Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Near surface ocean process : acoustical observations, ambient sound, and Langmuir circulation Zedel, Len 1991

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1991_A1 Z32.pdf [ 13.66MB ]
Metadata
JSON: 831-1.0053237.json
JSON-LD: 831-1.0053237-ld.json
RDF/XML (Pretty): 831-1.0053237-rdf.xml
RDF/JSON: 831-1.0053237-rdf.json
Turtle: 831-1.0053237-turtle.txt
N-Triples: 831-1.0053237-rdf-ntriples.txt
Original Record: 831-1.0053237-source.json
Full Text
831-1.0053237-fulltext.txt
Citation
831-1.0053237.ris

Full Text

Near Surface Ocean Processes: coustical Observations, Ambient Sound, and Langmuir Circulation by  Len Zedel B . S c , T h e University of V i c t o r i a , M . S c , T h e University of V i c t o r i a ,  1982 1985  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E OF D O C T O R OF PHILOSOPHY in  T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of  Oceanography)  W e accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A August 1991 © L e n Zedel, 1991  In  presenting this  degree at the  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  publication of  by  his  or  her  representatives.  for  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be It  is  granted  by the  understood  that  head of copying  my or  this thesis for financial gain shall not be allowed without my written  permission.  Department The University of British Columbia Vancouver, Canada  DE-6 (2/88)  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  n  Abstract This  thesis  describes  a study of near  surface  ocean  processes based on  observations m a d e with an instrument incorporating b o t h active acoustical  systems.  T h e topics addressed include the  clouds by L a n g m u i r circulation, the  a n d passive  organization of bubble  modulation of ambient  sound levels by  surface wave action, and the interactions of vortices associated w i t h L a n g m u i r circulation. Observations i n a deep ocean environment reveal bubble clouds organized into plumes of 100 m length and widths of about 5 m aligned w i t h the w i n d through the action of L a n g m u i r circulation. T h e depth of these plumes varies somewhat  with wind  speed with the  w i n d speeds of 13 ms . ms  - 1  between  of 12  occurring  m  at  are observed at 8 m depth within the bubble plumes.  Ambient sound observations at lationships  depths  Using acoustic Doppler techniques, downward vertical  -1  velocities of 0.06  greatest  wave  8 k H z are used to search for possible re-  breaking and L a n g m u i r circulation:  no  systematic  relationship is identified. T h i s investigation does reveal the occurrence of m o d ulations to ambient  sound levels i n phase w i t h the long (~  150  m)  waves passing over the instrumentation (positioned at 30 m depth).  surface  A model  of sound generation at the ocean surface suggests that individual sources must have spacings of less t h a n 6 m to reproduce the observations. Increased breaking activity (or greater source levels) are required at long wave crests to  ex-  plain these modulations: it could be caused either by interactions between long a n d short waves, or variations i n wind stress over the long waves. The  observations  of L a n g m u i r circulation reveal  of spacing between the windrows.  many  coexisting  scales  A mechanism capable of generating small  iii scale vorticity of the appropriate orientation through wave breaking a n d vortex stretching scale,  is developed.  T h e consequences  of interactions  between  this small  two dimensional vorticity is then explored using a Lagrangian  vorticity  model. T h i s model demonstrates that continuous injection of small scale vorticity close to the ocean surface can lead to circulation similar to that expected for L a n g m u i r circulation: welling  speeds  a distribution of circulations cell sizes results,  exceed upwelling speeds,  a n d the  cell spacing  down  scales vary  proportion to the depth at which a b o t t o m boundary is placed i n the model.  in  iv  Table of Contents  Abstract  ii  Table of Contents  iv  Figures  viii  Tables  xviii  Acknowledgements  xix  Preface  xx  1  Introduction  2  Background  3  1 •  8  2.1  A p p l i c a t i o n of Acoustics to Near Surface Processes  8  2.2  L a n g m u i r Circulation  10  2.3  Wave Breaking and A m b i e n t S o u n d  14  2.4  Objectives of Observations  16  Instrumentation  20  3.1  Instrument Deployment  21  3.2  Instrument M o t i o n  26  3.3  W i n d Speed Measurements  28  V  3.4  5  6  29  3.4.1  Vertical Sonar  29  3.4.2  Sidescan Sonar  33  3.4.3  Ambient Sound Record  35  3.5  4  Acoustic Characteristics  Data Recording  36  3.5.1  Conventional Instrumentation  36  3.5.2  Acoustical Data  37  Observations  40  4.1  Data Overview  42  4.2  Bubble Cloud Structure  49  4.3  Vertical Velocities  59  4.4  Discussion  62  4.5  Summary of Observations  65  Ambient Sound Modulations  68  5.1  Wave and Ambient Sound Analysis  68  5.2  Modulations of Sound Generation  78  5.3  A model of near surface sound  81  5.4  Model Results  86  5.5  Discussion of Model Results  91  5.6  Source Mechanisms  95  5.7  Summary and Conclusions  96  A Model of Langmuir Circulation  101  6.1  An Alternative Theory for Vorticity Generation  102  6.2  Analytical Formulation  104  6.3  Summary  108  . .  vi 7  8  9  A 2-D Lagrangian Vorticity M o d e l  110  7.1  M o d e l Requirements  Ill  7.2  A 2-D Lagrangian Vorticity M o d e l  113  7.3  M o d e l Implementation  114  7.4  M o d e l Subdivision Scheme  117  7.5  M o d e l Accuracy  120  7.6  M o d e l Scalings  126  7.7  S u m m a r y of Lagrangian Vorticity M o d e l  128  M o d e l Results  130  8.1  M o d e l Streamlines  130  8.2  B o t t o m Influence  133  8.3  L e n g t h Scale Distributions  136  8.4  Stability of Structures  136  8.5  Discussion of M o d e l Results  140  8.6  Conclusions  141  S u m m a r y and Conclusions  144  9.1  Instrumentation  145  9.2  Observations  146  9.3  A m b i e n t Sound Modulations  147  9.4  Langmuir Circulation  147  9.5  Concluding Remarks  149  10  References  152  A  Craik-Leibovich Theory  158  B  D a t a Acquisition  161  vii  C  D  E  F  B.l  A m b i e n t Sound Signal Conditioning  162  B.2  Sidescan Sonar Conditioning  162  B.3  Vertical Sonar Signal Conditioning  164  B.4  D i g i t a l Signal Processing Considerations  167  B. 5  D a t a Recovery  169  Vertical Sonar Processing  173  C. l  C o m p l e x Covariance M e t h o d  173  C.2  Z o r a n Processing  175  C.3  Velocity Processing  181  C.4  L o w A m p l i t u d e Bias  186  Sidescan Sonar Processing  196  D. l  Z o r a n Processing  196  D. 2  Sidescan Image Processing  198  A m b i e n t Sound Processing  203  E. l  207  A m b i e n t Sound C a l i b r a t i o n  Wave Measurement Details  210  F. l  Surface F i n d i n g a n d Velocity Determination  210  F.2  System Limitations  215  F.3  Waverider A c c u r a c y  220  F.4  Wave Spectral Analysis  221  F.5  Comparison of Spectra  222  F.6  Discussion  226  F.7  S u m m a r y and Conclusions  230  .  viii  Figures  Figure 2.1  11  Circulation pattern associated with L a n g m u i r circulation.  Figure 3.1  22  Deployment  configuration of the acoustics  platform.  T w o orthogo-  nally oriented sidescan beams sample bubble clouds i n narrow bands along the surface, the vertical sonar samples the penetration of bubble clouds i n a small area just above the package.  Figure 3.2 Diagram  24 of drifting  instrumentation package  identifying  the various  instrumentation a n d depth placement.  Figure 3.3  25  Details of acoustic instrumentation platform.  Figure 3.4  27  5 minute time series of the instrument attitude starting at 11:45 U T C , 27/10/1987.  a) sea surface displacement i n metres, b) instrument ver-  tical deviation about mean depth (derived f r o m accelerometer  record),  ix c) instrument vertical velocity (derived f r o m accelerometer record), d) X component of tilt, e) Y component of tilt, f ) instrument heading relative to true north.  Figure 4.1  41  T i m e line identifying periods of data availability f r o m various instrumentation groups (all times are i n U T C ) .  Figure 4.2  43  S u m m a r y of observations for the 21 hour period beginning at 22:00 U T C , 26/10/87; a) 10 m wind speed (dashed hne - anemometer speeds, solid line - ambient sound based), b) ambient sound level (7 to 9 k H z ) , c) significant wave height, d) average depth penetration of subsurface bubbles, e) depth integrated scattering cross section, M . Bars A , B , a n d C identify periods used to produce Figures 4.8a, b and c. v  Figure 4.3  47  Waterfall plot of surface wave spectra for the 21 hour p e r i o d beginning at 22:00 U T C , 27/10/87. Note the progression of locally w i n d generated waves to longer periods starting at 11:00 U T C , 27/10/87.  Figure 4.4.  48  Waterfall plot of ambient sound modulation spectra based on sound levels i n the b a n d between 5 k H z a n d 15 k H z for the 21 hour period beginning at 22:00 U T C , 27/10/87. T h e scaling i n this figure is identical to that of 4.3 to a i d comparisons.  Figure 4.5  50  E x a m p l e of 5 minutes of sidescan sonar data collected during 13 m s winds; a) is along the direction 1 9 0 ° true, a n d b) is along the d i rection 1 0 0 ° true. Instrument orientations for this period are shown - 1  X  in Figure 3.4. Line ' A ' identifies a surface wave disturbance, line ' B ' identifies a disturbance caused by instrument rotation (this event is identified as 'B' in Figure 3.4f).  Figure 4.6.  53  Simultaneous sidescan (top half of image) and upward looking sonograms (bottom half of image). Lines have been drawn up from the larger bubble plumes occurring in the vertical sonar image and along the average slope of the bands in the sidescan image to help in making associations.  Figure 4.7  56  Composite spatial map of subsurface bubble clouds observed during the period 11:10 - 12:00 U T C 27/10/87. The sectored line identifies the instruments track. Bubble clouds are collected into long narrow bands oriented parallel to the wind.  Figure 4.8  58  Histograms of windrow spacing based on sidescan sonar data. Observed winds were less than 7 ms (4.8a), about 10 ms (4.8b), and greater than 10 ms (4.8c). The time intervals over which the histograms were accumulated are shown by bars labeled A, B, and C in Figure 4.2a. -1  -1  -1  Figure 4.9 Contours of vertical velocity and backscatter cross-section for a conditionally sampled sequence of bubble clouds. To construct this cross section, data were averaged over a 2 hour period beginning at 12:10 U T C , 27/10/87.  62  xi Figure 5.1  70  S p e c t r u m of ambient quency  x  power)  sound fluctuations.  against  Data  are plotted as  a logarithmic frequency scale to  the relative contribution to signal variance. an average of 8 (overlapping),  (fre-  represent  T h e display is based o n  512 second data  samples  starting  at  12:10, 27/10/1987 U T C . T h e influence of wave motion is clearly visible at periods between 5 a n d 13 seconds.  Figure 5.2  71  Comparison  of surface  wave  displacement  a n d ambient  sound levels  (between 6000 a n d 9000 H z ) at 30 m depth for the 3 minute p e r i o d beginning at 12:13 27/10/1987 U T C ; a) ambient sound level (filtered to remove  fluctuations  at periods greater t h a n 20 seconds)  , b) sonar  determined surface displacements  Figure 5.3  73  Scatter plot of sound power at 30 m depth against wave displacement over a 40 minute period starting at 12:10 27/10/1987 U T C : b o t h wave and  ambient  sound data  have  been high pass  filtered  to eliminate  variations at periods longer t h a n 20 seconds.  Figure 5.4 Cross  74 spectral  analysis of 23  minutes of wave  and ambient  data starting at 12:10 27/10/1987 U T C ; a) wave spectra, of ambient sound fluctuations, c) coherence, is based o n averages over  d) phase.  This  20 separate frequency spectra.  confidence intervals are indicated by error  b)  sound spectra analysis  T h e 95%  bars for b o t h phase a n d  coherence.  Figure 5.5. T i m e series of wind speed a n d the phase a n d coherence between waves and ambient sound modulations for the 21 hour period beginning at  76  Xll  22:00 26/10/1987 U T C ; a) wind speed, b) average coherence at periods between 10.5 a n d 13.5 s, c) phase,  (95% confidence bounds are  indicated by error bars).  Figure 5.6  77  In the same format at used for Figure 5.5, the coherence a n d phase between wave motions and ambient sound are shown for a 44 hour period for fluctuations with a period of between  9.5 a n d 13 s are  displayed.  Figure 5.7  82  Geometry of modelled dipole sources and receiver.  Figure 5.8.  .  88  Comparison of observed a n d modelled ambient sound a 3 minute period. B ) intermittent  fluctuations  over  A ) quadratic dependence on wave displacement,  sources located at wave crests, a n d C ) quadratic de-  pendence o n wave displacement with sound sources restricted to long wave crests.  ( A l l models reproduce mean levels comparable to those  observed, b u t have been displaced to clarify the presentation).  Figure 5.9. Scatter plot of observed ambient sound levels against  90 those modelled  for the 40 minute period beginning at 12:10 27/10/1987 U T C . These data have been high pass filtered to remove all variations occurring at periods longer than 20 seconds.  Figure 7.1 M o d e l domain.  116  xiii Figure 7.2  123  Comparison of displacement differences between a normal model r u n , and one w i t h a time step reduced by a factor of 10,  (the small time  step model will have comparatively small errors a n d is considered as a reference),  a) Scatter plot of displacement differences, b) directional  dependence of displacement differences.  Figure 7.3  125  Difference i n computed displacements between a primitive vortex i n teraction  model a n d a model accelerated  by subdividing it into  640  regions; a) Scatter plot of displacement differences, b) Directional dependence of displacement differences.  Figure 8.1.  132  Contours of stream a steady of 4 m  2  negative  function occurring when the model has  state and there is no b o t t o m present. 5  -  1  has been used with values at  areas (characterized  A  contour  achieved interval  m a x i m a labelled a n d all  by clockwise oriented flow) have  been  shaded i n .  Figure 8.2  135  Contours of stream function occurring when the m o d e l has achieved a steady domain.  state with a b o t t o m located at A contour  interval of 2 m s~ 2  1  10 m  i n a 200  m  horizontal  has been used w i t h values  at m a x i m a labelled and areas characterized by clockwise oriented flow shaded i n .  Figure 8.3 Length scale dependence  137 on b o t t o m boundary depth.  are determined f r o m autocorrelations  L e n g t h scales  of the stream function and plot-  ted against the b o t t o m boundary depth used i n that model.  xiv Figure 8.4  138  C e l l spacing histograms for model results a)  10m b o t t o m b o u n d a r y  and b) 20m bottom boundary. Distinct cells are identified on the basis of vertical velocities exceeding —0.01  ms  - 1  .  Figure B . l  163  Example Dashed  of prewhitening filter effect  line is unfiltered ambient  on ambient  sound spectrum,  sound the  spectrum.  sohd line is  filtered.  Figure B.2  170  T y p i c a l processing steps used in recovering data f r o m V C R storage.  Figure C l . Data  177  acquisition processing  steps used for recovering  vertical  sonar  data.  Figure C.2 Dependence  187 of velocity bias on mean  signal amplitude based  on  6  hours of observation: signal amplitude is displayed as digitizer counts.  Figure C . 3 E x a m p l e of the  189 background spectral  content  of the  received  sonar  signal. T h i s power spectrum was acquired during a period of no active sonar operation a n d so provides the background "noise" spectrum for the sonar receiver. T h e large peak occurring at 0 H z is caused b y pick up of the carrier  frequency by the receiver,  of more  concern is  presence of a broadband noise floor with a peak at about 785 H z .  the  XV  Figure C.4  191  Bias i n mean frequency estimates associated  w i t h low amplitude sig-  nals when a spectrum is contaminated by coloured noise.  T h i s figure  is based on a simplified model of data contamination and is analogous to Figure C.2 which shows observations of velocity bias at low signal amplitudes.  Figure C.5 Plot  192  of inverse velocity bias ( 1 / V )  against  average signal amplitude.  Using the same data as shown i n F i g u r e C . 2 .  T h e straight  line is a  hnear regression fit to the data.  Figure C.6  194  Observed bias i n velocity data after correcting for the biasing effects using E q u a t i o n C.22.  A s i n Figure C.2, 6 hours of velocity data were  averaged according to the observed velocities a n d the results of these averages are presented here.  Notice that the velocity bias has largely  been eliminated except at amplitudes below about 3 counts.  Figure C . 7  195  Time for the  series  of  velocity  observations  amplitude bias effect;  before  and  after  a)  ocean  surface  vertical  backscatter amplitude observed at  10 m  depth, c) raw  correcting  velocity,  b)  (uncorrected)  vertical velocity at 10 m depth, d) 10 m velocities corrected for bias effect  and rejecting data where signal amplitudes fall below 3 binary  counts.  Figure D . l D a t a acquisition processing steps used for recovering sidescan data f r o m V C R storage.  197 sonar  xvi Figure D.2  200  Geometry of sidescan sonar deployment.  Figure D.3  202  T y p i c a l calibration curve used to correct sidescan sonar data for range dependent signal variations.  Figure E . l  204  D a t a acquisition processing steps used for recovering ambient sound data from V C R storage.  Figure E.2  205  Ambient data  sound data  are not  can  contaminated  sions a n d surface returns.  only be recovered  during intervals  b y sidescan a n d vertical sonar  when  transmis-  T h i s figure indicates the time intervals dur-  ing which the 7, 256 point F F T ' s are drawn during the data collection cycle.  Figure F . l Example  212 of an  acoustic  return  from the  ocean  surface:  a)  is  the  amplitude return, b) is the slope of the surface return, a n d c) is the complex demodulated signal.  Figure F.2  214  Comparison of 1 minute of surface wave observations: Waverider data,  b) is based on sonar range,  derived vertical velocity of the surface.  a n d c)  a) is based on is the  Doppler  xvii Figure F.3  216  5 minute time series of instrument attitude 27/10/1987.  starting at 11:45 U T C ,  a) sea surface displacement, b) instrument vertical devia-  tion about mean depth, c) instrument vertical velocity, d) X component of tilt, e) Y component of tilt, f) instrument heading relative to true n o r t h .  Figure F . 4  217  Schematic diagram of sonar sampling i n the presence of surface waves.  Figure F . 5  223  Flow chart of processing steps used i n spectral analysis of wave data.  Figure F . 6  225  Wave observations for the 20 minute period starting at 27/10/1987, 00:10 U T C . L o w w i n d speeds have prevailed for several hours a n d the wave field is dominated by ocean swell,  a) Waverider observations, b)  sonar range observations, c) sonar vertical velocity observations.  Figure F . 7  227  Wave observations for the 20 minute period starting at 12:10 U T C . W i n d ditions to about swell,  27/10/1987,  speeds have increased f r o m the earlier c a l m con-  lOms  - 1  at this time and i n addition to the ocean  there is now a developing sea.  a) Waverider observations,  sonar range observations, c) sonar vertical velocity observations.  b)  Tables  Table 3.1.  Sonar operating parameters  30  Table 3.2.  D a t a recording rates  37  Table 4.1.  R M S wave displacements inside and outside of windrows.  Table 5.1.  Sound source model parameters  Table 7.1.  Numerical viscosities resulting f r o m subdivision schemes. .  Table 8.1.  M o d e l r u n statistics  131  Table C l .  B i n gain factors  180  Table C.2.  C a l i b r a t i o n of frequency estimator  182  Table E . l .  Steps affecting ambient sound calibration  209  Table F . l .  Sonar effective footprints for various surface wavelengths.  Table F.2.  Wave energy densities determined by sonar a n d Waverider.  . . .  59 92  .  .  .  127  .  220  .  230  xix  Acknowledgements The successful completion of this project (and thesis) would not have been possible without the assistance and guidance of m a n y people. It is impossible to identify all those who have helped me for to do so would require many pages. T h e r e are however some individuals whose contributions have been so essential to me that I must recognize their efforts. The instrument design a n d construction required the skills of many experienced people. D o n R e d m a n completed the mechanical design. P a u l Johnson succeeded through skill a n d imagination i n designing analog circuitry capable of meeting m y most outrageous specifications. R o n Teichrob provided the digital circuit design and computer interfacing which allowed the convenient programm i n g of instrument operation. A l Stickland designed the mooring arrangement: I learned a great deal about working with people and moorings f r o m A l . None of the instrumentation would have been of any use except for the skill (and daring) of C a p t a i n P a u l Frost a n d the crew of the C . S . S . Parizeau who made deployment and recovery of the large instrumentation look easy. A great deal of computer processing a n d programming has been required at all stages of this project: there are many times that Grace K a m i t a k a h a r a K i n g has patiently listened to m y problems a n d provided me w i t h the perfect solutions. I always find the administrative requirements more confusing a n d complex t h a n any scientific problems. T h e r e are many times that C h r i s Mewis has led me through the administrative labyrinth of U B C . A t I O S , N e t t a Delacretaz and B o b L a k e have been most helpful i n eliminating bureaucratic problems. On m a n y occasions it is only m y fellow students have helped me to preserve m y sanity. I greatly value the m a n y discussions o n physics, oceanography, and life that I have had with D a n i e l a D i l o r i o , M i n g L i , C r a i g M c N e i l , D i m i t r i Menemenlis, Svein Vagle, and Y u n b o X i e . I must also thank m y supervisors for patience and support. Steve P o n d managed many administrative tasks on my behalf for which I a m indebted. D a v i d Farmer (too often) demonstrated the great skill of asking the right questions: m u c h of the work I have done resulted f r o m m y efforts to answer these irritating questions. F i n a n c i a l support for this project has come f r o m several sources. I have been supported by a N a t u r a l Sciences and Engineering Research C o u n c i l ( N . S . E . R . C . ) post graduate scholarship, a n d a Graduate Research Engineering a n d Technology G . R . E . A . T . award. Costs for instrumentation have been met through support f r o m the Panel o n Energy Research a n d Development, and the U n i t e d States Office of Naval Research. Finally, I would like to thank m y parents and my wife E l i z a b e t h for waiting a n d believing in me despite the ever slipping schedule.  XX  Preface Some of the material in this thesis has been previously published as a paper in the May 15, 1991 edition of the Journal of Geophysical Research (Volume 96, No. C5, pages 8889-8900). This publication is entitled "Organized Structures in Subsurface Bubble Clouds: Langmuir Circulation in the Open Ocean" by Len Zedel and David Farmer. I completed most of the work leading to this publication: David Farmer provided assistance to improve the initial manuscript and through discussions about the project as the work proceeded.  David Farmer  xxi  1 have seen A curious child, who dwelt upon a tract of inland ground, applying to his ear The convolutions of a smooth-lipped shell; To which, in silence hushed, his very soul Listened intensely; and his countenance soon Brightened with joy; for from within were heard Murmurings, whereby the monitor expressed Mysterious union with its native sea. William Wordsworth  i  Chapter 1 Introduction Wave  action,  turbulence and the  complexities of two-phase flow  present  significant challenges to the study of ocean surface phenomena. A l t h o u g h new measurement approaches are evolving to meet this challenge, our understanding of near  surface  processes  by the  ocean  remains limited.  For example,  one-  dimensional models continue to be used for the prediction of ocean m i x e d layer response ( M c C o r m i c k  and Meadows, 1988).  Such models b u r y the details of  m i x i n g and m o m e n t u m transfer i n approximate parameterizations. T h e purpose of the present  study is to  contribute to the growing b o d y of knowledge on  two and three dimensional mechanisms that underlie these processes.  F o r this  purpose, measurements were focussed on the processes at and just beneath the ocean surface using various acoustical techniques. The acoustical study of surface processes and passive devices.  can be made b o t h with  A c t i v e sonar is effective i n identifying the surface itself  and the clouds of bubbles that occur beneath a w i n d driven surface. measurement  of the  active  Passive  naturally occurring sound is particularly useful for  the  study of breaking waves, which appear to be a dominant acoustical source, as well as providing a background signal level that is closely related to the wind speed. There have been numerous reports o n bubble clouds created by breaking waves.  These include various optical a n d acoustical attempts to infer bubble  size distributions (for example, W a l s h a n d M u l h e a r n , itz, 1989,  Farmer and Vagle,  1989)  1987,  M e d w i n a n d Bre-  as well as echo-sounder studies of bubble  2 concentration Vaindruk  a n d spatial patterns such as those pioneered b y Aleksandrov a n d  1974 (as referenced  T h o r p e a n d colleagues.  in Thorpe  In particular,  1982) a n d vigorously  developed by  T h o r p e a n d H a l l (1983) obtained  images  of horizontal features aligned with the w i n d which they attribute to the effects of L a n g m u i r circulation. T h e presence of L a n g m u i r circulation i n the open ocean has been demonstrated b y Weller a n d Price averaging  current  meters  (1988).  (VACM's)  Weller a n d Price  used modified vector  deployed from R . P . F L I P  so as to ob-  tain three dimensional velocity profiles through the ocean mixed layer. revealed windrows  a downward  component  associated w i t h  of velocity  Langmuir  could not make instantaneous  as great  circulation.  as 0.3  ms~  A l t h o u g h Weller  These beneath  1  a n d Price  profiles with depth, their extensive set of mea-  surements showed that the m a x i m u m vertical velocities occurred at about 20 m depth a n d that there was a m a x i m u m i n the horizontal downwind velocity of about the same magnitude located i n the same location. Doppler (coordinated  sonar  observations  of the velocity  with the observations  field  b y S m i t h et a l .  (1987)  of Weller a n d Price) showed that some of  the L a n g m u i r cells documented b y Weller a n d Price h a d spacings of u p to 100 m. V i s u a l observations of windrows indicated coexisting smaller scales down to several metres but their sonar system was restricted to a 23 metre resolution. T h e large windrows were u p to 2 km long a n d persisted for periods of at least 2 hours. These studies help to identify the processes that are important layer  dynamics.  Breaking wind waves are important  m e n t u m between the atmosphere a n d ocean;  to mixed  to the transfer of m o -  they also inject bubbles into the  3 ocean  surface.  W h e n present,  will rapidly transport mixed layer.  L a n g m u i r circulation  (at  a variety  of scales)  any properties such as heat a n d m o m e n t u m through the  A s is clear from the range of observations  of other  researchers,  it is necessary to measure many different processes simultaneously (such as the wind,  wave  field,  wave breaking,  current  gle the relationships between them.  speeds  etc.)  i n order  to disentan-  In addition, these processes are occurring  on a great range of length scales from several metres up to at least  several  hundred metres. Acoustical sampling techniques provide the flexibility a n d resolution to sample effectively i n this environment b u t there remains for much more comprehensive implementation.  potential  T h o r p e a n d Hall's (1983) sides-  can observations were restricted to a coastal environment; T h o r p e et a l . (1985) developed systems with a mid-ocean capability but these measurements limited to sidescan observations,  were  although at two separate frequencies (80 a n d  248 k H z ) . T h o r p e (1986) used only one frequency of upward looking sonar a n d S m i t h et a l . (1987) h a d a limited spatial resolution of 23 m . In addition, for comprehensive observations of the variety of near surface processes it is desirable to combine simultaneous observations b o t h i n the vertical a n d horizontal dimensions. T h e O c e a n Acoustics group at the Institute of Ocean Sciences been developing various acoustical the deep ocean environment. freely drifting instrument  approaches  for near surface observations i n  Such observations  with acoustical  (IOS) has  are typically obtained with a  sensors suspended by an extensible  cord from a surface buoy so as to decouple it f r o m surface wave motion.  This  system was first deployed i n 1985 during the Frontal A i r Sea Interaction E x periment ( F A S I N E X ) to make simultaneous video, ambient sound a n d upward looking echo sounder observations.  T o provide a more  complete  set of near  4 surface observations i n the present  study, I organized the installation of two  (upward pointing) vertical sonars (50 rected  100  k H z and 200  k H z ) , two orthogonally d i -  k H z sidescan sonars, a n d an ambient sound recording system w i t h  22 k H z b a n d w i d t h o n a similar platform. D a t a were recorded using conventional V H S video cassette recording systems which provide an economical, high quality data systems  are  quencies.  storage format.  however only suitable for the recording of signals at  I developed a system  capable of accurately  These  audio fre-  recording sonar  phase  information o n these systems by using an implicit clock sampling scheme and carefully consulting with the electronics technicians who designed a n d built the hardware.  T h e phase recording capability is important because  it allows for  Doppler velocity processing of vertical sonar data. A  drawback of the V H S data storage system is the streaming nature  data recovery:  it is not possible to start a n d stop the data stream  losing substantial amounts of data.  of  without  T o overcome this limitation, I developed  an extensive package of signal processing software operating o n a Z o r a n V S P 161  vector  signal processor  controlled by an I B M - A T  personal computer.  By  using the high speed processing capability of the Z o r a n system, data could be processed i n real time (as  they were recovered f r o m the video cassette).  It is  only through the combination of the high speed signal processing capabilities of the Z o r a n system with the high data storage rates provided by V H S video cassettes that the variety and quality of acoustic data presented i n this thesis could be collected by an autonomous instrument.  The 15,  1987,  instrument was deployed during the period October 19 to November from the  CSS P A R I Z E A U  i n the  North  Pacific within  a  50  km  5 radius of 4 8 ° N , 1 3 9 ° W .  T h e cruise formed part  of the O C E A N  STORMS  experiment aimed at understanding the response of ocean circulation to storm forcing.  Meteorological, hydrographic and near surface velocity  microstructure  data were collected from the ship, a n d a large array of oceanographic ings (including weather  stations) were located  i n the  area thus  moor-  providing  a  reasonably comprehensive set of supporting environmental data. T h i s thesis presents  the acoustical observations made during this experi-  ment and interprets the more striking features  of these data.  C h a p t e r 2 pro-  vides a background on the use of acoustics for the study of near surface ocean processes, L a n g m u i r circulation, ambient sound a n d wave breaking. T h e general concepts of the Craik-Leibovich m o d e l of L a n g m u i r circulation are introduced there, but greater detail is left to A p p e n d i x A . Following this background, the initial objectives of the observation program are identified serving to explain m y choice of instrumentation. T h e instrumentation itself is described i n C h a p t e r 3.  A variety of conven-  tional oceanographic instruments have been used i n this study but the  nature  of their deployment is not discussed i n great detail as they do not f o r m the focus of the thesis.  T h e acoustical instrument package itself represents a novel  approach to studying near surface processes a n d its operation is described to provide a reference for the resulting observations.  T h e recording of the  acous-  tic data i n this study represents a substantial technical achievement and these recording techniques are documented. T h r o u g h Chapter 3 several technical issues are raised which are detailed i n a series of appendices. A p p e n d i x B describes the signal conditioning and data processing I developed for the various data types.  A l s o described i n A p p e n d i x  6 B is the Z o r a n V S P - 1 6 1 vector signal processing system for which I developed software to analyze all the recorded data. A p p e n d i x C explains how I extracted velocity estimates from the vertical sonar data.  T h e processing I developed to  convert sidescan sonar data into useful diagrams is presented i n A p p e n d i x D . A p p e n d i x E explains the processing and calibration I incorporated for ambient sound data. F i e l d observations first  are  presented i n C h a p t e r 4:  general observations  presented followed b y a detailed description of the  various data  are  types.  A l t h o u g h a total of 80 hours of data were recorded, this detailed discussion is restricted to a 21 hour period of increasing winds which provides a variety of sea state conditions a n d demonstrates the progressive changes to the subsurface bubble clouds. T h e influence of L a n g m u i r circulation is clearly demonstrated i n the d a t a a n d several characteristics of this phenomenon are presented. Ambient sound data were collected w i t h the intention of investigating any relationship between wave breaking and L a n g m u i r circulation but no significant interdependence could be found. currence of modulations at  Instead,  these observations identified the oc-  surface wave periods i n ambient sound and these  modulations are the topic of Chapter 5.  T h e modulations not only occur  at  surface wave frequencies, but are shown to be i n phase with the wave motions directly above the recording position.  I have investigated the implications of  this observation with the aid of a simple m o d e l of sound generation.  Through-  out this analysis, I have extracted surface wave observations f r o m upward looking sonar:  details of this technique and its accuracy are presented in A p p e n d i x  F. T h e most striking characteristic  of the sidescan data is the coexistence  m a n y scales of L a n g m u i r cells and the evidence for much smaller scales  of  than  7 are normally seen i n the open ocean.  T h e C r a i k - L e i b o v i c h theory of L a n g m u i r  circulation does not explicitly predict the presence of many coexisting scales or the presence of these very small scale structures.  Chapters 6, 7, a n d 8 explore  a possible explanation for this observation based on the consequences of a two dimensional upscale cascade of vorticity.  F i r s t , i n C h a p t e r 6,  I introduce an  alternative mechanism for the source of this vorticity based o n its generation by breaking waves and the subsequent distortion by wave currents.  I explore  the fate of such vorticity (or that of any other origin such as vorticity generated by the Craik-Leibovich mechanism) w i t h a two dimensional discrete  vortex  m o d e l which assumes only that the source of the vorticity has a small initial scale a n d is introduced close to the surface.  Chapter 7 describes the details of  the m o d e l as I have implemented it, and C h a p t e r 8 describes the results  of  m o d e l trials. Chapter 9 completes the thesis with a summary of results a n d observations a n d suggestions for future areas of research.  8  C h a p t e r2 Background 2.1  Application of Acoustics to Near Surface Processes Gas bubbles in water are excellent sources of acoustic backscatter because  of their resonant properties (Clay and Medwin 1977).  The action of wave  breaking introduces many bubbles into the mixed layer and these bubbles provide the targets for acoustic backscatter measurements near the ocean surface. Subsurface bubbles act in some ways hke tracers of current motion in the mixed layer; however, because they have buoyancy and are absorbed into solution their behavior is not trivial.  Larger bubbles rise fastest through the  water and consequently stronger downwelling currents are required to retain these bubbles beneath the surface. In principle, the size distribution of bubbles with depth provides some information on the vertical current component. Some bubbles eventually escape the downwelling currents and return to the surface, others are absorbed into the water. The distribution of bubbles seen at any one time represents the steady state balance between these various causes of attrition and bubble generation through wave breaking. The process of wave breaking is itself a source of acoustic energy. By monitoring the mean strength of ambient sound in the ocean, it is possible to infer wind speeds (Farmer and Lemon 1984, Vagle et al. 1990). In addition, the modulations of the ambient sound field can be used to determine breaking wave densities (Farmer and Vagle 1988). Studies on the bubbles themselves were initially done using bubble traps (Blanchard and Woodcock 1957, Glotov et al. 1962, Kolovayev 1976). Medwin  9 (1970), a n d Johnson a n d Cooke (1979), used photography to determine bubble size distribution. M e d w i n (1970) was first to apply acoustics ments of bubble distributions.  to the measure-  These studies revealed that the time  averaged  distribution of bubble density decreased exponentially w i t h depth ( W u 1981). T h e time averaged distribution of bubbles c a n be useful i n estimating gas exchange w i t h the atmosphere, driving the exchange process.  b u t it does not reveal much of the dynamics T h e short term behavior of subsurface bubbles  can better be studied b y the use of upward looking sonar such as used by T h o r p e et a l . (1985), T h o r p e (1986) a n d Crawford a n d Farmer (1987).  These  studies have demonstrated that the subsurface bubble distribution is characterized by dramatic changes i n bubble penetration depth. In fact, the bubbles are seen to form localized clouds or plumes rather than a continuous horizon of bubbles.  T h o r p e a n d H a l l (1983) mounted a sidescan sonar system on the sea floor a n d directed the beams upwards along the surface.  W i t h the sidescan i n this  configuration, the horizontal distribution of bubble clouds was clearly revealed. Individual wave breaking events could be identified b y the sudden of a bubble patch on sonogram images.  These patches of bubbles are seen to  be advected by the local surface currents after they appear. set were  of data,  they  coincident  observation  long narrow  with the observation  is very  sidescan sonar implies that  observed many  important  C r a w f o r d a n d Farmer  (1987),  In one particular  rows of bubble plumes which  of windrows o n the sea surface.  because  can be used to observe  the intermittent  appearance  it demonstrates  that  L a n g m u i r circulation.  upward  This  looking  In addition, it  clouds of bubbles seen by T h o r p e (1982), and were  caused  by L a n g m u i r circulation.  Thorpe  10 et al. (1985) report on more extensive observations of the sea surface using upward looking sidescan sonar mounted on a towed body. These previous studies demonstrate the utility of acoustic systems to the study of near surface processes. They have all however been restricted in some way by the power and data recording requirements of acoustic systems. As signal processing and data recording technology have improved dramatically in recent years, these restrictions have been eliminated (as is demonstrated by this thesis) providing many opportunities for acoustic applications. 2.2  Langmuir Circulation  Windrows aligned parallel to the wind have been famihar to mariners since men first went to sea. The first real study into windrows was done by Langmuir (1938) who reported on observations of windrows at sea and described a series of experiments he undertook to investigate their cause. He found that the windrows were associated with current vortices aligned parallel to the wind and arranged in counter-rotating pairs (so called Langmuir circulations). There have been many subsequent field studies on Langmuir circulations which are well documented by three reviews on the topic; Faller (1971), Pollard (1977), and Leibovich (1983). Weller and Price (1988), and Smith et al. (1987) report on a very complete set of observations combining current meter and acoustic observations. Together, these studies have established the essential characteristics of Langmuir circulation and identify the conditions necessary for its occurrence. Figure 2.1 shows a schematic diagram of the current flow associated with Langmuir circulation. The surface streaks of foam (or floating particles) form  11 because of convergence occurring above regions of downwelling.  T h e regions of  downwelling are more concentrated than the upwelling regions a n d have vertical speeds  of the  order of 1%  of the  wind  speed.  Coincident w i t h  the  vortex  motion are down-wind components of velocity which are greatest i n the regions of downwelhng and are comparable to the downwelling speeds.  This  current  regime will establish itself within a few minutes of the onset of w i n d speeds as low as 3 ms . -1  If a shift i n w i n d direction occurs, the L a n g m u i r cells will  reahgn themselves with the w i n d direction (again) within a few minutes of the change.  Figure 2.1:  Circulation pattern associated with L a n g m u i r circulation.  12 T h e spacings of the cells are not always regular, i n fact there is often a hierarchy of scales (Assaf et al. 1971, Harris a n d L o t t 1973, S m i t h et a l . 1987). T h e cells will form even i n the presence of a stable density profile ( S m i t h et al.  1987) although there is evidence that stability conditions m a y influence the  penetration  depth a n d shape of the cells ( T h o r p e 1982).  T h e depth  penetra-  tion of the circulations is ultimately limited b y the first significant pycnocline. Leibovich (1983) notes that the aspect ratio of L/2D observed to be approximately  for the largest  1 where L is the distance between  cells is  convergence  zones, a n d D is the mixed layer or b o t t o m depth. Despite the more t h a n adequate observational description of L a n g m u i r circulation, plausible theoretical models have only appeared quite recently. models  are all wave  current  interaction  models;  one proposed  by  These Garrett  (1976), a n d the C r a i k - L e i b o v i c h models (summarized by Leibovich 1980). T h e Garrett model is heuristic i n nature lows.  If a wave breaks,  troduces at  it transfers  a n d can be summarized as fol-  some m o m e n t u m into the water a n d i n -  a n increased velocity component i n the down w i n d (wave) direction  the point  cal current of somewhat  where  anomaly  the wave they  broke.  A s other  are slightly refracted  increased wave energy.  Garrett  waves  pass  through  inwards, producing a region  then assumed that the frequency  of wave breaking was proportional to wave energy.  This  assumption imphes  an increased probability of wave breaking i n the region of the initial anomaly reinforcing that from either drifts.  This  anomaly.  T h e wave  side, producing a convergence convergence  results  this lo-  field  current  would be focused inwards  zone due to the opposing  i n a downwelling region under  Stokes  the  current  anomaly providing a driving force for vortex-like L a n g m u i r circulation.  Obser-  vations of increased wave height i n the windrows by M y e r (1971) support the  13 Garrett  model;  however,  Thorpe and Hall  (1982), a n d Kenney (1977)  both  report no preferential wave breaking i n windrows. B o t h variations of the C r a i k - L e i b o v i c h m o d e l are based o n the same equations: driven.  they only differ i n the mechanism by which the L a n g m u i r circulation is These models describe the generation of L a n g m u i r cells resulting f r o m  interactions  of the surface  currents  with vorticity  associated  with the w i n d  stress a n d Stokes drift. These interactions can be seen from one of the simpler developments b y C r a i k a n d Leibovich (1976) which is outlined i n A p p e n d i x A . F r o m this development, the vorticity equation a ^ i + r!—- +(—-  ay  results.  Using  the coordinate  is the vorticity, u direction),  s  (u, v,w)  az  system  = v-^ + w-^-  ay  2.1  oz  displayed i n Figure 2.1, where  (i,r),()  is the unidirectional Stokes drift (aligned i n the downwind is the mean  surface  current  (excluding the Stokes  drift),  a n d a is a scaling factor for the eddy viscosity. T h e term a V £ represents the 2  diffusion of vorticity, n ^ - + C^£r represents the deformation of vortex hnes by the Stokes drift, a n d  -f  Wjf£  represents the convection of vorticity.  In one solution to E q u a t i o n 2.1, C r a i k  a n d Leibovich (1976) consider a  free surface boundary condition w i t h a directionally symmetric wave field, a n d assume no m o t i o n at infinite depth. (Leibovich (1983) labels solutions based on this approach the C L - I mechanisms: est of consistency.)  this label will be used here i n the inter-  Streamlines based o n this formulation agree very well with  the observations of Langmuir circulation. T h e solutions exhibit convergence at the  location of m a x i m u m downwind current,  vortices  aligned parallel to the  w a v e / w i n d direction, a n d more intense downwelling t h a n upwelling.  T h e spac-  ing of windrows for this solution are of the order of the dominant wavelength.  14 T h e major criticism of this theory is that the crossed wave trains must r e m a i n phase locked for many cycles to produce cross w i n d variations i n the Stokes drift: a condition which is very unlikely to be met i n a real sea. Faller (1978) however has demonstrated that such circulations can be set u p i n a laboratory wave tank.  Leibovich  (1977) solves the p r o b l e m f r o m the point of view of stability  (following Leibovich 1983, this approach will be referred to as the C L - I I mechanism).  T h e requirement  of crossed  wave  stress a n d stratification are considered. tion,  L e i b o v i c h demonstrates  grow until viscous effects  trains  is relaxed,  W h e n subject  that under most  and both  to a n initial  perturba-  conditions the disturbance  balance the driving force.  wind  will  T h e streamlines for this  solution are basically the same as those of the C L - I solution since b o t h models are  based o n the same equations.  T h i s m o d e l estabhshes  a preferred length  scale for L a n g m u i r cells which for most conditions is of the same order as the dominant surface wavelength (Leibovich a n d Paollucci, 1981).  T h e r e is still no observational evidence capable of refuting outright any of the existing models. In fact, it is possible that the different mechanisms could work i n concert to produce the observed circulations.  These remaining uncer-  tainties about Langmuir circulation invite more extensive observational studies which can contribute to the understanding of this fascinating phenomenon.  2.3  Wave Breaking and Ambient Sound Wave breaking is probably the most obvious physical process that c a n be  observed o n the ocean. atmosphere  It is involved i n the transfer of m o m e n t u m f r o m the  to the ocean, the introduction of air bubbles into the ocean a n d  15 therefore air-sea gas exchange, the ocean surface.  a n d the generation of turbulence which  mixes  T h e process of wave breaking is highly non-linear m a k i n g  theoretical analysis difficult, and because there are no automated methods for observing wave breaking i n the conventional sense, expensive a n d time consuming.  experimental studies are  It is for these reasons  that  ambient sound  studies of wave breaking hold so m u c h promise for future studies.  Wave  breaking studies are normally restricted  to visual  observations of  white capping ( M o n a h a n a n d O ' M u i r c h e a r t a i g h , 1980) which do not lend themselves to quantitative comparisons with theory. characteristics  T h e understanding of m a n y  of wave breaking could benefit from further field investigations.  First a n d foremost are the interactions between waves that ultimately mine the limiting wave spectrum i n a wind forced sea (Phillips 1985).  deter-  Phillips  (1981) describes how short waves can be modified b y long waves a n d this m o d ification bears on the problem of how short wave breaking might lead to long wave growth (Garrett  a n d S m i t h 1976).  Donelan et a l . (1972) reported wave  breaking i n wave groups, acoustic evidence for which was found by Farmer and Vagle (1988).  T h e characteristics of wave breaking m a y also play a role i n the  presence of secondary flows (ie. L a n g m u i r circulation) i n the upper ocean. T h e association of ocean ambient sound with wave breaking was first suggested by Wenz (1962).  T h i s association is clearly demonstrated b y field ob-  servations of Farmer a n d Vagle (1988), a n d laboratory tank studies of B a n n e r and  Cato  (1988).  Despite this  clear  relationship, the actual  mechanism of  sound generation is not well understood. T h e experiments by B a n n e r a n d C a t o (1988) a n d theoretical studies by M e d w i n and B e a k y (1989) suggest  that  cre-  ation of air bubbles is important to the sound generation. In contrast, analysis  16 by G u o (1987) suggests that this mechanism is unlikely because the presence of surface images associated with any subsurface sound source would severely restrict the acoustic source level of such a mechanism. T h e y suggest that sound is generated b y spray droplets striking the water surface. A s well as being associated w i t h wave breaking, overall sound levels have been found to vary i n strict proportion to the wind speed as first reported by K n u d s e n et a l . (1948) for frequencies of 100 H z to 25 k H z . M a n y subsequent studies have  demonstrated  L e m o n et a l . 1984). makes  this relationship (Wenz  1962, Evans et a l .  1984,  Vagle et a l . (1990) provide an empirical relation which  possible the accurate estimation of w i n d speeds f r o m ambient  sound  levels. T h e r e are clearly m a n y aspects of wave breaking a n d the associated  gen-  eration of ambient sound which invite further investigation. In particular, the combination of ambient  sound observations  w i t h wave  field  and wind  speed  measurements has the potential for clarifying many of the interactions between these mechanisms.  2.4  Objectives of Observations From  the success ( a n d failure) of previous studies it has become  clear that to make any progress  i n studying m i x e d layer dynamics,  quite  observa-  tions of m a n y contributing processes must be made simultaneously. T h e Ocean Storms p r o g r a m provided a n ideal opportunity for such a study because of the diverse observational program being arranged i n this large collaborative effort. M y objective within this framework was to make a thorough acoustical survey of upper ocean processes.  W h i l e trying to make the observation p r o g r a m as  17 general as possible, I have focused special attention o n recording the interactions of w i n d forcing, wave breaking, a n d L a n g m u i r circulation. Observations by Weller a n d Price (1988) have demonstrated that vertical velocities as great as 0.3 m s  - 1  can occur i n the mixed layer i n the presence of  L a n g m u i r circulation. A s well, it is obvious that i n order for bubbles generated by wave breaking to penetrate and  Farmer  to depths of 10 or 20 m as seen by C r a w f o r d  (1987), some significant vertical velocities must exist.  Knowledge  of these vertical velocities is crucial to understanding the energetics near surface processes.  of these  Direct measurements of these velocities are possible (as  demonstrated b y Weller a n d Price 1988), b u t the technique they used requires a large stable platform not generally available.  In contrast,  acoustic  Doppler  sampling techniques provide a means of measuring near surface velocity profiles remotely a n d f r o m a relatively small platform.  Such observations  are a  logical extension to simple echo sounder measurements a n d can provide a very important contribution to the present enquiry.  Observations by T h o r p e a n d H a l l (1983) demonstrate  that sidescan sonar  can provide a graphic view of the organization of subsurface bubbles b y near surface currents.  T h o r p e a n d H a l l (1983), a n d S m i t h et a l . (1987) have made  observations of the windrows of L a n g m u i r circulations w i t h sidescan sonar systems.  S m i t h et al. (1987) used Doppler sonar techniques with sidescan sonar  systems present  to make  current  velocity estimates  within  L a n g m u i r cells.  F o r the  study, these systems could greatly increase the understanding of near  surface processes. Aside from acting  as tracers of near  surface  water  motions,  bubbles are important i n themselves for the role they play i n ocean  subsurface atmosphere  18 gas exchange.  These bubbles are generated b y the breaking of waves, m a k i n g  this process of interest to the present study. Wave breaking is also of possible importance to the generation of L a n g m u i r circulation (Leibovich, 1983). Farmer and  Vagle (1988)  have  demonstrated  that  ocean  can be used to monitor wave breaking activity.  ambient  sound fluctuations  In addition, ambient sound  observations provide a n accurate measure of surface wind speed i n the open ocean (Vagle et a l . 1990).  T h e previously cited studies demonstrate  a range of important  processes  occurring i n the upper ocean a n d provide some clues on how they might be observed. O n e problem c o m m o n to the acoustical studies has been the need for large power supplies a n d a large data recording capacity.  These problems have  forced the use of deployment platforms which are less t h a n ideal i n some way (ie.  ships, special platforms such as R . P . F L I P , or coastal locations).  A neces-  sary first objective to fulfilling the scientific goals of this program has been the development of a suitable platform for deploying acoustical instrumentation i n the deep ocean. T o make the range of observations of demonstrated importance upward looking  sonar,  sidescan  sonar,  a n d ambient  sound recording  systems  were required. Vertical sonar is useful i n providing details of subsurface bubble concentrations, Doppler processing).  surface wave action, a n d vertical velocity profiles (through Sidescan sonars were required to reveal the spatial distri-  bution of subsurface bubbles. T h e ambient sound system was included for the study of wave breaking processes a n d to determine local wind speed. T h e r e were several processes of known importance that the acoustics package  could not monitor (or h a d not previously been used to monitor).  included surface wave data,  w i n d speed, pycnocline depth, a n d ocean  These surface  19  currents.  Some of these additional observations were known to be available as  part of the overall Ocean Storms experiment, but in the interest of autonomy and convenience, an effort was made to make local observations of these parameters by using various conventional instruments.  20  Chapter 3 Instrumentation My  objective for the acoustic  periment was to characterize as available resources  observations  during the  O c e a n Storms  ex-  the dynamics of the ocean surface as completely  a n d instrumentation would allow.  Conventional oceano-  graphic instrumentation was used to measure w i n d speed and direction, the one dimensional surface wave field, current shear and temperature mocline.  across the  ther-  Acoustical methods were used to determine vertical velocities within  the m i x e d layer, surface wave characteristics,  the horizontal and vertical dis-  tribution of subsurface bubbles, and ambient sound levels.  T h i s chapter  describe the implementation of instrumentation during the O c e a n Storms  will ex-  periment, a n d for the acoustic systems provide some details on system capabilities.  The  Ocean Storms  environment  placed  the deployment of acoustic instrumentation.  several  specific requirements  on  A stable, self contained platform  was required that could position acoustic transducers  within 40 metres of the  ocean surface and record developments through the evolution of a storm of 48 hours duration. Acoustic instrumentation required for the desired observations included two vertical (upward looking) sonars kHz, a  two  orthogonally oriented  hydrophone for detecting  sidescan  ambient  operating at  sonars  operating  sound levels at  200 at  k H z and  100  50  k H z , and  audio frequencies.  The  upward looking sonar systems were included to determine the vertical extent of subsurface bubbles. T h e choice of two frequencies was made with the intent  21 of inferring the relative bubble size distibution within  the bubble  clouds as  described by Farmer a n d Vagle (1989). However, no attempt was made to infer bubble size distributions with this data set. O n l y the 200 k H z system has been used i n subsequent analysis a n d so the characteristics  of the 50 k H z system  will not be described. T h e sidescan sonars display the horizontal extent and distribution of bubble clouds. Vertical velocity estimates are made by applying acoustic D o p p l e r techniques to the vertical sonar systems.  3.1  Instrument Deployment The  need to  place  acoustic  instrumentation, o n a  stable p l a t f o r m close  to the ocean surface i n deep water poses a significant deployment challenge. A  solution  1985  to  this problem was  developed for a similar  project  during  the  Frontal A i r Sea Interaction Experiment ( F A S I N E X ) : a surface float was  attached by means of an extensible rubber cord to a package containing acoustic instrumentation positioned at  20  m  depth.  T h e data collected w i t h this  configuration during F A S I N E X demonstrate that the rubber cord effectively decouples the large surface wave motions from the instrument package a n d does not interfere with the vertical sonar systems:  the rubber cord is essentially  transparent to acoustical energy when compared to the gas bubbles of interest near the  ocean surface.  from F A S I N E X  Video  camera  records  and the  ambient sound  data  showed that the elastic tether allows the buoy to follow  surface waves without creating significant agitation or acoustic emissions. ure 3.1  demonstrates  the Fig-  the deployment scheme and identifies the areas of the  surface sampled by the active sonar systems. For the Ocean Storms deployment, observations of wave heights a n d thermocline shear were required i n addition to  the acoustic observations.  These  22  Ballast  192 m  A  Figure 3.1: Deployment configuration of the acoustics platform. Two orthogonally oriented sidescan beams sample bubble clouds in narrow bands along the surface, the vertical sonar samples the penetration of bubble clouds in a small area just above the package.  23 measurements  were provided by using a Datawell Waverider buoy as the  sur-  face float, a n d placing Interocean S4 current meters at 41 m a n d 125 m depths spanning the thermocline depth of 50 m . because  of their ability to operate  ( T h e S4 current meters were chosen  in deployments subject  to wave motion).  Figure 3.2 displays the final instrumentation configuration used. T h e electronics required for the acoustical measurements were placed within two large pressure cases of 0.37  m  diameter  and w i t h heights of 1.45  a n d 1.1  m.  These  were  mounted within a 2.0 m tall open instrument cage w i t h 1.2 m diameter closed plates at each end. to 0.9  T w o stabilizing fins extending f r o m the package axis  rn radius a n d separated by 6 0 ° were mounted to maintain the  in a stable orientation. identifying the placement  T h e package  out  package  configuration is sketched i n F i g u r e  3.3  of acoustic transducers a n d various sensors used for  recording package orientation.  A  significant portion of the instrumentation associated with the  package  (Figure  3.2)  was included to insure that  and recovery operations were fail safe. to  locate  event  the  that  instrument  array  these concerns  was  at  instrument positioning  Specific areas of concern were the need  i n rough weather  a failure should occur  the  acoustics  some  and  point i n the  addressed by fitting an  to  recover  array.  Argos satellite  it  in  T h e first  beacon  onto  the of the  Waverider buoy to provide a record of instrument position. In addition to the Argos beacon, two V H F beacons and two flashing strobes were attached to the Waverider to allow an attending ship to monitor its location. Buoyancy for the drifting array was very carefully adjusted to position the acoustics  package at the desired 30  a buoyant element  metre  depth.  or the parting of a cable (the  A s a result,  any failure of  rubber cord i n particular)  24 Radio Beacons Waverider Buoy  SL  n .- 6 3  6  Acoustics Package  Current Meter  Floatation  Current Meter Locator Beacon  Floatation  []•  Pressure Release Floatation  192 m —  Acoustic Release Ballast  Figure 3.2:  Diagram of drifting instrumentation package identifying the  ous instrumentation and depth placement.  vari-  25  Mooring Ring  Pressure Sensor  Figure 3.3:  Compass  Details of acoustic instrumentation  platform.  0.5m  26 would cause the lower part of the array to be lost. T o avoid this consequence, a pressure sensitive release was included i n the array. If the array were to sink, the pressure release would part  allowing the acoustic release  model)  with the ballast,  to  sink to the  bottom  mooring to rise to the surface.  A  "witness"  (a high  but leaving the rest of  buoy would rise to the  uncovering a separate Argos beacon, V H F beacon, and strobe. of transmissions  from the  notification of a system  the  surface  T h e appearance  normally submerged Argos beacon  failure a n d assist  pressure  would provide  i n recovering the instrumentation.  W i t h luck, the high pressure acoustic release could be located by means of its acoustic transponder a n d could be recovered separately.  3.2  Instrument  Motion  T h e sonar data are sensitive to platform motions because to  make  measurements  of speed  a n d distance.  E v e n though  they are an  used  effort  was  made to provide a stable platform, not all motions could be eliminated a n d a record of platform m o t i o n was needed to allow for data interpretation. F o r this purpose, two axes of instrument tilt, vertical acceleration, a n d compass heading were recorded at  a rate of 2 H z . A 5 minute sample of these data  together  with surface wave displacements, collected during wind speeds of 13 m s displayed i n Figure 3.4. i n Figure 3.4  ,  is  T h e vertical displacement and vertical velocity shown  were b o t h determined by integration of the vertical  data subject to a 0.02  - 1  H z high pass  filter.  acceleration  These time series clearly show the  dominant role that wave forcing plays in instrument motion. T h e periodic vertical motions of the package with amplitudes of about  0.5  m can be seen from Figure 3.4 to be i n phase with the surface displacements. T h i s behaviour indicates that this m o t i o n is due to residual wave action  at  27  Vertical Displacement  11:45:00  11:46:40 time  Figure 3.4:  11:48:20  11:50:00  (UTC)  5 minute time series of the instrument attitude starting at 11:45  U T C , 27/10/1987. a) sea surface displacement i n metres, b) instrument vertical deviation about mean depth (derived from accelerometer vertical velocity (derived from accelerometer  record), c) instrument  record), d) X component of tilt, e)  Y component of tilt, f) instrument heading relative to true north.  28 30 m depth a n d not to the forcing from the elastic tether. T h i s observation is consistent w i t h the forcing terms acting o n the package:  the vertical force due  to extensions of the rubber cord has a m a x i m u m value of about 100 is insignificant when compared to the  1600  N  N which  amplitude drag forcing which  can arise f r o m residual wave motion at the instrument depth.  The  tilt meters (Figure  3.4d  and e)  similarly show periodic motions  surface wave frequencies, they show a mean tilt of about deviations having amplitudes of about coincident consistent  w i t h the  passage  of a  2°  large  a n d reach  wave  group.  at  1 . 5 ° with periodic  a m a x i m u m tilt T h e instrument  of 5 ° tilt  is  w i t h directional changes i n tension as the surface float is advected  horizontally by the passing surface waves.  T h e compass record shown i n F i g u r e 3.4f (accurate to about that  ± 2 ° ) shows  the instrument heading maintains a mean bearing w i t h variations of 5 °  or 1 0 ° occurring over periods of about motion  1 minute.  In contrast  a n d tilt there is little indication of surface  to the vertical  wave periods.  T h e slow  oscillations seen in heading are likely caused by the periodic shedding of eddies from the large pressure cases.  3.3  Wind  Wind  Speed  Measurements  speed measurements  were included at  several locations  as part  of  the overall Ocean Storms program but these observations were not positioned close to the site of acoustic observations. in the vicinity of the acoustics  package  A meteorological buoy was deployed to provide w i n d speed and direction  measurements for comparison w i t h the acoustic observations.  29  3.4  Acoustic Characteristics In the interpretation of the acoustic data, the various system  characteris-  tics must be considered. Frequency response determines the scale at which i n formation is provided, the sampled space is restricted by the transducer  beam  pattern a n d for the active sonar systems, further spatial definition is achieved through t i m i n g a n d the acoustic pulse length.  T h e vertical sonar system  be described first because it requires consideration of all sonar thereby introducing all of these topics. systems  will  characteristics  T h e sidescan sonar a n d ambient sound  can then be considered, without detailed background on any of the  operating parameters.  T h e system characteristics  are summarized i n T a b l e  3.1;  all of the parameters  identified i n Table 3.1 will be defined through descrip-  tions of the the individual sonar systems i n the following section.  3.4.1  V e r t i c a l Sonar The  choice of sonar operating frequency involves a compromise  several competing factors. and  High  between  frequencies allow for better range resolution  Doppler performance but are limited i n m a x i m u m range due to acoustic  absorption.  For the present  application to subsurface bubbles, it is necessary  to select a frequency at which these bubbles will resonate a n d so provide adequate acoustic backscatter. frequency was selected significant  F o r the vertical sonar system, a 200 k H z operating  which responds to 32 fim diameter bubbles of which  numbers are expected  i n near  surface bubble clouds (Farmer and  Vagle 1989).  An narrow  I T C model 5298 transducer acoustic  beam.  (serial number 2) was used to provide a  50% of the energy  transmitted by this transducer is  30  Sonar  Frequency  Ping  3 d B Beam  Pulse  Range  Rate  width  Length  Resolution  ms  m  kHz  Hz  Sidescan  100  2  2° x 50°  0.1  .075  V-Sonar  200  6  3°  2.6  2  Ambient  2-20  -  360°  -  -  T a b l e 3.1:  Sonar operating parameters  projected along a b e a m of 3 ° w i d t h (this angle is the 3dB beam width) and ensonifies a disk of 3 m  diameter at the surface of the ocean.  T h e frequency  response of this transducer is wide compared to the b a n d w i d t h of the recording system used a n d so the b a n d w i d t h of the data is restricted to 22 k H z . The  transducer  b e a m can only constrain the direction of data sampling  a n d a pulsed active sonar system is required to provide range discrimination. When  a short  pulse of sound is transmitted,  the range to any object  which  scatters sound can be determined by considering the speed of sound i n water a n d the time elapsed.  Depending somewhat  speed of sound in water is about C = 1475  on temperature  ms" . 1  and salinity, the  A t any time t after a pulse  of sound has been transmitted, the acoustic backscatter  will be received f r o m a  31 distance d = Ct/2. For the present application, E q u a t i o n 3.1  3.1  essentially bounds the rate at which  vertical sonar data can be collected: for the instrument located at 30 m depth, the acoustic returns f r o m the ocean surface are not received until 40 ms  after  transmission. Some margin must also be allowed for deployment variations and so conservatively, 80 ms was allowed between transmissions. A n additional factor is imposed by the recording technique: the data rate must be reduced by half because b o t h vertical sonar systems were recorded onto a single recording channel. In the end, sonar profiles are collected at a rate of 1 every 160 ms  or  approximately 6 every second. T h e range resolution of a sonar system is controlled by the length of the acoustic  pulse used.  This  limitation can  determine the range of acoustic edge of a n acoustic pulse.  be  backscatter  seen by using E q u a t i o n 3.1  for b o t h the leading and trailing  T h e signal received at  some point i n between these boundaries. at time t = 0, the acoustic backscatter  to  any time must  For a pulse of length r  come from transmitted  at time t after the start of transmission  must come from a range,  (LII) < < e i . P  C  2  ~  ~  3.2  0  2  T h e range interval indicated by E q u a t i o n 3.2 results i n a range uncertainty of for the range  estimated  be controlled by adjusting r  to  any acoustic  scatterer.  Range resolution can  so long as there is sufficient acoustic  backscatter  power to be distinguished f r o m noise levels. For general echo sounder applications very short pulse lengths can be used (in practice down to about  0.01ms),  32 but i n the present  application where Doppler processing is intended,  velocity  resolution must also be considered. W h e n sound is transmitted a n d reflected from m o v i n g bodies its frequency becomes surements  D o p p l e r shifted;  it is this effect which allows remote velocity  to be made acoustically.  sound returning to a transmitter  where /  mea-  For a backscatter system, the frequency of  will be shifted by an amount,  is the acoustic frequency, v is the relative velocity between the trans-  ducer a n d scatterer, and C is the speed of sound: inversely to determine the speed of a scatterer.  this relation can be used  E q u a t i o n 3.3  is only  strictly  valid for a single frequency but a modulated pulse composed of many frequencies must be used to provide finite range resolution (as 3.2).  dictated by E q u a t i o n  Theriault (1986) demonstrates that this finite frequency b a n d w i d t h leads  to a velocity uncertainty of, C ATVJT.  Considering Equations 3.2 not This  a n d 3.4  it is clear that fine range resolution is  compatible with fine speed resolution and some problem is considered  i n more  application, a pulse length of 2.6  ms  compromise  detail i n A p p e n d i x C . For  is required. the  present  was chosen providing a range resolution  of 195 c m and a single sample velocity uncertainty of about 0.23  ms  - 1  .  Such a  speed uncertainty may appear unacceptably large, but it must be realized that 6 independent velocity estimates can be realized each second and the error be rapidly reduced through averaging.  can  33 B o t h the velocity and range estimates of the vertical sonar are made relative  to the instrument  instrument  package.  package  and so are  M o t i o n of the  package  contaminated along the  that velocity directly into the sonar velocity estimates. ity component, the accelerometer  by motions of the  sonar  axis  introduces  T o remove that veloc-  data was adjusted to correct for the varying  component of gravity caused by instrument tilt and then integrated to provide an axial velocity estimate for the instrument.  T h e accelerometer  data was sim-  ilarly used used to correct range estimates for instrument motion. tilt will cause horizontal current the vertical sonar beam.  Instrument  components to be resolved along the axis of  N o correction  could be made for such errors  even  with knowledge of the instrument tilt because only one component of velocity is measured i n the present application.  3.4.2  Sidescan Sonar Sidescan sonar systems  are most  tion of structures on the ocean the entire  floor.  commonly used to display the distribuT h e present  system is turned upside-down to  ocean surface.  application is similar, only  look at  bubble clouds along  No attempt was made to develop this hardware for the  application; the transducers  and amplifiers f r o m an E D O M o d e l 606,  the  present 100 k H z  sidescan sonar were modified to meet the needs of the present apphcation. T h e 100 k H z system was selected because 50 fim diameter bubbles resonate at this frequency a n d there are large numbers of such bubbles located near the  ocean  surface (Farmer and Vagle 1989). Sidescan sonar systems have transducers with fan shaped beams to provide fine horizontal resolution, but poor vertical resolution.  ( T h e E D O transducers  have a 3 d B beam w i d t h that is 5 0 ° i n the vertical a n d 2 ° i n the horizontal  34 sense).  For the special case of acoustic  scatterers localized along a plane sur-  face, such as bubbles at the ocean surface, the system samples the line along which the f a n beam intersects the  plane surface.  In effect,  the  beam  shape  provides the horizontal resolution, while the surface provides the vertical resolution.  E q u a t i o n 3.1  is used to determine the exact point along the line of  intersection from which data are received.  Details of the spatial sampling of  the sidescan sonar are given in A p p e n d i x D ; range resolution is about 7.5  cm,  along a 2 ° ray extending along the ocean surface. Unlike the vertical sonar systems, there is no limit to the range over which data can b e collected except that imposed by the signal to noise limitations a n d sonar power. range  was  For the sidescan system as deployed, the m a x i m u m usable  approximately  200  m.  Based  on E q u a t i o n 3.1,  are required for sound to return f r o m such a range,  267  a n d so this  limits the m a x i m u m sample rate of the sidescan sonar.  ms  of  requirement  It was not  desirable  to have the various sonar transmission rates independent of each other any  sonar  transmission would contaminate  data  on all other  sonar  T h e vertical sonar systems were operating with a cycle time of 160 sidescan systems were therefore operated at one transmission every 480  A  single sidescan b e a m can only provide information projected  spatial component defined by the beam axis.  because systems.  ms.  The  ms.  onto  the  For the study of bubble clouds,  it is of value to know how structures are organized i n two dimensions. sidescan transducers  data  were oriented orthogonally to each other  i n Figure 3.1 and will be further discussed i n Chapter 4).  Two  (as is indicated  35 3.4.3  A m b i e n t Sound Record T h e purpose of the ambient sound recording system was to observe sound  generated  naturally at the ocean surface.  These sounds are generated  at fre-  quencies less than 100 k H z by w i n d stress, breaking waves, a n d rain ( K n u d s e n et a l . 1948).  Sound levels must be recorded over a b r o a d b a n d of frequencies  i n order to study the general characteristics  of these sounds.  For this application, a n I T C 6050C hydrophone was employed as it has a flat frequency response for signals between 2 k H z a n d 40 k H z a n d a n o m nidirectional response. active  sonar,  Because the ambient sound recording system is not an  the pulse travel  time delay (Equation 3.1)  determine the range to a source. is that  it must  lie somewhere  cannot  A l l that is known about  within  be used to  a source location  the angular receiving area of the hy-  drophone. T h e localization of ambient sound sources at the ocean surface leads to  somewhat  finer spatial sampling due to the dipole characteristic  surface sources (Vagle et a l . 1990). depth,  of near  F o r the hydrophone placement at a given  a circular region at the ocean surface centered above the hydrophone  location c a n be identified as providing 50% of the received signal power (analogous to the 3dB b e a m pattern for a transducer).  F o r the deployment geometry  used (Figure 3.2) the effective listening area is a disk of 60 m diameter.  Unhke  the active  sonar  systems,  there is no pulsed nature  sound  a n d so the data  can be recorded  continuously.  sonars  are removed i n frequency f r o m the ambient  to  Although  sound system,  ambient  the  active  the high  power transmissions contaminate the ambient sound data a n d so these portions of the data must be discarded. P r i o r to system deployment, it was not known if g o o d quality data could be recovered between such contaminated data. T h e  36 active  sonar systems  were disabled for a 10 minute period every hour so as  to insure good quality ambient sound data i n this situation.  In fact,  ambient  sound data could be recovered at all times (using the techniques described i n Appendix E) the  and so continuous ambient sound data were recorded.  hydrophone responded to frequencies  recorded digitally at  a 44  as  high  k H z sampling rate.  as  40  k H z , the  T o accommodate  Although data  the  was  22 k H z  b a n d w i d t h of the recording system, the data were filtered to eliminate frequencies greater than 22 k H z .  3.5  Data Recording D a t a recording for the conventional oceanographic instruments employ es-  sentially estabhshed techniques which will not be discussed further.  Only  the  data rates used and some of the considerations leading to the choice of those data rates will be discussed. In contrast, acoustical data are quite novel.  the recording techniques used for the  T h e essential characteristics  of these recording  techniques will be discussed here, but details of these procedures are presented separately i n Appendices B , C , D , and E .  3.5.1  Conventional Instrumentation The  time  scales  of interest  during  the  the order of minutes for a period of about  instrument a week.  deployments were  of  T h e recording rates for  the various instruments needed to be as r a p i d as possible consistent  with the  recording m e d i a available a n d the power supply of the instruments. T h e choice of sampling rates was selected based on this requirement; these are summarized in Table The  3.2. data recording for the Datawell Waverider buoy was modified some-  what to meet  the conditions encountered during the  Ocean Storms  program.  37  Instrument  Waverider  Sample P e r i o d  m  s  0  .5  S4  C/M  41  30  S4  C/M  125  30  0  5  Met.  T a b l e 3.2:  Depth  Stn.  D a t a recording rates.  T h e Waverider buoy is normally used in a near shore configuration i n which it transmits Such  a continuous record of wave data to a receiving station on shore.  a configuration could have  been used i n the  present  application if an  attending ship had been available to provide a reliable receiving station, such a ship was unavailable during the deployment.  T h i s problem was  but over-  come by installing a Seadata model 639-8 Wavelogger recording package i n the Waverider buoy thereby  converting the  system  into a self-contained  package.  T h i s approach restricts the Waverider resolution from that realized by the buoy itself because of the finite storage space available a n d the eventual  recording  configuration was necessarily a compromise. Wave data were recorded at a rate of 2 H z continuously during the deployments of the acoustics package.  3.5.2  Acoustical D a t a The  recording requirements  of the  acoustical  data provided several  stantial challenges not the least of which was the volume of data itself.  subThere  38 are four separate sonar systems (two vertical sonars, the sidescan sonar, a n d an ambient sound hydrophone) each generating data w i t h a characteristic width of order 10 k H z . In addition, i n order to meet Ocean  Storms  of several  project,  a  the objectives of the  capability of continuously recording for  days was required.  These objectives  were  band-  met  a  period  by recording  data  with conventional V H S video cassette recorders ( V C R ' s ) combined with a Sony Pulse C o d e M o d u l a t i o n ( P C M ) digital interface. with an 8 hour recording capacity,  B y combining 10 V C R ' s  each  the system was capable of recording data  continuously for 80 hours. There  are  three types  video channel providing  of storage formats  available o n a V H S V C R ; a  two digital channels of 16  bit resolution at  a  44.2  k H z sampling rate (through use of the Sony P C M ) , two H i - F i analog channels capable of recording a 20 k H z b a n d w i d t h with a d y n a m i c range of about dB,  and a low quality audio track.  T h e ambient  sound data  were  80  recorded  onto one of the digital channels while the two vertical sonars shared the other. The  sidescan sonars were recorded onto the H i - F i analog channels, data from  one transducer on each of the two channels. T h e low grade audio channel was used to store ancillary data (such as time a n d instrument attitude)  by means  of a 2400 b a u d modem. T h e r e is little signal processing required to record most of the data: A p pendix B provides details of such processing as is necessary.  T h e vertical sonar  data presents special problems because of the need to recover signal phase for Doppler speed estimates.  For this purpose, an implicit clock sampling scheme  has been employed as described i n A p p e n d i x C . T h i s scheme allows b o t h data channels resulting from a complex gle digitizer.  demodulation to be recorded with a  sin-  There is a degradation i n data quality with such a simplifying  39 approach:  since b o t h complex channels are stored onto a single channel,  the  bandwidth of the recorded signal is reduced from 20 k H z to 10 k H z . A s a whole, the acoustical instrument package collects data at a rate of 176800 16  bit samples every second m a k i n g it prohibitive to analyze all the  data that this system could generate over a several week period. In a d d i t i o n , the  package  is restricted  to an 80  hour recording life so that  if continuous  observations are made, the entire acoustical instrument array would have to be recovered a n d redeployed every 4 days. Such a procedure would not be possible in  severe  interest an the  weather  conditions and  these  are  exactly  i n the study of near surface dynamics.  acoustic  release  was modified to  instrument package.  Through  the  conditions of  most  T o overcome these problems,  provide an acoustical  use of this system,  the  control h n k with package  could be  controlled remotely f r o m an attending ship and o p t i m a l use could be made of the system's recording life.  40  Chapter4 Observations T h e acoustical observations presented i n this chapter were made as part of the O c e a n Storms project  aimed at improving the understanding of the  response to storm forcing.  T h i s project  ocean  a series of ship surveys.  moorings as well as  involved a large array  ocean  of long  T h e acoustical  term  observa-  tions were not an integral part of the coordinated study, but the participation as part  of the  Ocean Storms program insured a complete  suite of ancillary  observations. T h e acoustical instrumentation deployed as a drifting instrumentation array is described i n Chapter 3: platform of acoustic  it consisted of a Datawell Waverider buoy, a  instrumentation,  a n d two Interocean  S4  current  meters.  T w o successful deployments of the acoustical instrumentation were made f r o m C S S Parizeau during a survey cruise f r o m October 12, 1987 until November 11, 1987. 26, was 157.5  T h e first deployment lasted 21 hours beginning at  and is characterized a more extensive  18:00  U T C October  by a period of increasing w i n d speeds.  deployment starting  at  02:30,  October 29  hours during which 70 hours of acoustic data were collected.  T h e second a n d lasting A drifting  meteorological buoy was also deployed and provides w i n d speed data  during  the longer acoustics package deployment. A time hne identifying the periods of data collection with the various instruments is shown i n Figure 4.1.  In this chapter,  observations from the first (21  considered i n detail as they  demonstrate  hour) deployment will be  the evolution of subsurface bubble  41  Ocean S t o r m s Acoustic Data  Parlzeau Cruise  12  ^_  12:00 2130  Acoustics Platform  23:15  230  17:00 h  H I — I  raao  5:oo  is:oo  1B:00  21:45 I  Waverlder & S4  1  C/M'S  23:00 1 h  15:00  Met. Stn. Aanderaa data  i 2 2  Z1:  4.1:  18K30  18:00  ^_ 16,-oa  1  1  1  1  1  1  1  1  1  1  1  1  2 3  2 4  2 5  2 B  2 7  2 B  3 9  3 0  31  1  2  3  October  Figure  230 I  1387  1 -  4  1  i  1  1  1  1  5  B  7  8  9  1 0  1 11  November 19B7  T i m e line identifying periods of data  availability f r o m various  instrumentation groups (all times are i n U T C ) .  clouds while the wind speed increased f r o m near 0 to 13 provide a perspective  on the observations,  ms' .  In order  1  an overview of wind speed,  state, a n d average bubble cloud properties is first given i n Section 4.1. discussion of measurement for a proper  to  wave Some  techniques is included i n this overview where needed  interpretation  of the  data.  Section 4.2  describes  the  tion of bubble clouds as seen i n sidescan and vertical sonar data.  organizaT h e pres-  ence of bubble clouds below the surface indicates downward vertical velocities. These vertical velocities are investigated i n Section 4.3  using acoustic  Doppler  42 techniques applied to the vertical sonar system. heavily averaged i n time to get  Because  these data must  be  the required velocity resolution, a conditional  averaging scheme is employed to determine a velocity section across an idealized (average) bubble plume.  4.1  D a t a Overview T h e d a t a presented i n this chapter  are drawn f r o m a 21 hour period of  increasing w i n d speed. A summary of the sea state and bubble cloud response to this w i n d forcing are given i n Figure 4.2. The the  near  record of w i n d speed is important surface  processes.  During  since it  this first  drives the  deployment, the  energetics  of  meteorological  buoy h a d not yet been deployed a n d so accurate anemometer w i n d speeds were not available. W i n d speed estimates  are instead obtained from the established  relation between ambient sound levels and w i n d speed: 1Q  V= In E q u a t i o n 4.1,  V  SSL /20 0  j  _  b  .  is the w i n d speed (corrected  4.! to  10 rn height),  the ambient sound source level i n a 1 H z b a n d w i d t h about in d B relative to a signal of \\iPa /'Hz 2  at 1 m range (ie.  d B re -1  respectively.  is  0  8 k H z expressed  and S a n d b are calibration constants with values 52.87 fiPa/ms pPa  SSL  lfiPa /Hz), 2  a n d -80.94  Using these constants Vagle et al. (1990) demonstrated that  E q u a t i o n 4.1 provides a robust measure of surface w i n d speed with an accuracy of about ± 0 . 5 m s  - 1  in the deep ocean.  W i n d speeds derived f r o m E q u a t i o n 4.1  are shown i n Figure 4.2a,  Figure  4.2b shows the ambient sound levels u p o n which these observations are based.  43  fi  V Bubble Depth i  -12  1  d  150  >  100  3  2 6 / 1 0 22:00  2 7 / 1 0 05:00  27/10  12:00  27/10  19:00  time (UTC)  Figure  4.2:  Summary of observations for the 21 hour period beginning at  22:00 U T C , 26/10/87; a) 10 m w i n d speed (dashed line - anemometer sohd line - ambient sound based), significant  wave height,  b) ambient sound level (7 to 9 k H z ) , c)  d) average depth penetration  e) depth integrated scattering  speeds,  cross section,  M.  periods used to produce Figures 4.8a, b a n d c.  v  Bars  of subsurface bubbles, A , B , a n d C identify  44 Near calm conditions occurred at the beginning of the deployment w i t h speeds gradually increasing to a m a x i m u m of 13 servations as part  are  ms  - 1  .  available for this period f r o m a meteorological buoy deployed  of the  long term  Ocean Storms  program which was located  50 k m of the acoustic instrumentation at 4 7 ° 58' are shown by the sectored line i n Figure 4.2a). the  acoustically derived w i n d speeds:  of small scale  A d d i t i o n a l w i n d speed ob-  features  are  expected  N , 1 3 9 ° 15' W  within  (these data  These observations agree with  differences i n the time a n d magnitude because  of the  distance  separating  the  observations.  T h e high frequency echo sounder on the instrument can be used to provide an effective and accurate measure of sea-state.  T h e errors that could be  introduced by instrument motion i n the present application have been removed by  using the  accelerometer  data  available.  Echo  sounder estimates  of wave  height are preferred to Waverider data because the data are then collected using a c o m m o n clock:  comparisons between Waverider and echo sounder wave  records i n this data set have demonstrated the accuracy Appendix F).  Significant wave heights (E~i/ )  of this approach  (see  are shown i n Figure 4.2c;  they  increase gradually i n proportion to the wind speed, but detailed features  (such  3  as the squall passing at 03:00) do not appear clearly i n the wave records. Such insensitivity of - f f i / period waves.  3  is to  be expected  since it  is dominated by the  W h e n the wave data were filtered to isolate only the  longer shorter  period waves there was still no clear correlation with short term events.  T w o measures of the subsurface bubble field provide a graphical summary for comparison with wind a n d wave data:  the average penetration  bubble clouds, a n d the integrated volume of subsurface bubbles.  depth of  Figure  4.2d  45 shows a time series of mean bubble penetration depth.  T h e general t r e n d i n  these data is towards increasing penetration depth w i t h increasing w i n d speed. T h e observed bubble depth of about  1 m which persists at low w i n d  is likely due to the presence of biological scatterers.  speeds  A n interesting feature is  the abrupt occurrence of bubbles at about 6 metres for a limited time around 03:00 U T C , 27 October during  a squall observed i n the wind speed record.  T h e bubble plumes subsequently disappear when the w i n d speed subsides, and do not reappear until the wind speed again exceeds 7 m s  - 1  . T h i s behaviour  suggests that there may be a threshold wind speed of about 7 m s before subsurface bubbles can be detected with the acoustic  required  - 1  systems.  A n indicator of subsurface bubble volume can be obtained b y determining the scattering  cross section per unit volume M „ , detected  by a vertical  echo  sounder as described by T h o r p e (1982): Rv e 2  M, where  R is the range,  h  2  2nR  = « J ^ _ ,  uj is the output  voltage  4.2 recorded at the receiver,  is the acoustical attenuation due to chemical absorption (0.0131 m k H z sound), a n d Q is a constant a n d sonar  characteristics.  of the total  for 200  for geometry  Integration  v  c a n only be used to indicate relative of M  v  changes  over each profile provides an indicator  volume of bubbles interacting with the particular echo  frequency (with diameters of order 32 fim for the 200 k H z sonar). of this estimator  1  T h e value of Q has not been determined for the  sonar systems used a n d so M i n bubble volume.  scaling factor which accounts  -  n  sounder  T h e value  for the 200 k H z system is shown i n Figure 4.2e; the verti-  cal scale is arbitrary a n d only provides a relative indication of the entrained bubble volume.  It is interesting to note that the volume of bubbles injected  46 during the squall at about  03:00 is small compared to the volumes injected  during the subsequent period of sustained high winds, even though the depth of penetration at b o t h times is similar. A more complete representation of the sea state development is seen i n the evolution of wave spectra  (Figure 4.3).  M o s t of the wave energy is contained  in the swell with period between 8 a n d 12 seconds.  T h e waves generated by  local w i n d forcing appear at around 12:00 U T C . T h e p e r i o d is initially about 5 seconds, but systematically shifts to a longer period as the sea state develops. Toward the end of the data record, the sea could be considered fully developed since the w i n d waves have achieved a period of about 8 seconds a n d waves of this period are the longest that the 13 ms  -1  wind can generate based o n wave  speed ( L e B l o n d a n d M y s a k 1978). T h e wave field must directly control the incidence of wave breaking and thus might be expected to modulate the ambient sound variability as discussed by Farmer spectra  a n d Vagle (1988).  In order to illustrate this relationship, power  of the modulations of the ambient  same format  and scale as the wave spectra  an increased level of ambient  sound field are displayed i n the (Figure 4.4).  sound, the spectra  Whenever there is  show a strong m o d u l a t i o n  at surface wave frequencies. T h i s result differs from the coastal observation of Farmer  a n d Vagle (1988)  and visual observations by D o n e l a n et.  al.  (1972)  where breaking wave events occurred at half the dominant wave frequency. These results provide a picture of developments during a period of increasing wind.  Associated w i t h the increase i n wind speed is a rise i n significant  wave height a n d the appearance  of shorter  period waves.  plumes w i t h an average penetration depth of about  Subsurface bubble  6 metres occurred when  Power  ated waves to l o „ e g  r  P ^ ^ ^ n ^ ' J ^ ^ ^  ™ ^  48  Power 0  10000  i  1  22:00  Time  Figure  4.4:  —  1  1  ,  1  05:00  Waterfall  1  —  1  — "  %  1  |  4  19:00  sound m o d u l a t i o n  spectra based on  5 k H z a n d 15 k H z for the 21 hour period  beginning at 22:00 U T C , 27/10/87. that of 4.3 to aid comparisons.  — • — " —  26-27/10/87  of ambient  sound levels i n the b a n d between  1  12:00  (UTC)  plot  — — p —  T h e scaling i n this  figure  is identical to  49 wind speeds exceeded  a threshold of approximately  7 ms .  subsurface bubble plumes d i d not imply a large increase of subsurface  bubbles; total  T h e presence  -1  of  i n the total volume  bubble volume does however  appear  to  be  well  correlated w i t h wind speed.  4.2  Bubble Cloud  Structure  T h e sonar data, b o t h vertical a n d sidescan, yield more detailed information on  the  structure  a n d dynamics of the  bubble clouds.  T h e sidescan  images  provide an indication of the way i n which subsurface bubbles are distributed along the surface, as first shown by T h o r p e a n d H a l l (1983). F i g u r e 4.5  shows  an example of 5 minutes of sidescan sonar data from the two orthogonal beams computer  processed  into a sonogram images;  Figure 4.5a  shows data  from a  b e a m oriented horizontally at approximately 1 9 0 ° true, and F i g u r e 4.5b is from a b e a m oriented along 1 0 0 ° true.  Details of the processing required to produce  these figures is found i n A p p e n d i x D . T h e wind speed at this time is 13 from  1 7 0 ° true.  To aid i n the  chosen for display i n Figure 4.5  interpretation  of these data,  the  5  ms  -1  minutes  corresponds to the period displayed i n Figure  3.4 (page 27).  T h e bands seen i n Figure 4.5 in  Figure 4.5a  these groups are  while i n Figure 4.5b  are caused by discrete stable bubble groups, slowly approaching the  their ranges remain nearly constant.  instrument  Individual bands re-  tain their identity for the 5 minutes displayed i n Figure 4.5; time  series  the bands remain distinct a n d coherent  package,  i n more  extensive  for periods of u p to  20  minutes as they slope across 100 m of range i n the sidescan image. T h i s upper limit  is constrained by the  sonar's  range  (approximately  200  m)  and by  the  50  Acoustic  11:45:00  Baclcscatter  11:47:30 Time  11:50:00  (UTC) 27/10/87  F i g u r e 4.5: Example of 5 minutes of sidescan sonar data collected during 13 ms  - 1  100°  winds; a) is along the direction 1 9 0 ° true, and b) is along the direction true.  Instrument  orientations  for this period are shown i n Figure  3.4.  Line ' A ' identifies a surface wave disturbance, line ' B ' identifies a disturbance caused by instrument rotation (this event is identified as ' B ' i n Figure 3.4f).  51 speed w i t h which they  are  advected  through the b e a m .  It  is quite possible  that they remain coherent over greater temporal and spatial scales. Surface waves travelling across the bands cause coherent bances which slope steeply across the sonar image.  periodic distur-  T h e disturbance is caused  by the periodic wave currents advecting acoustical scatterers and the slope reveals the phase velocity of the waves,  resolved along the sidescan b e a m .  example of such a disturbance is shown by line ' A ' i n Figure 4.5a. turbance travels about 145 ± 8 ms~ ; 1  data  m i n 5.8  An  T h i s dis-  s indicating a speed along line ' A ' of 25  this same wave is not apparent i n the orthogonally oriented sidescan  of Figure 4.5b  indicating that  the true phase speed is about  25  ms~  l  i n a northerly direction. Large uncertainties i n this calculation result f r o m the difficulty i n estimating the short time differences a n d the unsteady  instrument  heading (see  themselves  Figure 3.4  page  27).  T h e constant  heading changes  cause a distinctive disturbance to these images; a simultaneous change i n range is seen i n all the scatterer bands with the degree of distortion depending on the range.  A n example of this effect is identified by line ' B ' i n Figure 4.5a  the 1 0 ° heading sweep that caused it is labelled ' B ' i n Figure 3.4.  and  Individual  bands often retain their identity through such heading swings for as m u c h as 40 metres of arc length. B y taking account of the apparent range changes and corresponding heading variations, the orientation of the bands can be derived. T h e y are typically aligned to within 1 5 ° of the w i n d direction consistent  with  similar observations by T h o r p e et al. (1985).  T h e correspondence  of the bands appearing i n the sidescan images,  the bubble clouds familiar i n images obtained using vertically oriented is illustrated with simultaneous presentations  with  sonars,  of b o t h data types (Figure  4.6).  52 T h e echo sounder data provides a record of the vertical extent of  subsurface  bubble clouds revealing a uniform cloud of bubbles close to the surface with periodic plumes of bubbles extending downward to depths of about The  arrival  coincides  of scatterer bands  w i t h the  at  zero range  in the  sidescan  appearance of a bubble cloud i n the  8 metres.  sonar  usually  echo sounder  data.  Lines have been drawn u p from the bubble plumes and along the mean  slope  of the sidescan image to associate bubble plumes w i t h respective bands i n the sidescan image.  In must  considering  be  born  Figure  in m i n d .  4.6, The  the  distortions  wave action (identified i n Figure 3.4) data i n this presentation. at  small ranges (cf.  limitations  of the  caused  by  sidescan  instrument  sonar  system  motions  tend to b l u r the highly averaged  and  sidescan  In addition, the poor range resolution characteristic  E q u a t i o n D.2)  makes  identification of the  exact  arrival  time of any bubble plume difficult. Because the slope of the bands i n Figure 4.6  remain constant, it is possible to identify bands at  extend t h e m  along the  prevailing slope to  determine  greater distances and  the  arrival times.  bands and plumes are time evolving and finite i n space so that i n the image structures appear  a n d disappear suddenly.  The  sidescan  In view of these limitations,  it cannot be expected that a scatterer b a n d could be identified for each bubble plume observed.  T h e number of scatterer bands arriving is certainly  compara-  ble to the number of bubble plumes observed and i n most cases a plume can be associated with a scatterer b a n d , suggesting that most if not all plumes are associated with scattering bands. A two dimensional image of the subsurface bubbles could be obtained by correctly accounting for the motion and orientation of the acoustical  instrument  53  Time  Figure  4.6:  sonograms  Simultaneous  (UTC)  sidescan  (bottom half of image).  bubble plumes occurring  i n the  (top  27/10/87  half of image)  and upward looking  Lines have been drawn up from the  vertical  sonar  image  and along  slope of the bands i n the sidescan image to help i n m a k i n g  the  associations.  larger  average  54 package relative to the drifting surface layer a n d projecting plots of the sidescan data onto a surface i n the correct orientation.  A requirement for such a  representation is a record of the instrument motion relative to the near surface bubble clouds.  A s pointed out b y S m i t h et a l . (1987), although it is possi-  ble to estimate  the speed of the package relative to the surface by measuring  the slopes of coherent structures i n the images, such measurements would only yield the component orthogonal to the parallel bands of scatterers. A n alternative approach makes use of the current meter observations obtained f r o m below the instrument at 41 m depth. If it is assumed that the water i n the m i x e d layer moves uniformly w i t h respect  to depth, this velocity is a valid  estimate  of the relative motion between the bubble clouds (in the m i x e d layer) a n d the instrument package.  T h i s assumption is only an approximation, b o t h the 3-  dimensional structure of L a n g m u i r circulation a n d shear associated with Stokes drift are being ignored. Current meter measurements  through the mixed layer  show that the effects of L a n g m u i r circulation are smaller at depth (Weller and Price,  1988).  T h e current  meter positioned above the thermocline will record  the mean relative mixed layer speed with  fluctuations  caused b y the passage of  successive L a n g m u i r cells. T h e averaged observations should therefore provide a reasonable estimate of the mean relative speed. A n a posteriori  confirmation of  the success of this processing is provided when the two sidescan beams create a consistent image during changes i n the instrument drift velocity.  Figure  4.7 shows  a subsurface bubble m a p created  transformed by this m e t h o d based on current of 50 minutes.  meter  using sidescan  records  data  for an interval  T h e resulting m a p is not as clear as the original sonograms  because wave motion a n d t e m p o r a l changes smear the location of the targets.  55 T h i s particular example was selected because the image created above a n d below the instrument track are produced by individual (separate) beams allowing a direct comparison of their respective maps. It is obvious that the images created b y the beams are qualitatively consistent showing a n elongation of bubble plumes along a direction of about instrument  1 6 0 ° . A b o u t midway across the m a p , the  speed a n d direction change abruptly, resulting i n some distortion,  but the gross features are preserved the procedure.  Uncertainties  a n d thereby  i n the navigational data preclude accurate  parisons of row alignment with w i n d direction. 4.7  demonstrate the viability of com-  T h e image presented i n Figure  does demonstrate that bubble clouds are collected into 10 m wide paral-  lel bands w i t h length of about about It  100 metres a n d separated f r o m each other by  10 m . is immediately  tempting  to associate  these  bubble plumes  w i t h the  windrows of L a n g m u i r circulation (Langmuir 1938). Similar banding i n sidescan sonograms  was reported  b y T h o r p e and H a l l (1983) who observed  (caused by Langmuir circulation)  i n coastal waters.  windrows  S m i t h et a l . (1987)  also seen evidence of Langmuir circulation w i t h sidescan sonar.  have  T h o r p e (1984a)  assumed that bubble plumes visible i n an upward looking sonar were caused by passing L a n g m u i r cells; these d a t a support that assumption. Further circulation  support  for the association  of the bubble rows  can be obtained by determining their  orientation  with  Langmuir  w i t h respect to  the wind. If the rows are caused by Langmuir circulations they are expected to be aligned w i t h the wind direction (Leibovich 1983). F o r the example of Figure 4.7  the bubble plumes  are oriented  approximately  1 6 0 ° true,  a n d the wind  direction was from 1 7 0 ° consistent with that expected for L a n g m u i r circulation.  56  Acoustic Backscatter  (dB)  0  12  160 X F i g u r e 4.7:  Position  320 (m)  Composite spatial map of subsurface bubble clouds observed dur-  ing the period 11:10  - 12:00  U T C 27/10/87.  T h e sectored line identifies  the  instruments track. B u b b l e clouds are collected into long narrow bands oriented parallel to the wind.  57 Some idea of the evolution of windrows can be gained by looking at the cell spacings observed w i t h the sidescan sonar over a n extended period. These scales  are most  corrected  easily measured off the sidescan sonograms  (rather t h a n the  surface maps) because of the greater clarity of the sonograms. T h e  spacings measured f r o m a single sidescan b e a m are the cell spacings projected onto that b e a m .  T o estimate  the actual spacings it is assumed that the two  orthogonal sidescan beams sample windrows which have the same distribution of spacings a n d consequently the same mean spacing. B y comparing the mean spacing observed by each relative  of the two beams,  to the windrows can be determined,  the orientation  of the  beams  a n d the distributions can be  corrected for orientation. Figure 4.8 shows three cell spacing histograms speed increased from near making <  these histograms  7 ms  - 1  ,  about  0 to 13 m s  - 1  .  accumulated as the wind  T h e observation intervals used i n  are indicated i n Figure 4.2a:  10 m s  - 1  ,  and >  10  ms~  l  the w i n d  correspond  to histograms  Figure 4.8a, b a n d c respectively. A t wind speeds below 7 m s the cell spacing ranges  speeds of  - 1  of  (Figure 4.8a),  from 1 to 10 m with a mean of a r o u n d 4 m.  The  observed spacing shifted to larger scales with increasing wind as shown b y the histograms of Figure 4.8b and c. W h e n the w i n d increases to greater t h a n 10 ms"  1  the spacing varies between 2 and 20 m with a mean value around 8 m  (Figure 4.8c). A t any time a range of scales coexist with a tendency for larger scales to occur at higher wind speeds. those presented by T h o r p e a n d H a l l  These histograms agree i n general with (1982) based on temperature  anomalies  seen by a towed thermistor chain. A  characteristic  of L a n g m u i r circulation predicted b y some theories  is a  difference i n wave heights occurring i n windrows f r o m those occurring elsewhere  58 100-  a) o  U, < 7 m/s 0  75-  a0  u 0 0  50-  o 1)  > 25-  0)  0100-  b) U = 10 m/s l0  0) u Cl u  75-  o 0  50-|  o  LTL  250)  o100-  c) U,o > 10 m/s  •>—'  0  75-  d In  CJ 0 50-  o >  25-  • rt  (fl «  0-r-L  5  10  15  Spacing  Figure  4.8:  (m)  Histograms of windrow spacing based o n sidescan sonar  Observed winds were less t h a n greater t h a n  20  10  ras  -1  (4.8c).  7 ms  - 1  (4.8a),  about  10 m s  - 1  data.  (4.8b), and  T h e time intervals over which the histograms  were accumulated are shown by bars labeled A , B , a n d C i n Figure 4.2a.  59 (Leibovich 1983).  T o test for this characteristic,  root mean square (rms) wave  displacements were determined f r o m the vertical sonar, bubble clouds were seen to penetrate  using data for which  to greater t h a n 5 m depth, a n d sepa-  rately when bubble plumes were not seen beyond 5 m depth. In this approach it is assumed that the presence of bubbles beyond 5 rn depth is a n indication of the presence of a windrow. Values were accumulated over 2 hour periods starting at 07:00 U T C a n d continuing to 19:00 w i t h no significant differences appearing between the two rms values (Table  4.1).  D a t a from before this  period d i d not have sufficient occurrences of deep bubble plumes to allow accurate estimates.  In W i n d r o w  No Windrow  cm  cm  7:10  72 ± 1  71 ± 1  9:10  77 ± 1  77 ± 1  11:10  85 ± 1  85 ± 2  13:10  89 ± 1  88 ± 2  15:10  95 ± 2  92 ± 2  17:10  91 ± 2  89 ± 2  Time ( U T C )  T a b l e 4 . 1 : R M S wave displacements inside a n d outside of windrows.  4.3  Vertical Velocities The  windrows of L a n g m u i r circulation f o r m  downwelling sites.  W e therefore  expect  at  local  convergence  to observe downward velocities  cident w i t h the bubble plumes. T h e Doppler processing of vertical sonar  and coindata  60 as described i n A p p e n d i x C allow estimates to be made of the vertical component of these currents.  T h i s technique does have the advantage  remote non-invasive velocity estimates, system characteristics  The the a  standard  present  sampling can  i n the  data  0.75  ms  - 1  ,  ms~  l  files.  - 1  sonar  ).  ms  - 1  noise and  T h e observations  which is consistent  pected uncertainties caused by wave motion (1.2 ms  is limited by  caused by instrument  be reduced by averaging.  deviation of about  sampling (0.25  accuracy  as outlined i n A p p e n d i x C .  r a n d o m errors  Doppler  but the  of m a k i n g  )  show  with the  and incoherent D o p p l e r  M e a n velocity estimates with accuracies of about  are needed requiring the averaging of about  1000  ex-  0.01  individual speed pro-  Such a n average requires 3 minutes of data while single bubble plumes  are only visible for about 5 minutes. Clearly the instrument travels too quickly to provide a useful velocity section through an individual bubble plume when using the 3 minute sampling p e r i o d required. In order to create a velocity section representative bubble plume a conditional averaging scheme locity profiles (generated at  of the velocities i n a  was employed.  Unaveraged ve-  a rate of 6 H z ) were accumulated into one of 6  profiles depending on the depth to which bubbles were observed. For example, if bubbles penetrated  to  would be added into the 4  and 6  metres depth.  4.5  metres i n a velocity profile, that  average profile for bubbles penetrating Using  this method,  the  observations  of bubble plumes could be accumulated into one representative method  does  entire profile  include all plumes  that  might  be  created  t h a n L a n g m u i r circulation (such as wave breaking).  by  to  between  from hundreds average.  This  processes  other  A l s o , the plumes are  as-  sumed horizontally symmetrical as no distinction is made between regions of  61 increasing or decreasing bubble depth.  T o a d d a spatial dimension, the aver-  age instrument drift rate is used to scale position according to the number of observations made at a given profile location. Figure 4.9 is an example section  of an averaged  velocity a n d scattering  cross-  through a bubble plume for the period 11:00 to 13:00 U T C during  which time the wind speed was 13 m s  - 1  which there was no acoustical backscatter  . Those regions of the section for o n which to base  speed  estimates  have been left blank. T h e data displayed are based on a n array of 6 horizontal profiles (doubled b y reflection across the center equally i n depth.  T h e velocity estimates  tainties of about 0.01 ms  -1  location),  a n d 6 bins spaced  i n these bins have statistical  a n d none are greater t h a n 0.02 m s  - 1  . In spite of  the sparse section that results, the general f o r m agrees well w i t h that for L a n g m u i r cells (Leibovich 1983):  uncer-  expected  downward vertical velocities are observed  near the center of the plume with the magnitudes decreasing towards the edges of the plume. T h e m a x i m u m vertical velocity occurs at 8 metres depths, w i t h values of about 0.06 m s  - 1  at 8 metres.  A l t h o u g h these seem to be large mean  vertical velocities so close to the surface, they are nevertheless consistent w i t h observations made by Weller a n d Price (1988) who found vertical velocities of 0.3 m s '  1  at 20 metres depth.  Accurate averaged velocity profiles could only be created lected during winds of 7 r n s  - 1  from data  col-  or greater: at w i n d speeds below this level the  reduced bubble concentration provided inadequate signal levels for the D o p p l e r processing.  Within  the limited range  of wind speeds  during which averaged  vertical velocity sections could be obtained there was no significant change i n downwelling magnitudes.  62  Averaged Section  Representative  Figure a  4.9:  Contours of vertical  conditionally sampled sequence  section,  data  were  averaged  over  Position  velocity  (m)  and backscatter  of bubble clouds.  cross-section  T o construct  a 2 hour period beginning at  this  12:10  for cross  UTC,  27/10/87.  4.4  Discussion  T h e short period of data displayed i n this report hints at some intriguing relationships between w i n d T h e data demonstrate  speed,  the expected  sea state,  a n d subsurface  bubble activity.  relationships between w i n d forcing, mean  63 ambient sound levels, and sea state. It is the appearance of the wave spectrum in modulations of the ambient sound signal, observations of spatial distribution and vertical velocities seen i n the bubble plumes that are new. T h e velocity estimates presented by the acoustic Doppler technique are not those of the water itself, but the acoustic scatterers carried by the water.  In  the present application, subsurface bubbles form the dominant source of scattering a n d these will have an upward component of velocity due to buoyancy. For the  200  k H z sonar system being used, the dominant source of  acoustic  backscatter is from bubbles of approximately 32 (im diameter and these have a negligible rise rate of about 0.0006 m s  - 1  .  T h e observations of vertical velocity are subject  to several biasing terms  due to instrument tilt a n d coupled motion (as discussed i n A p p e n d i x C ) . However,  an analysis of these bias terms  suggests  that  any such bias would  be  towards upward velocities. T h i s fact provides increased confidence i n the downward components reported and suggests that even these may be underestimates of the true values. A d d i t i o n a l confidence i n the observations is provided by the reduced velocities occurring near the surface as these observations are the most likely to be affected by surface coupled motions. Some small upward velocities are expected between the windrows of L a n g m u i r cells, but the ability to obtain useful measurement is limited by the absence of scatterers i n these regions. A has  conditional sampling scheme  been used to  determine  circulation convergence of plumes observed are  zones.  the  based  on data  vertical velocity  from all bubble plumes  field  within  It is believed that i n these data,  caused  the L a n g m u i r the  by L a n g m u i r circulation a n d so this  provides a representative velocity section.  majority scheme  64 T h e data show the r a p i d increase i n bubble penetration depth to a mean of 6 metres,  associated  27/10.  event  7  This  w i t h a brief increase  suggests  m s " ) for the existence 1  i n w i n d speed at  a possible threshold i n wind of bubble plumes since  03:00 U T C ,  speed  (of around  the plumes  disappeared  subsequent to the squall a n d reappeared only when the w i n d again increased. The  lag between  peak  plumes would suggest  ambient some  sound levels a n d the appearance  finite  response  of bubble  between bubble plume formation  a n d w i n d forcing. T h e r e is however the question of ambient sound response to w i n d forcing a n d a more extensive data set would be needed to investigate this relationship.  T h e depth penetration of bubble clouds d i d not depend linearly  on wind speed. In contrast, the total volume of bubbles a n d the ambient sound level b o t h varied i n proportion to wind speed consistent production b y breaking waves (Farmer  a n d Vagle 1988)  with ambient sound a n d bubble injection  controlled by wave breaking. T h e penetration depth of the bubbles must then be controlled i n part  by processes  other t h a n wave breaking, a n d L a n g m u i r  circulation is a likely candidate. Based icant  o n root  mean  difference between  windrows.  square wave  surface  displacements,  displacements  there was no signif-  occurring inside a n d outside of  T h i s result must be qualified by the limited horizontal resolution of  the sonar determined by the acoustical beam pattern.  T h e smallest wavelength  that can possibly be resolved with this system is 6 m a n d so the present result is only valid for wavelengths greater than 6 m. T h e spacings between L a n g m u i r cell windrows derived from the sidescan sonar provided length scales windrows i n deep water. sure  that are generally smaller t h a n other reports of  These histograms  of the relative importance  cannot  be considered as a mea-  of these various scales  since no measure  of  65 power is made. Also, any large scale circulation that m a y include smaller scale structures penetrate  will not have been resolved.  A l t h o u g h there are some plumes that  to depths of 12 m , most plumes only extend to 8 m depth or less.  T h i s result, i n addition to the distribution of spacings seen i n the histograms (Figure 4.8), suggests being advected  the possibility of a cascade of scales w i t h smaller cells  (and possibly engulfed) by larger ones.  With  a m i x e d layer  depth of 45 m , L a n g m u i r cells of scales greater than 90 m should be seen (Leibovich 1983, S m i t h et a l . , 1987). It is quite possible that at the time of these observations, the bubbles went into solution at depths b e y o n d 12 m m a k i n g it impossible for acoustical observations to distinguish the larger scales. T h e occurrence of energy at surface wave frequencies i n the ambient sound record is another with  wave  interesting result.  breaking has been  Farmer a n d Vagle 1988, Farmer  a n d Vagle report  T h e association of ambient  well established through  and laboratory some  ambient sound levels) to occur  field  sound levels  observations of  studies by Banner a n d C a t o  (1988).  evidence for wave breaking (as observed b y at half the dominant wave period i n a fetch  limited environment a n d this observation is consistent  w i t h visual records of  breaking  It  i n wave  groups  reconcile the present  by Donelan  observations  et  al.  (1972).  is not possible to  with these previous reports  existing concepts of wave breaking a n d sound generation.  based o n the  T h i s problem will be  investigated further i n C h a p t e r 5 through the use of a simple model of sound generation a n d more detailed analysis of the data.  4.5  S u m m a r y of Observations This  chapter  has reported  on observations  made  using a freely  drifting  acoustics platform deployed i n the N o r t h Pacific ocean as part of the O C E A N  66 STORMS  experiment in the fall of 1987.  face wave  height,  acoustical  backscatter  Acoustical observations include surfrom bubble clouds,  sidescan  sonar  representations of the spatial distribution of bubble clouds, ambient sound levels, and mean vertical velocities.  T h e response of sea state a n d bubble clouds  is described for a 21 hour period of increasing w i n d speed to a m a x i m u m 13 ms .  A m b i e n t sound levels increase i n proportion to the wind while the wave  -1  field  shows the evolution of short  an increase  i n wave height.  period w i n d waves to longer periods and  D u r i n g this time,  subsurface bubble plumes  observed when wind speeds are greater than about 7 ms" . 1  are  These plumes pen-  etrate to m a x i m u m depths of about 12 metres w i t h slightly deeper penetration seen during higher wind speed. The is likely  existence tied to  of a threshold wind the  subsurface bubbles.  energetics It  speed for bubble plume observation  of wave breaking;  the  most  likely  source  of  is not possible to tell if the vertical velocities which  draw the bubbles down into plumes existed before the bubble plumes are seen since without bubbles to serve as flow tracers, there is insufficient acoustical backscatter for Doppler speed estimates. Sidescan sonar data provide evidence for L a n g m u i r circulation (through the presence of organized bands of scatterers) throughout the 21 hour deployment presented.  These bands h a d widths of order 2 to 5 metres,  about  metres a n d were aligned with the wind.  100  were about 5 metres at wind speeds below 10 m s of 10 to 20 metres at greater w i n d speeds. coexisted.  - 1  a n d lengths  Spacings between  of  bands  a n d increased to spacings  A t all times a variety of spacings  T h e scales observed here are much smaller t h a n those often reported  i n the deep ocean (Leibovich 1983). T h i s result is more likely due to the concentration of our measurements on smaller scales rather than to the absence of  67 the larger scales.  E v e n if larger scales were present, they would not be appar-  ent i n the sidescan data because their would be m a n y smaller scale  structures  present between the downwelling regions of the larger cells. Vertical velocity estimates  made using a n upward looking echo  revealed downward speeds of 0.06  ms  - 1  sounder  at 8 m depth i n the bubble plumes.  T h e m a x i m u m velocity was located i n the middle of the bubble plumes with reduced downward velocities occurring towards the edges. Speed estimates  were  restricted to the bubble plumes because of inadequate signal levels elsewhere.  68  C h a p t e r5 Ambient Sound Modulations Ambient sound data were collected with the objective of m a k i n g observations of wave breaking i n the presence  of L a n g m u i r cells.  T h e possibility of  such analysis is suggested by Farmer a n d Vagle (1988) who observe signatures  from individual wave breaking events  i n a fetch limited  acoustic sea. N o  correlation could be estabhshed between wave breaking a n d the L a n g m u i r circulation. However, the analysis of ambient sound data lead to the identification of persistent wave period fluctuations (see Figures 4.3 a n d 4.4) not previously reported. The objective of this chapter is to identify mechanisms that could introduce surface  wave modulations i n the ambient sound  field.  T h i s question is  pursued first by considering the relationships between the w i n d and wave data in detail. T h a t analysis reveals that the sound modulations are i n phase with surface  wave displacements directly above the acoustic  package.  A model of  surface sound sources is used to investigate how source level variations driven by wave parameters  could account for the modulations seen.  T w o possibilities  are suggested; the interaction of short waves w i t h long waves, a n d the variation of w i n d stress over the wave  5.1  field.  Wave and Ambient Sound Analysis Fluctuations i n ambient sound levels can be caused by many  processes,  some of which could be frequency dependent (Farmer a n d Vagle 1989). In the present analysis however, such frequency dependence is not of interest, a n d a m bient sound is represented by a sound signal level ( S S L ) determined at some  69  characteristic by  frequency and b a n d w i d t h . T i m e series of S S L are  fluctuations  over many time scales;  the  fluctuations  to the signal variance are identified i n Figure 5.1 x  power), log frequency plot.  which contribute  by means  of a  most  (frequency  P l o t t i n g the data i n this format preserves  relative contribution to variance of each spectral component. ure 5.1  characterized  the  T h e data i n F i g -  are based o n approximately 38 minutes of data collected during w i n d  speeds of 12 m s " , with the instrument package (described i n C h a p t e r 3) posi1  tioned at 30 m depth. A l t h o u g h there is energy at all frequencies i n the ambient sound signal, most of the signal variance comes f r o m  fluctuations  at periods of less than 15 seconds. T h e cause of the low frequency  occurring fluctuations  is not investigated here, rather attention is focused o n the modulations which occur at surface wave frequencies. T h e persistence of surface wave modulations i n the ambient sound has already been demonstrated i n C h a p t e r 4 (Figures 4.3 a n d 4.4),  but the averaging  nature of power spectral analysis obscures the details of the interaction. A better understanding of this phenomenon can only be achieved by a more detailed analysis of the data. wave driven  Time  fluctuations  series over short periods show the dominance of  i n the ambient sound record.  F i g u r e 5.2a  displays 3  minutes of ambient sound signal levels recorded i n a 3 k H z b a n d w i d t h at  8  k H z and the wave observations for the same time period are shown i n F i g ure 5.2b. ms . -1  W i n d speeds during the time of these observations were about  12  These data are typical examples and demonstrate how peaks of about  5 d B in the wave field.  ambient sound level occur coincident with peaks i n the  Modulations such as these are apparent  surface  over the entire observed  frequency b a n d (from 2 to 20 k H z ) , but larger amplitude modulations are seen at higher frequencies.  70  2236-1  CD QJ  1136-  • Q.  36200  133  time:  Figure  5.1:  (frequency  x  B9  59  27/10  ~i  against  1 26  16  12  a  i  5  P e r i o d CsD  12:27  Spectrum of ambient power)  40  sound fluctuations.  Data  are plotted as  a logarithmic frequency scale to represent  relative contribution to signal variance.  the  T h e display is based o n a n average of  8 (overlapping), 512 second data samples starting at 12:10, 27/10/1987 U T C . T h e influence of wave motion is clearly visible at periods between 5 a n d 13 seconds.  71  Figure  5.2:  C o m p a r i s o n of surface  levels (between  wave  displacement  a n d ambient  sound  6000 a n d 9000 H z ) at 30 m depth for the 3 minute p e r i o d  beginning at 12:13 27/10/1987 U T C ; a) ambient sound level (filtered to remove fluctuations at periods greater t h a n 20 seconds)  , b) sonar determined  surface  displacements  Scatter  plots  of ambient  sound against  surface  wave  displacement  were  made to investigate the proportionality of sound modulations to wave heights. T h e low frequency variability causes offsets to occur i n scatter plots made over long time periods and so it was desirable to remove this variability before making the comparisons.  A 4 t h order Butterworth high pass filter with a cutoff  72 frequency of 20 seconds was applied to the data to eliminate this unwanted variation. subject  B o t h ambient sound a n d wave data were  filtered.  A scatter plot  to such processing is presented i n Figure 5.3 based on 40 minutes of  data starting f r o m 00:10 27/10/1987 U T C when the wind speeds were 8 ms . -1  T h e plot demonstrates  about  substantial scatter (the cross correlation be-  tween these variables is 0.65), but there is a well defined axis w i t h a slope of 36 fJ,Pa m  _  1  . T h i s slope remains relatively constant i n the 60 hours of obser-  vations w i t h w i n d speeds varying from 5 to 15 m s 36 ± 8 (J,Pa m  -  1  - 1  and has a n average of  .  Cross spectral  analysis of surface wave displacement a n d ambient sound  modulations (at 8 k H z frequency) was made to further investigate the correlation between these data.  Figure 5.4 shows a n example of such analysis based  on 23 minutes of data starting at 12:10 27/10/1987 U T C during w i n d speeds of approximately 10 m s  - 1  . Based o n visual observations, the dominant waves  at this time are oriented at about 4 5 ° to the wind direction. F i g u r e 5.4a a n d b show the surface wave a n d S S L spectra respectively. coherence  Figure 5.4c shows the  a n d Figure 5.4d is the relative phase between the two time series.  T h e m o d u l a t i o n spectrum (Figure 5.4b) shows an energy increase i n the frequency b a n d of surface wave activity, and there is enhanced coherence observed at these frequencies (Figure 5.4c). T h e phase relationship between these data is 0 at the 95% confidence level at those frequencies of high coherence. Coherence  analysis  can demonstrate  the relationship  between  ambient  sound levels a n d wave displacements for limited time intervals, but it does not demonstrate  how those  signals evolve through changing sea a n d wind  condi-  tions. T h e time dependent character of the coherence was investigated by plotting time series of coherence  a n d phase over a selected frequency b a n d w i d t h .  73  Surface  F i g u r e 5.3: ment  D i s p l a c e m e n t Cm]  Scatter plot of sound power at 30 m depth against wave displace-  over a 40  minute period starting  at  12:10  27/10/1987 U T C : b o t h wave  and ambient sound data have been high pass filtered to eliminate variations periods longer than 20  seconds.  at  74  F i g u r e 5.4:  Cross spectral analysis of 23 minutes of wave a n d ambient sound  data starting at 12:10  27/10/1987 U T C ; a) wave spectra, b) spectra of ambient  sound fluctuations, c) coherence, d) phase. over 20 separate frequency spectra.  T h i s analysis is based on averages  T h e 95% confidence intervals are indicated  by error bars for b o t h phase a n d coherence.  75 T h e 21 hour period beginning at 19:00 26/10/1987 U T C is characterized by i n creasing w i n d speeds a n d a developing sea ( C h a p t e r 4) and so presents a range of sea a n d wind conditions. F i g u r e 5.5a displays the wind speeds observed at this time, a n d the coherence a n d relative phase of the wave a n d sound field at periods between 10.5 a n d 13.5 seconds are shown i n Figure 5.5b a n d c.  It is  seen that as the wind speed picks u p , the coherence increases with a modest decrease when wind speeds are maintained at about  13 m s  - 1  . This  decrease  may be related to the sea state which is known to become fully developed at this time (see Chapter 4).  In spite of the variations i n coherence, the relative  phase during this period remains 0 (within 95% confidence bounds).  It must  be noted that the wind direction d i d not change appreciably during this p e r i o d remaining at about 4 5 ° to the prevailing swell. In a n effort to determine the importance of the crossed w i n d a n d waves occurring i n the data of F i g u r e 5.5, a second time series of wave displacements and sound modulation was analyzed. 44 hour period beginning at  18:00,  T h e only other data set available is a 2/11/1987  U T C during which the wind  speeds slowly decreased but d i d not change direction. period,  T h r o u g h o u t that  visual observations recorded the swell oriented at  about  data  3 0 ° to the  wind direction. Using the same format as F i g u r e 5.5, Figure 5.6 displays the wind speed, coherence a n d phase observed during this time interval. F o r this sample period, the phase a n d coherence are determined at periods between 10 and  13 seconds to bracket  remains  consistently high  the dominant wave period.  Again,  the coherence  a n d the phase remains relatively constant  with  a  mean value of 0.17T radians (indicating waves lead sound) but this value is at no time significantly different f r o m 0 as shown by the error 5.6c.  bars i n Figure  76  1.0 CD  a c  l |i|  \\ m  np  wPn  Pi] ^ p[i j *  n fj  jp [pj iij  CD  Coherence  -C  o G Q_  .00-  m cn co x:  .00-  1.0-  ll  ^  nil m L  n i l  m  g  i nil  l u  i^  i j IJ  I]I  j\ JiJ I]] Phase  •1. 26/10 22:00  27/10 0B:30 TIME  F i g u r e 5.5: waves  27/10 13:00  CUTC]  T i m e series of w i n d speed a n d the phase a n d coherence  a n d ambient  22:00 26/10/1987  between  sound modulations for the 21 hour period beginning at  U T C ; a) w i n d speed, b) average coherence  at periods be-  tween 10.5 a n d 13.5 s, c) phase, (95% confidence bounds are indicated b y error bars).  j | ji j | i i|  77  15-  Q  5-  Wind  Speed  1.0-  QJ  cj  c  tu c_ QJ .C  .50-  o U  Coherence .00-  cu cn CD  02/11  03/11  1B:00  T I M E  Figure phase  5.6:  In the same format  between  wave motions  at  16:00  04/11  CUTC)  used for F i g u r e 5.5,  a n d ambient  14:00  sound are  the coherence  shown for  a 44  and hour  p e r i o d for fluctuations with a p e r i o d of between 9.5 and 13 s are displayed.  78 The  suggestion of some slight phase difference i n this later  intriguing,  data  set is  b u t better quality data would be required to claim confidence i n  this small departure from 0 phase.  In the present data, the absolute t i m i n g  accuracy i n each of these data sets is ± . 2 5 s time series  alignment could account  0.1 7r radians at a 10 s period.  so that the cumulative error i n  for a phase uncertainty of as m u c h as  It is however extremely unlikely that such a  timing error would retain a constant offset for the entire 44 hours analyzed.  5.2  M o d u l a t i o n s of S o u n d G e n e r a t i o n T h e observations demonstrate that the modulations of ambient sound are  strongly driven b y surface wave motion. T h i s behaviour indicates that whatever mechanism is responsible for the generation of sound, it is strongly influenced by the phase of long waves.  T h e generation of ambient sound i n the ocean  is known to b e associated with wave breaking a n d i n particular by the i n troduction of small bubbles into the ocean surface ( M e d w i n a n d B e a k y 1989). It must b e concluded that either sound propagation is strongly influenced by surface wave m o t i o n or, the breaking of waves responsible for sound generation occurs at or near the crests of the longer period (swell) waves.  The  suggestion of wave breaking controlled by long wave phase  unreasonable:  is not  short waves can be disturbed b y longer wave currents a n d this  disturbance can trigger wave breaking as discussed by Phillips (1981) a n d G a r rett  and Smith  (1976).  T h e convergence of water  which occurs  towards the  crests of the long waves advects shorter waves towards the long wave crests. This  convergence at wave crests leads to a shortening i n the wavelength of  the short waves and consequently increases their steepness towards a m a x i m u m  79 at  the long wave crest.  A s demonstrated by Garrett  a n d S m i t h (1976), for  parallel wave trains, the wave steepness ak varies as  ak = aofc (l + kid] cos 6)  5.1  2  0  where ao is the undisturbed short wave amplitude, ko is the undisturbed short wave wavenumber, a/ a n d k} are the long wave amplitude a n d wavenumber, a n d 6 is the long wave phase. at  T h e steepness  of the short  waves occurring  the long wave crests would increase the probability of these short  waves  breaking a n d so lead to increased sound generation. T h e scale of breaking waves need not be large; K o l a i n i et a l . 1991 demonstrate that significant sound can be generated by the action of capillary wave breaking.  T h e y note that even i n the absence of breaking gravity waves, par-  asitic capillary waves occur just ahead of short gravity waves as described b y Longuet-Higgins  (1963).  Capillary  waves  are characterized  b y sharp  troughs  a n d r o u n d e d crests a n d break when adjacent crests actually pinch off a trough (Crapper  1957).  Kolaini  et a l .  1991 observe  that  breaking capillary waves  generate significant sound a n d offer this explanation of sound observed i n the absence of breaking gravity waves ( K n u d s e n et al. 1948). If this sound generation mechanism is important (even at high wind speeds when gravity waves break), t h e n sound generation could occur o n a very small scale governed b y the interactions of capillary waves. A n indirect mechanism which may be important to the variations i n sound generation could be the variability i n w i n d stress over the long wave phase. Gent a n d Taylor (1976) have demonstrated that w i n d stress is m o d u l a t e d b y wave f o r m with a m a x i m u m occurring on the u p w i n d  wave slope a n d this  80 result is consistent with observations by Zilker et al. (1977). T h i s variability i n stress could influence the occurrence of wave breaking (and consequently sound generation)  through the mechanism proposed by B a n n e r a n d Phillips (1974) i n  which near surface shear i n the water destabilizes waves. be expected  that  Alternately, it would  capillary waves would respond quickly to changes  stress a n d so capillary wave generated  i n wind  sounds could be closely tied to wind  stress. Comparisons of wind stress w i t h mean ambient sound levels b y Vagle et al. (1990), demonstrate a strong correlation following the relation, r oc P where P  5.2  2  is the sound pressure level, a n d r  is the w i n d stress.  This  empiri-  cal relationship is based o n one hour averages a n d it is not obvious that it should be valid for short time scale variations.  However, if it is assumed that  E q u a t i o n 5.2 is applicable over short time scales, then the stress variations over a wave f o r m measured by Gent a n d Taylor (1976) the  variability of sound generation  can be used to  with E q u a t i o n 5.2.  T h e curves  estimate of wind  stress variation observed by Gent a n d Taylor can be approximately modelled as varying as the square of the wave displacement, r oc (a — a where r is the stress, a — a i m  n  m t n  )  2  cos(f? + <f>,)  5.3  is the surface displacement above some reference,  <j> is the phase of stress variations  (relative  to the surface  waves),  8 is the  surface wave phase (ie. 6 = kx — ut, with k the wavenumber a n d u the angular frequency).  C o m b i n i n g equations 5.2 a n d 5.3 provides a prediction of sound  variation over a wave profile, P  2  a (a — a  m i n  )  2  cos(A;x — ut + (f>).  5.4  81 It is not  unlikely that  several sound generation mechanisms might work  together to generate the observed ambient sound  fluctuation.  However, because  of the direct influence w i n d stress has o n near surface processes, it is particularly likely that wind stress variations play some role.  Certainly, variations i n  w i n d stress would influence the breaking of capillary waves as well as gravity waves a n d so could indirectly lead to sound level modulations.  5.3  A m o d e l of near surface s o u n d It is not immediately clear which, if any, of the source mechanisms iden-  tified could account for the observed sound modulations. Indeed, it is entirely possible that  some  aspect  of acoustic  propagation  or  instrument  flow  noise  might be responsible for the observations. A simulation of acoustic propagation assuming  a wave modulated sound source  was  developed to  investigate  question. T h i s simulation demonstrates that, for appropriate parameter  this  choices,  variations i n sound source level occurring over the gravity wave length could account for the present observations. Characteristics of the model provide some insight into possible sound sources. The  assumption is made  that  near the ocean surface consistent received by a hydrophone can be  sound sources  are  confined to  with the mechanisms discussed.  be  at  or  T h e sound  determined by integrating over the  ocean  surface a n d accounting for spherical spreading and acoustic propagation losses. E v e n acoustic sources far f r o m the hydrophone contribute to the total received signal, but at some point, depending on the instrument geometry,  the contri-  b u t i o n becomes  negligible. T h a t radius about  contributes 50%  of the total acoustic power is a suitable measure of the lis-  tening area important  to  the  system:  the instrument location which  this area is the  half power or  3  dB  82 listening area. For the deployment geometry i n question with a hydrophone at 30  m  depth, and assuming dipole sources at  the surface  (consistent with  the  approach used by Vagle et al. 1990), the listening area has a radius of 29  m.  T h i s configuration is indicated i n Figure 5.7 which identifies all components  of  the model geometry.  F i g u r e 5.7:  It  is desirable to be able to  vations. above ing  Geometry of modelled dipole sources a n d receiver.  model results  directly with  obser-  T o do so, it is necessary to recreate the surface wave field occurring  the instrument  radius  of 29  m.  i n an area that is large compared A  vicinity of the instrument above  compare  the  representative  surface  can  be  to the  3 d B listen-  reconstructed  for  the  by phase shifting the wave height spectra observed  listening position to  successive  positions  according  to  the  surface  83 wave dispersion relation.  In the absence  of directional wave spectra,  the re-  sult is necessarily one dimensional, a n d will not provide good results wavelengths from the measurement  position.  F o r the present  many  application this  limitation is acceptable since the dominant wavelength is about 100 m w h i c h is already several times the 29 m listening radius. The  Fourier transform of the ocean surface m o t i o n at any point c a n be  expressed as °°  /  V  -oo  (x,t)\ e-^dt,  where r](x,t)\ —o is the observed sea surface x  x = 0.  5.5  x=Q  variation i n time at a position  T h e Fourier transform at any position x can be determined b y phase  shifting E q u a t i o n 5.5 by a distance / according to the linear dispersion relation S(u,l) The  = 5(w,0)e ' ,  u;2/  / .  5.6  ff  sea surface displacements at position / are then recovered f r o m E q u a t i o n  5.6 by the inverse Fourier transform,  1  »/('.*) = 5 - / It  is assumed that  r°° S(u,l)e du.  5.7  tut  this one dimensional wave  field  is propagating i n the x  direction a n d extends infinitely with no surface gradients i n the y direction. It is necessary to use finite transforms which distort the reconstructed sea surface. This  distortion is minimized b y transforming time  series  twice  the required  length a n d then using only the middle half of the adjusted data.  T h e length  of these time series was 1024 seconds thus including m a n y cycles of the longest period  surface  waves  (about  12 s).  T h e surface  reconstructed  far f r o m the  point of observations will not be accurate, but once again, it is well beyond  84 the effective listening radius at  the instrument depth and so should not  be  A c o u s t i c sources can be placed u p o n the reconstructed ocean surface  ac-  important.  cording to several possible schemes.  It was decided to describe the  acoustic  field w i t h a continuous distribution of sources with strengths varying i n proportion to some surface characteristics rather t h a n using randomly placed discrete sources. T h i s approach can be defended on the basis of the observations which are not characterized by a great deal of signal variability, and the subsequent success of the model.  T h i s approach also simplifies the model to one dimen-  sion substantially reducing computational requirements. Sound sources near the ocean surface are expected to behave as dipoles because of the image source across the water surface: this idea (Vagle et al.  observations of near surface ambient sound support  1990).  Subject to these assumptions, acoustic  are described b y dipole sources shown i n F i g u r e 5.7.  sources  distributed evenly over the ocean surface  as  O n the reconstructed surface, dipoles are oriented normal  to the surface at all points. In the absence of surface slopes i n the y direction (a result of the one dimensional reconstruction of surface waves), dipoles  are  arranged i n rows all tilted at the same angle to the horizontal.  T h e contribution to the signal strength received at some point due to any differential element of a dipole row is  where dp is the contribution of hne element dy with strength a at R  and <j> depends on b o t h position and surface slope.  a  Because the  range elements  are incoherent, the signal strength does not a d d linearly: instead, signal power  85 must  be integrated.  T h e contribution to the signal level then received  hydrophone by any infinite dipole row can be determined by integrating  at a along  that row a n d considering the spherical spreading that would occur, °° a  / where x,  R  2  = x  2  5.9  2  + y + d? is the range from element  ds to the receiver, a n d  2  y a n d d define the hydrophone position as i n Figure 5.7. F o r large ranges  or high frequencies, 5.9.  2  — cos (<f>(x,y))dy,  acoustic absorption would become  important  In the present case however, m a x i m u m ranges are about  highest  in Equation  500 m , a n d the  acoustic frequency being considered is 15 k H z : attenuation  for such a  signal is only 0.7 d B a n d so can be ignored without significant error. A range dependent  effect which could also be important  subsurface  bubbles observed b y Farmer  is the scattering of sound b y  a n d L e m o n (1984).  T h i s scattering is  not included i n the simple model discussed here. Equation infinite  5.9 c a n be integrated  row of dipole sources  with  to determine a  fixed  angle  the contribution of tilt  will  that a n  make  to the  received intensity:  o 1=  r  cos U  5.10  2  T h e contribution of the individual lines must  be integrated  to determine  the signal level at a receiver due to many such dipole lines,  SSL=  I  fl2<  ^  , cos U(x))dx. 2  where <f> depends on b o t h position a n d surface slope at that position,  5.11  86 a n d a is now position dependent.  Because r)(x,t) is determined from observa-  tions, E q u a t i o n 5.11 must be numerically integrated out to a range at which no further contribution is made.  In practice this s u m converged after integra-  tion to 500 m . T h e source strength parameter resent characteristic  i n E q u a t i o n 5.11 must be adjusted to rep-  signal strength  at any point along the wave surface.  In  particular, the strength must be adjusted i n proportion to some wave characteristic consistent  with the source mechanisms proposed. R a t h e r t h a n  special functions for each  mechanism investigated,  a general  creating  f o r m w i t h ad-  justable parameters was chosen,  a = AQ + A + (s - s ) C  s>s  a = A  S < S f,  2  2  where  AQ, A , C , s  surface  r e  /,  Q  2  0  5.13  re  a n d so are adjustable  dependent parameter  r e f  parameters  a n d s is any sea  such as wave displacement or acceleration. T h e  values for parameters i n E q u a t i o n 5.13 required to best m a t c h  model sound  variations with the observations provide insight into the nature  of the source  mechanism. source, depend  Adjustment  of sref  allows for an intermittent  character i n the  the values of Ao a n d A provide for a background level that does not o n the wave parameter,  dependence.  A linear source  and C  allows for a quadratic  level dependence  was initially  source  level  included but it  provided no improvement i n model results a n d so it was discarded.  5.4  Model Results T h e format of E q u a t i o n 5.4 was chosen to allow m a x i m a l flexibility subject  to the explicit constraints of the model. A s part of this generality, no specific  87 wave  parameter  is obvious that  ( 5 ) is imposed u p o n the the parameter  system.  used must  displacements at the instrument position.  F r o m the  observations  be nearly i n phase with the  would be derived from these measurements. introduce small errors  and the  to the wave displacements.  result  only surface wave  Adjustment of parameters i n E q u a t i o n 5.13  sonable qualitative agreement  parameter  would largely be a value proportional  For these reasons,  of the m o d e l .  one  Such derivations would inevitably  itself has been explored as a wave parameter i n E q u a t i o n  linear characteristics  wave  Surface wave displacements are  of the direct observations being made and any other wave dependent  it  displacement  5.13.  was complicated by the  non-  Parameters were adjusted to achieve  rea-  w i t h observations over a short time series  (the  3 minute interval shown i n F i g u r e 5.8).  Once approximate  parameter  values  h a d been selected, the correlation between the observed ambient sound fluctuations a n d the model predictions was made using a more extended time consisting of the 40 minute p e r i o d beginning at parameter  values were  then  adjusted  to  12:10  maximize  the  series  27/10/1987 U T C . T h e correlation  coefficient  between the simulated a n d observed ambient sound levels for this period. evaluating these correlations, the low frequency fluctuations present in the were removed using a filter with a pass b a n d of between 3 s a n d 20  s.  In  data To  avoid difficulties of phase distortion through filtering, b o t h model simulations a n d data were filtered i n b o t h the forward a n d backward directions. T h e model was first used to investigate fluctuations consistent in E q u a t i o n 5.13  with the observations.  (by setting s / r e  if E q u a t i o n 5.4  could reproduce  T h e threshold term was disabled  = —00). For this configuration of the model  the fitting procedure was used to determine the values of the three remaining  88  /Kj-,  ,  12:13:00  ,  12:14:00  ,  12:15:00  12:1B:00  Tinie  F i g u r e 5.8:  Comparison of observed and modelled ambient sound  over a 3 minute period. intermittent wave  sources located at  displacement  fluctuations  A ) quadratic dependence o n wave displacement,  B)  wave crests, a n d C ) quadratic dependence on  with sound sources  restricted  models reproduce mean levels comparable displaced to clarify the presentation).  to  long  wave  to those observed,  but  crests.  (All  have  been  89 parameters;  the quadratic scaling ( C ) was set to 5000 /J,Pa m~ , 2  term A was set to 50000 / x P o m 2  _ 1  , a n d the offset displacement so  —2 m (the approximate m i n i m u m wave displacement). AQ becomes arbitrary.  the constant  3  With s  r e  w  a  s  s e  t to  / set to —oo,  A three minute time series based o n these  parameter  choices is identified as trace " A " i n Figure 5.8 a n d can be compared w i t h the observed modulations. A further visual comparison between observations a n d model predictions can be presented by a scatter plot between the two time series such as shown i n Figure 5.9.  Figure 5.9 is based o n the 40 minutes  period beginning at 12:10 27/10/1987 U T C a n d demonstrates the agreement of the model with observations (the correlation coefficient for this comparison is 0.55).  T h e r e however remains substantial scatter throughout the plot w i t h no  obvious explanation for the limited correlation. The  source  mechanisms  of wave  breaking localized to long wave  crests  suggests the existence of a sound source mechanism localized at wave crests. T h i s mechanism was investigated by adjusting the threshold parameter s that sound was only generated  r e  / so  near wave crests with no variation i n signal  level i n proportion to wave displacement. made without using the parameter  A t first, trials of this m o d e l were  Ao which allows for a background sound  source distributed uniformly over the ocean surface.  W i t h o u t this background  source, large signal variations occurred i n the reconstructed sound signal that could only be reduced by adjusting s  r e  /.  T h e character of the signal level  variations simulated was not peaked upward (as are the observed variations), but rather they appeared as signal drop-outs, peaked i n a downward sense. A n example of such drop-outs can be seen i n the example time series as trace " B " i n Figure 5.8 generated with A = 180000 ^ P a m 2  —0.95 m.  _ 1  identified  , and s f re  =  T h e correlation between this model a n d the observations could not  90  LTJ TJ  H  cn cn UJ  •  '.\.T.  -H  D  *  « \ ... J'»  *  .•£<;... .. i . . . ' .  .  .  -3 -1  OBSERVED  F i g u r e 5.9:  S S L CdB]  Scatter plot of observed ambient sound levels against those m o d -  elled for the 40 minute period beginning at 12:10  27/10/1987 U T C . These data  have been high pass filtered to remove all variations occurring at periods longer t h a n 20  seconds.  91 be increased beyond 0.45 without using some form of signal level increase at wave crests. peaks  W h e n such additional modulation was used to recover the sharp  observed,  s f re  still h a d to be adjusted to small values to avoid the  sudden signal drop-outs. The  inability  of simulations with localized source  the observed sound constant  component.  fluctuations  regions  to reproduce  identifies the need for a sound source with a  T h e background source term  (AQ) was introduced into  E q u a t i o n 5.13 for this purpose. T h e model parameters were once again reconfigured to optimize the agreement with the observed fluctuations leading to the values; A = 100000 fiPa m~ , 2  0  C = 10000 fiPa m- . 2  this parameter  z  l  A = 0 u.Pa m~ , 2  x  s f re  = 0.2 m , s = —2 m , and 0  T h e time series i n F i g u r e 5.8 labelled " C " results from  selection.  A comparison of this m o d e l output was made with  the observations for the 40 minute period beginning at 12:10 27/10/1987 U T C for which a correlation of 0.5 is recovered.  5.5  Discussion of Model Results T h e comparisons between simulated a n d observed sound modulations pro-  vide some support for the concept  that sound level  waves c a n account for the observations.  fluctuations  over  surface  Results f r o m the model configurations  presented are summarized i n Table 5.1.  A l l variations of the model required some source level offset to reproduce the  mean  sound levels observed.  This  requirement  is a direct  result  small listening area of the instrument: the model assumes line sources  of the  arranged  parallel to unidirectional waves a n d for this geometry,  the 60 m listening d i -  ameter is i n fact reduced to a line of 36 m length.  In the model, if signal  92  Model  A  Ao  Pa m2  1  arb.  A  C  Pa m2  1  so  Pa m2  Z  •Sre/  m  m  50000  5000  -2  —oo  0.55  B  0  180000  0  arb.  -.95  0.45  C  100000  0  10000  -2  0.2  0.50  T a b l e 5.1:  Comment  R  stress  model  localized sources all  parameters  Sound source model parameters.  levels become very small at any point along the wave curvature,  then signal  level variations become much larger than those observed. Increasing the effective listening area (by changing to a monopole source) reduces  this problem  but eliminates the ability to simulate the large peaks seen i n the observations. For  the case of a continuous source  term  such as used i n M o d e l " B "  (Table 5.1), the use of the offset term (Ao or A) represents signal level of the source term.  an offset i n the  W h e n applied to a discontinuous source  as the case of M o d e l " C " i n T a b l e 5.1), this t e r m implies the existence  (such of a  second source mechanism independent of wave motion. A very likely cause for this term  could be the need to account  the surface f r o m the ocean b o t t o m .  for sound that is reflected back to  T h e ocean depth at the observation site  was about 2000 m : 8 k H z sound generated at the surface a n d reflected off the b o t t o m back to the surface is attenuated by about 3 d B through acoustic absorption a n d 10 d B due to the b o t t o m interaction. B y applying a simple model of such sound generation it was found that this signal has a 3 d B footprint of  93 about 8000 m diameter a n d can account received directly from the surface.  for a signal level comparable to that  A n additional contribution to such a con-  stant signal level term could be through the action of sound scattering near  surface  bubbles)  away f r o m the  or  refraction  serving to  distribute  the  source  (from  location  surface.  T h e simulations failed to reproduce  the peaked structure of the  observed  sound level modulations. It was not difficult to get modulations of the desired magnitude,  but  i n all cases some  means  of enhancing signal levels at  wave  crests was needed to approximate the sharp peaks observed i n the sound m o d ulations. Use of a linear term i n E q u a t i o n 5.13  was inadequate for this purpose  a n d i n all cases, a quadratic term was needed.  Scatter i n the comparisons be-  tween model and observations (such as shown in Figure 5.9)  made it impossible  to recognize any improvement i n model results when including b o t h linear and quadratic The  terms. scatter  evaluations about  0.5  than 0.55.  i n comparisons  of model variations but  of the difficult.  no variation of the  model a n d  observations  also  makes  A l l models produced correlations  model could produce  correlations  of  greater  T h i s limitation could result from approximations made by the model  such as the 1-dimensional wave representation for a 2-dimensional ocean, or the use  of line sources to  are  those processes not  represent  sound generation  represented  by the  model.  terms. Figure  O f more 5.2  concern  demonstrates  significant fluctuations i n ambient sound not obviously driven by wave motion. U s i n g the spectral character of the modulations as a guide (Figure 5.1),  much  of this variability can be eliminated by filtering out periods longer t h a n those associated  with surface  waves.  This  filtering  has been done prior to m a k i n g  94 correlation comparisons between the m o d e l a n d observations. reason  to  expect  entirely absent  the  at  mechanism causing the  wave periods  and it may  long period  B u t , there is no fluctuations  be responsible for some  to of  be the  discrepancies. Based o n the correlation coefficients achieved by the various models ( T a ble 5.1),  a best configuration is not obvious.  T h e combination of parameters  required i n any given case does however provide some insight into the possible source ment it  mechanisms.  T h e m o d e l relying only on variations  to produce modulations (model  closely models the  requires  the  expected  adjustment  action  of w i n d  of three parameters.  localized to  wave crests suggest  account  the  for  " A " i n Table 5.1)  observed  of wave  displace-  is attractive i n that  stress variations  T h e concept  and it only  of wave breaking  that the localization of sound sources  sound modulations.  observed fluctuations by this means  A n attempt  (using model " B " )  to  clearly  could  reproduce  the  demonstrated  that such localized sound sources lead to signal drop-outs not seen i n the observations.  T h e restriction of sources  to specific areas of the wave cannot  by  itself account for the observed modulations. T h e two approaches of models " A " a n d " B " were combined i n M o d e l " C " where a background source level acting at  all points at  the  surface  is included.  A s is demonstrated  of m o d e l " C " , the introduction of the additional parameter provement i n the results.  by the  results  provides little i m -  In addition, the need for a constant  source t e r m is  somewhat inconsistent with an intermittent source model: the mechanisms that suggest  sources  at  wave crests (short wave instabihties or parasitic  waves),  i m p l y that these sources  should be absent  i n troughs.  capillary  W h e n sound  generation is localized only at long wave crests, an additional source term must be introduced i n the m o d e l to reproduce sound level variations comparable those observed.  to  95  Source Mechanisms  5.6  T h e m o d e l demonstrates that the observed sound modulations can be described using a continuous distribution of sources.  Such a continuous distribu-  tion implies that several active sources must be present within the 60 m d i a m eter listening area at any time. These sources must then be small compared to the listening area suggesting a scale of about 6 m between independent sources (jQ  the length of the listening area).  th  A l t h o u g h the actual sound generating mechanism remains to be identified, sound generation  is strongly associated  w i t h breaking waves a n d the injection  of air bubbles into the water ( M e d w i n a n d B e a k y 1989). If individual breaking waves  are responsible for the sound fluctuations observed,  wave must be occurring at any time on a scale of about  then one breaking 6 m.  H w a n g et a l .  (1989) indicate that for small w i n d forced waves, the ratio of breaking to nonbreaking waves is about 0.1; this ratio provides a n upper limit of 0.6 m for the wavelength of breaking waves responsible for sound generation. H a v i n g estabhshed a scale for sound sources of 6 m (implying wavelengths of breaking waves  of about  0.6 m ) lends support  scale continuous source mechanism. statistical  variability,  to the concept  It is however quite possible that  randomly placed  sources with an increased  of occurrence at wave crests could produce similar results. i n the observations  which might be used to distinguish  variability from that caused  of a small through  probability  O n e characteristic wind-stress-regulated  by sources at wave crests, is the presence of a  phase difference between the wave crests a n d sound m a x i m a . In general, wave-wave interactions  cause short waves to have a m a x i m u m  steepness at the crests of long waves whereas the location of m a x i m u m wind  96 stress is not so restricted.  Several analyses of wind stress variation over wave  fields have predicted peak wind  stress values to occur  upwind  of the wave  crests (Zilker et al. 1977, O k u d a et a l . 1976, Gent a n d Taylor 1976). F o r the wave fields encountered i n the present observations it is not clear that such a phase shift would be significant:  comparing the steepness  of long waves and  wind speeds occurring i n the present data with the laboratory observations b y Zilker et a l . in by  (1977),  the absence Okuda  Gent  et  phase lags would be expected  of wave breaking. al.  (1976),  In contrast,  Buckles et  al.  to be vanishingly  small  laboratory observations  made  (1984),  a n d numerical studies b y  a n d Taylor (1976) show that relative phase lag is strongly affected by  wave breaking so that the lags reported b y Zilker et a l . (1977) m a y not be representative of a real ocean. In  the present observations, the phase between sound a n d wave displace-  ments was 0 ± 0.1 7r radians when the w i n d a n d wave field were crossed at about  4 5 ° but the phase  remained positive at 0.1 ± 0.1  wave displacement leading sound) directions were separated  during  by 3 0 ° . Under  7r radians (that is  observations when w i n d  a n d wave  these conditions (with large  angles  between the w i n d and waves), it is likely that any phase difference would be significantly reduced while the stress would still vary somewhat between crests and an  troughs.  In contrast,  the interaction of short waves with long waves at  angle would be reduced approximately as the cosine of the angle between  short  a n d long waves  (Garrett  and S m i t h  1976),  substantially reducing the  significance of such interaction.  5.7  S u m m a r y and Conclusions Observations of b r o a d b a n d ambient sound levels (2 k H z to 20 k H z ) at  30 m  depth i n the N o r t h  Pacific Ocean show modulations at surface  wave  97 frequencies. wave  Cross-spectral analysis between ambient sound levels a n d surface  observations  (made  directly above  the  acoustic  measurements)  demon-  strate strong coherence between these data at frequencies with significant wave energy.  In addition, at  those  frequencies where strong  coherence  exists,  the  relative phase of the signals is small (0 at the 95% confidence level). T w o extended periods of data are analyzed. T h e first is a 21 hour period characterized by a growing sea state w i t h the locally generated w i n d waves all times 4 5 ° to the 10 second period swell. m a x i m u m of 13 m s deployment.  - 1  T h e w i n d speed increased to  at a  producing a fully developed sea towards the end of the  D u r i n g this time, the phase remains fairly constant  at 0 ± 0.1 TT  radians while the coherence shows some variability a n d falls off slightly when the sea is fully developed. D u r i n g the second 44 hour deployment, m a x i m u m wind speeds were only about  10 m s  - 1  slowly decreasing through the deploy-  ment while maintaining a constant direction. D u r i n g this period when the swell was oriented within 3 0 ° of the w i n d , the coherence remains high a n d the wave displacements lead the ambient sound  fluctuations  by about 0.1 ± 0.1 TT radians  (that is m a x i m u m sound upwind of the wave crests).  T h i s phase difference is  however just at the limit of the instrument resolution as demonstrated by the 95%  confidence bounds.  T h r o u g h o u t b o t h these data sets, the slope of scat-  ter plots made between wave displacement a n d ambient sound levels remains constant at 36 ± 8 fiPa  The suggests  m  strong coherence that  face waves.  -  1  independent of w i n d speeds.  of ambient sound  the dominant ambient  fluctuations  sound source  with the wave  field  is modulated by the  sur-  For this modulation to occur, the source mechanism must have a  scale that is small compared to the dominant wavelength. T h i s conclusion was  98 explored by simulating ambient sound observations using a continuous distribution of sources along the surface with source levels adjusted i n proportion to surface wave parameters.  T h i s model reproduces ambient sound fluctuations  similar to those seen i n the data however correlations between the m o d e l a n d the observed modulations are limited to about R = 0.5.  T h e accuracy of the  model is critically dependent o n the accurate representation of the ocean surface a n d the model's limited accuracy undoubtedly results f r o m inaccuracies i n the ocean surface representation. ent sound  fluctuations  T h e ability of the m o d e l to reproduce ambi-  comparable to those observed does provide insight into  the possible sound source mechanisms. present  Based on the m o d e l results a n d the  observations sound generation must occur o n a scale of 6 m or less.  If breaking gravity waves are involved, then they must have a wavelength as short as 0.6 m to have one breaking event occurring at any time over any 6 m length (based o n the breaking rates for short gravity waves given by H w a n g et al., 1989). W i n d stress variations a n d short wave, long wave interactions are offered as a possible causes for the observed sound modulations. T h e r e is no strong evidence i n the model or the observations that can eliminate either of these mechanisms.  M u c h of the indirect evidence does however favour the action of  wind stress.  T h e observations show that scatter plots of sound level  against  wave displacements (Figure 5.3) have a constant slope at all w i n d speeds.  This  behaviour is consistent with the expected w i n d stress variation over the wave field  as given by Gent a n d Taylor (1976); stress variations would be purely de-  pendent o n wave amplitude regardless of wind speed. In addition, w i n d stress would not be expected unlikely event that  to vanish i n the long wave troughs,  except  i n the  a long wave should break, thus supporting the existence  99 of continuous distribution of sound sources. strates that just in troughs  as short  so that  waves  In contrast,  are steepened  E q u a t i o n 5.1 demon-  at crests,  this mechanism would suppress short  they  are  flattened  wave breaking a n d  sound generation i n wave troughs. T h e m o d e l results clearly demonstrate if regions of no sound generation are present  along the surface waves,  that large  drop outs i n sound level would occur; these are not seen i n the observations. Finally,  Vagle et al. (1990) show that average sound levels are proportional  to wind stress a n d close inspection of their displayed time series suggests sound levels c a n respond within  that  10 minutes to wind speed variations.  It is  hard to imagine that a sound source dependent o n long wave structure  could  respond so quickly to w i n d speed changes.  stress  (even when mediated by small waves)  Sound generated  by wind  is more likely capable of a r a p i d re-  sponse.  V i s u a l observations b y Donelan et al. (1972), a n d acoustic observations b y Farmer a n d Vagle (1988) have shown wave breaking to occur i n wave groups which would produce modulations at frequencies less t h a n those of the surface waves themselves. T h e observations of Farmer a n d Vagle were made i n a fetch limited sea with sea  no ocean  a n d laboratory  swell.  were  restricted  et al.  conditions a n d speculate  waves could affect the observations. here  Donelan  to a limited  that  comment  o n a variety of  the occurrence  of crossed  Unfortunately, the observations presented variety  of wave  conditions a n d it is not  possible to investigate the influence of mixed wave states o n the ambient sound modulations.  A  consistent  requirement  i n model parameterizations  large signal offsets to achieve the signal levels observed.  was the need for T h i s requirement is  100 likely due to the need to represent sound reflected off the ocean b o t t o m which greatly increases the listening area of the instrument.  T h e importance of this  term is frequency dependent as higher frequency sound suffers greater tion through absorption.  T h e observations are consistent  attenua-  with this explanation  displaying modulations more clearly at the higher frequencies. T h i s presentation  has focused attention  on those fluctuations of the  bient sound field occurring at surface wave periods.  T h e r e are  am-  fluctuations  to  this signal occurring at much lower frequencies as can be seen i n F i g u r e  5.1  but these do not contribute substantially to the signal variance. frequency  fluctuations  These lower  could be due to gusts i n the wind, consistent  w i t h the  speculations presented here, but wave breaking associated with wave groups documented by Donelan et al. 1972, equally viable explanation.  and Farmer a n d Vagle 1988)  (as  provides an  Clearly there is much to be learned about the short  term variation i n ambient sound levels.  101  Chapter6 A Model of Langmuir  Circulation  The data presented i n Chapter 4 demonstrates are not confined to a fixed scale, of coexisting lengths  scales  scales.  This  that L a n g m u i r circulations  but seem to be characterized  observation is not unique;  have been seen b y many  researchers  by a variety  similar distributions of as noted  i n the review  paper by Leibovich (1983). W h a t is striking i n the present data is the presence of L a n g m u i r cell spacings as small as 1 m while typical scales  i n the deep  ocean are of order 50 m (Smith et al. 1987). It is possible that larger  scales  are present at the time of these observations, but cannot be distinguished from the clutter of small scale structures occurring i n the sonogram images. The  presence  of m a n y coexisting length scales  i n this 2 - D flow  could be caused by an upscale energy cascade characteristic  pattern  of 2-D turbulence.  T h i s idea is further supported by reports of vortex pairing and the gathering of smaller structures into larger ones (Faller and A u e r 1988, a n d Leibovich 1983). The accurate description of this characteristic been  demonstrated  theoretically  of L a n g m u i r circulation has not  although Leibovich  a n d Paollucci (1981) do  suggest that such a tendency exists i n their numerical models It is m y speculation that the multiplicity of scales is not a  characteristic  of the generation mechanism of L a n g m u i r circulation, but is more likely a consequence of the 2-dimensional flow that results.  In that case, any mechanism  which could introduce 2 - D vorticity into the upper region of the m i x e d layer could result i n the flow field that is characterized as L a n g m u i r circulation.  102 T o pursue this idea, the next three chapters consider a possible source of near surface vorticity a n d how interactions i n the flow might produce the m u l tiple scale flows seen i n L a n g m u i r circulation. T h e present chapter a vortex  introduces  generation mechanism based on the interaction of waves w i t h near  surface turbulence. C h a p t e r 7 a n d 8 extend this result by considering the flow field resulting from unidirectional vorticity introduced by any means close  to  the ocean surface.  6.1  A n Alternative Theory for Vorticity Generation T o explain the relatively small scales of L a n g m u i r circulation seen i n the  deep ocean, a mechanism operating on scales small compared to the dominant surface wavelength was considered. It was realized that initially isotropic vorticity could acquire a directional character through the flow distortions caused by surface waves.  W h e n a parcel of water is distorted, there is an intensifica-  tion of the vorticity i n any vortex tube that is stretched.  (Stretching of vortex  tubes is what causes the flow singularity above a bathtub drain.) For the case of surface waves, a parcel of water initially located at the wave crest must be stretched  along the axis of wave propagation as that parcel of water  is ad-  vected from the wave crest to the following trough. T h r o u g h this distortion, an intensification of that component of vorticity aligned parallel to the direction of wave propagation will occur.  Naturally, this process is reversed as a parcel of  water is advected from a trough to a crest. It  is well known that  waves  tend to  break  at  their  crests because  the  acceleration associated w i t h wave motion serves to stabilize troughs a n d destabilize crests.  T h r o u g h the  erentially generated  at  act  of breaking, turbulence in the water  the wave crests.  A s the wave continues to  is pref-  propagate,  103 the patch of turbulence is left b e h i n d and is advected by the wave f r o m the crest position to the wave trough.  For a wave propagating i n the x direction  (with z defined as upward), this motion causes the fluid to be stretched i n the x direction a n d contracted  i n the z direction.  Associated with this distortion  there will be an intensification of the x vorticity a n d a suppression of the  z  vorticity; the y component will not be affected other than through advection. If the vorticity injected at the wave crests has equal magnitudes i n the x and z directions, there will be a tendency for the the x vorticity to dominate due to the fluid distortions identified. T h e y directed vorticity may be introduced independent  of this process  shown to not  affect  from the  the present  wind stress,  argument.  but  this vorticity will  be  T h e subsequent passage of waves  will introduce a periodic modulation of the vorticity, but the average effect is to increase the magnitude of the x component a n d to decrease that of the  z  component over that which was introduced at the wave crests.  It is realized that most of the vorticity introduced by breaking waves will be i n the y direction. characteristic  However, for a sea with a directional wave field (as is  of a developing sea),  breaking waves are normally short  crested.  T h e occurrence of finite regions of wave breaking requires the presence of some x directed vorticity. T h i s argument  does not  consider how turbulent  interactions  may  act  to  degrade the vorticity field into an isotropic state, but it does provide an answer to the fundamental problem of identifying a source of x directed vorticity. It is clear that once such vorticity exists i n the upper ocean it can remain stable for extended periods of time as demonstrated by the existence of L a n g m u i r circulation.  104 The  mechanism suggested  here is independent  of, but not incompatible  with, the theory of C r a i k a n d Leibovich. T h e C r a i k - L e i b o v i c h model suggests that a down wind component of vorticity arises f r o m the interaction the ity has  Stokes drift and vertical vorticity.  T h i s interaction leads to an instabil-  giving rise to L a n g m u i r circulation which under n o r m a l oceanic a  characteristic length  comparable  (Leibovich a n d Paolucci 1981).  between  to the dominant  surface  conditions wavelength  T h e vortex stretching model presented i n this  chapter predicts modifications to vorticity through wave motion. It is suggested that if vorticity is introduced isotropically at wave crests, then the wave distortion will lead to an anisotropic mean state.  There is no reason that these  two mechanisms could not work together w i t h the wave distortion mechanism introducing small scale vorticity while the larger structures are controlled by the C r a i k - L e i b o v i c h instability.  6.2  Analytical Formulation I wish to demonstrate  efficiency of the mechanism  the viability of the preceding argument described.  In order  to determine  a n d the  the effect  of  surface wave distortions on vorticity near the surface of the ocean, the vorticity equation is used:  du — + u • V w = u • V u + vV u, dt ' n  6.1  2  where u = (£, rj, C) is the vorticity vector a n d u — (u,v,w) tor.  is the velocity vec-  E q u a t i o n 6.1 can be expanded into three component equations to identify  which terms are important for the present situation,  d£  ,  d£  * <"5 +  d( + e  d£  5 "flS +  .^.du  s  )  =  %  +  du ,  *  +  c  >  3u.  &  )  +  ,  '  v  ^  6 2  105  dri  ,  dri  dri  dri  % ug.+vg + „g.) = +l  dt  dx  dy  T h e terms of interest  ,  dv  « £ + n £  dz  dx  and to§§)  a  x  ignored.  e  dv  ,  + & ) + »V%  dy  6.4  dz  are those that cause a change i n vorticity through  fluid distortions, not through transport: (uj§,u|£,  dv  for this reason,  Velocities associated  the advection terms  with vorticity will be  considered small compared to wave motions a n d vorticity is treated as a passive scalar i n the wave m o t i o n . In this case, the velocity field can be described by the irrotational wave m o t i o n alone which will contribute nothing to the vorticity.  F o r the case of a monochromatic, unidirectional wave field, u can then  be written as,  (u, v, w)  where  a is wave  =  ( 0 7 cos(kx  height,  7  — ~ft)e , kz  is the wave  0,  ay  sin(fcx — y t ) e  angular  k z  frequency,  ),  6.5  a n d k is the  wavenumber. Using the assumptions identified, Equations 6.2, duced to,  6.3, a n d 6.4 can be re-  106 E q u a t i o n 6.6  describes the evolution of £ subject to wave motion; £ dx  presses intensification due to stretching,  represents the interaction between  vertical vorticity a n d vertical shear i n the horizontal velocity, a n d f V £ 2  diffusion due to 6.8  but because  viscosity.  Analogous terms are  of the assumption that v =  or velocity interaction terms. equation a n d because  ex-  is the  found i n Equations 6.7  0, E q u a t i o n 6.7  A s a result, E q u a t i o n 6.7  and  has no vorticity  reduces to a diffusion  the y component of vorticity is not itself of interest i n  the present discussion, only the x and z components will be considered. Equations 6.6  and 6.8  can now be analyzed to  determine  how vorticity  introduced at wave crests would be modified by wave motion. T h e length scale of any vortex tube will be considered small compared to the surface wavelength so that the spatial variations in fluid distortion are not important. In addition, we are not interested i n the viscous diffusion of vorticity which will be caused by viscosity.  Values of eddy viscosity as large as 0.05  the ocean m i x e d layer ( P o n d a n d Pickard, 1983).  m s~ 2  1  are suggested i n  T h e present  objective is to  describe the motions which such a large eddy viscosity is intended to a n d so for the present viscosity {y = 1 0  - 6  m s 2  represent  case, a value of viscosity more like that of molecular - 1  ) would be appropriate.  In that case, it is reasonable  to ignore the viscous terms i n equations 6.6 a n d 6.8 leaving,  6.9  6.10  Equations 6.9  and 6.10  constitute  a coupled equation pair but an under-  standing of the physics can be gained by considering the problem when one  107 component  is zero.  For  the  case of no  vertical  component  of vorticity  (ie.  C = 0), E q u a t i o n 6.9 is easily solved by substituting the expression for E q u a t i o n 6.5  from  directly into E q u a t i o n 6.9 giving;  at  = -£akrf  sm(kx - >yt)e .  6.11  kz  Since vorticity is introduced by wave breaking close to the ocean surface, of the case of z = 0 is adequate.  A n additional simplification can be made by  considering processes which occur only at further simplifications, E q u a t i o n 6.11  _  where £ when  ^  0  e . ak  the  point  x =  0.  Subject  to  these  can be solved to give,  ak(l-cos(—f*))  e  6.12  f  is the value of £ at t = 0. =  use  E q u a t i o n 6.12  In breaking waves ak ~  0.4  has its m a x i m u m at t =  ( L e B l o n d and M y s a k 1978)  ^ so  that this m a x i m u m i n vorticity would be a factor of 1.5 above its initial value. An  average can be similarly arrived at  degree to which the x component  as having a value of about  1.2.  The  is intensified will oscillate w i t h the passage  of each wave, but as more vorticity is introduced selectively  at wave crests,  a  net increase i n x vorticity will be realized.  E q u a t i o n 6.10  can similarly be solved for the case of no horizontal vortic-  ity (ie. £ = 0) giving a related solution:  JL  =  e  a f c  (  C 0 S  (-T<))  g  13  o where  £o is the  value of £ at  average by a factor of 1/1.2 of horizontal vorticity.  t — 0.  This  equation  suggests a  decrease on  subject to the same assumptions used for the case  Vorticity originally oriented at some arbitrary  angle will  108 have its components subject to the variations predicted by Equations 6.13 6.12  but with the added complication of the interaction terms ( C § 7 and £ § 7 ) . It is worth noting that the term £ | j (in E q u a t i o n 6.9)  is a component of  the vortex force term identified i n the C r a i k - L e i b o v i c h theory (Leibovich, when the term  and  Stokes drift is considered.  of the  f o r m r/|^  because  ( T h e C r a i k - L e i b o v i c h theory  gradients  i n the  y direction are  1980)  also has  considered.)  In their development, they consider u to have some average z dependence. such a term were considered i n the present to the x  component of vorticity.  a  development, it would  If  contribute  T h i s action also serves to preserve  the  2-D  nature of the flow because there is no comparable term operating on the other components of vorticity.  6.3  Summary T h e development presented i n this chapter demonstrates  can serve to selectively intensify the x  that wave motion  component of vorticity when vorticity  with random orientation is introduced preferentially at  wave crests.  Although  this mechanism would appear to be periodic i n character ( E q u a t i o n 6.11), on average, it tends to a net increase in x vorticity because of the phase at which vorticity is introduced.  The processes.  simplifying steps used i n this development  ignore several  important  Viscosity would act to cause an outward diffusion of vorticity involv-  ing more fluid i n the circulation. T h e action of (eddy) viscosity would also be essential i n acting to diffuse the vorticity down through the m i x e d layer. addition, interactions between the vortices will act mon  to merge vortices  sign, a n d conversely annihilate vortices of opposite signs.  In  of com-  U l t i m a t e l y the  109 persistence on cay  whether  of this organized vorticity (or that of any other origin) will depend or not  the rate of vorticity introduction exceeds the rate of de-  through instabilities a n d viscous d a m p i n g .  vortices  will be highly non-linear a n d they  analytical considerations.  T h e interactions  do not  easily lend themselves  the to  T h e fate of two dimensional vorticity introduced close  to the ocean surface is considered i n Chapters 7 a n d 8. equally valid regardless  between  T h i s analysis will be  of the source mechanism of that vorticity and can  be  considered purely as an investigation into the dynamics of existing L a n g m u i r circulation.  no  C h a p t e r7 A 2-D Lagrangian Vorticity Model In  Chapter  vorticity  6 it was  injection at  demonstrated  wave  crests,  that  through the  it is possible to  preferred orientation at small scales.  action  of  selective  produce vorticity w i t h a  A major assumption i n that development  is that the velocities associated with vorticity are small compared to wave velocities.  T h i s assumption eliminates the interactions between vortices which is  acceptable  as long as there are few vortices.  A s more vortices are introduced  through continued wave breaking, a point will eventually be reached when vortex interactions must become important. turbulence which acts to cumstances,  destroy  Such interactions are the hallmark of  any organized  flow.  U n d e r the present  cir-  there is some reason to suspect that the flow could retain its two  dimensional characteristic.  A mechanism acting to enhance a single component  of vorticity has been described, and the development of Chapter 6 identifies some processes which might serve to retain the resulting two dimensionality. In addition, it is known f r o m observations that (two dimensional) L a n g m u i r cells can remain stable for long periods i n the ocean. If a flow retains a two dimensional character, then the vortex interactions lead to a cascade to larger  will not be destructive  but  will  scales identified with two dimensional turbulence  ( K r a i c h n a n 1967).  The  interactions  leading to a vorticity cascade are highly non-linear and  are most conveniently studied through use of a computer model. T h i s  chapter  describes the development of a computer model for this purpose and  presents  Ill some evaluation of that model's capabilities.  A discussion of the model results  specific to the problem of L a n g m u i r circulation is deferred until C h a p t e r 8.  7.1  Model Requirements T h e r e are many numerical models that might be suitable for analyzing a  system of two dimensional vorticity. In selecting a model for a particular application, consideration must be given to computational efficiency a n d tractability of the p r o b l e m . commodate  F o r the case of L a n g m u i r circulation,  a large range of important  to  horizontal, but there is a natural the b o t t o m  ac-  scales f r o m the domain size down to  resolving the smallest possible structure. the  the model must  T h e domain is normally unlimited i n length scale determined b y the depth  or the first significant pycnocline (typically 100 m i n a deep  ocean environment but 50 m i n the observations presented i n C h a p t e r 4). T h e smallest scales can be drawn f r o m the sidescan observations of C h a p t e r 4 a n d so must be approximately 1 m , consistent  with the introduction of vorticity b y  breaking waves since such vorticity will be constrained to have scales b o u n d e d by the horizontal extent of these breaking waves (about 1 m based o n observations presented i n Chapter 5). T h e model domain must then be several the depth scale limit of 50 m because the largest L a n g m u i r cells have  times  spacings  that are 2 to 3 times the mixed layer depth (Weller and Price 1988); a horizontal extent of at least 100 m is needed. T h e time scales that are relevant to such a system are as great as 30 minutes as seen i n the observations. A  suitable model for this problem is the Lagrangian vorticity model first  described b y C h o r i n (1973). imated  In this model, the vorticity of a flow is approx-  b y a distribution of many  point  vortices.  In a n inviscid  evolution of flow is described solely by the subsequent  fluid,  the  advection of vortices  112 through their  mutual interactions.  number flows where the neglect  T h e model is suitable for high Reynolds  of viscosity is acceptable.  A great economy of  computation is realized with such models because increased resolution is automatically provided i n areas of high shear b y the accumulation of many i n such areas. investigate bulence:  vortices  A form of this model was used by Siggia a n d A r e f (1981) to  characteristics of the inverse energy cascade i n two-dimensional tur-  their work provides some  motivation for this choice of m o d e l . F o r  the present application, such a model has the additional intuitive advantage of representing vorticity-dominated flow by a distribution of vorticity. A weak point i n the model is the assumption that viscosity is small. T h i s assumption is not a n issue if only the value of molecular viscosity  is used,  but estimates of eddy viscosities for ocean mixed layers are typically of order 0.05 m s~ 2  1  ( P o n d a n d Pickard 1983).  T h e use of a n inviscid model i n this  d o m a i n can be defended from the point of view that the model is attempting to reproduce exactly those turbulent motions that the eddy viscosities attempt to parameterize. to  fully  T h e position of considering the inviscid results is taken not  explain nature,  but to provide some  greater insight  towards  a full  explanation. A l t h o u g h this model has been developed to extend the idea of vortex i n jection through wave breaking presented i n Chapter 6, it makes no restrictions on the source of the vorticity. W h a t is considered is how two-dimensional vorticity will interact i n the presence of an image surface. results present,  can be considered to model the interactions whatever  the origin of that  F o r this reason, the  of L a n g m u i r cells  when  circulation might be. In particular,  the  m o d e l results are as applicable to vorticity introduced by the C r a i k - L e i b o v i c h mechanism as to that by the mechanism introduced i n Chapter 6.  113  7.2  A 2-D Lagrangian Vorticity Model The  concept  of solving the inviscid Navier-Stokes equations  grangian vorticity approach is suggested that  this  simple approach  can  by C h o r i n  accurately  using a L a -  (1973) who demonstrates  model the  complex  turbulent  flow  past a cylinder. T h e basic ideas of the technique are discussed by Christiansen (1973), who provides several example  applications.  T h e approach is based on  the vorticity equation for inviscid flow a n d the continuity equation;  V  •  u = 0,  where £ is vorticity, u is the two dimensional velocity, and t is time.  In a two  dimensional domain, the vorticity and stream function,  e= vx  u  , 7.2  u = V x -<f> can be used i n Equations 7.1 to give  V 4> =  7.3  2  For any spatial distribution of vorticity considered, the vorticity field can be approximated  by an appropriate  distribution of many point vortices  such  that «*,z) =  X>  7.4  If stream functions which satisfy Poisson's equation ( E q u a t i o n 7.3)  are assigned  to each point vortex, then the stream function for the entire flow can be approximated by summing over the stream functions of the constituent  4>{x,z) = ^2 (f> . /  i  vortices  7.5  114 G i v e n that the stream function is known, the velocity of each of the point vortices can be determined a n d the motion of those vortices can be approximated to estimate the evolution of the vorticity field. f r o m the new distribution of vortices  T h e stream function resulting  can again be calculated f r o m E q u a t i o n  7.5 thereby modelling the evolution of the flow.  O n e difficulty characteristic of this model arises from the infinite velocities encountered  at small distances  from a point vortex.  H a l d a n d D e l Prete  (1978) outline a variety of methods that have been developed to deal w i t h this problem.  T h e concept  common to all of these approaches  is to smooth out  the vorticity distribution so that the point vortices are replaced by some distribution of vorticity.  F o r the present  finite  model, a modification suggested b y  C h o r i n (1973) is used i n which the stream function of the discrete vortices is described as Mr.\  7.3  (  2 7 r  )  _ l l  °g  r  (  r  > )  7 fi  a  Model Implementation T h e implementation of the Lagrangian vortex model requires  of the b o u n d a r y conditions to be used. dynamics  of the changing vortex  individual vortices  becomes  introducing image  surfaces.  consideration  B o u n d a r y conditions must m a t c h the  locations  otherwise  location dependent. T h e geometry  the stream function of  A n easy way to do so is by  of the problem at h a n d is simple  under this approach, a single image surface is used at the ocean surface with a  second  desired.  image  surface  introduced  to simulate  a bottom  or thermocline if  These boundaries are realized i n the model by introducing images of  each vortex introduced into the model.  115 T h e horizontal d o m a i n is essentially unbounded a n d so would be best represented by a periodic boundary condition. Such a boundary is not for the present  model because vortex interactions  itly for each vortex a n d image represented  practical  must be determined explic-  i n the model.  Instead,  a periodic  boundary condition is approximated by repeating the domain once on each side of the m o d e l . W i t h this approach, interactions are considered for the  replicates  of all vortices within one model d o m a i n w i d t h of the finite model: the existing beyond this range  vortices  would contribute only marginally to the resulting  stream function. T h e length scale i n the model is set  by the size of vortices a n d b y  the  periodic domain size so that m o d e l results are naturally non-dimensionalized by these and related scalings. because  throughout  Results are however presented i n dimensional units  the model development, the observations  to gauge the model results.  have been used  For that purpose, a horizontal domain of 200  is always considered (consistent  with the sidescan sonar range),  resolution (as determined by the vortex diameter) model domain is shown schematically i n Figure  of 1 or 2 m  m  a n d a length is used.  The  7.1.  Vortices of diameter 2a are introduced into the model i n stable pairs with a spacing of 2cr  0  constant  at  a  depth of a.  introduced at  a  rate at at r a n d o m locations along the horizontal domain. T h e model  is stepped forward i n time existing velocity displacement vortices  These vortex pairs are  field.  by advecting  of the  point vortices  T h e time step is adjusted so that  is limited to  be small compared  (typically displacements  steps i n the model are  each  were restricted  adjusted at  to to  the  the  diameter  a/10).  all times to accomodate  by  largest  vortex  of the  point  In this way, the most  spaced vortices. N o vortex displacement will exceed this limit of  a/10.  the  time  closely  116  V  |  V  V  V  V  V  V  V  V  *  V  V  V  V  V  V  T  Image Surface  V tb  •  ' . 1  T  T  T  T  T  t  t  t  t  t  r\  T  [  T  T  T  1  T  T  t  |  f  T  1  t  T  T  T  T  T  T •  T  T  T  T  T  f  T  T  t  .Test Point  t  '1 *  T  T  T  T  T  T  1T  T  T  T  |  t  t  T Periodic Boundary  Optional Image Surface  Periodic Boundary  M o d e l domain.  Vortices that  approach  close  to  the  surface  locities through interactions w i t h their images. vortex trajectories that pass within cr/2 a  •  • ,  •*  F i g u r e 7.1:  V  »  \t * •  |  depth of cr/2:  acquire large  horizontal ve-  T o control these motions,  of the surface  are reflected back  a similar procedure is used when required where a  b o u n d a r y is present.  any to  bottom  117 Models based on point interactions requirements  that  increase  as  n  between vortices  where  2  present configuration uses a constant  n  is the  have  computational  number of vortices.  The  vortex injection rate and so the number  of vortices grows linearly, inexorably reducing the model execution speed. addition  to  this  computational difficulty,  it  is not  reasonable  to  In  expect  the  enstrophy of the flow to increase indefinitely. T h i s problem is addressed b y diffusing the vortex diameters w i t h time i n a manner that is somewhat  analogous  to viscous diffusion. T h e rate of vortex growth is given by  a  When  the  eliminated  vortex  diameter  f r o m the  2  increases  m o d e l thereby  =  2vt.  to  7.7  some specified value,  limiting  the  that  vortex  number of vortices  in  is the  system. The from the resented  method  of eliminating vortices  m o d e l a n d represents by the  after  some  time  a f o r m of dissipation.  model are essentially inviscid;  or eliminated within the m o d e l domain. the enstrophy is by eliminating vortices  removes  enstrophy  T h e interactions  vorticity cannot  be  rep-  generated  T h e only method available to  hmit  and the method being used removes  those that have been i n the model the longest.  A s s u m i n g that the action of  viscosity will have degraded the strength of these vortices, this m e t h o d can be considered as a means of representing viscous dissipation.  7.4  Model Subdivision Scheme T h e m o d e l stream  function at  over all the individual vortex  any point is approximated by integrating  contributions.  W h e n large numbers of vortices  are involved, this process requires a great deal of computing time to determine  118 the  contributions  of the  from distant  stream function.  vortices  which have  little effect on the  value  T h i s situation has been avoided by determining  the  vorticity contained within subdivided regions a n d computing the stream function based o n the vorticity of these regions. retaining i n d i v i d u a l vortex interactions point of interest.  M o d e l accuracy is recovered  for vortices  i n close proximity to  by the  Nearby vortices are identified as those falling w i t h i n the same  subdivided region as the point of interest,  or those regions lying immediately  adjacent to it. Special conditions must be considered when determining the stream function close to the model domain boundaries.  Close to image surfaces, images of  b o t h the individual vortices and the subdivided regions are required. A t horizontal boundaries, the adjacent vortices are actually those located at the  other  side of the model because of the periodic domain used. Figure 7.1 outlines the model geometry a n d subdivision scheme by identifying the vortices contributing to the stream function computation for an example test point. large arrows  represent the collected  arrows represent discrete vortices: The number  computational and  size of the  In Figure  vorticity of subdivided regions  arrows are inverted across image  advantage of this approach subdivided regions.  7.1,  a n d small surfaces.  critically depends on  T h e relative  advantage can  determined by considering the number and type of computational  the be  operations  required for b o t h the primitive a n d the subdivided versions of the m o d e l .  For  the primitive version of the model, the stream function must be determined at each vortex location which requires  considering the influence of all the  other  vortices at that location. T h e time required for this computation is  T = 6n(n -  1)  7.8  119 where  8 is  the  time  required to  determine  the  influence of one  vortex  on  another a n d ra is the number of vortices. In contrast  to the  " p r i m i t i v e " version of the m o d e l , the subdivided ver-  sion of the model requires three distinct operations i n order to determine  the  stream function at any point. F i r s t , the vorticity contained within each subdiv i d e d region must be determined a n d that vorticity assigned to a representative vortex located at the center of the region. T h e contribution of these collected vortices to the stream function at the point i n question must then be mined.  Finally, the contribution to the stream function f r o m all those  vortices identified as being close to the point of interest  deterdiscrete  must be determined.  T h e time required for these calculations can be represented as  9 Ti c  =  c  an + Bnm +  7.9  6—ra , 2  m where m  is the total number of subdivided regions, ra is the total number of  vortices, a is a scaling for the time to sort a vortex into its appropriate region, 8 scales the time to determine the stream function at any vortex location due to the vorticity contained within a region, and 6, as i n E q u a t i o n 7.8,  scales the  time to determine the stream function at a vortex location due to the ~  9ra/m  vortices located close to the test point (assuming vortices are distributed evenly over the m o d e l domain). What  is important  is not  the  actual  processing  time,  but  the  relative  advantage of using the subdividing algorithm;  T  cic  T  =  an + 8nm +  6±n  2  8n(n-l)  T h e factor a is known to be small and it is linear i n ra so this term can be ignored for large ra. T h e operations to determine stream function at  a point  120 are  identical whether  they  are for individual vortices,  or for the subdivided  regions so that 8 ~ 8. U s i n g these two simplifications, E q u a t i o n 7.10  reduces  to ^ = m / n For  a given  models  value  of n ,  + 9/m.  7.11  ^ p - is minimal when  to be considered  incorporate  1500  m =  vortices:  3n  - 1  / . 2  Most  of the  the optimal number of  subdivdided regions for such cases is 116 for which a computational advantage of  = 0.15 is realized. T h e subdivision scheme clearly saves computation time, but it also intro-  duces  errors by limiting  the resolution of the model.  This  loss of accuracy  has not been considered i n this discussion, it will be considered i n the following section  on model accuracy through comparisons  of models with different  operating parameters.  7.5  Model The  Accuracy  question of convergence  and ultimate  considered by H a l d a n d D e l Prete (1978), approximations  accuracy of vortex models is  and Hald  (1979).  Subject  of the model, they find that the approach converges  an error proportional to the diameter of the discrete vortices. with any numerical scheme  to the a n d has  A n o t h e r concern  is the effect of numerical diffusion o n the results;  errors in the stream function, a n d the finite time step (displacement  step) of  the model cause errors i n the trajectory of the point vortices. The  effect of (random) errors i n vortex displacements  random component This  effect  to the vortex  can be seen  is to introduce  a  motion which acts to diffuse the vortices.  by considering how the model would represent the  121 motion of passive point tracers about  a single vortex.  T h i s system w o u l d be  completely stable with the tracers orbiting the vortex, but the r a n d o m errors in the model would lead to a slow diffusion of tracers outward from the vortex. For (as  the  vortex model,  this  discussed by C h o r i n ,  diffusion is analogous  1973).  to  the  action  of viscosity  T h e variance i n vortex displacements  can  be  related to viscosity through the relation,  x  where x time.  2  2  = 2ut,  7.12  is the variance i n position, v is the viscosity, and t is the  elapsed  T h e effects of this numerical viscosity are insignificant as long as  they  are small compared to the effects of molecular or eddy viscosity. It is not possible to determine the absolute error i n vortex  displacements  occurring i n the model since the correct displacements are not actually known. It  is however possible to  start models with various parameter  from a given state, a n d then compare these models.  If the  models  have  the vortex displacements  identical errors,  will be identical and nothing can be learned. subdivision  scheme  subdivided)  model,  isolated  can and  be  isolated  the  errors  by comparing models  by  the  vortex  configurations predicted by displacements  However, the errors due to  comparing  arising from  w i t h different time  against a  a primitive  finite time step values.  step  the  (non-  can  be  Displacement  errors will be different (and it is assumed independent) in these comparisons so that the variance i n the distribution of vortex displacements can be related viscosity through E q u a t i o n The  to  7.12.  first comparison to be considered is made between two models start-  ing from a c o m m o n state but proceeding with different time steps for 2 s of  122 model  time.  O n e model incorporates  a  time  step regulated  by  a  maximum  vortex displacement of cr/10, while the second model is constrained to by displacements models  are  of cr/100 (resulting i n time identical in all other  steps  respects  ~  t  of the  h  spanning 200  first model).  m  The  horizontally, u n -  b o u n d e d vertically, and incorporating 3000 individual vortices.  In Figure  7.2a,  a visual comparison of differences between these models is obtained by p l o t t i n g the differences i n horizontal and vertical displacement as x a n d y positions for each of the vortices in the models. If it is assumed that the displacement differences do not depend o n position within the model d o m a i n , then F i g u r e can  be interpreted  occurring between  as  portraying the  these models.  distribution of displacement  If the  errors  differences  occurring i n these models  r a n d o m , then the variance of displacement errors will a d d .  7.2a  are  T h e model based  on small time steps makes only a small contribution to this variance a n d it is assumed that all of the scatter seen i n Figure 7.2a f r o m the use of a larger time step.  is due to errors resulting  A t worst, this assumption leads to an over  estimation of the variance generated by the m o d e l . Subject to this assumption, the amount of scatter seen i n Figure 7.2a a viscosity of 1 0  - 6  m 5 2  - 1  .  translates through E q u a t i o n 7.12  to  T h i s value is of the order of as that of molecular  viscosity a n d is obviously insignificant i n the present study.  A key concern with the model is the degree to which the observed scatter in vortex displacements is isotropic since isotropy is required for the tation of this scatter i n terms of viscosity. apparent direction. model  Figure 7.2a  interpre-  is characterized  by an  isotropic scatter w i t h some anomalous displacements i n a downward These anomalous points are  treatment of vortices  interacting  not  unexpected,  w i t h the  they  surface.  result  from  the  T h e r e is only one  123  .02A  nj  LD O CL o.oo-  > I  cn • CL  >  .02-  .02  .01  —I  .01  XPOS1-XPOS2  .02  CmD  .02n B  QJ  .01-  c  to LX  X  0.00-3.14  -1.05 Angle  Figure run,  7.2:  1.05  3.14  CradJ  Comparison of displacement differences between a normal m o d e l  a n d one with a time step reduced by a factor  of 10,  (the  small time  step m o d e l will have comparatively small errors a n d is considered as a reference),  a) Scatter plot of displacement differences, b) directional dependence of  displacement differences.  124 time step required in the model using a long time step a n d any escaping vortices are arbitrarily replaced at never  a depth of z =  escape in the m o d e l with shorter  CQ/2.  M a n y of these  time steps a n d they  vortices  will appear  depths greater t h a n CTQ/2 resulting i n anomalously large negative  at  displacement  differences i n the comparison. T o further  quantify the  degree of isotropy,  plotted as a function of direction i n Figure 7.2b.  the  displacement  variance  It is seen that the variance is  essentially isotropic except for an increase i n downward variance related to surface interacting vortices.  is  F r o m this comparison it is clear  the  that time steps  regulated by m a x i m u m displacements of O.lcr produce m i n i m a l errors through numerical diffusion. A  similar evaluation can be made to quantify the diffusive effects intro-  duced by the model subdivision scheme.  For this  primitive version of  the m o d e l was executed until a steady state was achieved a n d that m o d e l result was used as subdivided  model.  the  initial condition for b o t h the  T h e vortex  displacements  primitive m o d e l a n d  predicted  i n these two  were compared after a two second time step h a d been completed.  the  models  Figure  7.3a  shows the distribution of displacement differences between the primitive model a n d a m o d e l that has been subdivided into 640  rectangular  regions 3.13  m in  the horizontal by 5 m i n the vertical. A feature of the distribution i n Figure 7.3a tex  displacements.  is the horizontal line of vor-  It is caused by vortices interacting w i t h the surface  image  boundary, but because the time step is the same i n b o t h models, (in contrast to the two models compared i n Figure 7.2a), many of the same vortices escape the b o u n d a r y i n b o t h models a n d are returned to the same depth (resulting i n a 0 vertical displacement).  125 .02-  A  ru cn •  CL >I  o.oo.:'7*-' ;  CD • CL  .02-.02  I  -.01  1 .01  —•i  .02  X P D S 1 - X P O S 2 Cm] .02-1  B  E QJ Dl C CD  .01-  CE  X  o.oo-3.14  -1.05 Angle  F i g u r e 7.3:  1.05  3.14  Crad]  Difference i n computed displacements between a primitive vortex  interaction model and a model accelerated by subdividing it into 640 a)  Scatter plot of displacement  placement differences.  regions;  differences, b) Directional dependence of dis-  126 Figure 7.3b shows a plot of variance as a function of direction to quantify the degree of isotropy i n the scatter plot of Figure 7.3a.  T h e only distortions  in this plot are those expected i n the horizontal which result f r o m the b o u n d ary interacting vortices.  T h e amount of variance present in this comparison is  similar to that seen i n F i g u r e 7.2 vision scheme,  and so it is concluded that for this subdi-  there is neither (significant) increase i n displacement scatter or  introduction of any undesirable bias. Based on the minimization of E q u a t i o n 7.11,  there is an o p t i m a l choice for  the number of subdivided regions but this estimate does not account for model accuracy. the  Comparisons were repeated  sensitivity of the  results  to  the  with a variety of models to size of the  comparing against the same primitive model). of these  tests i n terms  the resulting variance.  of the  In all cases tested,  subdivided regions,  Table  horizontal and  determine  7.1  vertical  provides a summary viscosity  implied  64x10 (3.13  7.6  m x 5 m)  by  the viscosities are of the order of  molecular viscosity and so the subdivisions should not adversely affect Based on the results shown i n Table 7.1,  (always  results.  models have been s u b d i v i d e d into  regions.  Model Scalings It  is a  worthwhile exercise to  consider the  scahngs  that  are  present  the m o d e l a n d the implications that these might have on the results.  in  Aside  from the restrictions imposed by the model design, the parameters which can be freely explored include the vortex injection rate, the vortex initial size and strength, time).  viscosity and m a x i m u m vortex size (which controls  the  vortex life  It is the results which have some physical meaning which are of interest  a n d not those that are a consequence of the model design.  127  x-dimension  y-dimension  m  m  m s~  1  10  10  2 x 10  -6  4 x 10"  7  2  10  5  2 x 10  -6  1 x 10"  6  3  5  5  3 x 10  -6  9 x 10~  4  2.5  2.5  1 x 10"  Trial  Table 7.1:  2  2 —1 m s  1  7  9 x 10~  5  6  Numerical viscosities resulting from subdivision schemes.  T h e vortex  life time is determined by the size of injected vortices,  the  m a x i m u m allowed vortex size, a n d the rate of vortex diffusion. F r o m E q u a t i o n 7.7,  the vortex life time can be found as:  (2  2\  j 23  rp _ \°~m ~ o) a  2v where o~  m  is the m a x i m u m vortex  radius i n meters,  radius i n meters, and v is the viscosity i n m s~ . 2  cr  0  is the initial  vortex  T h i s time scale is largely a  l  result of the model design and so it must be determined that the results  are  not strongly dependent on this term. T h e model is ultimately a balance between the enstrophy input a n d the rate at which dissipation erodes this enstrophy. T h e values of viscosity used i n E q u a t i o n 7.12  were kept small (less than 1 0  _ 3  m s 2  - 1  ) to be consistent w i t h the  concept of an inviscid model. A consequence of this low value was a tendency  128 to extend vortex life times as regulated by E q u a t i o n 7.13. tices active i n the model is a direct consequence rate V  p  a n d the m a x i m u m vortex diameter cr . m  of the viscosity, the injection In order to keep vortex n u m -  m  bers low i n the model, the value of a  T h e number of vor-  was decreased  to values of order 2cTo.  In this case, the elimination of vortices is a separate non-physical form of viscosity.  T h e only argument  old vortices  that can be made i n support this approach is that  have a tendency to appear at greater depths i n the model where  density gradients (not considered by the model) would act to absorb vorticity.  Numerical  viscosity  is also  active i n the  Values for this term are however of order 1 0 so they  should have  to increase  a very  7.7  - 5  discussed previously.  as identified i n T a b l e 7.1  small effect on m o d e l outcomes.  It  and  is possible  the viscosity of the model by introducing random motions to  vortices according to E q u a t i o n 7.12, model  model as  the  this approach has not been explored i n the  experiments.  Summary of Lagrangian Vorticity Model T w o dimensional flow close to an image b o u n d a r y is a characteristic fun-  damental to L a n g m u i r circulation.  A Lagrangian model of vorticity has  been  developed to improve the understanding of interactions between vortices i n this geometry.  This  model is particularly suited to  multiple scales seen i n L a n g m u i r circulation.  investigating the  presence of  T h e model makes no distinction  as to the origin of vorticity a n d so it is equally applicable to any model of L a n g m u i r circulation." It is developed in this instance to determine if vorticity introduced at very small scales can account for the larger structures recognized as L a n g m u i r circulation.  129 T h e m o d e l is based o n solving the inviscid equations of fluid m o t i o n and so the results are only valid for high Reynolds number flows (when viscosity is unimportant).  T h e model recreates the vorticity distribution of the flow with  many discrete vortices. B y integrating over the stream function of each discrete vortex,  the  stream  function of the  entire  flow  can  be determined.  For  the  present problem, discrete vortices are introduced as stable pairs r a n d o m l y along the surface image boundary of the model's periodic horizontal d o m a i n . T h e r e is no explicit need for a b o t t o m boundary because of the Lagrangian nature of the m o d e l . In practice,  the use of point vortices is difficult since they can introduce  infinite velocities i n the flow. T h i s problem is avoided by using finite regions of vorticity.  W i t h such a system, the accuracy of the model is restricted by the  dimensions of these individual vortices ( H a l d 1979). limit on the number of vortices  There is also a  practical  used since the execution time of the model  increases as the square of the number of vortices.  Since the m o d e l introduces  vortices at a continuous rate, it is necessary to ehminate vortices i n some m a n ner to avoid excessive  computational requirements;  a n d are removed from the m o d e l when they  reach  the vortex  regions diffuse  some arbitrary  diameter.  T h i s approach approximates the action of viscous dissipation. T h e number of active vortices i n the model eventually reaches a balance between the rate of vortex injection and the life time of vortices. T h e m o d e l cannot  be relied u p o n to study the energy budget of a cir-  culation pattern because it does not accurately represent the m o d e l can be expected  to represent  energy  flow.  Rather,  the interaction between many point  vortices, the effects of a b o t t o m boundary (if included), and the velocity distrib u t i o n w i t h i n the circulations that are generated.  130  Chapter8 Model Results E v a l u a t i o n of model results can be carried out at two levels; a qualitative consideration of model characteristics, parameters  a n d results.  on exact parameter this chapter.  a n d a quantitative comparison of model  Qualitative characteristics  are not strongly dependent  choices and these general results will be presented first i n  Progressively, more quantitative results will be considered which  offer more information but are more sensitive to the m o d e l characteristics. The Table  results that are presented are based o n nine model runs identified i n 8.1.  indicators  In addition to model parameters, of the model results:  the  Table 8.1  displays some general  significance of these indicators  will  be  discussed i n detail as they are encountered through the discussions presented i n this chapter.  8.1  Model Streamlines A  convenient overview of model characteristics  can be obtained b y con-  sidering the streamlines predicted by the model after it has reached a  steady  state. Streamlines are constructed by contouring the stream function o n a grid of 3 by 3 m over the model d o m a i n . Contouring o n this grid filters out small scale structures  consistent  with the model's finite resolution as determined by  the discrete vortex dimension (of order ao). As  a  first  example,  typical streamlines  produced by the  absence of a b o t t o m boundary are displayed i n F i g u r e 8.1,  m o d e l in  these  the  streamlines  131  C  D  E  F  G  H  3.0  3.0  1.5  3.0  3.0  3.0  3.0  3.0  .004  .002  .002  .004  .004  .002  .002  .002  .002  0.27  0.27  0.27  0.54  0.27  0.27  0.27  0.27  0.27  cr (m)  0.5  1.0  2.0  1.0  2.0  1.0  1.0  1.0  1.0  cr (m)  1.5  1.62  2.37  1.62  2.37  1.62  1.62  1.62  1.62  0.005  0.01  0.02  0.01  0.02  0.01  0.01  0.01  0.01  3076  1205  1318  1118  2148  1342  1232  1230  1216  oo  oo  oo  oo  oo  oo  15  10  500  325  326  197  168  264  276  228  216  0.14  0.11  0.11  0.13  0.06  0.09  0.09  0.07  0.07  -.02  -.03  -.05  -.03  -.10  -.03  -.05  -.04  -.04  37  44  33  48  34  35  14  11  20  Model  (s x 10 )  T  3  Km^^lO" ) 3  0  m  as- ) 1  Vortices Domain  (rn)  T & (.s) 0  s  Tobs/T  V  max  {ms~ ) x  FWHM  (m)  A  B  3.7  .  I  20  T a b l e 8 . 1 : M o d e l r u n statistics.  are drawn from M o d e l C identified i n Table 8.1. figure is 4 m s~ 2  1  T h e contour interval i n this  with only the values at m a x i m a labelled. Regions of largely  clockwise rotation have been shaded to distinguish adjacent vortex cells.  Figure  8.1 displays the entire 200 m horizontal domain of the model a n d 30 m i n the vertical. T h e flow has organized itself into a few well defined cells w i t h the obvious  132  Horizontal Scale (m)  Figure  8.1:  Contours of  achieved a steady of 4 m s~ 2  1  stream  function occurring  when  state a n d there is no b o t t o m present.  has been used with values at  the  model  has  A contour interval  m a x i m a labelled a n d all negative  areas (characterized by clockwise oriented flow) have been shaded i n .  presence  of several  length scales.  There is some  indication that  regions  of  clockwise flow are pressed towards the right against balancing counter-clockwise flows.  T h e resulting crowding of downward directed streamlines between these  regions results model,  i n downwelling velocities exceeding  m a x i m u m downwelling velocities are about  those  upwelling.  —0.05 m s  - 1  For  compared  this to  133 0.03 m s  - 1  for upwelling.  The occurrence of larger downwelling velocities than upwelling velocities is an observed characteristic of Langmuir circulation (Smith et al. 1987), and it is an obvious result of the flow geometry: each clockwise region has a counterclockwise image balancing it across the surface and pushing it to the right. The reverse is true for counter-clockwise regions. An additional consequence of the flow geometry is that maximum velocities must occur somewhat below the surface since there is the restriction of no flow across the image surface. A key consideration in attempting to match the model output to observations was the magnitude of vertical velocities. From the observations it is known that downwelling speeds of about 0.06 m s  - 1  are expected for the scales  that the model attempts to simulate. Maximum velocities were averaged over many (independent) flow field realizations to determine characteristic velocities from the model. The results of these averages are shown in Table 8.1 as V xma  Model C (see Table 8.1) provides downward velocities of —0.05 m s comparable to the values of —0.06 m s  - 1  - 1  which is  observed in the field (see Chapter 4)  and this model was used to produce the streamlines shown in Figure 8.1.  8.2  Bottom Influence The flow field depicted by Figure 8.1 is compelling in its similarity to that  expected for Langmuir circulation. A characteristic that one is immediately tempted to test is the dependence of length scales on the presence of a bottom boundary. Langmuir circulation is known to be sensitive to the presence of a bottom boundary with the maximum length scale restricted to 2 or 3 times the bottom depth (Weller and Price 1988, and Smith et al. 1987). Such a  134 boundary  was  introduced  at  10  m  into a model trial identical i n all  respects to that shown i n Figure 8.1. are shown i n Figure 8.2.  other  T h e streamlines that result from this test  A s for Figure 8.1,  m a x i m a have been labelled and  regions of clockwise flow have been shaded in; a contour interval of 2 has been used.  In Figure 8.2,  m s~ 2  the entire model d o m a i n is displayed; 200  i n the horizontal and 10 m i n the vertical.  Figure 8.2  shows some  1  m  streamlines  crossing the b o t t o m image b o u n d a r y : this does not result from flow across the model boundary, but is an artifact of the contouring package used i n making the figure.  In comparing Figure 8.1  w i t h Figure 8.2  it is immediately clear that  the  presence of the b o t t o m boundary has altered the horizontal length scales (bear in  mind  horizontal  the  different  vertical  coherence of the  scales used in p r o d u c i n g these figures).  stream  function at  a  fixed  depth  was  The  used  to  quantify this result:  P(p,z)=  (^Jj(x,z)(f>(x +  p,z)dx^ ,  8.1  where <f)(x,z) is the stream function, p is the horizontal displacement, z  are  horizontal and vertical  spatial  coordinates,  average.  T h e horizontal coherence is somewhat  bounded  models  it  is calculated  at  and  (  )  indicates  depth-dependent;  m i d depth,  a n d i n the  for  a  x  and  time  bottom  model with  no  b o t t o m boundary it is computed at 15 ro depth. T h e time average is achieved by repeating  the  the full w i d t h at used as a measure  calculation over many (independent) half m a x i m u m  (FWHM)  of the  of model horizontal length scale.  runs is listed i n Table 8.1.  model realizations  autocorrelation  and  function is  T h i s value for all model  135  0  Horizontal Scale (m)  Figure 8.2: achieved  Contours  a steady  zontal domain.  of  stream  function  state with a b o t t o m  A contour interval of 2 m s~ 2  m a x i m a labelled and areas characterized  It  is not  immediately  unbounded models,  but the  clear what  dependence  1  at  10  when m  the  in a  model 200  m  has hori-  has been used w i t h values  at  by clockwise oriented flow shaded i n .  parameters control  introduction of the b o t t o m  stricts length scales i n proportion to the the  occurring  located  boundary  the  FWHM  boundary  depth.  in  the  clearly  re-  Figure 8.3  shows  of length scales on bottom boundary depth for M o d e l s G , H  a n d I. These models are identical i n all respects except for the  depth of the  136 bottom boundary. Figure 8.3 shows that length scales vary in direct proportion to the boundary depth consistent with observations of Langmuir circulation in the presence of a thermocline or bottom (Leibovich 1983). 8.3  Length Scale Distributions A primary objective of this modelling was to determine if the interaction  of many point vortices could lead to the variety of length scales observed in the sidescan data. The model does not simulate bubble cloud activities, but vertical velocities can be used to identify regions of downwelling and so distinguish windrows in the model domain. Using the model velocity field, individual cells were identified by the presence of downward velocities exceeding an adjustable threshold. The spacings between the cells defined in this way were then measured and these values accumulated into a histogram based on many model realizations.  This result is sensitive to the choice of velocity  threshold, but the form of the histograms is consistent and comparisons can be made between models run with similar input parameters.  Figure 8.4 displays  two such histograms based on models with a 10 m and 20 m bottom boundary (model runs H and I). As demonstrated by the coherence analysis, the bottom depth markedly alters the length scales observed with larger scales occurring only with the deepening of the bottom boundary. The form of these histograms can be compared with those of sidescan data (Figure 4.8 page 58) and they demonstrate distributions consistent with those observed. 8.4  Stability of Structures An important aspect of the model is the stability of individual vortex  structures since it provides an indication of how instabilities destroy the organized flow. In the observations, stability is manifested in the life time of  137  D o m a i n D e p t h Cm]  Figure 8.3:  Length  scale dependence  on b o t t o m  scales are determined from autocorrelations  boundary  depth.  Length  of the stream function and plotted  against the b o t t o m boundary depth used i n that model.  138 100n  ^  Spacing  (m)  lOO-i  0)  10m  o  bottom  U  0  o  o  > •H  -P i—I  (1)  Spacing  Figure 8.4:  (m )  C e l l spacing histograms for model results a) 10m b o t t o m b o u n d -  ary and b) 20m b o t t o m boundary. Distinct cells are identified o n the basis of vertical velocities exceeding —0.01  ms . -1  139 identifiable structures lar sort of measure  i n the sidescan data;  about 20 to 30 minutes.  A  simi-  could be used for the model results based on similarities  between successive streamline patterns,  but this approach would be  time consuming to implement a n d would not easily be repeatable qualitative nature of the definition. been used which is based on the  extremely  due to  the  Instead, a more quantitative approach has coherence  between the stream functions of  successive model realizations. T h i s approach is not directly comparable to the observations, but since the alternative of visual estimates ture  life time  is no better  in this regard,  the  more  of streamline  struc-  quantified approach is  favoured. For the purpose of estimating structure life times, the coherence is defined as, n  r  x  =  { T )  (f <Kx,t)<l>(x,t + T)dx) J <f)*(x,t)dxJ <f>*(x,t + T)dx 2  x  x  x  where (f>(x,t) is the model stream function. T h e life time (T b ) is defined as 0  that time lag beyond which the coherence falls below 0.7  (ie.  s  H(T b ) 0  3  =  0.7)  T h i s fairly high choice for the coherence threshold results i n shorter life times, but  the resulting values are more stable t h a n those  generated  using smaller  values where the results are very sensitive to r a n d o m fluctuations. T h e results of these calculations are presented i n Table 8.1 considered:  the model life times are about 200  the parameter  to 300  seconds depending on  choice.  T h e m o d e l life times are m u c h shorter life times  for all the model variations  observed i n the  sidescan data  than the 30 minute (or  but  as has  already  1800  s)  been indicated,  the m o d e l life times are arbitrarily determined based o n the coherence of Longer life times could be achieved by using a smaller coherence  0.7.  threshold,  140 but comparisons between model results would then become difficult because of the lack of stability i n these estimates.  T h e observed life times are those  of  the longest lived structures, not the mean life times and this difference further distorts comparisons with model results. A be  concern  with the  determined by the  themselves.  The  model was  vortex  extent  to  that  life time which  the  and  this  life  not  occurs  time by the  can  be  of structures vortex  might  interactions  evaluated  by  non-  dimensionalizing the observed life times by the vortex life times,  T* = T /T.  8.3  0b3  T h e values of this indicator are also shown i n Table 8.1 a n d , while the scaling value remains  close  to  0.1,  significant changes  rameters (vortex injection rate V  p  occur  i n particular).  w i t h some  Clearly vortex  of the  pa-  life times do  not dominate the variability i n the structure life times, suggesting that  vortex  interactions are a significant influence.  8.5  D i s c u s s i o n of M o d e l R e s u l t s Results from a two dimensional Lagrangian model of vorticity interactions  have  been presented.  This  model does  not  consider vorticity generation,  it  assumes that vorticity appears randomly and spontaneously i n time and space close  to  an  image  surface.  T h e flow  that  results  is determined by  vortex  interactions and by the geometrical constraints of the model d o m a i n . T h e first notable result of this model is that it reproduces streamlines consistent w i t h those expected for L a n g m u i r circulation. In particular, it predicts downwelling  speeds  in excess of upwelling  speeds  with the  m a x i m u m down  141 ward velocity somewhat below the surface. T h i s result is a consequence of the model geometry and the interaction of vortices with their images. T h e response of the m o d e l to the presence  of a b o t t o m boundary is another  geometrical  result consistent with observations. T h e m a x i m u m length scale is seen to vary linearly with variations i n the d o m a i n depth. Quantitative comparison of model length scales tograms  with observations are  (Figure 8.4)  difficult, but qualitatively the m o d e l his-  agree i n appearance with those generated f r o m sidescan  sonar data (Figure 4.8 page  58).  Some inaccuracy of the m o d e l scalings is suggested by comparing the life times of structures  seen i n the m o d e l with the predictions of E q u a t i o n  7.13.  These differences can be seen b y forming the ratio of observed structure  life  times w i t h the life time scaling (from E q u a t i o n 7.13)  8.1.  as shown i n Table  T h i s variation demonstrates that there are mechanisms acting which determine structure stability i n addition to the effects of vortex elimination. the structure  Comparing  life time of M o d e l E with that of M o d e l C is revealing:  these  models differ i n the doubling of the vortex injection rate but the outcome is a halving of the structure life times. some way acts to disrupt structures  Clearly the r a n d o m injection of vortices i n already existing and thus reduces the life  times of these structures.  8.6  Conclusions In C h a p t e r 6,  it was  demonstrated that  isotropic turbulence introduced  selectively at wave crests can result i n an enhancement of the vorticity component oriented parallel to the waves by a factor of 1.2.  It is suggested that this  mechanism could be responsible for the phenomenon of L a n g m u i r circulation by means of a two dimensional vorticity cascade to larger scales.  T h e motivation  142 for advancing this explanation over the more established C r a i k - L e i b o v i c h theory is its direct explanation of small scale cells that are seen to coexist with larger structures i n the observations presented i n Chapter 4. A two dimensional Lagrangian vorticity model described i n C h a p t e r 7 was developed to investigate the behaviour of vorticity introduced close to an image surface  (the  ocean surface).  T h i s model does not involve any source  mecha-  n i s m for vorticity but only considers how such vorticity must evolve after it has  been introduced.  T h e model results  are  consequently applicable to  any  model of near surface vortex generation, including that presented by the  the-  ory of C r a i k a n d Leibovich, w i t h the provision that it ignores any generation term. T h e experiments performed with this Lagrangian vortex m o d e l have been discussed i n the present  chapter  through considerations of m o d e l streamlines,  velocities, structure life times, a n d length scales. T h e f o r m of the streamlines produced by the model are observations  of L a n g m u i r circulation, with pairs of counter  occurring at a variety of length scales.  consistent rotating  with  vortices  In these streamlines, there is some sug-  gestion that clockwise regions press to the right against  counter clockwise re-  gions. Sections of vertical velocity through the model verify this behaviour with downwelling velocities exceeding upwelling velocities.  T h e occurrence  welling velocities i n excess of upwelling velocities is a characteristic  of down-  that is ob-  served i n L a n g m u i r circulation a n d , based o n model results, it can be explained by the interaction of vortices w i t h their image pairs. Regions of clockwise vorticity image  are  advected  vorticity,  towards  the  and conversely,  a clockwise region encounters  right by the  corresponding counter-clockwise  counter-clockwise regions to  the  left.  When  a counter-clockwise region, they are pressed to-  gether by their images and the observed assymetry results.  143 Spacings between cells i n the model have been determined by identifying vertical velocity m i n i m a (regions tograms  of spacings  estimated  of downwelling) i n the m o d e l results.  i n this way  agree i n form with  His-  comparable  histograms made from sidescan sonar observations. T h e introduction of a bott o m b o u n d a r y restricts the largest length scales and forces the peak i n spacing histograms to smaller scales.  T h e characteristic  length scale determined from  the spatial correlation of the stream function varies linearly w i t h changes i n b o t t o m b o u n d a r y depth. T h i s behaviour is i n agreement w i t h observations that windrow spacings are h m i t e d to 2 or 3 times the water (or m i x e d layer) depth (Leibovich 1983,  Smith et al. 1987).  W i t h any modelling simulations, there is the concern that  characteristics  of the m o d e l might influence the flow fields predicted. A particular weakness i n the discrete vortex m o d e l presented here is the existence of a totally artificial time scale imposed by the life times of individual vortices. Comparisons between m o d e l configurations w i t h markedly different vortex  life times  have  demonstrated that the life times do not dominate the persistence of structures i n the model.  Instead,  it is the rate at  controls the persistence of structures:  which vorticity is introduced which  the persistence of model structures varied  inversely w i t h the rate of vortex injection.  144  Chapter 9 Summary and Conclusions  Near matter  surface  between  m a n y important world  the  at  the  mediate  atmosphere  processes  budget  CO2  occurring  processes  can  ocean  the  exchange  a n d ocean.  including ocean  only  be  surface.  of heat,  momentum,  and  A n improved understanding of  circulation, climate,  a n d even  achieved by understanding the Observations of near  surface  however complicated by the destructive action of surface waves.  the  interactions  processes  are  In addition,  m a n y instruments that might survive the energetic motions of the wave zone can cause disturbances rendering their observations meaningless. T h e objective of this thesis has been to develop acoustic instrumentation capable of m a k i n g remote measurements i n this hostile environment, a n d to use those observations to improve the understanding of near surface processes.  T h i s thesis reports on the development of instrumentation which combines vertical sonar, sidescan sonar, a n d ambient sound observations i n a freely drifting,  autonomous package capable of operating i n the deep ocean.  T h i s system  was used to observe the dynamics of near surface processes i n the deep ocean as they respond to various wind forcing conditions. T h e organization of subsurface bubble clouds into long rows parallel to the w i n d reveals the  occurrence  of L a n g m u i r circulation. These observations motivate a study of the generation and  interactions of Langmuir circulation.  Ambient sound observations demon-  strate modulations at surface wave periods and the causes (and implications) of such modulations have been investigated.  145 9.1  Instrumentation  The  observations presented  i n this thesis were made possible by an  ex-  tensive p r o g r a m of instrumentation development. A l t h o u g h m u c h of this development has involved the application of proven techniques, several  components  were developed specifically to meet the present requirements.  The recorded The  16  of 44.1  large  quantities  of  data  generated  using video cassette recorders bit  data  recorded  and  by this system  by a  the Sony  can only  acoustic  systems  P C M digital be recovered  were  interface. at  a  rate  k H z and these data must be analyzed i n real time because no com-  puter system could (conveniently) store such a large volume of raw data.  A  Z o r a n V S P - 1 6 1 vector signal processing system was employed to allow this real time processing.  Software was developed for the Z o r a n system which allowed  spectral analysis of ambient sound data and complete analysis of sidescan and vertical sonar data.  W i t h o u t the high performance digital processing capabili-  ties of the Z o r a n system, the data presentation of this thesis would not have been possible.  T h e need to record phase information with a single digitizing channel led to the use of an implicit clock sampling scheme. was complicated by the need to  A p p h c a t i o n of this technique  synthesize specific frequencies to m a t c h  the  (fixed) P C M digitizing rate. T h i s need led to the development (largely by P a u l Johnson of IOS) of a novel frequency synthesizing circuit based on a  quartz  oscillator to provide the required frequency stability. D a t a collected with this system provided accurate phase recording for the vertical sonar data making Doppler speed estimates possible.  146 A  key component to the observational program was a record of surface  wave m o t i o n a n d so wave observations were made using a Datawell Waverider buoy.  Wave observations are however also possible w i t h upward looking sonar  systems.  In the present  application, sonar wave observations have the advan-  tage of being referenced to the same clock as other observations allowing for more accurate time correlations. A direct comparison between wave heights determined by Waverider data a n d sonar has demonstrated that the sonar can provide observations  of comparable  accuracy  to  those  of the  data  Waverider.  Based o n the success of this comparison, future acoustic studies can determine surface wave records w i t h confidence using vertical sonar systems.  9.2  Observations Observations were made using the package of acoustic instrumentation i n  the mid-Pacific Ocean as part of the O C E A N S T O R M S program. These observations provide detailed documentation of a 21-hour period of increasing wind speed (to a m a x i m u m of 13 m s  - 1  ).  T h r o u g h these observations, the sea state  is observed to build to a fully developed state a n d the evolution of subsurface bubble plumes is documented. Short  period analysis  of ambient  sound records  (2-20  k H z ) have  been  demonstrated to contain signals generated by breaking waves (Farmer a n d V a gle 1989). In studying the short period fluctuations of ambient sound in these data,  it is demonstrated  that fluctuations occur at  surface wave periods and  are i n phase with waves passing over the instrumentation.  Sidescan sonar data at 150 k H z provide evidence for L a n g m u i r circulation (through the presence of organized bands of scatterers) throughout the 21 hour  147 deployment presented.  These bands h a d widths of order 2 to 5 metres,  and  lengths of about 100 metres and were aligned with the wind. Spacings between bands were about  5 metres at w i n d speeds below 10 m s  - 1  a n d increased  to  spacings of 10 to 20 metres at greater wind speeds. Vertical velocity estimates  made using an upward looking, 200  sounder reveal downward velocities of 0.06  ms  - 1  k H z echo  at 8 m depth i n the bubble  plumes. T h e m a x i m u m velocity was located at 8 m depth i n the m i d d l e of the bubble plumes with reduced downward velocities occurring towards the Speed estimates  were restricted  to the bubble plumes because  edges.  of inadequate  signal levels elsewhere.  Ambient Sound Modulations  9.3 A  simple model of surface  sound generation  was developed to  assist  in  the understanding of the wave period modulations seen i n the ambient sound data.  Comparisons between the  model predictions a n d observations  suggests  that sound sources must be restricted to surface dimensions of 6 m or less account  for the continuous nature  of sound levels i n the observations).  (to  Two  possible source mechanisms are considered: short wave, long wave interactions; a n d variations i n wind stress over the long surface waves. T h e present data are characterized by swell at approximately 9 0 ° to the prevailing w i n d m a k i n g it impossible to distinguish between these two mechanisms.  9.4  Langmuir Circulation T h e sidescan sonar observations of L a n g m u i r circulation demonstrate  occurrence of many coexisting length scales.  the  In this thesis it is speculated that  this distribution is caused by a two dimensional vorticity cascade f r o m small to larger scales.  148 A  possible source of small scale vorticity is suggested as the preferential  stretching of vorticity by breaking surface waves:  this stretching i n the direc-  tion of wave propagation can enhance vorticity by about 25%. component of vorticity is generated at  Once a single  small scales, it is possible that  larger  scales can arise out of two dimensional vortex interactions. A  computer model of interactions between discrete, two dimensional, vor-  tices has been developed which illustrates the evolution of the stream function field resulting from continuous injection of small scale vortices close to an i m age surface (the ocean surface).  T h i s model is not restricted to any one source  of vorticity, it only considers the fate of the vorticity once generated.  In this  sense, the model results are equally valid for any generation m o d e l of L a n g m u i r circulation (such as that of C r a i k a n d Leibovich). T h e discrete vortex model successfully reproduces many characteristics Langmuir  circulation:  a range  of vortex  length scales  is seen,  of  down-welling  speeds exceed upwelling speeds, a n d m a x i m u m length scales are restricted i n proportion to the domain depth.  These results suggest  that the concept of a  two dimensional up-scale cascade  is consistent with the observations of L a n g -  muir circulation. T h e model clearly identifies the cause of the asymmetry seen i n L a n g m u i r circulation (down welling speeds exceeding upwelling speeds): across  the  image surface  advects  clockwise regions of flow to  counter-clockwise regions of flow to  the  left.  Eventually, the  the circulation the right and flow  organizes  itself into stable pairs of clockwise regions (moving to the right) blocked by counter-clockwise regions (moving to the left).  Oppositely formed pairs (clock-  wise on the right and counter-clockwise on the left) are not stable a n d they  149 slowly drift apart.  T h i s asymmetrical migration leads to a crowding (and con-  sequent intensification) of downwelling streamlines. The  occurrence of asymmetry in models of L a n g m u i r circulation has been  identified as  a key requirement for any m o d e l of L a n g m u i r circulation (Lei-  bovich 1983). T h e present results indicate that the asymmetry (as well as the length scale  dependence o n b o t t o m  boundary depth)  is a result  of two d i -  mensional vorticity and the domain geometry germane to L a n g m u i r circulation. A n y m o d e l introducing two dimensional vorticity close to an image surface will demonstrate these basic The  m a i n purpose of the vortex interaction m o d e l was to investigate  behaviour The  characteristics.  of small scale  vorticity introduced by  m o d e l results clearly demonstrate  that  selective  vortex  the  stretching.  small scale vorticity can lead to  flow structures similar to those observed i n L a n g m u i r circulation. Near surface flow is however much more complicated t h a n the representation offered by this simple m o d e l .  T h e presence  of vertical shear  i n the near surface water  will  ultimately introduce the vortex forcing identified by the C r a i k Leibovich mechanism.  T h e discrete vortex  m o d e l cannot  represent  such interactions  a n d so  cannot provide any insight into their nature. It is quite possible that these two mechanisms could coexist  with the vortex  stretching mechanism seeding small  scale structures which are then sustained by the C r a i k Leibovich mechanism. A more complete understanding of these complicated interactions will require the development of a more sophisticated (three dimensional) model.  9.5  Concluding Remarks T h i s thesis has touched o n only a few of the important  processes occurring at the ocean surface:  a n d interesting  m u c h work remains to be done. T h e  150 action of wave breaking, L a n g m u i r circulation, gas exchange, m o m e n t u m transfer and m i x i n g all interact in this complex physical system. to provide a complete  description of any one component  It is not possible  without  considering  several (if not all) of these processes. A c o u s t i c sampling techniques provide a valuable tool to probe these near surface  processes.  mine vertical display  the  In this  velocities,  thesis,  make  horizontal extent  mensional wave spectra,  acoustic  qualitative  analysis  has  estimates of bubble  of subsurface  bubble plumes,  a n d identify certain  used  to  deter-  concentrations,  measure  one di-  characteristics of wave breaking.  T h i s is only a partial list of the capabilities of acoustic C a l i b r a t e d sonar systems can be used to determine passive  been  arrays can track individual sound sources,  sampling techniques.  bubble size distributions, coded sonars can  achieve  m u c h improved Doppler speed estimates, and D o p p l e r enabled sidescan sonars can be used to determine directional wave spectra a n d near surface horizontal currents.  A s signal processing capabilities improve, even more advanced  tic sampling systems will be developed.  T h e r e remain many  acous-  possibilities for  further applications of these systems to the study of near surface processes.  T h e observations circulation vations  over  presented indicate the  a two  week  period.  These  continuous presence of L a n g m u i r observations,  by Weller and Price (1988), contribute  and  similar  to the growing evidence  L a n g m u i r circulation is a c o m m o n phenomenon in the open ocean.  obserthat  A n y model  of m i x e d layer dynamics must therefore account for the enhanced vertical mixi n g this circulation can cause; the concept  of a fixed eddy viscosity is clearly  inappropriate. It is therefore essential that an understanding of how and when L a n g m u i r circulation occurs be gained.  151 T h e evaluation in this thesis demonstrates that many observed characteristics of L a n g m u i r circulation can be reproduced by a two dimensional cascade of vorticity.  A possible vorticity source is presented as vortex generation by wave  breaking a n d its subsequent intensification by wave action. cannot verify or refute this concept:  T h e available data  an extended set of observations (preferably  under controlled conditions) will be required for such an evaluation. Wave period modulations i n ambient sound data have been described b y a m o d e l w i t h source amplitude variations i n proportion to surface wave displacement.  This  model implies that  ambient  sound is generated  preferentially  at  wave crests. T h e implications of this result are far reaching: if long wave, short wave interactions  are responsible for this phenomenon, then the  could be contributing energy to the long waves (Garrett the other h a n d , the observations are also consistent  short  waves  and S m i t h 1976). O n  with sound levels being  proportional to wind stress variations over the long waves.  For this explana-  tion to be valid, sound levels must respond very quickly to changes i n w i n d stress providing an extremely sensitive stress measuring approach. Future work will be needed to resolve this question because of its importance to b o t h wave growth a n d to wind measurements derived from ambient sound.  152  Chapter 10 References Allender,  J . , T . A u d u n s o n , S . F . Baxstow, S. Bjerken,  Steinbakke, WADIC  L . Vartdal,  project:  instrumentation. Anderson,  a  L . E . Borgman,  comprehensive  field  H . E . Krogstad,  and C . Graham, evaluation  P.  1989: T h e  of directional  wave  Ocean E n g n g , 16, 505-536.  Tannehill, and Pletcher,  1984:  Computational  fluid  mechanics  Assaf, G . , R . Gerard a n d A . L . G o r d o n , 1971: Some mechanisms  of oceanic  a n d heat transfer., Hemisphere publishing corp., p . 513.  m i x i n g revealed i n aerial photographs. Alexsandrov,  J . Geophys. Res., 76, 6550-6572.  A . P . a n d E . S . V a i n d r u k , 1974: i n The investigation of the  variability of hydrophysical fields in the ocean, R . O z i m d o v ed., N a u k a Publishing Office, Moscow. Banner,  M . L . and O . M . Phillips, 1974: O n the incipient breaking of small  scale waves. J . F l u i d M e c h . , 65, 647-656. Banner  M . L . and D . H . C a t o ,  1988: Physical mechanisms  tion b y breaking waves - a laboratory  of noise genera-  study. In: Sea Surface Sound., B .  K e r m a n , E d . Kluwer, 429-436. Blanchard, D . C . and A . H . Woodcock,  1957: B u b b l e formation a n d modifi-  cation i n the sea a n d its meteorological Buckles,  J . , T . J . Hanratty,  significance. Tellus 9, 145-158.  and R . J . A d r i a n ,  1984:  Turbulent  flow  over  large-amplitude wavy surfaces. J . F l u i d M e c h . , 140, 27-44. Chorin,  A . J . , 1973:  Numerical  study  of slightly  viscous  flow.,  J.  Fluid  M e c h . , 57, 785-796. Christiansen,  J . P . , 1973: Numerical simulation of hydrodynamics  b y the  m e t h o d of point vortices. J . C o m p . P h y s . , 13, 363-379. Clay, C . S . a n d H . M e d w i n , 1977: Acoustical Oceanography:  Principles and  Applications. John W i l e y a n d Sons. 544 p p . Crapper,  G . D . , 1957: A n exact solution for progressive  arbitrary amplitude. J . F l u i d M e c h . , 2, 532-540.  capillary waves of  153 Craik,  A.D.D.,  a n d S. Leibovich,  1976:  A rational  model for L a n g m u i r  circulations. J . F l u i d M e c h . , 73, 401-426. Crawford, G . B . a n d D . M . Farmer, 1987: Observations of the spatial distrib u t i o n of ocean bubbles. J . Geophys. Res., 92, 8231-8243. Donelan, M . , M . S . Longuet-Higgins a n d J . S . T u r n e r , 1972: Periodicity i n Whitecaps. Nature, 239, 449-451. Evans,  D . L . , D . R . Watts,  D . Halpern,  a n d S. Bourassa,  1984:  Oceanic  winds measured f r o m the sea floor. J . Geophys. Res., 89, 3457-3461. Faller, A . J . 1971: Oceanic turbulence a n d the L a n g m u i r circulations. A n n . R e v . E c o l . Syst. 2, 201-236. Faller, A . J . 1978: Experiments with controlled L a n g m u i r circulations.  Sci-  ence 201, 618-620. Faller, A . J . and S . J . A u e r , 1988: T h e roles of L a n g m u i r circulations i n the dispersion of surface tracers. J . P h y s . Oceaonogr., 18, 1108-1123. Farmer,  D . M . , a n d D . D . L e m o n , 1984: T h e influence of bubbles o n a m -  bient noise i n the ocean  at high w i n d speeds.  J . Phys. Oceanogr.  14  1762-1778. Farmer, surface  D . M . a n d S. Vagle, wave  1988:  O n the determination  distributions using ambient  of breaking  sound. J . Geophys. Res., 93,  3591-3600. Farmer,  D . M . a n d S. Vagle,  1989:  Waveguide  propagation  of  ambient  sound i n the ocean surface bubble layer. J . A c o u s t . Soc. A m . , 85, 18971908. Garrett,  C.J.R.,  1976:  Generation  of L a n g m u i r  circulations  by  surface  waves - a feedback mechanism. J . M a r . Res., 34, 117-130. Garrett, C . and J . Smith, 1976: O n the interaction between long a n d short surface waves. J . Phys. Oceanogr., 6, 925-930. Gent, P . R . a n d P . A . Taylor, 1976: A numerical m o d e l of the air flow above water waves. J . F l u i d M e c h . , 77, 105-128. Gill,  A . E . a n d J . S . Turner, 1976: A comparison of seasonal  models with observations. Deep-Sea Research, 23, 391-401.  thermocline  154 Glotov,  V . P . , P . A . Kolobeav a n d G . G . N e u i m i n ,  1962: Investigation of  scattering of sound by bubbles generated by a n artificial w i n d i n sea water a n d the statistical distribution of bubbles sizes. Sov. P h y s . A c o u s t . , E n g l . Transl., 7, 341-345. G u o , Y . P . 1987: O n sound generation by weakly nonlinear interactions of surface gravity waves. J . F l u i d M e c h . , 181, 311-328. Hald,  O . H . , 1979: Convergence of vortex methods for Euler's equations.  II. S I A M J . N u m e r . A n a l . , 16, 726-755. Hald,  0.  a n d V . M . D e l Prete,  1978: Convergence of vortex methods for  Euler's equations. Mathematics of C o m p u t a t i o n , 32, 791-809. Harris, G . P . a n d J . N . A . L o t t , 1973: Observations of L a n g m u i r circulations i n lake Ontario. L i m n o l . Oceanogr. 18, 584-589. Hwang, P . A . , D . X u a n d J . W u , 1989: Breaking of wind-generated waves: measurements a n d characteristics.  J . F l u i d M e c h . 202, 177-200.  Johnson, B . D . , a n d R . C . Cooke, 1979: B u b b l e populations a n d spectra i n coastal  waters:  A photographic  approach,  J . Geophys. Res., 84, 3761-  3766. Kenney, B . C . 1977: A n experimental investigation of the fluctuating currents responsible for the generation  of windrows. P h . D . thesis.  Univ.  Waterloo, O n t . , 163 p p . K n u d s e n , V . O . , R . S . A l f o r d a n d J . W . E m l i n g , 1948: Underwater  ambient  noise. J . M a r . Res., 22, 410-429. K o l a i n i , A , R . A . Roy, L . A . C r u m , 1991: T h e production of high-frequency ambient noise by capillary waves, to appear i n Natural Physical Sources of  Underwater  Sound,  B . K . Kerman  E d . , Kluwer  Academic  Press,  Boston. Kolovayev, size  D . A . 1976: Investigation  of the concentration  a n d statistical  distribution of wind-produced bubbles i n the near-surface  ocean.  Oceanology, E n g l . Transl., 15 p. 659-661. K r a i c h n a n , R . H . , 1967: Inertial ranges Physics of Fluids, 10, 1417-1423.  i n two-dimensional  turbulence.  L a n g m u i r , I., 1938: Surface m o t i o n of water induced by wind. Science, 87, 119-123. Leblond,  P a u l H . a n d Lawrence  A . Mysak:  1978: Waves  Elsevier, p p . 602, A m s t e r d a m , T h e Netherlands.  i n the Ocean.  155 L e i b o v i c h , S. 1977: Convective instability of stably stratified water i n the ocean. J . F l u i d M e c h . 82, 561-85. L e i b o v i c h , S., 1980: O n wave-current  interaction theories of L a n g m u i r cir-  culations. J . F l u i d M e c h . 99, 715-724. L e i b o v i c h , S., 1983: T h e form a n d dynamics of L a n g m u i r circulations. A n nual Review of F l u i d Mechanics, 15, 391-427. L e i b o v i c h , S. and S. Paolucci, 1981: T h e instability of the ocean to L a n g muir circulations. J . F l u i d M e c h . , 102, 141-167. Lemon,  D . , D . Farmer,  D . Watts,  1984: Acoustic measurements  of wind  speed a n d precipitation over a continental shelf. J . Geophys. Res., 89, 3462-3472. Longuet-Higgins,  M . , 1963:  T h e generation  of capillary  waves  b y steep  gravity waves, J . F l u i d M e c h . , 16, 138-159. Longuet-Higgins, M . S . , 1988: Mechanisms of wave breaking, i n NATO Series  C, vol. 238,  edited  by B . R . K e r m a n ,  p. 1, K l u w e r  ASI  Academic  Publishers, Dordrecht, T h e Netherlands. McCormick,  M . J . a n d G . A . Meadows, 1988: A n intercomparison of four  m i x e d layer models i n a shallow inland sea. J . Geophys. Res., 93, 67746788. M e d w i n , H . , 1970: Acoustic  fluctuations  due to microbubbles i n the near-  surface ocean. J . Acoust. Soc. A m . 56, 1100-1104. M e d w i n , H . , and M . M . Beaky,  1989: B u b b l e sources of the K n u d s e n sea  noise spectra. J . Acoust. S o c , 86, 1124-1130. M e d w i n , H . a n d N . D . Breitz, 1989: A m b i e n t a n d transient bubble spectral densities i n quiescent seas a n d under spilling breakers. J . Geophys. Res., 94, 12751-12759. Miller, K . S . , and M . M . Rochwarger,  1972: A covariance approach to spec-  tral moment estimation. I E E E Trans, on Inform. Theory, 18, 588-596. M o n a h a n , E . C . , and I. O ' M u i r c h e a r t a i g h , 1980: O p t i m a l power law description of oceanic  whitecap  coverage dependence  on w i n d speed, J . P h y s .  Oceanogr., 10, 2094-2099. M y e r , G . E . , 1971: Structure  a n d mechanics  of L a n g m u i r circulations o n a  small inland lake. P h . D . dissertation. State U n i v . N . Y . , A l b a n y .  156 Okuda,  K . S . , M . Kawai, M . Tokuda and Y . Toba,  vations  of the wind-exerted  surface  1976: Detailed obser-  flow by use of flow visualization  methods. J . Oceanogr. Soc. Japan, 32, 53-64. Phillips, O . M . , 1981: T h e dispersion of short wavelets i n the presence of a dominant long wave. J . F l u i d M e c h . , 107, 465-485. Phillips, O . M . , 1985: Spectral and statistical properties of the equilibrium range i n wind-generated gravity waves. J . F l u i d M e c h . , 156, 505-531. Pollard,  R . T . , 1977:  Observations a n d theories  of L a n g m u i r  circulations  a n d their role i n near surface mixing. In: A Voyage of Discovery: George Deacon  70'th Anniversary  Volume, ed. M . A n g e l .  Oxford:  Pergamon.  235-251. Pond,  S. a n d G . L . Pickard, 1983: Introductory  dynamical  oceanography.,  Pergamon press, p p . 329, Siggia,  E . D . , a n d H . Aref, 1981: Point-vortex  simulation of the inverse  energy cascade i n two-dimensional turbulence. P h y s . Fluids 24, 171-173. Smith,  J . , R . Pinkel  and R . A . Weller,  1987: Velocity structure  i n the  m i x e d layer during M I L D E X . J . Phys. Oceanog., 17, 425-439. T h e r i a u l t , K . B . , 1986: Incoherent  multibeam Doppler current  profiler per-  formance. I E E E J . Ocean. E n g i n . , 11, 7-15. Thorpe,  S . A . , 1982: O n the clouds of bubbles formed by breaking wind-  waves i n deep water, a n d their role i n air-sea gas transfer. P h i l . Trans. Roy. S o c , A-304, 155-210. T h o r p e , S . A . , 1984a: T h e effect of Langmuir circulation on the distribution of submerged bubbles caused by breaking w i n d waves. J . F l u i d 142,  Mech.,  151-170.  T h o r p e , S . A . , 1984b: A m o d e l of the turbulent diffusion of bubbles below the sea surface. J . Phys. Oceanog., 14, 841-854. Thorpe,  S . A . , 1986:  Measurements  with  an automatically  recording i n -  verted echo sounder; A R I E S a n d the bubble clouds. J . P h y s . Oceanog., 16,  1462-1478.  T h o r p e , S . A . and A . J . H a l l , 1982: Observations of the thermal structure of L a n g m u i r circulation. J . F l u i d M e c h . 114, 235-250. T h o r p e , S . A . and A . J . H a l l , bubble  clouds,  1983: T h e characteristics  a n d near-surface  Shelf Res. 1, 353-384.  currents  of breaking waves,  using side-scan  sonar.  Cont.  157 T h o r p e , S . A . , A . J . H a l l , A . R . Packwood a n d A . R . Stubbs, 1985: T h e use of a towed side-scan sonar to investigate processes near the sea surface. C o n t . Shelf Res. 4, 597-607. Vagle, Svein, W i l l i a m G . Large, a n d D a v i d M . Farmer,  1990: A n evalua-  tion of the W O T A N technique of inferring oceanic winds f r o m underwater ambient sound. J . A t m o s . Oceanic Tech., 7, 576-595. W a l s h , A . L . a n d P . J . M u l h e a r n , 1987: Photographic measurements  of b u b -  ble populations f r o m breaking waves at sea. J . Geophys. Res., 92(cl3), 14553-14565. Weller, R . A . and J . F . Price, 1988: Langmuir circulation within the oceanic m i x e d layer. Deep Sea Res. 35, 711-747. Wenz,  G . M . , 1962:  Acoustic  ambient  noise  i n the ocean:  spectra  and  sources. J . Acoust. Soc. A m . , 34, 1936-1956. W u , J . , 1981: Bubble populations and spectra i n near-surface ocean: summary a n d review of field measurements. Zedel,  L . J . and J .  Church,  1987:  J . Geophys. Res. 86, 457-463.  Real-time  screening  techniques  for  D o p p l e r current profiler data. J . A t m o s . Oceanic Tech., 4, 572-581. Zilker, D . P . , G . W . C o o k a n d T . J . Hanratty, 1977: Influence of the amplitude of a wavy wall on a turbulent flow. Part I. Non-separated flows. J . F l u i d M e c h . , 82, 29-51.  158  Appendix A Craik-Leibovich Theory This ity  appendix provides a  brief outline of the  derivation of the  vortic-  equation describing L a n g m u i r circulations after the C r a i k L e i b o v i c h theory.  T h i s development is taken from C r a i k and Leibovich (1976). Consider the total water velocity for the water surface  q can be broken  into two parts £ =  where e is the waves slope, eu and  tv 2  is everything else.  w  «M  ul  + « w,  A.l  2  is the irrotational wave component of m o t i o n ,  It is assumed that the velocity due to wave mo-  tion is significantly larger t h a n the non-wave velocity components.  With  this  decomposition, the vorticity equation for a Boussinesq fluid can be written as  u  t  = V x (q x w) + u V u e  2  A.2  where w = V x q. T h e expression for u> can be expanded by substituting i n the expression for q from E q u a t i o n A . l to give w = e (Vxu).  A.3  2  Notice that there is no vorticity introduced from the irrotational wave component u^,. B o t h the non-wave velocity component v_ and the vorticity u_ can be  ex-  panded into a series of the f o r m ,  n — y_o + -i + ev  +  -A-4  159 In addition, each of the terms of this expansion can be broken into a mean and  fluctuating  component of the f o r m  Vj — Vj+  <  Vj  A.5  >,  where the overbar refers to a mean value, a n d the < • • • > dependent component.  refers to the time  T h e vorticity equation can be broken down into several  relations equating the successive orders of e. T h e second order relation (that is for 0J2) is the lowest order to provide a non-zero mean solution.  - a V u J = V x (Fo~ x uTo") + V x (u x < o; >) 2  0  where the eddy viscosity u  w  e  A.6  :  has been assumed to be approximately e a. 2  This  relation can be time averaged over a period short compared to the development time of the L a n g m u i r circulation, but long compared to the wave period to produce a time averaged vorticity equation. -aV U 2  0  = (u£-  V)(^-rM )-(Ho+M )Vwo s  a  A.7  where u* is the Stokes drift,  u = {judt- V)u s  A.8  t E q u a t i o n A . 7 describes how the vorticity and surface currents motion) interact.  (including wave  Craik a n d Leibovich (1976) simplify the problem b y assuming  that the Stokes drift is unidirectional (implying a directionally symmetric wave spectrum).  T h e velocity field a n d vorticity become, M  = K(y,*),o,o)  UQ"  = (u, v, w)  s  A.9  160 When  these  simplifications are  substituted  into  Equation A.6  the  vorticity  equation becomes, ,  «v f + ^  du*  Equation  A.10  circulation.  forms  the  du  + C  2  basis  of the  In this equation, a V f 2  1  di  3  7  = v ^  d( +  ^  Craik-Leibovich  Aid theory  for L a n g m u i r  represents the diffusion of vorticity, r / ^  represents the deformation of vortex lines by the Stokes drift, a n d u>H  represents the convection of vorticity.  -  + +  161  Appendix B Data Acquisition Storage of acoustic d a t a is made possible by using the Sony P C M system together w i t h the video a n d H i - F i signal storage available on conventional video cassette recorders  (VCR's).  These systems are designed to record h i g h quality  audio frequency signals i n a continuous mode for periods as long as 8 hours. T h e y are a convenient m e d i u m for many applications but, any signal that is recorded widths.  must  be conditioned to  be compatible with audio frequency b a n d -  In addition, the data can only be recovered in a continuous  streamed  mode so either the data must be transferred to a conventional storage m e d i u m or it must be processed i n 'real time' as it is recovered.  Transferring the  data  is not a tenable solution since each video tape contains the equivalent of gigabytes of data. ing  5.1  B u t , to implement the alternative, powerful signal process-  systems which can keep u p with the streamed data rate must be used to  analyze the data.  T h i s A p p e n d i x describes the data conditioning required to store the ious  data  types  onto  VCR's  are  pendix  C , D , and E  respectively.  the  V C R medium.  Details of data  recovery  var-  from  the  considered i n separate appendices for the various data types; A p for vertical  sonar,  sidescan  sonar,  and ambient  sound  A l t h o u g h sidescan sonar is digitized during data playback while  ambient sound and vertical sonar are digitized during data storage, the processing configuration on playback is fundamentally the same i n all cases.  A  general outline of the processing steps a n d instrumentation used i n d a t a  re-  162 covery will  be given rather t h a n  detailing the  slight differences between  the  individual cases.  B.l  A m b i e n t S o u n d Signal C o n d i t i o n i n g O f the  data recorded,  only ambient sound lends itself to storage w i t h a  streaming audio frequency system and it consequently required a m i n i m u m of signal  conditioning.  ocean  ambient  T h e only consideration  sound levels are  i n recording these data  known to have  is  a coloured spectrum  that  with  a  level that decays at about 20 d B per decade at increasing frequencies ( K n u d s e n et  al.  1948).  accommodate  This  colouring would require system  the high power,  of higher frequency signals.  gain levels to  be set  to  low frequency signals compromising resolution  T o offset  this effect,  a prewhitening  filter  with  response,  (R  2  \/u C fl  +  2  2  2  B.l  R where, C = B.l  V;  n  is the input voltage,  834 x 1 0  - 1 2  F,  and u  V  out  is the  output  voltage,  R  =  12414  is the signal angular frequency, was used.  fi,  Figure  displays a typical ambient sound spectrum before and after whitening with  this  filter.  B.2  Sidescan Sonar C o n d i t i o n i n g The  (one  sidescan sonar data is recorded on the two H i - F i channels of the V C R  channel for each of the  two sidescan sonars).  These channels  are only  capable of recording a 20 k H z b a n d w i d t h but the sidescan sonar is on a k H z carrier: used.  100  i n order to record this signal some f o r m of demodulation must be  163  Figure trum. filtered.  B.l: Dashed  Example  of prewhitening filter effect on ambient  line is unfiltered  ambient  sound  spectrum,  the  sound specsolid  line  is  164 F o r the  sidescan sonar, the frequency  content of the signal is not  impor-  tant, it is the modulations on that received signal that contain the information o n bubble distributions.  T o isolate this signal from the  received signal is multiplied with a 137.5 information at  17.5  taining only the  100  k H z carrier,  the  k H z reference producing a signal w i t h  k H z , a n d 257.5 k H z . T h i s signal is low pass filtered  17.5  k H z signal for recording  remaining carrier is subsequently  onto the H i - F i  channels.  reThe  removed through the data recovery process-  ing.  B.3  Vertical Sonar Signal Conditioning T h e vertical  lems.  sonar systems provide the  challenging recording  prob-  T h e complexity stems f r o m the desire to make Doppler speed estimates,  a n d so, i n addition to the requirement  of matching the carrier frequency to  recording bandwidth, the signal phase must applications,  data  recording  is  normally  sonar signal w i t h a reference oscillator signal w i t h a 0 mean down" out  most  frequency.  at  also be preserved.  done the  by  mixing  T o recover the  W i t h Doppler  the  sonar frequency  backscattered to produce  phase from such  signal, the process is repeated using a reference oscillator  of phase with the first.  These  two signals f o r m a complex  the  a  a  "mixed  that is 9 0 ° number  pair  from which the original received signal can be reconstructed with an accuracy that  is only  constrained  by  the  recording  bandwidth.  A  draw-back  of  this  scheme is that it requires two channels a n d i n the present application, b o t h of the digital P C M channels this restriction,  could not be committed  a technique  to vertical sonar.  T o avoid  known as implicit clock sampling is employed  to  allow complex data to be stored onto a single digitized channel. Consider that a signal is received with the form s(t) = A(t) cos(u>i + <p(t))  B.2  165 here,  t is time,  u  is the  carrier  frequency of the  signal, <f>(t)  contains  Doppler shifts and any other phase information i n the signal, a n d A(t)  the  is the  amplitude envelope of the signal. T h i s received signal is mixed w i t h a reference oscillator of frequency u giving, S{t)  - A(t) cos(wi + <f>(t)) cos(wi)  = ^2. c o s ( (  - u)t +  w  m) +  cos  (^ + +  B3  T h e high frequency component of this signal is filtered off leaving,  c(t) = u  cos((> - u)t + <f>(t)).  can be selected so that (a> — UJ) is exactly 1/4  the digitization rate.  BA c(r)  is  then sampled whenever  i = tj =  *  J  ~s  ;=0,1,2,...  .  B.5  E q u a t i o n B.4 can now be rewritten as  c(tj)  =  A(t) ^  ~  ~  [cos(u; — u)tj cos <f>(tj) — sin(u> — u>)tj sin <f>(tj)]  B.6  and, substituting in the values of tj,  c(*o) = ^ C O S ^ ( t o ) 4f^sM(*i) ?(<2) = ^ c o s ^ )  B.l  =^-sm<f>(t ) 3  ?(*4) =  If (^(r)  a n d A(t)  A{i  2  * cos^(t ) ]  4  change slowly i n a time of ir/(2(u — UJ)) then the two con-  secutive samples from c(r)  can be considered as the i n phase and quadrature  terms of a single complex data sample and conventional analysis schemes  can  166 be used. T h e only complication to the data is that sign alterations  are intro-  duced to the data at every second pair of entries (note the negative signs i n Equation B.7). T h e consequences  of assuming a slow rate of phase change  compared to  the sampling interval can be investigated b y considering typical values i n the present observed,  application.  the value of ^  In the case that a radial velocity of 0.2 ms  -1  will be 1.8 x 1 0  frequency  error  is small compared to the velocities that  the  data,  to a speed  - 3  This  is acceptable.  leads  expected  s  estimate that  - 1  is  (for the 200 k H z sonar).  is low b y 0.01  ms  - 1  :  this  are being investigated a n d so  Use of this final assumption is only a convenience i n processing  i f the resulting errors  are too large,  the values can be recovered  completely by accounting for the actual sample times as given i n E q u a t i o n B . 7 . It kHz  was necessary  to heterodyne  to apply the implicit clock  the sonar  scheme  signals onto carriers  to the P C M application.  of 11.025 This  fre-  quency is exactly 1/4 the P C M digitization frequency. In order to preserve the signal phase between successive  sonar transmissions,  it was essential that the  osciUator providing the mixing frequency be phase locked to b o t h the P C M digitizing clock, a n d the sonar carrier frequencies. Such phase coherence is usually achieved by using a c o m m o n oscillator and dividing it as appropriate to achieve the various frequencies required. In the present case, such a n approach is not possible because of the combination of frequencies used a n d the inflexibility of the digitization clock. T o overcome this problem, a phase locked loop circuit was devised by P a u l Johnson (a technologist at the Institute of O c e a n Sciences) PCM  which allowed the beating up of a reference  clock.  B y using a reference  clock derived from the  clock of 787.5 H z , it was possible to gen-  erate any frequency required to within 787.5 H z . T h e choice of 787.5 H z was  167 made because it could generate b o t h the required m i x frequencies of 200 k H z ±  11.025 k H z and 50 k H z ±  11.025 k H z . A l t h o u g h this system worked when  based o n a conventional phase locked loop circuit, a large amount of energy appeared at 787.5 H z i n the m i x e d signals. T h i s noise was intolerable because it interfered with Doppler frequency shifts. T h i s problem was eliminated b y replacing the conventional phase locked loop with custom made crystal oscillators a n d assembling phase locked loops based o n these oscillators. T h e narrow b a n d characteristic  eliminated m u c h of the reference  feed through,  although  some  evidence for signal contamination from this source d i d appear i n the data: its removal is discussed i n A p p e n d i x C . T h e entire vertical sonar processing scheme was developed specifically for the present  application a n d some means of testing its operation was needed  even before building the circuitry.  T h i s testing was done using a simple com-  puter m o d e l of the signal processing steps. T h i s m o d e l included two fundamental steps:  a backscatter signal was created to simulate the expected signal f r o m  a r a n d o m distribution of acoustic scatterers; a n d this synthetic signal was then subjected  to the processing described for sonar  signals.  Using  this  package,  tests of various combinations of transmitted pulse lengths a n d scatterer densities were made and the feasibihty of the processing scheme was demonstrated. For the large scatterer densities expected i n subsurface bubble clouds, the processing provided accurate velocity estimates for a m o d e l w i t h 0.75 m s  B.4  - 1  (for example, velocities  came to 0.73 m s  - 1  estimated  )  D i g i t a l Signal P r o c e s s i n g C o n s i d e r a t i o n s D a t a once recorded using V C R systems must be recovered i n a streaming  fashion.  It is not convenient to simply transfer the data to a standard record-  ing m e d i u m because of the enormous volumes of data involved (5 gigabytes on  168 each video cassette). Instead, the d a t a are analyzed as they are recovered from the V C R so that the volume of d a t a can be reduced before storing it on computer system.  A variety of recently developed high speed signal  offer the capabilities required for this task; for the present corporations V S P - 1 6 1 was  processors  application, Z o r a n  selected.  Zoran produces a circuit b o a r d compatible w i t h the I B M Personal puter complete with interfacing software their V S P - 1 6 1 .  a  that allows convenient  Com-  apphcation of  T h i s board is equipped w i t h a F I F O (first i n first out) register  that allows buffering of input data on the b o a r d itself. B y taking advantage of the Zoran F I F O ' s , P C M data could be captured directly onto memory residing on the Z o r a n board and conveniently processed. T h e Z o r a n V S P achieves  high speed processing by vectorizing commonly  used signal processing operations including: ucts,  conjugations,  erations processor  and modulations.  on arrays of up to 128  capabilities.  H i g h speeds  complex  does no logical operations  are  sums, dot p r o d -  achieved by doing op-  16 bit numbers simultaneously.  The  explicitly a n d has very restricted looping  T h e limitations i n looping a n d logic were overcome  program running in parallel on the host major  F F T ' s , products,  by using a  I B M A T , a n d they have not  posed  restrictions.  A significant limitation of the Zoran system is the 16 bit resolution of the processor;  all operations must be arranged to avoid the risk of an overflow or  underflow condition.  T h e Zoran processor  assists in this matter by providing  block floating point solutions for the F F T operations:  data are scaled automat-  ically through the F F T process to avoid overflows. T h e required scaling factor is recoverable  and can be taken into consideration  i n subsequent  processing.  169 W h e n computing products, numbers being multiplied must be chosen as large as possible since the Z o r a n retains only the bit  product:  if this characteristic  is not  16 most  significant bits of a  considered, substantial loss i n  32  data  resolution can result.  B.5  Data Recovery T h e d a t a recovery f r o m video tapes was essentially the same for each of  the three data types processed w i t h the Z o r a n system (sonar, and  ambient  sound).  This  processing  approach  will  be  sidescan sonar,  described here,  see  A p p e n d i x C , D , and E for details of processing vertical sonar, sidescan sonar, a n d ambient sound respectively. The  most  convenient  Hewlett-Packard  (H/P)  system  A900  for  ultimately  minicomputer.  This  analyzing the system  data  a  offered convenient  d a t a archiving o n 6250 B P I  9-track computer tapes and adequate  age space provided by a 600  M b y t e disk.  disk  stor-  In addition, the H / P provided fast  processing of data with the use of firmware vectorized commands. VSP  was  T h e Zoran  operating on the I B M A T must, however, first be used to condense the  d a t a f r o m its recorded form before the data could be transferred f r o m the I B M A T to the H / P system. AT  could only  T h i s step was a potential bottleneck because the I B M  store about  1 hour of processed  for every hour of data recovered. was arranged  where the data  data  necessitating  transfers  T o avoid this problem, a pipelined system  flowed from the  Zoran, through the I B M A T ,  to the H / P A900 in a continuous fashion. T h e Z o r a n system conditioned and compressed data and passed it onto the I B M A T for logical a n d higher level operations.  D a t a was then passed to the H / P for file organization all i n real  time (Figure B.2 shows a block diagram of this data aquisition sequence).  170  Typical Processing Serial Data  VCH  L-out PC  Digital Data  Key Pulse Detector  Key Pulse  Interface  Data  Zoran VSP1B1  Control  Data  IBM/AT  GPIB  HPA900  F i g u r e B.2: age.  Disk Tape  T y p i c a l processing steps used i n recovering d a t a f r o m V C R stor-  171 T i m e synchronization is critical i n all cases to determine target ranges for the active  sonars  ( E q u a t i o n 3.1),  or i n the case of ambient sound data,  select data not contaminated by active sonar systems.  T h e necessary  to  timing  was achieved by the encoding of key pulses onto the sonar channels to mark the times of sonar transmissions. These key pulses are detected using a circuit operating m u c h like an oscilloscope trigger:  when a key pulse is detected i n  the data stream, the detector issues a trigger pulse that is used to gate data acquisition by the Zoran system. Once the presence of key pulses is accurately identified, the time positioning of all sonar data within a transmission cycle is easily achieved by counting data records received by the Z o r a n F I F O ' s . A c c u r a t e absolute time information is critical i n coordinating observations f r o m the m a n y instruments being used a n d between data types recovered f r o m video tapes.  T i m e data was recorded onto the low grade audio channel of the  V C R ' s every 500  ms  cessing sonar data.  and it was necessary to recover these times while pro-  It is not possible to monitor this time stamp continuously  because the time stamps are recorded asynchronously with respect to the sonar data and as much as 0.5 latest time stamp.  seconds can be consumed while waiting to read the  T h i s complication is overcome by sampling the time only  every 15 seconds as determined by the number of processing cycles completed. Because the sonar repetition rate is known, the correct time can be estimated by  counting cycles since the last known time.  record transferred to ms  the  Using this m e t h o d , each  data  H / P is labelled with a time stamp providing  precision (but only ± 2 5 0  ms  can be claimed because of the time  100  stamp  resolution). D a t a once transferred to the H / P are placed into direct access files which contain data for the 50 minutes of every hour during which active sonar data  172 were  collected.  For  the  ambient  sound data  additional files of  10  minutes  duration are created because these data were recorded continuously. W i t h this approach,  data can be randomly accessed for any time during an instrument  deployment with a resolution of 250  ms.  173  Appendix C Vertical Sonar Processing Vertical sonar  data  are  processed  vertical velocities from acoustic wave measurements  and data  to  recover  Doppler estimates,  alignment.  pects of vertical sonar signal processing;  normal echo and range  sounder to  data,  surface  for  T h i s appendix deals w i t h three  as-  general Doppler velocity estimation,  implementation of the required processing through the data acquisition system, and velocity data  conditioning.  Estimates  of Doppler frequency shift can i n  principle be made through a Fourier analysis. Such processing is extremely i n efficient, a n d the complex covariance spectral estimation technique used instead will  be  described.  Details of signal pre-conditioning and  the  actual  mentation of the complex covariance technique will be presented.  Also,  implethose  processing steps required to provide accurate final velocity estimates will  be  explained.  C l  Complex Covariance Method A c c u r a t e estimates of Doppler shifts i n acoustic data represent  a challeng-  ing problem because of the trade-offs between space and speed resolution. W i t h an incoherent backscatter system as used i n the present application, spatial resolution (cr ) x  is ultimately determined by the length of the acoustic pulse;  where C is the speed of sound i n water a n d t is the acoustic pulse length. In contrast, the accuracy of speed determination is optimized by having a narrow  174 peak i n the frequency spectrum requiring a long (narrow bandwidth)  acoustic  pulse; 1  C.2  T h e ultimate choice of pulse length must take into consideration the observation requirements and the restrictions imposed b y Equations C . l a n d C . 2 . A detailed discussion of these competing terms is presented b y T h e r i a u l t (1986). For the practical computation of Doppler velocities, it is desirable not to restrict the range resolution beyond that given by E q u a t i o n C . l by limitations in  the signal processing.  In particular,  if mean frequency shifts were deter-  m i n e d by considering frequency spectra,  then the length of Fourier  used would become a restriction to the range resolution.  transform  T h i s complication is  completely avoided by estimating mean frequency shifts through consideration of the derivatives of the signal autocorrelation tral moments.  which can be related to spec-  T h i s approach is known as the complex covariance m e t h o d for  D o p p l e r speed estimation (Miller a n d Rochwarger 1972).  For a power spectrum P ( / ) , the mean frequency based o n the first moment is,  " ~  fp(f)df  c  If the corresponding autocorrelation function is R(h),  z  then it is easily shown  that dR(h)  fi =  -^hr R(h) v  '  CA h=Q.  T h e autocorrelation function can be expressed as  R(h) = A ( f t ) e ' *  (ft)  C.5  175 where A ( h ) expresses the amplitude a n d (j>(h) the phase at lag h. expression for R(h) given by E q u a t i o n C . 5 ,  ®  . affile dt  Equation  C . 6 is simplified  +  A  becomes,  (  dt  h  first  )  '  K  by using  Using the  i  ? m  e  CM  ^ .  dt  difference  approximations  for the  derivatives a n d assuming that (for any autocorrelation function) A(h)  is even  and <j>(h) is o d d . E q u a t i o n C . 4 can then be used to estimate the frequency as;  d<f> Cl 1  ~ 2irh  x  (ImR{T)\  \ReR(T) J '  where R(T) is the autocorrelation function determined at some small time lag (as discussed b y Miller a n d Rochwarger 1972). T h e complex covariance method makes velocity estimates possible for each estimation of the autocorrelation very  function.  simple a n d can be applied to data  T h i s technique is computationally windows as small as the time lag  chosen, thereby imposing no artificial restriction o n the range resolution.  C.2  Zoran Processing Signal amplitude a n d Doppler velocity must be extracted through process-  ing of the vertical sonar data. In addition, the data must be positioned relative to the ocean surface so that meaningful data averages can be made. T h i s processing is done as the data are recovered from the V C R with the Z o r a n V S P controlled by the I B M A T . T h e processing steps a n d computer  timing rela-  tionships are identified i n the flow chart of Figure C l : notice that while the Z o r a n system is waiting for a n d processing data f r o m one sonar return, the  176 IBM  A T is computing data products for the previous return.  T h e processing  steps outlined i n Figure C . l will be discussed i n the order i n which they  are  executed. The 48  m  Z o r a n system loads the 2816  data points (corresponding to 63 ms  of range) received immediately after the  sonar transmission.  Since  or the  instrument is known to be at about 30 m depth, this block of data necessarily includes the surface return. to  A first problem is encountered w i t h this step due  a hardware fault on the  Zoran b o a r d :  duplicate data point when a read request most  of the  applications,  a  the F I F O register  will generate a  is issued to an empty F I F O .  single duplicate data  point  For  is insignificant, but  when reading complex numbers such data duplications introduce spurious phase jumps.  Stating the obvious, this problem can be overcome by not  requesting  data f r o m an empty F I F O . Fortunately, status words available to the I B M A T indicate when the F I F O is half full a n d by monitoring this status word,  data  is requested only when there is data i n the F I F O . T h i s solution does have the drawback of keeping the I B M A T tied up monitoring the status word and it is not available for parallel processing much of the time. Once the the  data  are  P C M digitizer must  large  as  200  loaded,  be eliminated.  digitizer counts  estimations  become  introduced by  These offsets are  while good data  amplitudes as low as 5 counts: phase  D C offsets  a bias voltage  in  observed to be  as  signals can be recovered  if such offsets are not removed, the  meaningless.  T h e implicit clock  demonstrates  Re(i),  Doppler  sampling  provides a convenient means of correcting for these data offsets.  with  scheme  Equation B.7  that the data are received as a sequence;  Im(i),  -Re(i  + 1), -Im(i  + 1), Re(i + 2), Im(i + 2),... .  C.8  177  IBM/AT  ZORAN  Set Up Initialize Zoran  Grab Data  Walt for Interupt  Sign Change Remove Offset  Read Data Find Surface Disable Data  Find Surface  Start Zoran Enable Data  Issue Interupt  Velocity Magnitude Xfer to HP Compute Correlations Magnitude  Record Time if needed  Figure sonar  C l :  data.  Data  acquisition  processing  steps used for  recovering  vertical  178 If an offset (a)  is introduced into this signal, either as part of the  digitizing  process or through a voltage offset, the sampled signal will appear as:  Re(i) + a, Im(i) + a,  - Re(i + 1) + a ,  -Im(i  + 1) + a , C.9  Re(i + 2) + a , Im(i + 2) + a;, ... . T h i s offset can be estimated by adding successive (real or imaginary) values. F o r example,  (Re(i) + a) + (-Re(i + 1) + a) = Re{i) - Re(i + 1) + 2a.  C.10  Since the signal is slowly varying relative to the sampling rate, Re(i)  ~ Re(i  -f  1) a n d so,  Re(i) - Re(i + 1) + 2a ~ 2a  C.W  T h e estimate of a from equation C . l l is then used to correct the two entries. T h e entire 2816  point data block is processed i n this manner eliminating any  offsets that may be present. T h e d a t a of interest  are located at a n d just below the sea surface:  data  occurring appreciably b e y o n d the sea surface i n the sonar record is not meaningful. sonar  For this reason it is necessary return and adjust  the  data  to identify the surface location i n the  so that  it remains aligned to the moving  surface position. W i t h a normal echo sounder arrangement,  it is sufficient to  search the return signal for the m a x i m u m return which will identify the surface.  In the present application however, an acoustic pulse of 2.4  ms  is being  used to allow acoustic Doppler processing a n d this technique would introduce a ±0.98  m uncertainty i n surface location.  T h i s uncertainty is eliminated by  using the rising edge of the surface return as a surface indicator (this approach is described i n detail i n A p p e n d i x F ) . T h e Z o r a n processor is not capable of  179 the IBM  logic required to find the A T could not  surface  i n the  signal by any method,  possibly do the processing required in real  but  time.  the  These  problems are circumvented by conditioning the signal return into an amplitude record, smoothing it and determining a subsampled first difference (slope) on the Z o r a n system.  T h e resulting (reduced) d a t a is scanned by the I B M A T to  find the peak slope locating the surface to w i t h i n 0.1  m accuracy.  T h i s posi-  tion in the d a t a is then related back to the Z o r a n program which can continue processing relative to that point. W i t h the data aligned to the surface, can be directly determined. able since the 2.6 range resolution.  ms  a profile of backscatter amplitudes  T h e r e is no need to retain all of the d a t a avail-  pulse creates a backscatter profile w i t h only a 1.95  T h e d a t a are  the base of the topmost  blocked into  10  bins of 1.95  m  b i n coincident with the surface location.  b i n is retained because it records  the backscatter strength  also identifies the vertical velocity of the surface.  m  length with The  surface  of the surface  W i t h this system,  and  the max-  i m u m depth from which data are recorded is arbitrarily set to 18 m since no significant backscatter is received below this depth. Velocity estimates f r o m the vertical sonar d a t a are made using the plex  covariance  spectral  analysis.  technique  to  avoid the  computational  requirements  com-  of power  T o apply this method to the sonar data on the Z o r a n sys-  tem requires the computation  only of the signal autocorrelation  A l t h o u g h simple i n principle, these computations  at  some lag.  require multiplications which  can introduce underflow conditions in the Zoran processor.  T h i s problem was  reduced by amplifying data values (through multiple self additions) before any correlation analysis being careful not to create overflow conditions i n the process. T h e method used for this problem was to apply differing amplifications to  180 data as a function of depth below the surface:  signal levels are high near  surface a n d decay exponentially with depth. T h e amplification required at depth was determined by trial; Table  Bin  #  the each  C l indicates the factors chosen.  Depth  Gain  Factor  m 9 8 7 6 5 4 3 2 1 0  1 1 16 32 32 32 32 64 64 64  0 2 4 6 8 10 12 14 16 18  T a b l e C . l : B i n gain factors.  W i t h the data so amplified, autocorrelations the  data.  For each of the  10,  2.6  correlation function are made (not  ms  range  were computed directly f r o m  b i n , 64  all independent).  estimates of the  auto-  In order to convert  these  values into velocities it is necessary to determine the phase of the  autocorrela-  tions. T h i s phase determination cannot be done with the Zoran processor,  but  the A T could not possibly keep up computing all of the required arctangent calculations.  Instead, the Z o r a n is used to compute the average  autocorelation  slope for each b i n and this slope is then passed to the I B M A T . In addition to scaling all the frequency shifts into velocity estimates,  the data are  screened  to eliminate obvious errors based o n data quality indicators such as low amplitudes or large velocity anomalies as described i n Zedel and C h u r c h (1986).  181 These  screened  values are  then transferred to  the  H / P for subsequent  data  analysis. The  velocity processing contains several operations  before they could be relied u p o n for data recovery.  that  required testing  In particular, the combi-  nation of the implicit clock sampling scheme a n d the mean removal technique required testing before d a t a analysis could proceed w i t h confidence. A s a test of all the velocity processing operations, a function generator was used to provide a reference  signal which was digitized by the P C M a n d analyzed using  the velocity analysis processing package. A variety of frequency offsets f r o m the sonar carrier were analyzed w i t h this system and the hardware and provided  accurate measurements  tests are summarized i n T a b l e  C.3  of these frequency offsets.  software  Results of these  C.2 demonstrating the accuracy of the package.  Velocity Processing The  velocity data as processed and stored are i n a relatively crude f o r m .  T h e y have not been corrected for the vertical motion of the instrument platform  a n d they  are  subject  will discuss the accuracy  to  several potential biasing errors.  of the Doppler measurements,  This  section  the significance of the  potential biasing terms, a n d corrections applied to the data.  The  velocity measured using acoustical Doppler techniques is not actually  that of the water, but rather that of acoustical scatterers carried by the water. For  the 200  k H z sonar, acoustical scattering is dominated by 32 fj,m diameter  air bubbles which resonate at this frequency. A l t h o u g h these bubbles will have a vertical velocity due to buoyancy, their rise speed is only about 0.0006 (after T h o r p e 1984b) a n d so for the present  application they make  ms  - 1  excellent  182  Zoran  Input  Estimate  Hz  Hz  Hz  -1000  - 9 9 4 . 8 ± 2.3  - 5 . 2 ± 2.3  0.5  -800  - 7 9 5 . 7 ± 1.6  - 4 . 3 ± 1.6  0.5  -600  - 5 9 7 . 0 ± .3  - 3 . 0 ± 0.3  0.5  -400  -398.4 ± - 1 . 0  - 1 . 6 ± 1.0  0.4  -200  - 1 9 9 . 2 ± 0.5  - 0 . 8 ± 0.5  0.4  - 0 . 4 5 ± 0.01  oo  0  0.45 ±  Difference  % Error  Reference  0.01  (ref.  - est.)  200  199.6 ±  0.5  0.4 ±  0.5  0.2  400  398.6 ±  1.0  1.4 ±  1.0  0.4  600  597.3 ±  0.3  2.7 ±  0.3  0.5  800  795.7 ±  1.7  4.3 ±  1.7  0.5  1000  995.7 ±  2.3  4.3 ±  2.3  0.4  T a b l e C . 2 : Calibration of frequency estimator.  tracers of water motion. Some acoustical backscatter bles (with greater rise speeds).  will be f r o m larger bub-  However, at 200 k H z , a bubble diameter of  greater t h a n 800 fim is required to scatter energy comparable to that by resonant  scattered  bubbles a n d populations of such bubbles are typically l / 1 0 0 0  that of the 32 fj,m bubbles (Walsh and M u l h e a r n 1987).  t;i  D o p p l e r systems do  not make point measurements, but rather a n average over the volume of water ensonified by the acoustical beam.  F o r the data being considered, this volume  183 is a 2 m long cylinder w i t h a diameter of 3 m or less.  T h i s volume places a  fundamental limitation on the spatial resolution of the velocity Velocities are  estimates.  determined by frequency shifts occurring on the  tered signal and the accuracy  backscat-  of the velocity estimate is limited by the ability  to determine the frequency of the received signal. T h e 200  k H z echo sounder  was operated  F o r pulse-to-pulse  with a transmit  pulse length ( r )  incoherent Doppler, the speed uncertainty (a)  a = where,  C  ms.  for a single sample is given by  C  C.12  (47TT/)'  is the speed of sound a n d /  1986). For the present example a — .25 In addition to the uncertainty  of 2.4  is the operating frequency  (Theriault  ms~ . x  due to the Doppler speed estimation,  the  m e a n vertical velocities are masked by the periodic wave motion. A n estimate of the magnitude of this term can be made by using the linear wave equation a n d estimating vertical velocities f r o m knowledge of the swell p e r i o d and the wave height (approximately this approach,  10 second period with a 1.5 m amplitude).  the uncertainty  Using  i n speed estimates for a single sample due to  wave action alone is about 1.2 m s  - 1  at the surface.  P l a t f o r m motion along the b e a m axis introduces that velocity directly into the measure  of relative velocity;  even if the scatterer is not  moving, an ap-  parent velocity will be observed. T h i s error can only be removed b y recording platform m o t i o n along the direction of the beam axis. tion, a vertical accelerometer Figure 3.4), motion.  In the present applica-  was used to measure these vertical motions  and these data are used to correct profile velocities for  (see  package  184 T i l t i n g motions of the platform cause changes i n the acoustic b e a m direction a n d consequently change the  component  of speed being measured.  error cannot be eliminated since no measurement is  made;  strument  all that tilts.  can b e  done is to  T h i s requirement  of other velocity  minimize the  effect  components  by m i n i m i z i n g i n -  was considered when designing the m o o r i n g  package by maximizing the instruments righting moment. instrument  This  E v e n so, a record of  tilt was made so that the degree of data contamination could be  estimated f r o m geometrical considerations. Figure  3.4d  and e  about  two  orthogonal  tilts  package 3°  surface z  axes.  show an From  example  of observed  these records  it  instrument  is known that  the  can have a mean tilt of 3 ° or 4 ° with wave coupled oscillations of  about  be V  (page 27)  that mean.  current =  T h e average tilt will allow a portion of any horizontal  to be resolved onto the acoustic  V sin(0) where V  beam;  this contribution will  is the horizontal velocity, and 8 is the tilt  angle.  T h e actual horizontal velocities at the surface were not measured, but f r o m the S4 current  meter positioned at 41  layer relative to the instrument  m  depth, the mean velocity of the mixed  package  was about  0.3  ms .  Such a  -1  current resolved along the acoustic beam axis could introduce a 0.02 in the  vertical velocity estimates.  ms  - 1  mean bias  A l t h o u g h this bias could be of any sign,  the geometry of the instrument would most likely result i n a positive velocity: drag on the surface float will tilt the package i n the surface current and  the echo sounder beams will detect a velocity component  package  (a  net  positive velocity).  value for periods of the  response  This  bias would however  time of the  surface  wave  direction  away f r o m the be  a  field,  consistent and  variations occurring on time scales m u c h smaller t h a n that are of interest, such contamination would be obvious i n the data.  since any  185 T h e tilt oscillations coupled w i t h wave motion could also introduce velocity biases b y selectively sampling the velocity magnitude of this error, wave  field.  T o place a n estimate o n the  sampled velocities were computed for an ideal linear  a n d idealized sinusoidal instrument  motion.  A linear estimate  of the  velocity fluctuations close to the surface is given by u = A cos(fcx — u>t)e w = Asin(fcx — ut)e  kz  kz  ,  C.13  v = 0. W h e r e A is the m a x i m u m surface velocity, k is the wave number for a wave of frequency OJ, a n d x is the horizontal component  i n the direction of wave  propagation. T h e tilt angle 6 must vary periodically with frequency a n d so c a n be expressed as 6 = 7 s i n ( - w i + <£), where 7 is the magnitude of tilt, wave field.  C.14  a n d <j> is the phase of tilt relative to the  Doppler sonar systems measure the component of velocity resolved  onto the acoustical beam axis. T a k i n g x = 0 as a point o n the surface directly above the instrument location, the sampling position will be at x = s6 for a measurement  at range s from the instrument, the measured velocity will be  V = Acos(ks6 - ut)e  kz  sin0 + Asin(ks6 - ut)e  kz  cos6.  C.15  Since 9 is small (typically less than 5 ° , see Figure 3.4d, a n d e), E q u a t i o n C.15 can be simplified a n d an average over time will give 6=  +  1  }  sin(^)e*'.  C.16  If we assume i n the worst case that the phase term is a m a x i m u m (sin(<^>) = ±1)  a n d use representative  values for the other  parameters (k =  0.04 r n  - 1  ,  186 s =  30  ra,  7 =  6 = ±0.08 ms 180°  (see  - 1  .  2.5° =  0.04  radians,  A =  1.6  ms  - 1  ,  and  z =  0  m),  then  T h e observations indicate that the phase is actually close to  Figure 3.4c  a n d d); thus any such bias will be m u c h smaller than  this worst case estimate.  C.4  Low Amplitude Bias Preliminary plots of vertical  velocity revealed  a negative  bias  correlated  w i t h low signal levels: when signal levels became low, wave p e r i o d oscillations were still clearly seen i n profile time series, but they were biased to values.  T o investigate  this signal contamination,  negative  velocities were averaged  ac-  cording to their signal amplitudes (for example, all velocity estimates for which the signal amplitude fell between 10 a n d 15 binary counts would be  averaged).  T h e periodic wave velocities will average to zero and, because signal amplitudes a n d velocities should not be correlated, these velocity averages at selected amplitudes should also converge to zero. indicative of a systematic  A n y departure f r o m a zero average is  bias i n the data.  A n example of how this bias de-  pends on the amplitude is presented i n Figure C . 2 where the average velocities based on 12 hours of data- are plotted against occurred.  the amplitudes at which they  Figure C.2 shows that at high amplitudes, the averages do converge  reasonably to 0, but as amplitudes decrease, a consistent bias appears. A systematic  bias with amplitude is most likely introduced through some  signal contamination i n the electronics.  T o investigate the possible sources  of  this contamination, a low level signal was fed into the receiver amplifier for the 200  k H z sonar system a n d the output was observed on a spectrum  T h i s analysis revealed many peaks spaced at Hz.  constant  analyzer.  intervals of about  800  Considering the details of the receiver electronics, the only possible cause  187  -1-  1D.D Amplitude  F i g u r e C.2:  [counts]  Dependence of velocity bias on mean signal amplitude based on 6  hours of observation: signal amplitude is displayed as digitizer counts.  of these harmonics is the 787.5 H z reference oscillator used i n heterodyning the received signal (see A p p e n d i x B ) . T h e presence of this signal contamination can also be seen i n power spectra  made f r o m data received at  very low input signal levels.  Figure C.3  is  188 an example of such a power spectrum:  a large central peak occurs  at 0 H z  D o p p l e r shift, but the broadband background noise shows a peak that  occurs  at 785 H z . T h i s analysis of receiver processing clearly demonstrates data  contamination by the 787.5 k H z oscillator.  the occurrence of  B y knowing  the character  of this contamination, a n d considering the signal processing it is possible to remove the biasing effects. In the signal processing used, Doppler frequency shifts are estimated based on the first moment of the sonar backscatter spectrum. F o r such a system, the presence of coloured noise can introduce a bias even though the location of the spectral peak is itself still identifiable. T h e nature of this bias c a n be seen by considering the first moment of a power spectrum P ( f ) : u  _ S f P ( M fP(fW  C  1  7  a  i  7  If the power spectrum ( P ( / ) ) is made u p of a noise spectrum a n d a true sign a l spectrum, these constituent  spectra can be approximated by two gaussian  spectra with different means a n d variances:  S(f) = s e ^ r 1  C.18  a  where,  S(f)  is the signal spectrum with mean frequency F  variance a a n d B(f)  distributed with  is the noise spectrum with mean frequency p a n d vari-  ance a.  (These spectra can be expressed equivalently i n frequency or velocity  because  of the linear relationship between velocity a n d frequency.)  moment of this composite spectrum is then  _ ff(S(f) f(S(f)  + B(f))df + B(f))df •  T h e first  189  1D-i  Frequency  Figure  C.3:  E x a m p l e of the  H  background spectral  content  of the  received  sonar signal. T h i s power spectrum was acquired during a period of no  active  sonar operation and so provides the background "noise" spectrum for the sonar receiver.  T h e large peak occurring at 0 H z is caused by pick u p of the carrier  frequency by the receiver, of more concern is the presence of a b r o a d b a n d noise floor w i t h a peak at about 785 H z .  190 E x p a n d i n g these terms a n d integrating, the first moment becomes =  Fas + pab  C  2  Q  as + ab T h e biasing effect of noise i n the first moment estimation given by E q u a tion C.20  depends o n the  ratio of power i n the  noise compared to that i n  the signal (as regulated by the products ab, and as). with a low peak will have the same effect but  narrow spectrum.  the parameters  T o demonstrate  A broad noise spectrum  as noise with a high peak power  the behaviour of this bias,  values of  i n E q u a t i o n C.20 are set to typical values expected  based o n  the observed character of Figure C . 3 . b = .01, p = 750 Hz,  Choosing a = 1000  Hz , 2  a =  100  Hz , 2  and F = 0, the dependence of the first moment on signal  amplitude ( 5 ) is shown i n Figure C.4. Figure C.4 is plotted i n the same format as Figure C.2 except that the results are scaled as frequency rather t h a n velocity; for the purposes of this example, the linear scahng is not important.  For  high signal power relative to the noise, the first moment remains near zero but as the signal level decreases,  a progressively greater bias is observed similar to  that exhibited i n the data (Figure C.2). The  noise model presented  supporting  this  interpretation.  behaves This  very  similarly to  model can  now be  that  used to  means for removing the bias from the low amplitude data. that  the  noise power remains  constant  irrespective  of the  of the  data  provide  a  If it is assumed signal level,  and  that the signal mean frequency remains at zero (which is expected o n average) then equation C.20 can be used with the data to calibrate the biasing effects of the noise.  E q u a t i o n C.20 is rearranged  to a form that is linear i n signal  amplitude; 1  as  P  ab  1  + P-  = Ms + I  C.21  191  Figure signals  C . 4 : Bias i n mean frequency estimates associated when a  spectrum  is contaminated  by  with low amplitude  coloured noise.  This  figure is  based on a simplified model of d a t a contamination and is analogous to Figure C . 2 which shows observations of velocity bias at low signal amplitudes.  where, M =  and I =  K  For the assumptions made, the signal peak is at  0 frequency so that fi given by E q u a t i o n C.21 represents the expected bias for this situation. T h e data of Figure C . 2 were re-plotted against  1/v  recovering a  192 straight line as expected from E q u a t i o n C.21 (Figure C . 5 ) . U s i n g linear regres-  sion, these d a t a determine values of M a n d I as —1089.5 Hz  1236.9 Hz" : 1  1 5.0  O.D  Amplitude  tude.  ( c o u n t s ) , and -1  the hne defined by these parameters is indicated i n Figure C . 5 .  -4DH  Figure  -1  1 10.0  (counts)  C . 5 : Plot of inverse velocity bias ( 1 / V ) against average signal ampliU s i n g the same data as shown i n Figure  linear regression fit to the data.  C . 2 . T h e straight line is a  193 A s s u m i n g that these correction coefficients remain constant signal mean frequency F  irrespective of  (an assumption implicitly used i n the computation of  M and I), E q u a t i o n C.20 can be modified for the case of non-zero F  giving  /z(l + -J—) - ^ - = F. M —s Ms Knowing  that  frequency F  the  C.22  observed mean frequency is given by p,  can be recovered  the  true  signal  w i t h knowledge of the signal amplitude using  equation C.22. T o evaluate the effects of E q u a t i o n C.22, Figure C . 2 was repeated with corrected  the processing used to generate  data producing F i g u r e C . 6 .  T h e cor-  rection t e r m effectively removes the observed bias for amplitudes greater t h a n about 3 digital counts:  data received at amplitudes less t h a n this level cannot  be corrected and such data must be rejected. To  demonstrate  the final result  of correcting for the velocity bias  rejecting d a t a with amplitudes below 3 counts), before a n d after  corrections  (and  two minutes of velocity data  are displayed i n F i g u r e C . 7 .  T o provide a  refer-  ence, F i g u r e C . 7 a displays the surface vertical velocities and Figure C.7b shows the signal amplitudes i n b i n 5 (at  a depth of 8 m  below the surface):  this  particular data interval was selected because it shows a progression f r o m high to low signal amplitudes. demonstrate creases.  Uncorrected vertical velocities (Figure C.7c)  clearly  an increasing bias to negative values as the signal amplitude de-  A f t e r applying the  to negative bias is absent  velocity corrections  (Figure  C.7d),  although some gaps now appear at  the  tendency  those  intervals  where the signal amplitude persists below the threshold of 3 counts.  194  + 1  +  ++  0.0  +  +  + + +  +++++++++++++++++++-  • + + + + + + + ••  +  10 .0  5.0  Amplitude  [counts]  Figure C.6: Observed bias i n velocity data after correcting for the biasing effects using E q u a t i o n C.22. A s i n F i g u r e C . 2 , 6 hours of velocity data  were  averaged according to the observed velocities a n d the results of these averages are presented here.  Notice that the velocity bias has largely been eliminated  except at amplitudes below about 3 counts..  195  17:31:30  17:31:50  Time Figure C.7:  17:32:10  (UTC)  T i m e series of velocity observations before and after  for the amplitude bias effect; a) ocean surface vertical velocity, b) amplitude observed at 10 m depth, c) raw (uncorrected) m  17:32:30  correcting backscatter  vertical velocity at  10  depth, d) 10 m velocities corrected for bias effect a n d rejecting data where  signal amplitudes fall below 3 binary counts.  196  Appendix  D  Sidescan Sonar Processing Sidescan sonar data were collected with the intention of determining the horizontal  distribution of subsurface  the backscattered  bubble clouds.  signals must be reconstructed  T o meet  this  into sonogram images.  appendix describes the data processing and conditioning necessary backscatter  objective,  to  This  recover  signal strength f r o m the recorded d a t a and how that information is  used to produce meaningful sonogram images.  D.l  Z o r a n Processing Through  analog processing during data  recording, the  sidescan d a t a  are  placed onto a 17.5 k H z carrier and stored i n analog form on the H i - F i channels of the V C R . T o convert this data into a digital record, the H i - F i recording is fed is the  into a Sony P C M system a n d the resulting 44.1 captured data  using the  k H z , 16 bit data  Z o r a n V S P . Processing this data  interval of interest,  removal of offsets  stream  requires selection  (substantially  of  introduced by  the antialiasing filters of the P C M digitizer), extraction of the signal f r o m the carrier, a n d subsampling the resulting amplitude series.  These processing steps  are outlined schematically i n Figure D . l . The  sidescan data, by its nature, contains no useful information until after  the return from the surface. the first 43 ms  (1888  Since the instrument is located at  32  m  depth,  data points) of data after transmission are discarded. N o  effort is made to accommodate  wave action or variable instrument depth since  these changes of a few meters constitute only a small error compared to  the  197  Side S c a n  Processing  IBM/AT  Zoran D S P  Set Up Initialize Zoran  Wait for Zaran  Head Data  Start Zoran  Transfer Data To HP  Read in 1888 pts Data before surface  Read in 10240 pts  De-mean Rectify  8pt Running Average  Sub Sam pie Data  Issue Interupt  Figure D . l :  D a t a acquisition processing  sonar d a t a from V C R storage.  steps used for recovering  sidescan  198 200 m d a t a window being considered.  Following the discarded 43 ms interval,  232 ms of d a t a (10240 d a t a points) are captured into Zoran memory. W i t h the vertical sonar data, adjusted  to have  a zero  mean  implicit clock sampling allowed d a t a to be  value  over  successive  this m e t h o d is not possible for the sidescan  data,  data points.  Although  these data are still o n a  carrier a n d so averages can be used to remove any D C offsets.  F o r these data,  averages are accumulated for blocks of 128 d a t a points (representing  2.89 ms  or 2 meters of range) a n d the calculated offset is removed from that block. Since all that is needed f r o m the sidescan  d a t a is signal amplitude, the  d a t a are rectified and smoothed with a running average. has  a frequency of 17.5 k H z so that  ripple over successive  d a t a points.  T h e recorded  carrier  the rectified signal still has significant  T h i s ripple is eliminated b y filtering the  d a t a w i t h a n 8 point running mean.  T h e smoothing of this filter is consistent  w i t h the 0.1 ms transmit pulse used which would span 4 data points. E a c h block of sidescan data constitutes 10240 data points a n d these are received at a rate of 4 H z (between all the d a t a are retained, so,  i n the interest  each  the two operating sidescan  systems).  If  hour would generate 150 M b y t e of d a t a a n d  of storage economy,  subsampling is necessary.  Based on  inspection of the processed data, retention of only 1 i n 16 data points  retains  most variability seen i n the signal (providing range resolutino of about 0.3 ra). These subsampled arrays of 640 points are then transferred  through the I B M  A T a n d stored directly on the H / P A900 system.  D.2  Sidescan Image P r o c e s s i n g T h e sidescan  data format  conventional sonogram image.  is very simple a n d is most E v e n these basic acoustic  easily viewed as a  data can benefit sub-  stantially f r o m the signal conditioning made possible by computer  processing.  199 In particular, are of interest  it is the  spatial distribution of subsurface bubble clouds  that  and so it is desirable to clarify their representation i n the fi-  nal d a t a display. T h e bubble clouds are best demarked by changes i n acoustic backscatter  strength, not by the overall signal level so it is useful to eliminate  signal level variations w i t h range and  acoustic  absorption).  In  (such as result  addition, sidescan  from geometrical spreading sonar  data  naturally linear spatial scale as do conventional backscatter non-linearity must be corrected.  do  not  systems  have  a  a n d this  T h i s section will describe the implementation  of techniques to correct for these limitations of sidescan data.  A  sonogram image is created  from acoustic backscatter  data by p l o t t i n g  echo return strength against range as an image density or colour and plotting these progressively i n time. backscatter  A  first  requirement is to transform the  time series into a spatial representation  along the ocean surface.  of acoustic  acoustic  cross section  T h i s transformation is essentially a geometric  adjust-  ment determined from the deployment configuration indicated i n Figure D . 2 . In the data, the slant range at any time (t) can be determined by using E q u a t i o n 3.1; the range along the surface is then,  D.l  U s i n g E q u a t i o n D . l , the data are transformed into a linear range scale but this transformation does introduce a range dependent spatial resolution. T h e range uncertainty (p) for a given time resolution (I) in the sidescan sonar d a t a can be determined from E q u a t i o n D . l a n d is  -L (d  p==  C  2  + D)'. 2 1 2  D.2  200  1  r  Surface  3 dB Beam  Figure D.2:  Geometry of sidescan sonar deployment.  A t large ranges this approaches p = Cl/2 but  as the range approaches 0,  sidescan  sonar  to  (about 0.25  m for data as recorded),  p approaches infinity.  resolve structures  at  short  ranges  Clearly, the ability of is very poor  a n d this  characteristic is obvious i n the data (see Figure 4.5page 50). Sonogram images can be produced directly by plotting received signal level as a function of range. due  Such plots suffer from the changes i n backscatter level  to acoustic propagation losses and transducer b e a m pattern effects.  What  is actually of interest is the acoustic backscatter as a function of range which requires the correction of the data for any range dependent effects. ple,  In princi-  range dependence can be determined analytically by considering acoustic  absorption, spherical spreading a n d the transducer b e a m pattern, but accurate  201 calibration in such a manner is extremely difficult. A dynamic and more accurate way of affecting this correction in the present case is by determining the mean signal backscatter for a period of time and using that as the correction factor for sidescan data. This method is adequate where the scattering cross section is, on average, not range dependent (as in this case). Calibration curves for sidescan sonar from this data set were generated for each hour of operation. This method insured that as overall sea conditions change, the relative scaling in sonogram images was not affected. An example showing the complicated character of the necessary corrections is shown in Figure D.3. The large discontinuities occurring around 140 ms, 180 ms, and 220 ms are caused by sonar transmissions and reflections from the surface and the instrument package itself.  202  Figure D.3: T y p i c a l calibration curve used to correct sidescan sonar data for range dependent signal variations.  203  Appendix  E  Ambient Sound Processing The  ambient  sound data  are  the  most  convenient  to record  because  their n a t u r a l suitability to the P C M system but, they are also the most sitive to contamination. and remain consistent  of  sen-  A n y variation i n signal amplitude must be quantified to allow calibration of the ambient sound levels.  cessing these data from V C R storage to computer files involves:  Pro-  selection of  those data intervals not contaminated by active sonar transmissions, removal of offsets f r o m the data, tapering the data w i t h a cosine window, application of a Fourier transform, a n d averaging several transforms to increase d a t a stability. These steps,  and the division of processing between the Z o r a n V S P , a n d the  I B M A T are identified schematically i n Figure E . l . E v e n though the operating frequencies of the active sonars fall well beyond the receiving bandwidth of the hydrophone, the transmit pulses (and i n some cases the surface returns) contain significant energy within that b a n d w i d t h so that contamination of the ambient sound data occurs.  Selection of those inter-  vals that could be considered free of contamination was done b y observation of the  ambient  windows of 5.8  sound data ms  on an oscilloscope.  duration (corresponding to 7,  extracted from each 160  ms  Based on this evaluation, 256  7  point F F T ' s ) could be  sonar system cycle. Figure E . 2 identifies the  data  windows accepted and their placement i n the sonar cycle. As w i t h all data processed through the P C M system, signal offsets be eliminated prior to Fourier analysis.  For the ambient  sound records,  must this  204  Ambient Sound Processing Zoran DSP  IBM/AT  Load 644 pts =15 ms to Clear 50 kHz Transmit  Load 256 pts Remove Mean  X3  Window, FFT  Load 3128 pts =70.8 ms to Clear  Disable Data Flow  200 kHz Transmit  Read Data  Load 256 pts Remove Mean  Start Zoran  X3  Window, FFT  Enable Data Flow  Load 256 pts =17.4 ms to Clear 200 kHz Surface Return  Record Time  Load 256 pts Remove Mean  X1  Window. FFT  Scale F F T ' s Compute Magnitude Average  Issue Interupt  Figure E . l :  D a t a acquisition processing  sound d a t a from V C R storage.  D  steps used for recovering  ambient  205  50 kHz Surface Return  Key Pulse 50 kHz xmit  /  Key Pulse 200 kHz xmit  /  200 kHz Surface Return  1  3,  3, 256 pt FFT's  '  t '  N  J  i  25B pt FFT's 1, 25B pt FFT  1  40.  o.  Time  Figure E.2:  120.  80.  Ambient  sound data  160.  Cms)  can  only  be recovered  during  intervals  when d a t a are not contaminated by sidescan a n d vertical sonar transmissions a n d surface returns.  T h i s figure indicates the time intervals during which the  7, 256 point F F T ' s are drawn during the data collection cycle.  p r o b l e m is complicated because system gains h a d been selected too low during the  data  acquisition:  under some  conditions g o o d data  are  limited to  data  counts as low as 10 or 20. U n d e r these conditions, extreme care is needed to avoid underflow conditions o n the Z o r a n while at the same time not  applying  excessive amplification. T o deal with this special case, a cumbersome but safe m e a n determination scheme was used. E a c h 256 point data block was divided by 2 a n d then successive data points were added together halving the number of d a t a points but preserving the mean.  T h i s process was repeated until only  206 one data point remained and that single value was the mean to be removed from that 256 point data segment. Blocks of 256 data points were selected because these are very conveniently transformed i n one pass of the Z o r a n V S P . T h e d a t a were windowed w i t h a cosine taper,  and then directly transformed.  T h r o u g h this process,  the Z o r a n  system generates a scaling factor which applies to the entire transform. scaling factor  is retained to preserve  data  calibration through the  This  averaging  process. It is the power spectra themselves that are of interest, so the magnitudes of the Fourier transforms must be estabhshed.  Conversion to power spectra is  normally a straightforward computation through an inner product of complex conjugates,  but with the Zoran system, this procedure would reduce data  curacy by losing the 16 least significant bits of the 32 bit product.  With  acthe  present data, often characterized by low bit counts, such a loss i n accuracy is unacceptable.  T o avoid this problem, an iterative scheme to determine  magnitudes is incorporated which is based o n the fact that when the  vector  absolute  values of b o t h components of a complex number are taken, the phase of the resulting complex number is restricted to between 0 ° a n d 9 0 ° . B y rotating such a vector by 4 5 ° clockwise (easily done on the Z o r a n system using an internal cosine look-up table) and again taking absolute values of the components,  the  vector is further restricted to be between 0 ° a n d 4 5 ° . T h i s procedure can be repeated etc.)  using successively smaller rotation angles (90,  45,  22.5,  11.25,  5.125  constraining the phase of the vector to progressively smaller values. E v e n -  tually, when the phase angle is suitably b o u n d e d (to  5.125°  for these data),  the vector magnitude is effectively represented by the real component. A s with  207 m a n y Z o r a n algorithms, the sequence of operations appears the  processor's  speed makes it  an  acceptable  cumbersome,  but  approach a n d i n this case,  it  completely eliminates the need for multiplications. After  for  each  transform, they are converted to a c o m m o n scaling factor and averaged.  The  IBM  the  Zoran V S P has  completed  the  magnitude estimates  A T takes the averaged spectra based o n 7 256 point F F T ' s and transfers  these to the H / P system every 160 ms as they are generated. A slight variation i n ambient sound processing was possible during the  10  minutes out of every hour when no active sonar was operating. A t . t h e s e times, there is no contamination of d a t a  a n d the  processing system  was  operated  without synchronizing to the (then absent) sonar trigger pulses. In this mode, the system generates one averaged spectrum for each 150 ms of raw data.  E.l  Ambient Sound Calibration Ambient sound processing is largely completed through the data acquisi-  tion by computing power spectra.  T h e data as stored are suitable for display-  ing relative variations i n ambient sound power, but calibrations are needed for cross comparisons with other data sets.  T h e various considerations in ambient  sound calibration will be identified i n this section a n d the scalings that  they  apply will be noted. The  signal processing steps affecting ambient sound signal levels are iden-  tified i n Table  E . l . Starting w i t h the receiving transducer gain, the signal is  pre-whitened using an R C filter, amplified, converted to a digital signal with the P C M system and converted to power spectra by the Zoran processor. A l l of these terms can be represented i n a sonar equation,  SSL = S-T  S  + W-G  + R + PCM-Z-B,  E.l  208 where  SSL  (0 VU  =  =  Sound Signal Level i n d B re 1 (iPa /Hz,  32768 counts),  (for the I T C 5298), W = dB,  R =  T  =  s  Transducer sensitivity =  whitening filter response,  resistor bridge loss =  re 0 VU/V,  S  2  Z =  6 d B , PCM  =  G =  d B re 0  -157 d B re  =  VU  IV/pPa  amplifier gain =  Digitization gain =  gain through Z o r a n processing  to b a n d w i d t h i n the F F T =  =  30.5 d B , B  =  37.7  6.6 d B gain due  22.4 d B . T h e pre-whitening filter response is, b y  definition, frequency dependent:  knowing the resistance R, capacitance C , a n d  frequency, the relationship between input a n d output voltage  (Vi„, and V ) 0  is  given by,  v^  (jp + i / t d ' c ) / ^ 2  =  V ut  E  2  R  0  The  1  gain through b o t h the Zoran a n d P C M conversions were determined ex-  perimentally. In the absence of a standard sound source, could be made of the instrument parison of ambient  calibration.  was possible was a com-  Vagle et al. (1990) provide a relationship between wind  speed a n d S S L ( E q u a t i o n 4.1 i n the text); 8 k H z is expected to be 45 d B relfiPa l  What  end to end test  sound levels observed w i t h those expected for the wind  conditions encountered.  ms~  no complete  2  for a 5 m s  / Hz  - 1  wind,  the S S L at  a n d the value expected at  15  is 57 d B . In the present data, the observed values of S S L for these wind  conditions were observed to be 45 a n d 55 d B . These values are i n very good agreement supporting the accuracy of the calibration.  209  T a b l e E . l : Steps affecting ambient sound calibration.  Component  Gain  Hydrophone  (dB)  -157.7  Sensitivity Prewhitening Filter  -10 @  8 kHz  Amplifier  37.7  Resistor  -6  Bridge PCM  -6  Zoran  30  Processing FFT  22.4  Total  -90.2  210  Appendix  F  Wave Measurement Details M a n y of the parameters investigated i n this thesis have been driven either directly or indirectly by wave action. Wave height measurements were provided for with a conventional Datawell Waverider buoy. It was realized, however, that wave observations could be made directly by using vertical sonar to  measure  the range to the ocean surface. T o consider this o p t i o n may appear redundant w i t h the availability of the Waverider data, but for any analysis requiring precise relative timing between wave observations and other acoustic observations, it  is a great convenience to have b o t h data types referenced to  a common  clock. A n additional benefit exists since if this m e t h o d can be demonstrated to be accurate, it will be possible to free future acoustic studies of the need for independent wave height measurements.  T h i s appendix will outline the  tech-  niques used to determined wave heights (and spectra) from the vertical sonar systems  a n d compare  those to  the  more accepted  records  of the  Waverider  buoy.  F.l  Surface F i n d i n g and V e l o c i t y D e t e r m i n a t i o n The  ergy;  sonar data provide two somewhat independent measures of wave en-  first  there is the time series of range to the surface, a n d secondly, the  time series of the vertical velocity of that surface.  Identifying the surface with  the vertical sonar systems is not trivial, a 1.6 ms  (1.9  m ) long acoustic pulse  must be used to meet Doppler sonar requirements a n d this pulse length makes any  simple method of surface finding inaccurate  (as is discussed i n A p p e n d i x  211 C ) . Figure F . l a displays a typical acoustic return from the ocean surface using the 200 k H z sonar system. Based o n the location of the peak signal return, the resolution of the range to the surface is no better t h a n about ± l m . An  alternative  means of identifying the surface is provided by the  relative signal strength of the surface ume scattering). surface return  (about  20  d B above near  large  surface  vol-  B y identifying the characteristically steep leading edge of the (see  Figure F . l a ) ,  detection  is  possible. T h e first difference of the signal amplitude is computed (ie. dA/dt)  to  identify the leading edge.  a much more accurate surface  In using this approach, some smoothing of the am-  plitude return is required to reject large slopes associated with low amplitude noise.  F i g u r e F . l b shows a first difference amplitude return after smoothing:  the surface location is clearly identified by the large isolated peak.  T h e accu-  racy of this approach is limited by the amount of averaging that must be done to eliminate spurious peaks, with data from the 200  k H z sonar, surface  range  was provided with a precision of ± 0 . 1 0 m . It must be appreciated that the surface finding accuracy reported here is only a precision because the technique is not infallible and errors location do occur.  These errors  i n surface  are however never greater than about  ±1  m  because the algorithm used to identify the surface will always identify a point within the 2 m long interval which is returned f r o m the surface F.la).  For wave spectra  (see  determined from wave height, such errors  difficulty a n d they require filtering to remove spikes reducing the data in  time.  in  excess  Sonar surface of that  estimates  are  made  at  needed for meaningful wave  3 samples providing 0.5 analysis which follows.  Figure  do cause accuracy  a rate of 6 H z which is far measurements,  averages  s time resolution a n d have been used for the  over wave  212 1800-  a] Amplitude  cu  TD D •U  - 500a £ <  b] Amplitude Slope  c] Complex Signal  8192  B256  8319  Data Element  F i g u r e F . l : E x a m p l e of an acoustic return from the ocean surface: amplitude return, b) is the slope of the surface return, a n d c) is the demodulated signal.  a) is the complex  213 Once the range to the surface is established, the vertical velocity of the surface  can  be determined through the  Doppler  shift present  on the signal.  For velocity estimates f r o m volume scattered sound, the accuracy is limited to about ± 0 . 3 m s  - 1  (for the 200 k H z system as used) due to the required m o d -  ulation of the transmitted  acoustic  achieved f r o m velocity estimates  pulse.  M u c h greater accuracy  off the surface.  is however  Figure F . l c shows an  ple of the complex (real a n d imaginary) return f r o m the surface:  the  examsmooth  sinusoidal f o r m of data through the surface return testifies to the small bandw i d t h of this acoustic return. no incoherent  returns  essentially coherent.  T h i s small b a n d w i d t h occurs because there are  from any object T h e high estimate  other  t h a n the surface,  accuracy  the  possible because  signal is  of the  co-  herent surface return and the high vertical velocities of wave action (of order 1 ms  - 1  )  combine to provide a signal that requires no more averaging  that of the surface range data.  than  Figure F.2 compares one minute of Waverider  data, sonar surface ranges and sonar surface velocities and provides support for the comparable accuracies of these wave measurement  It range  is important to  timates.  the  surface  to note do not  that  the errors  techniques.  which occur i n determining the  introduce comparable errors  T h e velocity estimates  are  restricted  (determined by the acoustic pulse length used).  to  a range  in the  velocity es-  resolution of 1  m  Errors i n identifying the sur-  face which are less than 1 m are consequently insignificant. T h e crude  range  resolution of the velocity estimates is not itself a problem because vertical velocities associated  with the waves being measured (those with wavelengths of  12 m a n d greater) do not vary significantly over a depth of 1 m.  214  Figure F.2:  Comparison of 1 minute of surface  based o n Waverider data,  wave observations:  b) is based on sonar range,  derived vertical velocity of the surface.  and c) is the  a)  is  Doppler  215  F.2  System Limitations Measurements of b o t h range to the surface and surface velocity are rela-  tive to a freely moving package i n the present deployment configuration. T h i s m o t i o n must be accounted for if accurate wave measurements  are to be made  a n d this correction has been done by using a vertical accelerometer  a n d two  tilt meters (measuring orthogonal tilt components) mounted on the instrumentation package.  T h e accelerometer  data were corrected for errors  due to tilt,  high pass filtered using a 4'th order Butterworth filter with a cutoff period of 50 s and then integrated to recover velocities a n d displacements. In F i g u r e F.3, 5 minutes of surface wave data, instrument tilt a n d instrument vertical motion are  displayed along with surface wave height.  T h e strong wave period oscil-  lations seen i n these data clearly demonstrated the need to correct for these motions i n the final data.  T h e high frequency (high wavenumber) cutoff for sonar based wave measurements is determined either by the sampling rate (2 H z for these data), or by the surface footprint of the acoustic tern,  the  surface.  200  beam.  Based on a 3 d B b e a m pat-  k H z system would sample a 3 rn diameter disk o n the  T h e scattering  cross section of the surface is however about  ocean 20  dB  greater t h a n the bubble scattering just below the surface and so 3 d B of signal suppression is not adequate to eliminate surface returns from the larger side lobes.  F o r this reason, it is more appropriate to consider the sonar as having  an omnidirectional radiation pattern as shown i n Figure F.4  a n d to consider  the consequences of such sampling. In this case, the system resolution is determined by the region of intersection of a sphere centered o n the depth w i t h the wave covered ocean surface.  transducer  216  I *  -54 124-  Heading  „/\  M 116108-  w  10011:45:00  11:46:40 time  Figure F.3:  11:48:20  11:50:00  ( U T C )  5 minute time series of instrument  attitude  starting  at  11:45  U T C , 27/10/1987. a) sea surface displacement, b) instrument vertical deviation about mean depth, c) instrument vertical velocity, d) X component of tilt, e) Y component of tilt, f) instrument heading relative to true north.  217  \<  X \< I  :  Effective Footprint 3 dB Footprint  • | i  X Transducer  Figure waves.  F.4:  Schematic diagram of sonar sampling i n the presence of surface  218 As sonar R =  depicted in Figure F.4,  receives Ct/2,  acoustic  where  at  any time  t after sonar  backscatter f r o m a spherical surface  C is the  speed of sound i n water.  transmission,  the  w i t h a radius  of  Considering a two d i -  mensional projection of this backscatter region, the locus of points sampled is determined by, R = (x  2  + (z - d ) ) * ,  F.l  2  where d is the instrument depth, and x a n d z are horizontal and vertical spatial coordinates relative to a point at the surface directly above the location. ocean  ( A two dimensional projection is adequate  surface  is being characterized  i n this case because  by a unidirectional surface  ocean surface can be defined by a single representative  instrument  wave).  the The  wave component,  T] = a s\xi{kx — u>t),  F.2  where a is the wave amplitude, u> is the wave frequency and k is the wavenumber.  T h e range to  the  ocean  surface  will be  detected  m i n i m u m value of R which intersects the ocean surface. F.l  sonar  at  the  C o m b i n i n g Equations  a n d F . 2 , gives the m i n i m u m value of R as  R = (  x  At  by the  2  + (asm(kx - ut) - d) )^.  F.3  2  this point, a worst case estimate of the surface footprint is of interest  from inspection of Figure F.4,  the larges footprint will occur  when the  phase (kx — ut)  is j  sonar system).  For this situation, the m i n i m u m value of E q u a t i o n F . 3  and wave  evaluated at x — 0 (ie. the wave crest is centered over the occurs  when  x = (d — a cos kx)ak sin kx.  FA  219 For most applications, a «  d a n d E q u a t i o n F . 4 can be simplified to  x = akd sin kx,  F.5  and the sonar footprint can be determined f r o m this expression b y the value of x required to satisfy E q u a t i o n F . 5 . T h e footprint (2x) and  wave  becomes  slope:  smaller.  as  identified by E q u a t i o n F . 5  the  A t the  waves  smallest  system resolution to about data  set  become  3 m.  being considered are  longer  wavelengths,  is dependent on frequency  a n d less steep,  the  footprint  the 3 d B footprint limits the  A t longer wavelengths,  bounded by about  ak <  wave slopes i n the  0.1:  Table  F . l pro-  vides a comparison of detection ranges based on E q u a t i o n F.5 for various wave lengths assuming a fixed wave slope of 0.1. waves of 2.8  T h e m a x i m u m error is seen for  s period which have a footprint of 6 m .  A t longer  wavelengths,  the wave curvature becomes sufficiently small that the error is reduced. In addition, for a beam angle of 2 0 ° , the beam pattern provides 20 d B of side lobe suppression and will b o u n d the sonar footprint to 22 m . For the present set,  these resolution constraints  are  not  restrictive  since there is little  data wave  energy seen at periods shorter t h a n 5 seconds (corresponding to a wavelength of 40  m).  T h e deployment geometry being used places the Waverider above the sonar systems tethered by a rubber cord. T h i s placement makes comparisons between the  wave  measurement  systems  convenient,  but  introduces  the  possibility of  interference of the sonar system by the Waverider a n d rubber cord. T h e rubber cord itself has not introduced any significant problems when considering profile data f r o m the sonar systems a n d so is not expected to cause problems at  the  220  wavenumber  wave slope  footprint  period  wavelength  s  m  m"  1.1  1.8  3.5  .1  1.6  1.4  3  2.1  .1  2.6  2.0  6  1.1  .1  4.4  2.8  12  .53  .1  6  5  39  .16  .1  0  m  1  T a b l e F . l : Sonar effective footprints for various surface wavelengths.  surface.  T h e buoy itself could present  which serves as a proxy surface return.  a strong single target  at  the  surface  If this interferance occurred, it would  not affect the present application of wave measurements since the surface buoy itself follows the wave motions.  T h e r e remains the question of how the  sonar  systems might respond i n the absence of a surface float. T h e present data set cannot be used to investigate this problem, but previous applications of upward looking sonar have not h a d difficulties identifying the surface and it is unlikely that  the  absence  of a surface float would greatly  reduce the  surface  finding  ability.  F.3  Waverider Accuracy  The  Datawell 0.9  m  diameter  waverider buoy is used as  a reference  in  this comparison. T h i s buoy is a heave measuring buoy which determines wave height by integrating vertical accelerations.  T h e manufacturer  indicates  that  221 this instrument has a high frequency cutoff of about 0.5 H z which is imposed by the dimensions of the buoy itself.  In addition,  because of the high  pass  filter which must be applied before integration of the acceleration record, this instrument has a low frequency limitation of about 1/28  Hz.  T h e filtering ap-  plied by the Waverider system does not have a linear response to acceleration at low frequencies and data must be scaled to correct for this characteristic. T h e filter complex response is given by Datawell as  A =  x ..,  ^  l-y/2pi-p  .,„,  (l-?0  2  where p = ~ ,  1  g = ^ - , T i s the wave period, i is \f—l,  constants of 30.8  s and 460  s respectively.  F.6  3  and T\ a n d T  2  are time  Correction for this effect has been  applied to all of the data presented.  F.4  W a v e Spectral A n a l y s i s T h e time series shown i n Figure F.2  sonar to determine wave characteristics,  demonstrate  the potential of using  but because of the inevitable timing  difficulties, a quantified comparison is difficult.  Ultimately some f o r m of wave  spectrum is required, a n d because spectra are not as sensitive to t i m i n g errors as direct correlations, comparisons of measurements are made using spectra of wave energy density. F r o m surface wave heights, the energy density of a wave is, J = \pgo?,  F.l  where p is the water density, g is the acceleration due to gravity, a n d a is the wave amplitude. Spectra of wave energy can be directly generated f r o m wave height power spectra through scaling by  \pg.  222 Vertical  velocity data  must  also be converted  to  energy  densities.  This  conversion could be done by integrating the velocity data into vertical displacements  (essentially the same approach used to convert  velocity and displacement).  package acceleration  to  A n alternative method is to integrate the velocity  power spectrum with respect  to time:  consider some harmonic wave  compo-  nent, 77 = asin(fcx — u>t), where n is surface displacement,  F.8  k is the wavenumber, and u  is the  angular  frequency. T h e vertical velocity of the surface is given by, Qn  — = —au cos(kx — ut). at Comparing  Equations F.8  and F . 9 ,  will be scaled by a factor of u  2  is to divide through by u  2  F.9  it is seen that power spectra  over displacement spectra.  of velocity  A l l that is required  to convert a velocity power spectrum to a displace-  ment spectrum. Notice that as frequencies approach zero, this scaling tends to infinity a n d so this scaling becomes unstable at low frequencies. For all the data types, the same basic spectral analysis technique was used a n d these steps are identified i n Figure F.5. samples a n d 10, 512  D a t a were averaged into .5 second  point F F T ' s were computed using a cosine taper a n d an  overlap of 50 % . T h e power spectra from these F F T ' s were averaged a n d scaled depending on the d a t a type (wave height or velocity).  together  T h e spectra  that result from this processing are representative of 20 minutes of data.  F.5  C o m p a r i s o n of S p e c t r a 60 hours of observations were suitable for comparisons between the  a n d Waverider spectra.  sonar  D u r i n g a 20 hour period of increasing w i n d speeds,  a  Spectral Analysis  223  Haw D a t a  Loop X 10  512, 0 .5 s e c Sam pies  Cosine Taper  Scale Aaverage  Corret : t f o r Package Motion  FFT  Add P o w e r to Average  Back Space File 2 5 6 points C5Q°/o Overlap] Final Power Spectrum  Figure data.  F.5:  Flow chart of processing steps used i n spectral analysis of wave  224 complete range of sea states occurred varying f r o m ocean swell w i t h no winds, to a fully developed sea i n the presence of a crossed swell. T w o examples  will  be considered; one sea dominated by ocean swell, a n d the second d u r i n g the period of developing seas. Figure F . 6 shows wave spectra  based o n 20 minutes of data starting at  00:20 U T C o n October 27, 1987 when wind speeds h a d been c a l m for some time  a n d were just  increasing to about  f r o m Waverider data,  5 ms  - 1  . Figure F . 6 a is determined  Figure F . 6 b is determined f r o m the sonar range to the  surface, a n d Figure F.6c is determined from surface vertical velocity data. N o tice that although the spectra are normalized (by peak energy), the scales have been adjusted so that absolute comparisons are possible. T h e total energy density for these spectra  are 4.6 kJm~ ,  F.6a, b a n d c respectively. at  4.7 kJm~ ,  2  long period waves.  a n d 5.2 kJm~  2  2  for Figure  Figure F.6c shows some anomalous increased energy  T h i s energy is a result of the scaling to convert  velocity to amplitude spectra which tends to infinity at infinite periods.  from Aside  f r o m this one fault, comparison between these spectra demonstrates incredibly good agreement  A creased  especially the velocity a n d range to surface  more complicated sea state was encountered to 13 ms~  l  spectra.  when the w i n d speed i n -  a n d added a developing sea to the existing swell.  collected under these conditions are shown i n F i g u r e F . 7 with wave based  o n 20 minutes of data  starting  at  12:20 U T C on O c t o b e r  Data  spectra  27, 1987.  A s i n F i g u r e F . 6 , Figure F . 7 a displays data f r o m the Waverider buoy, Figure F . 7 b displays data based o n the sonar surface range record, a n d F i g u r e F . 7 c is based o n sonar surface velocities. densities are 9.4 kJm~ , 2  In these spectra,  9.9 kJm~  2  a n d 8.8 kJm~  2  the total observed  energy  for the spectra of Figure  225  Figure F . 6 : 27/10/1987,  Wave 00:10  observations  U T C . Low wind  for the speeds  20  minute  have  a n d the wave field is dominated b y ocean swell,  period  starting  prevailed for several  at  hours  a) Waverider observations, b)  sonar range observations, c) sonar vertical velocity observations.  226 F.7a, b and c respectively. A g a i n , the agreement between the three spectra is very good with the exception of the long period power that leaks through from the velocity processing.  F.6  Discussion Comparisons between wave measurement  systems  are always complicated  by the statistically non-stationary nature of ocean w i n d waves. comparison, method  this  itself:  problem is almost  the  two  sonar  completely  systems  In the present  eliminated by  sample exactly  the  is directly underneath the Waverider buoy within about  the sampling  same  area  3 or 4 m  which  (as  con-  trolled by the instrument tilt). W i t h this accuracy of instrument placement, all three observations are made at the same point to well within the wavelength of the waves being measured. T h e three systems have markedly different errors associated with the sampling they use. T h e Waverider is a heave measuring buoy and so must exclude horizontal accelerations from the vertical accelerations being measured.  In ad-  dition, the Waverider is advected horizontally by the wave currents and so it does not make true point measurements.  T h e Waverider cannot observe waves  with periods greater than 28 s because of the measured accelerations.  filtering  necessary  to  integrate  A short p e r i o d limit is imposed on the Waverider by  the response of the buoy to short  waves, the manufacturer suggests  a  short  period cutoff of about 2 s.  T h e sonar range to surface is a simple observation to make; required is to  identify the  location of the  surface  i n the sonar  all that is backscatter.  In the present study, range determination has been somewhat complicated by  227  TIME: 27/10 12:20  Figure  F.7:  27/10/1987,  Wave  observations  12:10 U T C . W i n d  conditions to about  Period  lOms  - 1  ( s )  for the  20  minute  period  starting  speeds have increased from the earlier  at  calm  at this time and i n addition to the ocean swell,  there is now a developing sea. a) Waverider observations, b) sonar range observations, c) sonar vertical velocity observations.  228 the use of long sonar pulses for Doppler velocity processing but it remains a fairly robust measurement.  T h e m e t h o d does not measure  the range  to  the  surface at a fixed point, but rather the m i n i m u m range from the sonar to the surface (as described by E q u a t i o n F.3).  In the present application this imposes  a wavelength restriction o n the waves being measured of about period of 3 s).  12  m  (or  a  For the present deep ocean application this limitation is not a  problem as their is comparatively little energy at periods of 3 s or less i n these data. T h e two methods of estimating wave spectra using the vertical sonar syst e m are largely independent techniques even though they are made with same sonar system.  the  T h e y do share the common difficulty of having a p o o r l y  defined sampling position caused by the finite sonar characteristics:  b o t h mea-  surements are made at some point within a 6 m diameter disk centered above the instrument location. T h i s limitation restricts b o t h methods to the measurement of wavelengths greater t h a n 12 m . For measurements based o n the range to the surface, errors identifying the surface result i n high frequency noise; this noise has been reduced i n the present data by averaging the successive estimates.  range  Velocity based wave spectra depend on the range to surface  to identify the location of the ocean surface. mination do not however translate  T h e errors i n the range  to errors i n the velocity estimates  data deter-  because  surface range errors are normally less t h a n about 1 m and the vertical velocity of the waves being measured does not vary significantly over this distance. It is difficult to quantify the accuracy of the velocity estimate itself since it clearly exceeds that expected for incoherent Doppler processing.  Based on  qualitative observations, averaging over .5 seconds of data (3 independent velocity  estimates) provides adequate  accuracy  for the  determination of wave  229 spectra presented here. spectra  at  Some error is introduced i n the velocity based wave  long periods because the velocity power spectrum must be scaled  by the ( f r e q u e n c y ) . -2  A s the frequency tends to 0 for long period waves, this  scaling amplifies noise in the spectrum to the point that it becomes significant a n d contaminates  the spectra:  this characteristic  is obvious i n the  examples  presented.  One potential problem with b o t h the sonar based wave measurements  is  the presence of significant subsurface bubbles. T h e surface detection algorithm employed relies on a characteristically large acoustic backscatter from the ocean surface. If significant quantities of subsurface bubbles are present, it is conceivable that the acoustic location of the surface may become ill defined.  Although  significant subsurface bubbles were observed during the period characterized by a  developing sea,  at  no time  d i d the  surface  detection algorithm fail.  m a x i m u m w i n d speeds encountered were however no greater t h a n 15 m s  The  - 1  and  this blocking effect may become a difficulty at greater wind speeds.  The  overall agreement  i n peak locations between the wave spectra pro-  vides strong evidence for the individual accuracy of each of these systems. agreement even small  between sonar range a n d velocity estimates details are reproduced i n these  The  is particularly striking;  two spectra.  Such  strong  agree-  ment does not demonstrate that these two methods are b o t h correct since they clearly suffer from some c o m m o n errors.  W h a t it does demonstrate is that the  errors not common to b o t h of these techniques (Doppler velocity estimation, surface  identification, a n d conversion from velocity to  tions) are not introducing significant errors.  amplitude  representa-  230 T h e r e is quite a bit of variance i n peak energy levels, but it is to be expected since slight changes in frequency can split the power between two adjacent frequency bins. T h e total energy density represented by the three methods provides a convenient benchmark for comparison avoiding this difficulty. the  two sea states considered, the  in Table  F.2.  observed energy  densities are  In both cases, the three observation techniques  For  summarized agree within  10% of each other i n total energy density. T h i s accuracy is comparable to that reported for the Waverider i n the comprehensive comparison by Allender et al. (1989).  Sonar Velocity  Range  Waverider  swell  4.6 x 1 0 J m "  2  4.7 x 10  3  Jm~  2  5.2 X 10  3  Jm~  2  9.4 x 10  2  9.9 x 10  3  Jm~  2  8.8 x 10  3  Jm~  2  3  mixed  Table F.2:  F.7  Sonar  Wave condition  3  Jm~  Wave energy densities determined by sonar and Waverider.  S u m m a r y and Conclusions  Wave measurements  have been made using an upward looking sonar  t e m positioned at 30 m depth i n a deep ocean environment. Wave spectra generated  using b o t h wave heights (sonar range to surface),  velocity of the surface using the same sonar. parison,  wave spectra  A l l data geometry:  and the  sysare  vertical  T o provide a reference for com-  determined using a Datawell Waverider buoy are used.  are sampled at essentially the same location due to the deployment the  waverider  is located  above  the  upward looking  sonar  on  the  231 same drifting instrumentation array.  T h i s geometry eliminates any question of  wave field coherence in the data comparison. Wave spectra observed during two distinct sea states have been presented. Comparisons of the spectra generated from the three techniques show remarkable similarities (Figure F.6 estimated f r o m these The  only  error  terms  a n d Figure F.7).  spectra  agrees within  common to  all three  T h e total wave energy density 10  % i n each case (Table  techniques are  those  F.2).  associated  with motion of the sampling platform (ie. the tendency of the observations to be Doppler shifted by instrument motion i n the long waves).  A l l other error  sources are absent i n at least one of the techniques: based o n these results, the collective effect of those errors is less than 10% i n wave energy density. These results demonstrate  that  vertical sonar can provide excellent  esti-  mates of surface wave motion even from a moving platform i n the deep ocean. W h e n corrections  are made for motions of that platform, results comparable  to those obtained with a heave measuring buoy can be achieved. For the applications of interest i n this study, the accuracy  of sonar wave  eliminates the need for independent wave observations.  measurements  M o r e generally, sonar  techniques could provide a m e t h o d of making wave observations where buoy observations are not suitable such as i n areas of heavy shipping, or areas prone to icing.  U n i v e r s i t y of Victoria, V i c t o r i a , B.C.  9/774/82  U n i v e r s i t y of Victoria, V i c t o r i a , B.C. U n i v e r s i t y of B r i t i s h Columbia Vancouver, B.C. M.Sc.  Field  Attendance dates  Name and location  Grade %  1982  81  9/822/85  Physics 1985 (acoustics)  94  9/86-  Oceanography 1991  89  Degree- 1985  Physics (honors)  Degree date  U n i v e r s i t y of V i c t o r i a V i c t o r i a , B.C. Canada  Thesis Topic E v a l u a t i o n of an Acoustic Doppler P r o f i l e r with Application to S t r a t i f i e d Flow i n a F j o r d Ph.D. Degree- 1991  U n i v e r s i t y of B r i t i s h Columbia Vancouver, B.C. Canada  CSIRO Marine Labs GPO 1538 Hobart Tasmania, 7001 Australia Phone: (002) 206-666 From 3/85 u n t i l  6/86  Seakem Oceanography L t d . 2045 M i l l s Rd., Sidney, B.C. Canada Phone: (604) 656-0881 from 5/82 u n t i l  Defense Research Establishment C.F.B. Esquimalt Esquimalt, B.C. Canada Phone: (604) 388-1921 from 1/80 u n t i l  9/82  Seakem Oceanography L t d . 2045 M i l l s Rd. Sidney, B.C. Canada Phone: (604) 656-0881 from 5/81 u n t i l  9/81  M i n i s t r y of T r a n s p o r t a t i o n and Highways G e o t e c h n i c a l and M a t e r i a l s T e s t i n g Branch 324 K i n g s t o n S t r e e t V i c t o r i a , B.C. Canada Phone: (604) 387-5828 from 9/80 u n t i l  1/81  5/80  Pacific  PUBLICATIONS Z e d e l , L . J . , D.M. Farmer, ( a c c e p t e d Dec. 1990), O r g a n i s e d s t r u c t u r e s i n s u b s u r f a c e b u b b l e c l o u d s : Langmuir c i r c u l a t i o n i n t h e open ocean, J o u r n a l of G e o p h y s i c a l Research. Z e d e l , L . J . , J.A. C h u r c h , 1987, R e a l - T i m e s c r e e n i n g t e c h n i q u e s f o r D o p p l e r c u r r e n t p r o f i l e r d a t a , J o u r n a l of A t m o s p h e r i c and O c e a n i c T e c h n o l o g y . 4, 572-581. S t a c e y M.W. , L . J . over the s i l l Oceanography.  Z e d e l , 1986, The t i m e d e p e n d e n t , h y d r a u l i c of O b s e r v a t o r y I n l e t , J o u r n a l of P h y s i c a l 16, 1062-1076.  flow  Z e d e l , L . J . , 1985, E v a l u a t i o n of an A c o u s t i c D o p p l e r P r o f i l e r w i t h a p p l i c a t i o n to S t r a t i f i e d flow i n a F j o r d , U n i v e r s i t y of V i c t o r i a M.Sc thesis. Z e d e l , L . J . , 1982, Development of a P r o t o t y p e I n e x p e n s i v e A c o u s t i c R e l e a s e , C o n t r a c t e r s R e p o r t t o Department o f F i s h e r i e s and Oceans Canada, (DSS F i l e no. 06SB.FP941-2-0452). J.  O z a r d , L . J . Z e d e l , 1981, D e t e c t i o n of an A c o u s t i c T a r g e t i n S h a l l o w Water by a B a r r i e r o f O m n i d i r e c t i o n a l S e n s o r s , D.R.E.P. T e c h n i c a l Manual 81-18.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0053237/manifest

Comment

Related Items