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

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Near Surface Ocean Processes: coustical Observations, Ambient Sound, and Langmuir Circulation by Len Zedel B . S c , The University of Victoria, 1982 M . S c , T h e University of Victoria, 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 R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Department of Oceanography) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A August 1991 © L e n Zedel, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of 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) A b s t r a c t n This thesis describes a study of near surface ocean processes based on observations made with an instrument incorporating both active and passive acoustical systems. T h e topics addressed include the organization of bubble clouds by Langmuir circulation, the modulation of ambient sound levels by surface wave action, and the interactions of vortices associated with Langmuir circulation. Observations in a deep ocean environment reveal bubble clouds organized into plumes of 100 m length and widths of about 5 m aligned with the wind through the action of Langmuir circulation. T h e depth of these plumes varies somewhat with wind speed with the greatest depths of 12 m occurring at wind speeds of 13 ms-1. Using acoustic Doppler techniques, downward vertical velocities of 0.06 m s - 1 are observed at 8 m depth within the bubble plumes. Ambient sound observations at 8 kHz are used to search for possible re-lationships between wave breaking and Langmuir circulation: no systematic relationship is identified. This investigation does reveal the occurrence of mod-ulations to ambient sound levels in phase with the long (~ 150 m) surface waves passing over the instrumentation (positioned at 30 m depth). A model of sound generation at the ocean surface suggests that individual sources must have spacings of less than 6 m to reproduce the observations. Increased break-ing 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 and short waves, or variations in wind stress over the long waves. T h e observations of Langmuir circulation reveal many coexisting scales of spacing between the windrows. A mechanism capable of generating small iii scale vorticity of the appropriate orientation through wave breaking and vortex stretching is developed. T h e consequences of interactions between this small scale, two dimensional vorticity is then explored using a Lagrangian vorticity model. This model demonstrates that continuous injection of small scale vortic-ity close to the ocean surface can lead to circulation similar to that expected for Langmuir circulation: a distribution of circulations cell sizes results, down welling speeds exceed upwelling speeds, and the cell spacing scales vary in proportion to the depth at which a bottom boundary is placed in the model. iv T a b l e o f C o n t e n t s Abstract ii Table of Contents iv Figures viii Tables xviii Acknowledgements xix Preface xx 1 Introduction 1 2 Background • 8 2.1 Application of Acoustics to Near Surface Processes 8 2.2 Langmuir Circulation 10 2.3 Wave Breaking and Ambient Sound 14 2.4 Objectives of Observations 16 3 Instrumentation 20 3.1 Instrument Deployment 21 3.2 Instrument Motion 26 3.3 W i n d Speed Measurements 28 V 3.4 Acoustic Characteristics 29 3.4.1 Vertical Sonar 29 3.4.2 Sidescan Sonar 33 3.4.3 Ambient Sound Record 35 3.5 Data Recording 36 3.5.1 Conventional Instrumentation 36 3.5.2 Acoustical Data 37 4 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 5 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 6 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 A 2-D Lagrangian Vorticity Model 110 7.1 M o d e l Requirements I l l 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 Summary of Lagrangian Vorticity M o d e l 128 8 M o d e l Results 130 8.1 M o d e l Streamlines 130 8.2 Bottom Influence 133 8.3 Length Scale Distributions 136 8.4 Stability of Structures 136 8.5 Discussion of Model Results 140 8.6 Conclusions 141 9 Summary and Conclusions 144 9.1 Instrumentation 145 9.2 Observations 146 9.3 Ambient 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 B . l Ambient Sound Signal Conditioning 162 B.2 Sidescan Sonar Conditioning 162 B.3 Vertical Sonar Signal Conditioning 164 B.4 Digital Signal Processing Considerations 167 B . 5 D a t a Recovery 169 C Vertical Sonar Processing 173 C . l Complex Covariance Method 173 C.2 Zoran Processing 175 C.3 Velocity Processing 181 C . 4 Low Amplitude Bias 186 D Sidescan Sonar Processing 196 D . l Zoran Processing 196 D . 2 Sidescan Image Processing 198 E Ambient Sound Processing 203 E . l Ambient Sound Calibration 207 F Wave Measurement Details 210 F . l Surface Finding and Velocity Determination 210 F.2 System Limitations . 215 F.3 Waverider Accuracy 220 F.4 Wave Spectral Analysis 221 F.5 Comparison of Spectra 222 F.6 Discussion 226 F.7 Summary and Conclusions 230 Figures viii Figure 2.1 11 Circulation pattern associated with Langmuir 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 in a small area just above the package. Figure 3.2 24 Diagram of drifting instrumentation package identifying the various instrumentation and 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 in metres, b) instrument ver-tical deviation about mean depth (derived from accelerometer record), ix c) instrument vertical velocity (derived from 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 from various instru-mentation groups (all times are in U T C ) . Figure 4.2 43 Summary 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 kHz) , c) significant wave height, d) average depth penetration of subsurface bubbles, e) depth integrated scattering cross section, Mv. Bars A , B , and C identify periods used to produce Figures 4.8a, b and c. Figure 4.3 47 Waterfall plot of surface wave spectra for the 21 hour period begin-ning at 22:00 U T C , 27/10/87. Note the progression of locally wind 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 in the band between 5 k H z and 15 k H z for the 21 hour pe-riod beginning at 22:00 U T C , 27/10/87. The scaling in this figure is identical to that of 4.3 to aid comparisons. Figure 4.5 50 Example of 5 minutes of sidescan sonar data collected during 13 m s - 1 winds; a) is along the direction 1 9 0 ° true, and b) is along the di -rection 1 0 0 ° true. Instrument orientations for this period are shown 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 sono-grams (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 mak-ing associations. Figure 4.7 56 Composite spatial map of subsurface bubble clouds observed during the period 11:10 - 12:00 UTC 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. Ob-served winds were less than 7 ms-1 (4.8a), about 10 ms-1 (4.8b), and greater than 10 ms-1 (4.8c). The time intervals over which the histograms were accumulated are shown by bars labeled A, B, and C in Figure 4.2a. Figure 4.9 62 Contours of vertical velocity and backscatter cross-section for a con-ditionally sampled sequence of bubble clouds. To construct this cross section, data were averaged over a 2 hour period beginning at 12:10 UTC, 27/10/87. xi Figure 5.1 70 Spectrum of ambient sound fluctuations. D a t a are plotted as (fre-quency x power) against a logarithmic frequency scale to represent the relative contribution to signal variance. T h e display is based on an 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 visi-ble at periods between 5 and 13 seconds. Figure 5.2 71 Comparison of surface wave displacement and ambient sound levels (between 6000 and 9000 Hz) at 30 m depth for the 3 minute period beginning at 12:13 27/10/1987 U T C ; a) ambient sound level (filtered to remove fluctuations at periods greater than 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 : both wave and ambient sound data have been high pass filtered to eliminate variations at periods longer than 20 seconds. Figure 5.4 74 Cross spectral analysis of 23 minutes of wave and 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. This analysis is based on averages over 20 separate frequency spectra. T h e 95% confidence intervals are indicated by error bars for both phase and coherence. Figure 5.5. 76 Time series of wind speed and the phase and coherence between waves and ambient sound modulations for the 21 hour period beginning at X l l 22:00 26/10/1987 U T C ; a) wind speed, b) average coherence at peri-ods between 10.5 and 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 and phase between wave motions and ambient sound are shown for a 44 hour period for fluctuations with a period of between 9.5 and 13 s are displayed. Figure 5.7 82 Geometry of modelled dipole sources and receiver. Figure 5.8. . 88 Comparison of observed and modelled ambient sound fluctuations over a 3 minute period. A ) quadratic dependence on wave displacement, B) intermittent sources located at wave crests, and C) quadratic de-pendence on wave displacement with sound sources restricted to long wave crests. ( A l l models reproduce mean levels comparable to those observed, but have been displaced to clarify the presentation). Figure 5.9. 90 Scatter plot of observed ambient sound levels against 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 7.1 116 Model domain. xiii Figure 7.2 123 Comparison of displacement differences between a normal model run, and one with a time step reduced by a factor of 10, (the small time step model will have comparatively small errors and is considered as a reference), a) Scatter plot of displacement differences, b) directional dependence of displacement differences. Figure 7.3 125 Difference in computed displacements between a primitive vortex in -teraction model and a model accelerated by subdividing it into 640 regions; a) Scatter plot of displacement differences, b) Directional de-pendence of displacement differences. Figure 8.1. 132 Contours of stream function occurring when the model has achieved a steady state and there is no bottom present. A contour interval of 4 m 2 5 - 1 has been used with values at maxima labelled and all negative areas (characterized by clockwise oriented flow) have been shaded in . Figure 8.2 135 Contours of stream function occurring when the model has achieved a steady state with a bottom located at 10 m in a 200 m horizontal domain. A contour interval of 2 m2s~1 has been used with values at maxima labelled and areas characterized by clockwise oriented flow shaded in . Figure 8.3 137 Length scale dependence on bottom boundary depth. Length scales are determined from autocorrelations of the stream function and plot-ted against the bottom boundary depth used in that model. xiv Figure 8.4 138 Cell spacing histograms for model results a) 10m bottom boundary and b) 20m bottom boundary. Distinct cells are identified on the basis of vertical velocities exceeding —0.01 m s - 1 . Figure B . l 163 Example of prewhitening filter effect on ambient sound spectrum. Dashed line is unfiltered ambient sound spectrum, the sohd line is filtered. Figure B.2 170 Typica l processing steps used in recovering data from V C R storage. Figure C l . 177 D a t a acquisition processing steps used for recovering vertical sonar data. Figure C.2 187 Dependence of velocity bias on mean signal amplitude based on 6 hours of observation: signal amplitude is displayed as digitizer counts. Figure C.3 189 Example of the background spectral content of the received sonar signal. This 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 up of the carrier frequency by the receiver, of more concern is the presence of a broadband noise floor with a peak at about 785 H z . XV Figure C.4 191 Bias i n mean frequency estimates associated with low amplitude sig-nals when a spectrum is contaminated by coloured noise. This 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.5 192 Plot of inverse velocity bias ( 1 / V ) against average signal amplitude. Using the same data as shown in Figure C.2. T h e straight line is a hnear regression fit to the data. Figure C.6 194 Observed bias in velocity data after correcting for the biasing effects using Equation C.22. A s in Figure C.2, 6 hours of velocity data were averaged according to the observed velocities and 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 T i m e series of velocity observations before and after correcting for the amplitude bias effect; a) ocean surface vertical velocity, b) backscatter amplitude observed at 10 m depth, c) raw (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 197 D a t a acquisition processing steps used for recovering sidescan sonar data from V C R storage. xvi Figure D.2 200 Geometry of sidescan sonar deployment. Figure D.3 202 Typical 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 sound data can only be recovered during intervals when data are not contaminated by sidescan and vertical sonar transmis-sions and surface returns. This 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 212 Example of an acoustic return from the ocean surface: a) is the amplitude return, b) is the slope of the surface return, and c) is the complex demodulated signal. Figure F.2 214 Comparison of 1 minute of surface wave observations: a) is based on Waverider data, b) is based on sonar range, and c) is the Doppler derived vertical velocity of the surface. xvii Figure F.3 216 5 minute time series of instrument attitude starting at 11:45 U T C , 27/10/1987. a) sea surface displacement, b) instrument vertical devia-tion about mean depth, c) instrument vertical velocity, d) X compo-nent of tilt, e) Y component of tilt, f) instrument heading relative to true north. Figure F.4 217 Schematic diagram of sonar sampling in the presence of surface waves. Figure F.5 223 Flow chart of processing steps used in 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 . Low wind speeds have prevailed for several hours and 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 27/10/1987, 12:10 U T C . W i n d speeds have increased from the earlier calm con-ditions to about l O m s - 1 at this time and in addition to the ocean swell, there is now a developing sea. a) Waverider observations, b) sonar range observations, c) sonar vertical velocity observations. T a b l e s 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. . . . 59 Table 5.1. Sound source model parameters 92 Table 7.1. Numerical viscosities resulting from subdivision schemes. . . . 127 Table 8.1. Model run statistics 131 Table C l . B i n gain factors 180 Table C.2. Calibration of frequency estimator 182 Table E . l . Steps affecting ambient sound calibration 209 Table F . l . Sonar effective footprints for various surface wavelengths. . . 220 Table F.2. Wave energy densities determined by sonar and Waverider. . 230 xix A c k n o w l e d g e m e n t s The successful completion of this project (and thesis) would not have been possible without the assistance and guidance of many people. It is impossible to identify all those who have helped me for to do so would require many pages. There are however some individuals whose contributions have been so essential to me that I must recognize their efforts. The instrument design and construction required the skills of many expe-rienced people. D o n Redman completed the mechanical design. Paul Johnson succeeded through skill and imagination in designing analog circuitry capable of meeting my most outrageous specifications. R o n Teichrob provided the digital circuit design and computer interfacing which allowed the convenient program-ming of instrument operation. A l Stickland designed the mooring arrangement: I learned a great deal about working with people and moorings from A l . None of the instrumentation would have been of any use except for the skill (and daring) of Captain Paul Frost and 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 and programming has been required at all stages of this project: there are many times that Grace Kamitakahara-K i n g has patiently listened to my problems and provided me with the perfect solutions. I always find the administrative requirements more confusing and complex than any scientific problems. There are many times that Chris Mewis has led me through the administrative labyrinth of U B C . A t IOS, Netta Delacretaz and Bob Lake have been most helpful in eliminating bureaucratic problems. On many occasions it is only my fellow students have helped me to pre-serve my sanity. I greatly value the many discussions on physics, oceanography, and life that I have had with Daniela Dilorio , M i n g L i , Craig M c N e i l , Dimitr i Menemenlis, Svein Vagle, and Yunbo Xie . I must also thank my supervisors for patience and support. Steve Pond managed many administrative tasks on my behalf for which I am indebted. D a v i d Farmer (too often) demonstrated the great skill of asking the right questions: much of the work I have done resulted from my efforts to answer these irritating questions. Financial support for this project has come from several sources. I have been supported by a Natural Sciences and Engineering Research Council ( N . S . E . R . C . ) post graduate scholarship, and a Graduate Research Engineer-ing and Technology G . R . E . A . T . award. Costs for instrumentation have been met through support from the Panel on Energy Research and Development, and the United States Office of Naval Research. Finally, I would like to thank my parents and my wife Elizabeth for waiting and believing in me despite the ever slipping schedule. X X P r e f a c e 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 xx i 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. W i l l i a m W o r d s w o r t h C h a p t e r 1 I n t r o d u c t i o n i Wave action, turbulence and the complexities of two-phase flow present significant challenges to the study of ocean surface phenomena. Although 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 mixed layer response (McCormick and Meadows, 1988). Such models bury the details of mixing and momentum transfer in approximate parameterizations. T h e purpose of the present study is to contribute to the growing body of knowledge on two and three dimensional mechanisms that underlie these processes. For 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 can be made both with active and passive devices. Active sonar is effective in identifying the surface itself and the clouds of bubbles that occur beneath a wind driven surface. Passive measurement of the 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 on bubble clouds created by breaking waves. These include various optical and acoustical attempts to infer bubble size distributions (for example, Walsh and Mulhearn, 1987, Medwin and Bre-itz, 1989, Farmer and Vagle, 1989) as well as echo-sounder studies of bubble 2 concentration and spatial patterns such as those pioneered by Aleksandrov and Vaindruk 1974 (as referenced in Thorpe 1982) and vigorously developed by Thorpe and colleagues. In particular, Thorpe and Hal l (1983) obtained images of horizontal features aligned with the wind which they attribute to the effects of Langmuir circulation. T h e presence of Langmuir circulation in the open ocean has been demon-strated by Weller and Price (1988). Weller and Price used modified vector averaging current meters ( V A C M ' s ) deployed from R . P . F L I P so as to ob-tain three dimensional velocity profiles through the ocean mixed layer. These revealed a downward component of velocity as great as 0.3 ms~1 beneath windrows associated with Langmuir circulation. Although Weller and Price could not make instantaneous profiles with depth, their extensive set of mea-surements showed that the maximum vertical velocities occurred at about 20 m depth and that there was a maximum in the horizontal downwind velocity of about the same magnitude located in the same location. Doppler sonar observations of the velocity field by Smith et al. (1987) (coordinated with the observations of Weller and Price) showed that some of the Langmuir cells documented by Weller and Price had spacings of up to 100 m. Visual 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 up to 2 km long and persisted for periods of at least 2 hours. These studies help to identify the processes that are important to mixed layer dynamics. Breaking wind waves are important to the transfer of mo-mentum between the atmosphere and ocean; they also inject bubbles into the 3 ocean surface. W h e n present, Langmuir circulation (at a variety of scales) will rapidly transport any properties such as heat and momentum through the mixed layer. 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 speeds etc.) in order to disentan-gle the relationships between them. 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 and res-olution to sample effectively in this environment but there remains potential for much more comprehensive implementation. Thorpe and Hall's (1983) sides-can observations were restricted to a coastal environment; Thorpe et al. (1985) developed systems with a mid-ocean capability but these measurements were limited to sidescan observations, although at two separate frequencies (80 and 248 kHz) . Thorpe (1986) used only one frequency of upward looking sonar and Smith et al. (1987) had a limited spatial resolution of 23 m . In addition, for comprehensive observations of the variety of near surface processes it is desir-able to combine simultaneous observations both i n the vertical and horizontal dimensions. The Ocean Acoustics group at the Institute of Ocean Sciences (IOS) has been developing various acoustical approaches for near surface observations in the deep ocean environment. Such observations are typically obtained with a freely drifting instrument with acoustical sensors suspended by an extensible cord from a surface buoy so as to decouple it from surface wave motion. This system was first deployed in 1985 during the Frontal A i r Sea Interaction Ex-periment ( F A S I N E X ) to make simultaneous video, ambient sound and upward looking echo sounder observations. To provide a more complete set of near 4 surface observations in the present study, I organized the installation of two (upward pointing) vertical sonars (50 k H z and 200 kHz) , two orthogonally di-rected 100 k H z sidescan sonars, and an ambient sound recording system with 22 k H z bandwidth on a similar platform. D a t a were recorded using conventional V H S video cassette recording sys-tems which provide an economical, high quality data storage format. These systems are however only suitable for the recording of signals at audio fre-quencies. I developed a system capable of accurately recording sonar phase information on these systems by using an implicit clock sampling scheme and carefully consulting with the electronics technicians who designed and 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 of data recovery: it is not possible to start and stop the data stream without losing substantial amounts of data. To overcome this limitation, I developed an extensive package of signal processing software operating on a Zoran V S P -161 vector signal processor controlled by an I B M - A T personal computer. B y using the high speed processing capability of the Zoran system, data could be processed in real time (as they were recovered from the video cassette). It is only through the combination of the high speed signal processing capabilities of the Zoran system with the high data storage rates provided by V H S video cassettes that the variety and quality of acoustic data presented in this thesis could be collected by an autonomous instrument. T h e instrument was deployed during the period October 19 to November 15, 1987, from the C S S P A R I Z E A U in the North Pacific within a 50 km 5 radius of 4 8 ° N , 139° W . The cruise formed part of the O C E A N S T O R M S 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, and a large array of oceanographic moor-ings (including weather stations) were located in the area thus providing a reasonably comprehensive set of supporting environmental data. This thesis presents the acoustical observations made during this experi-ment and interprets the more striking features of these data. Chapter 2 pro-vides a background on the use of acoustics for the study of near surface ocean processes, Langmuir circulation, ambient sound and wave breaking. T h e general concepts of the Craik-Leibovich model of Langmuir circulation are introduced there, but greater detail is left to Appendix A . Following this background, the initial objectives of the observation program are identified serving to explain my choice of instrumentation. T h e instrumentation itself is described in Chapter 3. A variety of conven-tional oceanographic instruments have been used in this study but the nature of their deployment is not discussed in great detail as they do not form the focus of the thesis. The acoustical instrument package itself represents a novel approach to studying near surface processes and 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. Through Chapter 3 several technical issues are raised which are detailed in a series of appendices. Appendix B describes the signal conditioning and data processing I developed for the various data types. Also described i n Appendix 6 B is the Zoran VSP-161 vector signal processing system for which I developed software to analyze all the recorded data. Appendix 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 in Appendix D . Appendix E explains the processing and calibration I incorporated for ambient sound data. F ield observations are presented i n Chapter 4: general observations are first presented followed by a detailed description of the various data types. Al though 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 and demonstrates the progressive changes to the subsurface bubble clouds. The influence of Langmuir circulation is clearly demonstrated in the data and several characteristics of this phenomenon are presented. Ambient sound data were collected with the intention of investigating any relationship between wave breaking and Langmuir circulation but no significant interdependence could be found. Instead, these observations identified the oc-currence of modulations at surface wave periods in 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 in phase with the wave motions directly above the recording position. I have investigated the implications of this observation with the aid of a simple model of sound generation. Through-out this analysis, I have extracted surface wave observations from upward look-ing sonar: details of this technique and its accuracy are presented in Appendix F . T h e most striking characteristic of the sidescan data is the coexistence of many scales of Langmuir cells and the evidence for much smaller scales than 7 are normally seen in the open ocean. T h e Craik-Leibovich theory of Langmuir circulation does not explicitly predict the presence of many coexisting scales or the presence of these very small scale structures. Chapters 6, 7, and 8 explore a possible explanation for this observation based on the consequences of a two dimensional upscale cascade of vorticity. First , in Chapter 6, I introduce an alternative mechanism for the source of this vorticity based on 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 gener-ated by the Craik-Leibovich mechanism) with a two dimensional discrete vortex model which assumes only that the source of the vorticity has a small initial scale and is introduced close to the surface. Chapter 7 describes the details of the model as I have implemented it, and Chapter 8 describes the results of model trials. Chapter 9 completes the thesis with a summary of results and observations and suggestions for future areas of research. C h a p t e r 2 B a c k g r o u n d 8 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 pro-vide 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 so-lution 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 ambi-ent 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), and Johnson and Cooke (1979), used photography to determine bubble size distribution. Medwin (1970) was first to apply acoustics to the measure-ments of bubble distributions. These studies revealed that the time averaged distribution of bubble density decreased exponentially with depth (Wu 1981). T h e time averaged distribution of bubbles can be useful in estimating gas exchange with the atmosphere, but it does not reveal much of the dynamics driving the exchange process. T h e short term behavior of subsurface bubbles can better be studied by the use of upward looking sonar such as used by Thorpe et al. (1985), Thorpe (1986) and Crawford and Farmer (1987). These studies have demonstrated that the subsurface bubble distribution is character-ized by dramatic changes in bubble penetration depth. In fact, the bubbles are seen to form localized clouds or plumes rather than a continuous horizon of bubbles. Thorpe and Hall (1983) mounted a sidescan sonar system on the sea floor and directed the beams upwards along the surface. W i t h the sidescan in this configuration, the horizontal distribution of bubble clouds was clearly revealed. Individual wave breaking events could be identified by the sudden appearance of a bubble patch on sonogram images. These patches of bubbles are seen to be advected by the local surface currents after they appear. In one particular set of data, they observed many long narrow rows of bubble plumes which were coincident with the observation of windrows on the sea surface. This observation is very important because it demonstrates that upward looking sidescan sonar can be used to observe Langmuir circulation. In addition, it implies that the intermittent clouds of bubbles seen by Thorpe (1982), and Crawford and Farmer (1987), were caused by Langmuir 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 L a n g m u i r Circulat ion 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 Lang-muir (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 acous-tic observations. Together, these studies have established the essential charac-teristics 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 and have vertical speeds of the order of 1% of the wind speed. Coincident with the vortex motion are down-wind components of velocity which are greatest in 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 wind speeds as low as 3 ms-1. If a shift in wind direction occurs, the Langmuir cells will reahgn themselves with the wind direction (again) within a few minutes of the change. Figure 2.1: Circulation pattern associated with Langmuir circulation. 12 T h e spacings of the cells are not always regular, in fact there is often a hierarchy of scales (Assaf et al. 1971, Harris and Lott 1973, Smith et al. 1987). T h e cells will form even i n the presence of a stable density profile (Smith et al. 1987) although there is evidence that stability conditions may influence the penetration depth and shape of the cells (Thorpe 1982). T h e depth penetra-tion of the circulations is ultimately limited by the first significant pycnocline. Leibovich (1983) notes that the aspect ratio of L/2D for the largest cells is observed to be approximately 1 where L is the distance between convergence zones, and D is the mixed layer or bottom depth. Despite the more than adequate observational description of Langmuir cir-culation, plausible theoretical models have only appeared quite recently. These models are all wave current interaction models; one proposed by Garrett (1976), and the Craik-Leibovich models (summarized by Leibovich 1980). T h e Garrett model is heuristic in nature and can be summarized as fol-lows. If a wave breaks, it transfers some momentum into the water and in-troduces an increased velocity component in the down wind (wave) direction at the point where the wave broke. A s other waves pass through this lo-cal current anomaly they are slightly refracted inwards, producing a region of somewhat increased wave energy. Garrett then assumed that the frequency of wave breaking was proportional to wave energy. This assumption imphes an increased probability of wave breaking in the region of the initial current anomaly reinforcing that anomaly. The wave field would be focused inwards from either side, producing a convergence zone due to the opposing Stokes drifts. T h i s convergence results in a downwelling region under the current anomaly providing a driving force for vortex-like Langmuir circulation. Obser-vations of increased wave height in the windrows by Myer (1971) support the 13 Garrett model; however, Thorpe and Hall (1982), and Kenney (1977) both report no preferential wave breaking in windrows. Both variations of the Craik-Leibovich model are based on the same equa-tions: they only differ in the mechanism by which the Langmuir circulation is driven. These models describe the generation of Langmuir cells resulting from interactions of the surface currents with vorticity associated with the wind stress and Stokes drift. These interactions can be seen from one of the simpler developments by Craik and Leibovich (1976) which is outlined in Appendix A . From this development, the vorticity equation a ^ i + r!—- +(—- = v-^ + w-^- 2.1 ay az ay oz results. Using the coordinate system displayed in Figure 2.1, where (i,r),() is the vorticity, us is the unidirectional Stokes drift (aligned in the downwind direction), (u, v,w) is the mean surface current (excluding the Stokes drift), and a is a scaling factor for the eddy viscosity. T h e term a V 2 £ represents the diffusion of vorticity, n ^ - + C^£r represents the deformation of vortex hnes by the Stokes drift, and -f Wjf£ represents the convection of vorticity. In one solution to Equation 2.1, Craik and Leibovich (1976) consider a free surface boundary condition with a directionally symmetric wave field, and assume no motion at infinite depth. (Leibovich (1983) labels solutions based on this approach the C L - I mechanisms: this label will be used here in the inter-est of consistency.) Streamlines based on this formulation agree very well with the observations of Langmuir circulation. T h e solutions exhibit convergence at the location of maximum downwind current, vortices aligned parallel to the wave/wind direction, and more intense downwelling than 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 remain phase locked for many cycles to produce cross wind variations in the Stokes drift: a condition which is very unlikely to be met in a real sea. Faller (1978) however has demonstrated that such circulations can be set up in a laboratory wave tank. Leibovich (1977) solves the problem from the point of view of stability (following Leibovich 1983, this approach will be referred to as the C L - I I mech-anism). T h e requirement of crossed wave trains is relaxed, and both wind stress and stratification are considered. W h e n subject to an initial perturba-tion, Leibovich demonstrates that under most conditions the disturbance will grow until viscous effects balance the driving force. The streamlines for this solution are basically the same as those of the C L - I solution since both models are based on the same equations. This model estabhshes a preferred length scale for Langmuir cells which for most conditions is of the same order as the dominant surface wavelength (Leibovich and Paollucci, 1981). There 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 in 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 can be observed on the ocean. It is involved in the transfer of momentum from the atmosphere to the ocean, the introduction of air bubbles into the ocean and 15 therefore air-sea gas exchange, and the generation of turbulence which mixes the ocean surface. The process of wave breaking is highly non-linear making theoretical analysis difficult, and because there are no automated methods for observing wave breaking in the conventional sense, experimental studies are expensive and time consuming. It is for these reasons that ambient sound studies of wave breaking hold so much promise for future studies. Wave breaking studies are normally restricted to visual observations of white capping (Monahan and O'Muircheartaigh, 1980) which do not lend them-selves to quantitative comparisons with theory. The understanding of many characteristics of wave breaking could benefit from further field investigations. First and foremost are the interactions between waves that ultimately deter-mine the limiting wave spectrum in a wind forced sea (Phillips 1985). Phillips (1981) describes how short waves can be modified by long waves and this mod-ification bears on the problem of how short wave breaking might lead to long wave growth (Garrett and Smith 1976). Donelan et al. (1972) reported wave breaking in wave groups, acoustic evidence for which was found by Farmer and Vagle (1988). The characteristics of wave breaking may also play a role in the presence of secondary flows (ie. Langmuir circulation) in the upper ocean. The association of ocean ambient sound with wave breaking was first sug-gested by Wenz (1962). This association is clearly demonstrated by field ob-servations of Farmer and Vagle (1988), and laboratory tank studies of Banner and Cato (1988). Despite this clear relationship, the actual mechanism of sound generation is not well understood. T h e experiments by Banner and Cato (1988) and theoretical studies by Medwin and Beaky (1989) suggest that cre-ation of air bubbles is important to the sound generation. In contrast, analysis 16 by Guo (1987) suggests that this mechanism is unlikely because the presence of surface images associated with any subsurface sound source would severely re-strict the acoustic source level of such a mechanism. They suggest that sound is generated by spray droplets striking the water surface. A s well as being associated with wave breaking, overall sound levels have been found to vary in strict proportion to the wind speed as first reported by Knudsen et al. (1948) for frequencies of 100 H z to 25 kHz. M a n y subsequent studies have demonstrated this relationship (Wenz 1962, Evans et al. 1984, Lemon et al. 1984). Vagle et al. (1990) provide an empirical relation which makes possible the accurate estimation of wind speeds from ambient sound levels. There are clearly many aspects of wave breaking and the associated gen-eration of ambient sound which invite further investigation. In particular, the combination of ambient sound observations with 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 (and failure) of previous studies it has become quite clear that to make any progress in studying mixed layer dynamics, observa-tions of many contributing processes must be made simultaneously. T h e Ocean Storms program provided an ideal opportunity for such a study because of the diverse observational program being arranged in this large collaborative effort. M y objective within this framework was to make a thorough acoustical survey of upper ocean processes. While trying to make the observation program as 17 general as possible, I have focused special attention on recording the interac-tions of wind forcing, wave breaking, and Langmuir circulation. Observations by Weller and Price (1988) have demonstrated that vertical velocities as great as 0.3 m s - 1 can occur in the mixed layer in the presence of Langmuir circulation. A s well, it is obvious that in order for bubbles generated by wave breaking to penetrate to depths of 10 or 20 m as seen by Crawford and Farmer (1987), some significant vertical velocities must exist. Knowledge of these vertical velocities is crucial to understanding the energetics of these near surface processes. Direct measurements of these velocities are possible (as demonstrated by Weller and Price 1988), but 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 pro-files remotely and from a relatively small platform. Such observations are a logical extension to simple echo sounder measurements and can provide a very important contribution to the present enquiry. Observations by Thorpe and Hall (1983) demonstrate that sidescan sonar can provide a graphic view of the organization of subsurface bubbles by near surface currents. Thorpe and H a l l (1983), and Smith et al. (1987) have made observations of the windrows of Langmuir circulations with sidescan sonar sys-tems. Smith et al. (1987) used Doppler sonar techniques with sidescan sonar systems to make current velocity estimates within Langmuir cells. For the present study, these systems could greatly increase the understanding of near surface processes. Aside from acting as tracers of near surface water motions, subsurface bubbles are important in themselves for the role they play in ocean atmosphere 18 gas exchange. These bubbles are generated by the breaking of waves, making this process of interest to the present study. Wave breaking is also of possible importance to the generation of Langmuir circulation (Leibovich, 1983). Farmer and Vagle (1988) have demonstrated that ocean ambient sound fluctuations can be used to monitor wave breaking activity. In addition, ambient sound observations provide an accurate measure of surface wind speed in the open ocean (Vagle et al. 1990). T h e previously cited studies demonstrate a range of important processes occurring in the upper ocean and provide some clues on how they might be observed. One problem common to the acoustical studies has been the need for large power supplies and a large data recording capacity. These problems have forced the use of deployment platforms which are less than ideal in 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 in the deep ocean. To make the range of observations of demonstrated importance upward looking sonar, sidescan sonar, and ambient sound recording systems were required. Vertical sonar is useful in providing details of subsurface bub-ble concentrations, surface wave action, and vertical velocity profiles (through Doppler processing). 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 and to determine local wind speed. There were several processes of known importance that the acoustics pack-age could not monitor (or had not previously been used to monitor). These included surface wave data, wind speed, pycnocline depth, and ocean 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 auton-omy and convenience, an effort was made to make local observations of these parameters by using various conventional instruments. 20 C h a p t e r 3 I n s t r u m e n t a t i o n M y objective for the acoustic observations during the Ocean Storms ex-periment was to characterize the dynamics of the ocean surface as completely as available resources and instrumentation would allow. Conventional oceano-graphic instrumentation was used to measure wind speed and direction, the one dimensional surface wave field, current shear and temperature across the ther-mocline. Acoustical methods were used to determine vertical velocities within the mixed layer, surface wave characteristics, the horizontal and vertical dis-tribution of subsurface bubbles, and ambient sound levels. This chapter will describe the implementation of instrumentation during the Ocean Storms ex-periment, and for the acoustic systems provide some details on system capabili-ties. The Ocean Storms environment placed several specific requirements on the deployment of acoustic instrumentation. 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 operating at 200 k H z and 50 k H z , two orthogonally oriented sidescan sonars operating at 100 k H z , and a hydrophone for detecting ambient sound levels at 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 and Vagle (1989). However, no attempt was made to infer bubble size distributions with this data set. Only the 200 k H z system has been used in subsequent analysis and 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 Doppler techniques to the vertical sonar systems. 3.1 Instrument Deployment T h e need to place acoustic instrumentation, on a stable platform close to the ocean surface in deep water poses a significant deployment challenge. A solution to this problem was developed for a similar project during the 1985 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 acous-tic instrumentation positioned at 20 m depth. T h e data collected with this configuration during F A S I N E X demonstrate that the rubber cord effectively de-couples the large surface wave motions from the instrument package and 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. Video camera records and the ambient sound data from F A S I N E X showed that the elastic tether allows the buoy to follow the surface waves without creating significant agitation or acoustic emissions. F ig-ure 3.1 demonstrates 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 and ther-mocline shear were required in addition to the acoustic observations. These 22 B a l l a s t 1 9 2 m A Figure 3.1: Deployment configuration of the acoustics platform. Two orthog-onally 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, and placing Interocean S4 current meters at 41 m and 125 m depths spanning the thermocline depth of 50 m . (The S4 current meters were chosen because of their ability to operate 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 with heights of 1.45 and 1.1 m. These were mounted within a 2.0 m tall open instrument cage with 1.2 m diameter closed plates at each end. T w o stabilizing fins extending from the package axis out to 0.9 rn radius and separated by 6 0 ° were mounted to maintain the package in a stable orientation. T h e package configuration is sketched in Figure 3.3 identifying the placement of acoustic transducers and various sensors used for recording package orientation. A significant portion of the instrumentation associated with the acoustics package (Figure 3.2) was included to insure that the instrument positioning and recovery operations were fail safe. Specific areas of concern were the need to locate the instrument array in rough weather and to recover it in the event that a failure should occur at some point in the array. The first of these concerns was addressed by fitting an Argos satellite beacon onto 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 metre depth. As a result, any failure of a buoyant element or the parting of a cable (the rubber cord in particular) 24 Radio Beacons Waverider Buoy SL n .- 6 192 m — Acoustics Package Current Meter 3 Floatation 6 []• Current Meter Locator Beacon Floatation Pressure Release Floatation Acoustic Release Ballast Figure 3.2: Diagram of drifting instrumentation package identifying the vari-ous instrumentation and depth placement. 25 Mooring Ring Pressure Compass 0.5m Sensor Figure 3.3: Details of acoustic instrumentation platform. 26 would cause the lower part of the array to be lost. T o avoid this consequence, a pressure sensitive release was included in the array. If the array were to sink, the pressure release would part allowing the acoustic release (a high pressure model) to sink to the bottom with the ballast, but leaving the rest of the mooring to rise to the surface. A "witness" buoy would rise to the surface uncovering a separate Argos beacon, V H F beacon, and strobe. T h e appearance of transmissions from the normally submerged Argos beacon would provide notification of a system failure and assist in recovering the instrumentation. W i t h luck, the high pressure acoustic release could be located by means of its acoustic transponder and could be recovered separately. 3.2 Instrument M o t i o n T h e sonar data are sensitive to platform motions because they are used to make measurements of speed and distance. Even though an effort was made to provide a stable platform, not all motions could be eliminated and a record of platform motion was needed to allow for data interpretation. For this purpose, two axes of instrument tilt, vertical acceleration, and 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 - 1 , is displayed in Figure 3.4. T h e vertical displacement and vertical velocity shown in Figure 3.4 were both determined by integration of the vertical acceleration data subject to a 0.02 Hz high pass filter. 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 in phase with the surface displacements. This behaviour indicates that this motion is due to residual wave action at 27 Vertical Displacement 11:45:00 11:46:40 11:48:20 11:50:00 t i m e ( U T C ) Figure 3.4: 5 minute time series of the instrument attitude starting at 11:45 U T C , 27/10/1987. a) sea surface displacement in metres, b) instrument vertical deviation about mean depth (derived from accelerometer record), c) instrument vertical velocity (derived from accelerometer record), d) X component of tilt, e) Y component of tilt, f) instrument heading relative to true north. 28 30 m depth and not to the forcing from the elastic tether. This observation is consistent with the forcing terms acting on the package: the vertical force due to extensions of the rubber cord has a maximum value of about 100 N which is insignificant when compared to the 1600 N amplitude drag forcing which can arise from residual wave motion at the instrument depth. The tilt meters (Figure 3.4d and e) similarly show periodic motions at surface wave frequencies, they show a mean tilt of about 1 .5° with periodic deviations having amplitudes of about 2 ° and reach a maximum tilt of 5° coincident with the passage of a large wave group. T h e instrument tilt is consistent with directional changes in tension as the surface float is advected horizontally by the passing surface waves. The compass record shown in Figure 3.4f (accurate to about ± 2 ° ) shows that the instrument heading maintains a mean bearing with variations of 5° or 10° occurring over periods of about 1 minute. In contrast to the vertical motion and tilt there is little indication of surface 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 W i n d S p e e d M e a s u r e m e n t s W i n d 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. A meteorological buoy was deployed in the vicinity of the acoustics package to provide wind speed and direction measurements for comparison with 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 in-formation is provided, the sampled space is restricted by the transducer beam pattern and for the active sonar systems, further spatial definition is achieved through timing and the acoustic pulse length. T h e vertical sonar system will be described first because it requires consideration of all sonar characteristics thereby introducing all of these topics. The sidescan sonar and ambient sound systems can then be considered, without detailed background on any of the operating parameters. T h e system characteristics are summarized in Table 3.1; all of the parameters identified i n Table 3.1 will be defined through descrip-tions of the the individual sonar systems in the following section. 3.4.1 Vertical Sonar The choice of sonar operating frequency involves a compromise between several competing factors. High frequencies allow for better range resolution and Doppler performance but are limited in maximum 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 and so provide ade-quate acoustic backscatter. For the vertical sonar system, a 200 k H z operating frequency was selected which responds to 32 fim diameter bubbles of which significant numbers are expected in near surface bubble clouds (Farmer and Vagle 1989). A n I T C model 5298 transducer (serial number 2) was used to provide a narrow acoustic beam. 50% of the energy transmitted by this transducer is 30 Sonar Frequency Ping 3 d B Beam Pulse Range Rate width Length Resolution k H z H z ms m Sidescan 100 2 2 ° x 5 0 ° 0.1 .075 V-Sonar 200 6 3° 2.6 2 Ambient 2-20 - 3 6 0 ° - -T a b l e 3 .1 : Sonar operating parameters projected along a beam of 3 ° width (this angle is the 3dB beam width) and ensonifies a disk of 3 m diameter at the surface of the ocean. The frequency response of this transducer is wide compared to the bandwidth of the recording system used and so the bandwidth of the data is restricted to 22 k H z . The transducer beam can only constrain the direction of data sampling and a pulsed active sonar system is required to provide range discrimination. W h e n 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 and the time elapsed. Depending somewhat on temperature and salinity, the speed of sound in water is about C = 1475 m s " 1 . A t any time t after a pulse of sound has been transmitted, the acoustic backscatter will be received from a 31 distance d = Ct/2. 3.1 For the present application, Equation 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 from 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 fac-tor is imposed by the recording technique: the data rate must be reduced by half because both 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 be seen by using Equation 3.1 to determine the range of acoustic backscatter for both the leading and trailing edge of an acoustic pulse. T h e signal received at any time must come from some point in between these boundaries. For a pulse of length r transmitted at time t = 0, the acoustic backscatter at time t after the start of transmission must come from a range, C(LII) < P < 0 e i . 3.2 2 ~ ~ 2 T h e range interval indicated by Equation 3.2 results in a range uncertainty of for the range estimated to any acoustic scatterer. Range resolution can be controlled by adjusting r so long as there is sufficient acoustic backscatter power to be distinguished from noise levels. For general echo sounder applica-tions very short pulse lengths can be used (in practice down to about 0.01ms), 32 but in the present application where Doppler processing is intended, velocity resolution must also be considered. W h e n sound is transmitted and reflected from moving bodies its frequency becomes Doppler shifted; it is this effect which allows remote velocity mea-surements to be made acoustically. For a backscatter system, the frequency of sound returning to a transmitter will be shifted by an amount, where / is the acoustic frequency, v is the relative velocity between the trans-ducer and scatterer, and C is the speed of sound: this relation can be used inversely to determine the speed of a scatterer. Equation 3.3 is only strictly valid for a single frequency but a modulated pulse composed of many frequen-cies must be used to provide finite range resolution (as dictated by Equation 3.2). Theriault (1986) demonstrates that this finite frequency bandwidth leads to a velocity uncertainty of, C ATVJT. Considering Equations 3.2 and 3.4 it is clear that fine range resolution is not compatible with fine speed resolution and some compromise is required. This problem is considered in more detail in Appendix C . For the present application, a pulse length of 2.6 ms was chosen providing a range resolution of 195 cm and a single sample velocity uncertainty of about 0.23 m s - 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 can be rapidly reduced through averaging. 33 Both the velocity and range estimates of the vertical sonar are made rel-ative to the instrument package and so are contaminated by motions of the instrument package. Motion of the package along the sonar axis introduces that velocity directly into the sonar velocity estimates. T o remove that veloc-ity component, the accelerometer 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. The accelerometer data was sim-ilarly used used to correct range estimates for instrument motion. Instrument tilt will cause horizontal current components to be resolved along the axis of the vertical sonar beam. No correction could be made for such errors even with knowledge of the instrument tilt because only one component of velocity is measured in the present application. 3.4.2 Sidescan Sonar Sidescan sonar systems are most commonly used to display the distribu-tion of structures on the ocean floor. T h e present application is similar, only the entire system is turned upside-down to look at bubble clouds along the ocean surface. No attempt was made to develop this hardware for the present application; the transducers and amplifiers from an E D O Model 606, 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 and 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. (The E D O transducers have a 3 dB beam width that is 5 0 ° in the vertical and 2 ° in 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 fan beam intersects the plane surface. In effect, the beam shape provides the horizontal resolution, while the surface provides the vertical res-olution. Equation 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 Appendix 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 be collected except that imposed by the signal to noise limitations and sonar power. For the sidescan system as deployed, the maximum usable range was approximately 200 m . Based on Equation 3.1, 267 ms of data are required for sound to return from such a range, and so this requirement limits the maximum sample rate of the sidescan sonar. It was not desirable to have the various sonar transmission rates independent of each other because any sonar transmission would contaminate data on all other sonar systems. T h e vertical sonar systems were operating with a cycle time of 160 ms. The sidescan systems were therefore operated at one transmission every 480 ms. A single sidescan beam can only provide information projected onto the spatial component defined by the beam axis. For the study of bubble clouds, it is of value to know how structures are organized in two dimensions. Two sidescan transducers were oriented orthogonally to each other (as is indicated in Figure 3.1 and will be further discussed in Chapter 4). 35 3.4.3 Ambient 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 wind stress, breaking waves, and rain (Knudsen et al. 1948). Sound levels must be recorded over a broad band of frequencies in order to study the general characteristics of these sounds. For this application, an I T C 6050C hydrophone was employed as it has a flat frequency response for signals between 2 kHz and 40 k H z and an om-nidirectional response. Because the ambient sound recording system is not an active sonar, the pulse travel time delay (Equation 3.1) cannot be used to determine the range to a source. A l l that is known about a source location is that it must lie somewhere within the angular receiving area of the hy-drophone. The localization of ambient sound sources at the ocean surface leads to somewhat finer spatial sampling due to the dipole characteristic of near surface sources (Vagle et al. 1990). For the hydrophone placement at a given depth, a circular region at the ocean surface centered above the hydrophone location can be identified as providing 50% of the received signal power (analo-gous to the 3dB beam pattern for a transducer). For 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 to ambient sound and so the data can be recorded continuously. Although the active sonars are removed in frequency from the ambient sound system, the high power transmissions contaminate the ambient sound data and so these portions of the data must be discarded. Prior to system deployment, it was not known if good 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 in this situation. In fact, ambient sound data could be recovered at all times (using the techniques described in Appendix E ) and so continuous ambient sound data were recorded. Although the hydrophone responded to frequencies as high as 40 k H z , the data was recorded digitally at a 44 kHz sampling rate. To accommodate the 22 kHz bandwidth of the recording system, the data were filtered to eliminate frequen-cies 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. O n l y the data rates used and some of the considerations leading to the choice of those data rates will be discussed. In contrast, the recording techniques used for the acoustical data are quite novel. T h e essential characteristics of these recording techniques will be discussed here, but details of these procedures are presented separately in Appendices B , C , D , and E . 3.5.1 Conventional Instrumentation T h e time scales of interest during the instrument deployments were of the order of minutes for a period of about a week. The recording rates for the various instruments needed to be as rapid as possible consistent with the recording media available and the power supply of the instruments. The choice of sampling rates was selected based on this requirement; these are summarized i n Table 3.2. T h e data recording for the Datawell Waverider buoy was modified some-what to meet the conditions encountered during the Ocean Storms program. 37 Instrument Depth Sample Period m s Waverider 0 .5 S4 C / M 41 30 S4 C / M 125 30 Met . Stn. 0 5 T a b l e 3.2: Data recording rates. T h e Waverider buoy is normally used in a near shore configuration in which it transmits a continuous record of wave data to a receiving station on shore. Such a configuration could have been used in the present application if an attending ship had been available to provide a reliable receiving station, but such a ship was unavailable during the deployment. This problem was over-come by installing a Seadata model 639-8 Wavelogger recording package in the Waverider buoy thereby converting the system into a self-contained package. This approach restricts the Waverider resolution from that realized by the buoy itself because of the finite storage space available and 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 Data T h e recording requirements of the acoustical data provided several sub-stantial challenges not the least of which was the volume of data itself. There 38 are four separate sonar systems (two vertical sonars, the sidescan sonar, and an ambient sound hydrophone) each generating data with a characteristic band-width of order 10 kHz. In addition, in order to meet the objectives of the Ocean Storms project, a capability of continuously recording for a period of several days was required. These objectives were met by recording data with conventional V H S video cassette recorders ( V C R ' s ) combined with a Sony Pulse Code Modulation ( P C M ) digital interface. B y combining 10 V C R ' s each with an 8 hour recording capacity, the system was capable of recording data continuously for 80 hours. There are three types of storage formats available on a V H S V C R ; a video channel providing 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 bandwidth with a dynamic range of about 80 d B , and a low quality audio track. The ambient sound data were recorded onto one of the digital channels while the two vertical sonars shared the other. T h e 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 and instrument attitude) by means of a 2400 baud modem. There is little signal processing required to record most of the data: A p -pendix B provides details of such processing as is necessary. The 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 in Appendix C . This scheme allows both data channels resulting from a complex demodulation to be recorded with a sin-gle digitizer. There is a degradation in data quality with such a simplifying 39 approach: since both complex channels are stored onto a single channel, the bandwidth of the recorded signal is reduced from 20 k H z to 10 kHz. As a whole, the acoustical instrument package collects data at a rate of 176800 16 bit samples every second making it prohibitive to analyze all the data that this system could generate over a several week period. In addition, 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 and redeployed every 4 days. Such a procedure would not be possible in severe weather conditions and these are exactly the conditions of most interest in the study of near surface dynamics. T o overcome these problems, an acoustic release was modified to provide an acoustical control hnk with the instrument package. Through use of this system, the package could be controlled remotely from an attending ship and optimal use could be made of the system's recording life. C h a p t e r 4 O b s e r v a t i o n s 40 The acoustical observations presented in this chapter were made as part of the Ocean Storms project aimed at improving the understanding of the ocean response to storm forcing. This project involved a large array of long term ocean moorings as well as a series of ship surveys. T h e acoustical 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 ar-ray is described in Chapter 3: it consisted of a Datawell Waverider buoy, a platform of acoustic instrumentation, and two Interocean S4 current meters. T w o successful deployments of the acoustical instrumentation were made from C S S Parizeau during a survey cruise from October 12, 1987 until November 11, 1987. T h e first deployment lasted 21 hours beginning at 18:00 U T C October 26, and is characterized by a period of increasing wind speeds. T h e second was a more extensive deployment starting at 02:30, October 29 and lasting 157.5 hours during which 70 hours of acoustic data were collected. A drifting meteorological buoy was also deployed and provides wind speed data during the longer acoustics package deployment. A time hne identifying the periods of data collection with the various instruments is shown in Figure 4.1. In this chapter, observations from the first (21 hour) deployment will be considered in detail as they demonstrate the evolution of subsurface bubble 41 Ocean Storms Acoustic Data Parlzeau 1 2 ^_ Cruise 12:00 Acoustics 230 2130 23:15 17:00 H I — I h Platform raao 5:oo is:oo 1B:00 21:45 2 3 0 23:00 I 1 I 1 h Waverlder & S4 C/M'S 15:00 18K30 18:00 Met. Stn. Z 1 :^_ Aanderaa data 16,-oa i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 2 2 2 3 2 4 2 5 2 B 2 7 2 B 3 9 3 0 3 1 1 2 3 - 4 5 B 7 8 9 1 0 11 O c t o b e r 1 3 8 7 N o v e m b e r 1 9 B 7 F i g u r e 4 .1 : T i m e line identifying periods of data availability from various instrumentation groups (all times are in U T C ) . clouds while the wind speed increased from near 0 to 13 ms'1. In order to provide a perspective on the observations, an overview of wind speed, wave state, and average bubble cloud properties is first given in Section 4.1. Some discussion of measurement techniques is included in this overview where needed for a proper interpretation of the data. Section 4.2 describes the organiza-tion of bubble clouds as seen in sidescan and vertical sonar data. T h e pres-ence of bubble clouds below the surface indicates downward vertical velocities. These vertical velocities are investigated in Section 4.3 using acoustic Doppler 42 techniques applied to the vertical sonar system. Because these data must be heavily averaged in time to get the required velocity resolution, a conditional averaging scheme is employed to determine a velocity section across an ideal-ized (average) bubble plume. 4.1 Data Overview T h e data presented i n this chapter are drawn from a 21 hour period of increasing wind speed. A summary of the sea state and bubble cloud response to this wind forcing are given in Figure 4.2. The record of wind speed is important since it drives the energetics of the near surface processes. During this first deployment, the meteorological buoy had not yet been deployed and so accurate anemometer wind speeds were not available. W i n d speed estimates are instead obtained from the established relation between ambient sound levels and wind speed: 1QSSL0/20 _ b V = j . 4.! In Equation 4.1, V is the wind speed (corrected to 10 rn height), SSL0 is the ambient sound source level in a 1 Hz bandwidth about 8 k H z expressed in dB relative to a signal of \\iPa2/'Hz at 1 m range (ie. dB re lfiPa2/Hz), and S and b are calibration constants with values 52.87 fiPa/ms-1 and -80.94 pPa respectively. Using these constants Vagle et al. (1990) demonstrated that Equation 4.1 provides a robust measure of surface wind speed with an accuracy of about ± 0 . 5 m s - 1 in the deep ocean. W i n d speeds derived from Equation 4.1 are shown in Figure 4.2a, Figure 4.2b shows the ambient sound levels upon which these observations are based. 43 fi > 3 - 1 2 150 100 V Bubble Depth i 1 d 26/10 22:00 2 7 / 1 0 05:00 27/10 12:00 27 /10 19:00 t i m e ( U T C ) F i g u r e 4.2: Summary of observations for the 21 hour period beginning at 22:00 U T C , 26/10/87; a) 10 m wind speed (dashed line - anemometer speeds, sohd line - ambient sound based), b) ambient sound level (7 to 9 kHz) , c) significant wave height, d) average depth penetration of subsurface bubbles, e) depth integrated scattering cross section, Mv. Bars A , B , and C identify periods used to produce Figures 4.8a, b and c. 44 Near calm conditions occurred at the beginning of the deployment with speeds gradually increasing to a maximum of 13 m s - 1 . Additional wind speed ob-servations are available for this period from a meteorological buoy deployed as part of the long term Ocean Storms program which was located within 50 k m of the acoustic instrumentation at 4 7 ° 58' N , 1 3 9 ° 15' W (these data are shown by the sectored line in Figure 4.2a). These observations agree with the acoustically derived wind speeds: differences in the time and magnitude of small scale features are expected because of the distance separating the observations. The high frequency echo sounder on the instrument can be used to pro-vide an effective and accurate measure of sea-state. T h e errors that could be introduced by instrument motion in 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 us-ing a common clock: comparisons between Waverider and echo sounder wave records in this data set have demonstrated the accuracy of this approach (see Appendix F ) . Significant wave heights (E~i/3) are shown in Figure 4.2c; they increase gradually in proportion to the wind speed, but detailed features (such as the squall passing at 03:00) do not appear clearly in the wave records. Such insensitivity of - f f i / 3 is to be expected since it is dominated by the longer period waves. W h e n the wave data were filtered to isolate only the 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 and wave data: the average penetration depth of bubble clouds, and the integrated volume of subsurface bubbles. Figure 4.2d 45 shows a time series of mean bubble penetration depth. T h e general trend in these data is towards increasing penetration depth with increasing wind speed. T h e observed bubble depth of about 1 m which persists at low wind speeds is likely due to the presence of biological scatterers. 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 in the wind speed record. T h e bubble plumes subsequently disappear when the wind speed subsides, and do not reappear until the wind speed again exceeds 7 m s - 1 . This behaviour suggests that there may be a threshold wind speed of about 7 m s - 1 required before subsurface bubbles can be detected with the acoustic systems. A n indicator of subsurface bubble volume can be obtained by determining the scattering cross section per unit volume M „ , detected by a vertical echo sounder as described by Thorpe (1982): R2vh2e2nR M, = « J ^ _ , 4.2 where R is the range, uj is the output voltage recorded at the receiver, n is the acoustical attenuation due to chemical absorption (0.0131 m - 1 for 200 k H z sound), and Q is a constant scaling factor which accounts for geometry and sonar characteristics. The value of Q has not been determined for the sonar systems used and so Mv can only be used to indicate relative changes in bubble volume. Integration of Mv over each profile provides an indicator of the total volume of bubbles interacting with the particular echo sounder frequency (with diameters of order 32 fim for the 200 kHz sonar). T h e value of this estimator for the 200 k H z system is shown in Figure 4.2e; the verti-cal scale is arbitrary and 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 both times is similar. A more complete representation of the sea state development is seen in the evolution of wave spectra (Figure 4.3). Most of the wave energy is contained in the swell with period between 8 and 12 seconds. T h e waves generated by local wind forcing appear at around 12:00 U T C . T h e period 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 wind waves have achieved a period of about 8 seconds and waves of this period are the longest that the 13 ms-1 wind can generate based on wave speed (LeBlond and Mysak 1978). The 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 and Vagle (1988). In order to illustrate this relationship, power spectra of the modulations of the ambient sound field are displayed in the same format and scale as the wave spectra (Figure 4.4). Whenever there is an increased level of ambient sound, the spectra show a strong modulation at surface wave frequencies. This result differs from the coastal observation of Farmer and Vagle (1988) and visual observations by Donelan 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 increas-ing wind. Associated with the increase in wind speed is a rise in significant wave height and the appearance of shorter period waves. Subsurface bubble plumes with an average penetration depth of about 6 metres occurred when P o w e r ated waves to l o „ g e r P ^ ^ ^ n ^ ' J ^ ^ ^ ™ ^ 48 P o w e r 0 10000 i 1 — 1 1 , 1 — — p — 1 — • — " — 1 — 1 — " % 1 | 4 22:00 05:00 12:00 19:00 T i m e ( U T C ) 2 6 - 2 7 / 1 0 / 8 7 F i g u r e 4.4: Waterfall plot of ambient sound modulation spectra based on sound levels in the band between 5 k H z and 15 k H z for the 21 hour period beginning at 22:00 U T C , 27/10/87. T h e scaling in this figure is identical to that of 4.3 to aid comparisons. 49 wind speeds exceeded a threshold of approximately 7 ms-1. T h e presence of subsurface bubble plumes did not imply a large increase in the total volume of subsurface bubbles; total bubble volume does however appear to be well correlated with wind speed. 4.2 B u b b l e C l o u d Structure T h e sonar data, both vertical and sidescan, yield more detailed information on the structure and dynamics of the bubble clouds. T h e sidescan images provide an indication of the way in which subsurface bubbles are distributed along the surface, as first shown by Thorpe and Hal l (1983). Figure 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 beam oriented horizontally at approximately 1 9 0 ° true, and Figure 4.5b is from a beam oriented along 1 0 0 ° true. Details of the processing required to produce these figures is found in Appendix D . T h e wind speed at this time is 13 ms-1 from 1 7 0 ° true. To aid in the interpretation of these data, the 5 minutes chosen for display in Figure 4.5 corresponds to the period displayed in Figure 3.4 (page 27). T h e bands seen in Figure 4.5 are caused by discrete stable bubble groups, in Figure 4.5a these groups are slowly approaching the instrument package, while in Figure 4.5b their ranges remain nearly constant. Individual bands re-tain their identity for the 5 minutes displayed in Figure 4.5; in more extensive time series the bands remain distinct and coherent for periods of up to 20 minutes as they slope across 100 m of range in the sidescan image. This upper limit is constrained by the sonar's range (approximately 200 m) and by the 50 A c o u s t i c B a c l c s c a t t e r 11:45:00 11:47:30 11:50:00 T i m e ( U T C ) 2 7 / 1 0 / 8 7 F i g u r e 4.5: Example of 5 minutes of sidescan sonar data collected during 13 m s - 1 winds; a) is along the direction 1 9 0 ° true, and b) is along the direction 1 0 0 ° true. Instrument orientations for this period are shown 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). 51 speed with which they are advected through the beam. It is quite possible that they remain coherent over greater temporal and spatial scales. Surface waves travelling across the bands cause coherent periodic distur-bances which slope steeply across the sonar image. T h e disturbance is caused by the periodic wave currents advecting acoustical scatterers and the slope re-veals the phase velocity of the waves, resolved along the sidescan beam. A n example of such a disturbance is shown by line ' A ' in Figure 4.5a. This dis-turbance travels about 145 m in 5.8 s indicating a speed along line ' A ' of 25 ± 8 ms~1; this same wave is not apparent in the orthogonally oriented sidescan data of Figure 4.5b indicating that the true phase speed is about 25 ms~l i n a northerly direction. Large uncertainties in this calculation result from the difficulty in estimating the short time differences and the unsteady instrument heading (see Figure 3.4 page 27). T h e constant heading changes themselves cause a distinctive disturbance to these images; a simultaneous change in range is seen in all the scatterer bands with the degree of distortion depending on the range. A n example of this effect is identified by line ' B ' in Figure 4.5a and the 1 0 ° heading sweep that caused it is labelled ' B ' in Figure 3.4. Individual bands often retain their identity through such heading swings for as much 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 15° of the wind direction consistent with similar observations by Thorpe et al. (1985). T h e correspondence of the bands appearing in the sidescan images, with the bubble clouds familiar in images obtained using vertically oriented sonars, is illustrated with simultaneous presentations of both 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 8 metres. T h e arrival of scatterer bands at zero range in the sidescan sonar usually coincides with the appearance of a bubble cloud in the echo sounder data. Lines have been drawn up from the bubble plumes and along the mean slope of the sidescan image to associate bubble plumes with respective bands in the sidescan image. In considering Figure 4.6, the limitations of the sidescan sonar system must be born in mind. T h e distortions caused by instrument motions and wave action (identified in Figure 3.4) tend to blur the highly averaged sidescan data in this presentation. In addition, the poor range resolution characteristic at small ranges (cf. Equation D.2) makes identification of the exact arrival time of any bubble plume difficult. Because the slope of the bands in Figure 4.6 remain constant, it is possible to identify bands at greater distances and extend them along the prevailing slope to determine the arrival times. The bands and plumes are time evolving and finite in space so that in the sidescan image structures appear and disappear suddenly. In view of these limitations, it cannot be expected that a scatterer band could be identified for each bubble plume observed. The number of scatterer bands arriving is certainly compara-ble to the number of bubble plumes observed and in most cases a plume can be associated with a scatterer band, 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 T i m e ( U T C ) 2 7 / 1 0 / 8 7 F i g u r e 4.6: 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. 54 package relative to the drifting surface layer and projecting plots of the sides-can data onto a surface in 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 by Smith et al. (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 alterna-tive approach makes use of the current meter observations obtained from below the instrument at 41 m depth. If it is assumed that the water in the mixed layer moves uniformly with respect to depth, this velocity is a valid estimate of the relative motion between the bubble clouds (in the mixed layer) and the instrument package. This assumption is only an approximation, both the 3-dimensional structure of Langmuir circulation and shear associated with Stokes drift are being ignored. Current meter measurements through the mixed layer show that the effects of Langmuir 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 by the passage of successive Langmuir 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 in the instrument drift velocity. Figure 4.7 shows a subsurface bubble map created using sidescan data transformed by this method based on current meter records for an interval of 50 minutes. T h e resulting map is not as clear as the original sonograms because wave motion and temporal changes smear the location of the targets. 55 This particular example was selected because the image created above and be-low the instrument track are produced by individual (separate) beams allowing a direct comparison of their respective maps. It is obvious that the images cre-ated by the beams are qualitatively consistent showing an elongation of bubble plumes along a direction of about 1 6 0 ° . About midway across the map, the instrument speed and direction change abruptly, resulting in some distortion, but the gross features are preserved and thereby demonstrate the viability of the procedure. Uncertainties in the navigational data preclude accurate com-parisons of row alignment with wind direction. T h e image presented in Figure 4.7 does demonstrate that bubble clouds are collected into 10 m wide paral-lel bands with length of about 100 metres and separated from each other by about 10 m . It is immediately tempting to associate these bubble plumes with the windrows of Langmuir circulation (Langmuir 1938). Similar banding in sidescan sonograms was reported by Thorpe and Hall (1983) who observed windrows (caused by Langmuir circulation) in coastal waters. Smith et al. (1987) have also seen evidence of Langmuir circulation with sidescan sonar. Thorpe (1984a) assumed that bubble plumes visible in an upward looking sonar were caused by passing Langmuir cells; these data support that assumption. Further support for the association of the bubble rows with Langmuir circulation can be obtained by determining their orientation with respect to the wind. If the rows are caused by Langmuir circulations they are expected to be aligned with the wind direction (Leibovich 1983). For the example of Figure 4.7 the bubble plumes are oriented approximately 1 6 0 ° true, and the wind direction was from 1 7 0 ° consistent with that expected for Langmuir circulation. 56 Acous t i c B a c k s c a t t e r (dB) 0 12 160 3 2 0 X P o s i t i o n ( m ) F i g u r e 4.7: 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. Bubble 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 with the sidescan sonar over an extended period. These scales are most easily measured off the sidescan sonograms (rather than the corrected surface maps) because of the greater clarity of the sonograms. T h e spacings measured from a single sidescan beam are the cell spacings projected onto that beam. To estimate the actual spacings it is assumed that the two orthogonal sidescan beams sample windrows which have the same distribution of spacings and consequently the same mean spacing. B y comparing the mean spacing observed by each of the two beams, the orientation of the beams relative to the windrows can be determined, and the distributions can be corrected for orientation. Figure 4.8 shows three cell spacing histograms accumulated as the wind speed increased from near 0 to 13 m s - 1 . T h e observation intervals used in making these histograms are indicated in Figure 4.2a: the wind speeds of < 7 m s - 1 , about 10 m s - 1 , and > 10 ms~l correspond to histograms of Figure 4.8a, b and c respectively. A t wind speeds below 7 m s - 1 (Figure 4.8a), the cell spacing ranges from 1 to 10 m with a mean of around 4 m. T h e observed spacing shifted to larger scales with increasing wind as shown by the histograms of Figure 4.8b and c. W h e n the wind increases to greater than 10 m s " 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. These histograms agree in general with those presented by Thorpe and Hall (1982) based on temperature anomalies seen by a towed thermistor chain. A characteristic of Langmuir circulation predicted by some theories is a difference i n wave heights occurring in windrows from those occurring elsewhere 58 o a 0 u 0 0 o 1) > 100-75-50-0) 0) u Cl u o 0 o 25-0-100-75-50-| 25-0) •>—' 0 d In CJ 0 o > • rt (fl o-100-75-50-25-a) U, 0 < 7 m/s b) U l 0 = 10 m/s L T L c) U,o > 10 m/s « 0-r -L 5 10 15 S p a c i n g ( m ) 20 F i g u r e 4.8: Histograms of windrow spacing based on sidescan sonar data. Observed winds were less than 7 m s - 1 (4.8a), about 10 m s - 1 (4.8b), and greater than 10 ras-1 (4.8c). T h e time intervals over which the histograms were accumulated are shown by bars labeled A , B , and C in Figure 4.2a. 59 (Leibovich 1983). To test for this characteristic, root mean square (rms) wave displacements were determined from the vertical sonar, using data for which bubble clouds were seen to penetrate to greater than 5 m depth, and 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 an indication of the presence of a windrow. Values were accumulated over 2 hour periods starting at 07:00 U T C and continuing to 19:00 with no significant differences appearing between the two rms values (Table 4.1). Data from before this period did not have sufficient occurrences of deep bubble plumes to allow accu-rate estimates. Time ( U T C ) In Windrow 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 T a b l e 4 .1 : R M S wave displacements inside and outside of windrows. 4.3 V e r t i c a l V e l o c i t i e s The windrows of Langmuir circulation form at local convergence and downwelling sites. We therefore expect to observe downward velocities coin-cident with the bubble plumes. T h e Doppler processing of vertical sonar data 60 as described i n Appendix C allow estimates to be made of the vertical com-ponent of these currents. This technique does have the advantage of making remote non-invasive velocity estimates, but the accuracy is limited by sonar system characteristics as outlined i n Appendix C . The random errors present in the data caused by instrument noise and the Doppler sampling can be reduced by averaging. The observations show a standard deviation of about 0.75 m s - 1 , which is consistent with the ex-pected uncertainties caused by wave motion (1.2 m s - 1 ) and incoherent Doppler sampling (0.25 m s - 1 ) . Mean velocity estimates with accuracies of about 0.01 ms~l are needed requiring the averaging of about 1000 individual speed pro-files. Such an 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 period required. In order to create a velocity section representative of the velocities i n a bubble plume a conditional averaging scheme was employed. Unaveraged ve-locity profiles (generated at a rate of 6 Hz) were accumulated into one of 6 profiles depending on the depth to which bubbles were observed. For example, if bubbles penetrated to 4.5 metres in a velocity profile, that entire profile would be added into the average profile for bubbles penetrating to between 4 and 6 metres depth. Using this method, the observations from hundreds of bubble plumes could be accumulated into one representative average. This method does include all plumes that might be created by processes other than Langmuir circulation (such as wave breaking). Also, the plumes are as-sumed horizontally symmetrical as no distinction is made between regions of 61 increasing or decreasing bubble depth. To add 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 of an averaged velocity and scattering cross-section 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 . Those regions of the section for which there was no acoustical backscatter on which to base speed estimates have been left blank. T h e data displayed are based on an array of 6 horizontal profiles (doubled by reflection across the center location), and 6 bins spaced equally in depth. The velocity estimates in these bins have statistical uncer-tainties of about 0.01 ms-1 and none are greater than 0.02 m s - 1 . In spite of the sparse section that results, the general form agrees well with that expected for Langmuir cells (Leibovich 1983): downward vertical velocities are observed near the center of the plume with the magnitudes decreasing towards the edges of the plume. The maximum vertical velocity occurs at 8 metres depths, with values of about 0.06 m s - 1 at 8 metres. Although these seem to be large mean vertical velocities so close to the surface, they are nevertheless consistent with observations made by Weller and Price (1988) who found vertical velocities of 0.3 m s ' 1 at 20 metres depth. Accurate averaged velocity profiles could only be created from data col-lected during winds of 7 r n s - 1 or greater: at wind speeds below this level the reduced bubble concentration provided inadequate signal levels for the Doppler processing. W i t h i n the limited range of wind speeds during which averaged vertical velocity sections could be obtained there was no significant change in downwelling magnitudes. 62 Averaged Section R e p r e s e n t a t i v e P o s i t i o n ( m ) F i g u r e 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. 4.4 D i s c u s s i o n T h e short period of data displayed in this report hints at some intriguing relationships between wind speed, sea state, and subsurface bubble activity. T h e data demonstrate the expected relationships between wind 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. The 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 scat-tering and 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 . The observations of vertical velocity are subject to several biasing terms due to instrument tilt and coupled motion (as discussed in Appendix C ) . How-ever, an analysis of these bias terms suggests that any such bias would be towards upward velocities. This fact provides increased confidence in the down-ward components reported and suggests that even these may be underestimates of the true values. Additional confidence in 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 Langmuir cells, but the ability to obtain useful measurement is limited by the absence of scatterers in these regions. A conditional sampling scheme based on data from all bubble plumes has been used to determine the vertical velocity field within the Langmuir circulation convergence zones. It is believed that in these data, the majority of plumes observed are caused by Langmuir circulation and so this scheme provides a representative velocity section. 64 The data show the rapid increase in bubble penetration depth to a mean of 6 metres, associated with a brief increase i n wind speed at 03:00 U T C , 27/10. This event suggests a possible threshold in wind speed (of around 7 m s " 1 ) for the existence of bubble plumes since the plumes disappeared subsequent to the squall and reappeared only when the wind again increased. T h e lag between peak ambient sound levels and the appearance of bubble plumes would suggest some finite response between bubble plume formation and wind forcing. There is however the question of ambient sound response to wind forcing and a more extensive data set would be needed to investigate this relationship. The depth penetration of bubble clouds did not depend linearly on wind speed. In contrast, the total volume of bubbles and the ambient sound level both varied in proportion to wind speed consistent with ambient sound production by breaking waves (Farmer and Vagle 1988) and bubble injection controlled by wave breaking. T h e penetration depth of the bubbles must then be controlled in part by processes other than wave breaking, and Langmuir circulation is a likely candidate. Based on root mean square surface displacements, there was no signif-icant difference between wave displacements occurring inside and outside of windrows. This result must be qualified by the limited horizontal resolution of the sonar determined by the acoustical beam pattern. The smallest wavelength that can possibly be resolved with this system is 6 m and so the present result is only valid for wavelengths greater than 6 m. The spacings between Langmuir cell windrows derived from the sidescan sonar provided length scales that are generally smaller than other reports of windrows in deep water. These histograms cannot be considered as a mea-sure of the relative importance of these various scales since no measure of 65 power is made. Also, any large scale circulation that may include smaller scale structures will not have been resolved. Although there are some plumes that penetrate to depths of 12 m , most plumes only extend to 8 m depth or less. This result, in addition to the distribution of spacings seen in the histograms (Figure 4.8), suggests the possibility of a cascade of scales with smaller cells being advected (and possibly engulfed) by larger ones. W i t h a mixed layer depth of 45 m , Langmuir cells of scales greater than 90 m should be seen (Lei-bovich 1983, Smith et al. , 1987). It is quite possible that at the time of these observations, the bubbles went into solution at depths beyond 12 m making it impossible for acoustical observations to distinguish the larger scales. T h e occurrence of energy at surface wave frequencies in the ambient sound record is another interesting result. The association of ambient sound levels with wave breaking has been well established through field observations of Farmer and Vagle 1988, and laboratory studies by Banner and Cato (1988). Farmer and Vagle report some evidence for wave breaking (as observed by ambient sound levels) to occur at half the dominant wave period in a fetch limited environment and this observation is consistent with visual records of breaking i n wave groups by Donelan et al. (1972). It is not possible to reconcile the present observations with these previous reports based on the existing concepts of wave breaking and sound generation. This problem will be investigated further in Chapter 5 through the use of a simple model of sound generation and more detailed analysis of the data. 4.5 S u m m a r y o f O b s e r v a t i o n s This chapter has reported on observations made using a freely drifting acoustics platform deployed in the North Pacific ocean as part of the O C E A N 66 S T O R M S experiment in the fall of 1987. Acoustical observations include sur-face wave height, acoustical backscatter from bubble clouds, sidescan sonar representations of the spatial distribution of bubble clouds, ambient sound lev-els, and mean vertical velocities. T h e response of sea state and bubble clouds is described for a 21 hour period of increasing wind speed to a maximum 13 ms-1. Ambient sound levels increase in proportion to the wind while the wave field shows the evolution of short period wind waves to longer periods and an increase i n wave height. During this time, subsurface bubble plumes are observed when wind speeds are greater than about 7 ms"1. These plumes pen-etrate to maximum depths of about 12 metres with slightly deeper penetration seen during higher wind speed. The existence of a threshold wind speed for bubble plume observation is likely tied to the energetics of wave breaking; the most likely source of subsurface bubbles. It 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 Langmuir circulation (through the presence of organized bands of scatterers) throughout the 21 hour deployment presented. These bands had 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 wind speeds below 10 m s - 1 and increased to spacings of 10 to 20 metres at greater wind speeds. A t all times a variety of spacings coexisted. T h e scales observed here are much smaller than those often reported in the deep ocean (Leibovich 1983). This result is more likely due to the con-centration of our measurements on smaller scales rather than to the absence of 67 the larger scales. Even if larger scales were present, they would not be appar-ent in the sidescan data because their would be many smaller scale structures present between the downwelling regions of the larger cells. Vertical velocity estimates made using an upward looking echo sounder revealed downward speeds of 0.06 m s - 1 at 8 m depth in the bubble plumes. T h e maximum velocity was located in 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. C h a p t e r 5 A m b i e n t S o u n d M o d u l a t i o n s 68 Ambient sound data were collected with the objective of making observa-tions of wave breaking in the presence of Langmuir cells. T h e possibility of such analysis is suggested by Farmer and Vagle (1988) who observe acoustic signatures from individual wave breaking events in a fetch limited sea. No correlation could be estabhshed between wave breaking and the Langmuir cir-culation. However, the analysis of ambient sound data lead to the identification of persistent wave period fluctuations (see Figures 4.3 and 4.4) not previously reported. The objective of this chapter is to identify mechanisms that could intro-duce surface wave modulations in the ambient sound field. This question is pursued first by considering the relationships between the wind and wave data in detail. That analysis reveals that the sound modulations are in 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. Two possibilities are suggested; the interaction of short waves with long waves, and the variation of wind stress over the wave field. 5.1 Wave and Ambient Sound Analysis Fluctuations in ambient sound levels can be caused by many processes, some of which could be frequency dependent (Farmer and Vagle 1989). In the present analysis however, such frequency dependence is not of interest, and am-bient sound is represented by a sound signal level (SSL) determined at some 69 characteristic frequency and bandwidth. T i m e series of S S L are characterized by fluctuations over many time scales; the fluctuations which contribute most to the signal variance are identified in Figure 5.1 by means of a (frequency x power), log frequency plot. Plotting the data in this format preserves the relative contribution to variance of each spectral component. The data i n Fig-ure 5.1 are based on approximately 38 minutes of data collected during wind speeds of 12 m s " 1 , with the instrument package (described in Chapter 3) posi-tioned at 30 m depth. Although there is energy at all frequencies in the ambi-ent sound signal, most of the signal variance comes from fluctuations occurring at periods of less than 15 seconds. The cause of the low frequency fluctuations is not investigated here, rather attention is focused on the modulations which occur at surface wave frequencies. The persistence of surface wave modulations in the ambient sound has al-ready been demonstrated in Chapter 4 (Figures 4.3 and 4.4), but the averaging nature of power spectral analysis obscures the details of the interaction. A bet-ter understanding of this phenomenon can only be achieved by a more detailed analysis of the data. T i m e series over short periods show the dominance of wave driven fluctuations in the ambient sound record. Figure 5.2a displays 3 minutes of ambient sound signal levels recorded in a 3 k H z bandwidth at 8 kHz and the wave observations for the same time period are shown in Fig-ure 5.2b. W i n d speeds during the time of these observations were about 12 ms-1. These data are typical examples and demonstrate how peaks of about 5 dB in the ambient sound level occur coincident with peaks i n the surface wave field. Modulations such as these are apparent over the entire observed frequency band (from 2 to 20 k H z ) , but larger amplitude modulations are seen at higher frequencies. 70 2236-1 CD QJ • Q. 1136-36-200 133 B9 59 t i m e : 2 7 / 1 0 1 2 : 2 7 ~ i 1 40 26 P e r i o d CsD 16 12 a i 5 Figure 5.1: Spectrum of ambient sound fluctuations. D a t a are plotted as (frequency x power) against a logarithmic frequency scale to represent the relative contribution to signal variance. The display is based on an 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 and 13 seconds. 71 F i g u r e 5.2: Comparison of surface wave displacement and ambient sound levels (between 6000 and 9000 Hz) at 30 m depth for the 3 minute period beginning at 12:13 27/10/1987 U T C ; a) ambient sound level (filtered to remove fluctuations at periods greater than 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 in scatter plots made over long time periods and so it was desirable to remove this variability before mak-ing the comparisons. A 4 th order Butterworth high pass filter with a cutoff 72 frequency of 20 seconds was applied to the data to eliminate this unwanted variation. B o t h ambient sound and wave data were filtered. A scatter plot subject to such processing is presented in Figure 5.3 based on 40 minutes of data starting from 00:10 27/10/1987 U T C when the wind speeds were about 8 ms-1. T h e plot demonstrates substantial scatter (the cross correlation be-tween these variables is 0.65), but there is a well defined axis with a slope of 36 fJ,Pa m _ 1 . This slope remains relatively constant in the 60 hours of obser-vations with wind speeds varying from 5 to 15 m s - 1 and has an average of 36 ± 8 (J,Pa m - 1 . Cross spectral analysis of surface wave displacement and ambient sound modulations (at 8 k H z frequency) was made to further investigate the correla-tion between these data. Figure 5.4 shows an example of such analysis based on 23 minutes of data starting at 12:10 27/10/1987 U T C during wind speeds of approximately 10 m s - 1 . Based on visual observations, the dominant waves at this time are oriented at about 4 5 ° to the wind direction. Figure 5.4a and b show the surface wave and SSL spectra respectively. Figure 5.4c shows the coherence and Figure 5.4d is the relative phase between the two time series. The modulation spectrum (Figure 5.4b) shows an energy increase i n the fre-quency band 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 and wave displacements for limited time intervals, but it does not demonstrate how those signals evolve through changing sea and wind condi-tions. T h e time dependent character of the coherence was investigated by plot-ting time series of coherence and phase over a selected frequency bandwidth. 73 S u r f a c e D i s p l a c e m e n t Cm] F i g u r e 5.3: Scatter plot of sound power at 30 m depth against wave displace-ment over a 40 minute period starting at 12:10 27/10/1987 U T C : both wave and ambient sound data have been high pass filtered to eliminate variations at periods longer than 20 seconds. 74 F i g u r e 5.4: Cross spectral analysis of 23 minutes of wave and 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. This analysis is based on averages over 20 separate frequency spectra. The 95% confidence intervals are indicated by error bars for both phase and coherence. 75 T h e 21 hour period beginning at 19:00 26/10/1987 U T C is characterized by in-creasing wind speeds and a developing sea (Chapter 4) and so presents a range of sea and wind conditions. Figure 5.5a displays the wind speeds observed at this time, and the coherence and relative phase of the wave and sound field at periods between 10.5 and 13.5 seconds are shown in Figure 5.5b and c. It is seen that as the wind speed picks up, 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 in coherence, the relative phase during this period remains 0 (within 95% confidence bounds). It must be noted that the wind direction did not change appreciably during this period remaining at about 4 5 ° to the prevailing swell. In an effort to determine the importance of the crossed wind and waves occurring in the data of Figure 5.5, a second time series of wave displacements and sound modulation was analyzed. T h e only other data set available is a 44 hour period beginning at 18:00, 2/11/1987 U T C during which the wind speeds slowly decreased but did not change direction. Throughout that data period, visual observations recorded the swell oriented at about 3 0 ° to the wind direction. Using the same format as Figure 5.5, Figure 5.6 displays the wind speed, coherence and phase observed during this time interval. For this sample period, the phase and coherence are determined at periods between 10 and 13 seconds to bracket the dominant wave period. Again , the coherence remains consistently high and 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 from 0 as shown by the error bars in Figure 5.6c. 76 1.0 CD a c CD -C o G Q_ .00-1.0-l | i | \m\np w P n Pi] ^  p[i j * n fj jp [pj iij j | ji j | i i | C o h e r e n c e m .00-cn co x: ll ^ nil Lm n i l m g i nil l u i ^  i j IJ I]I j\ JiJ I]] P h a s e •1. 26/10 22:00 27/10 0B:30 T I M E C U T C ] 27/10 13:00 F i g u r e 5.5: Time series of wind speed and the phase and coherence between waves and ambient sound modulations for the 21 hour period beginning at 22:00 26/10/1987 U T C ; a) wind speed, b) average coherence at periods be-tween 10.5 and 13.5 s, c) phase, (95% confidence bounds are indicated by error bars). 77 15-Q 5-QJ cj c tu c_ QJ . C o U 1.0-.50-.00-cu cn CD 02/11 1B:00 W i n d S p e e d C o h e r e n c e 03/11 16:00 T I M E C U T C ) 04/11 14:00 F i g u r e 5.6: In the same format at used for Figure 5.5, the coherence and phase between wave motions and ambient sound are shown for a 44 hour period for fluctuations with a period of between 9.5 and 13 s are displayed. 78 The suggestion of some slight phase difference in this later data set is intriguing, but better quality data would be required to claim confidence in this small departure from 0 phase. In the present data, the absolute timing accuracy i n each of these data sets is ± . 2 5 s so that the cumulative error in time series alignment could account for a phase uncertainty of as much as 0.1 7r radians at a 10 s period. It is however extremely unlikely that such a timing error would retain a constant offset for the entire 44 hours analyzed. 5.2 Modulat ions of Sound Generation T h e observations demonstrate that the modulations of ambient sound are strongly driven by surface wave motion. This 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 in the ocean is known to be associated with wave breaking and in particular by the in-troduction of small bubbles into the ocean surface (Medwin and Beaky 1989). It must be concluded that either sound propagation is strongly influenced by surface wave motion or, the breaking of waves responsible for sound generation occurs at or near the crests of the longer period (swell) waves. T h e suggestion of wave breaking controlled by long wave phase is not unreasonable: short waves can be disturbed by longer wave currents and this disturbance can trigger wave breaking as discussed by Phillips (1981) and Gar-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 in the wavelength of the short waves and consequently increases their steepness towards a maximum 79 at the long wave crest. A s demonstrated by Garrett and Smith (1976), for parallel wave trains, the wave steepness ak varies as ak = aofc 0(l + kid] cos 6)2 5.1 where ao is the undisturbed short wave amplitude, ko is the undisturbed short wave wavenumber, a/ and k} are the long wave amplitude and wavenumber, and 6 is the long wave phase. T h e steepness of the short waves occurring at the long wave crests would increase the probability of these short waves breaking and so lead to increased sound generation. T h e scale of breaking waves need not be large; Kolaini et al. 1991 demon-strate that significant sound can be generated by the action of capillary wave breaking. T h e y note that even in the absence of breaking gravity waves, par-asitic capillary waves occur just ahead of short gravity waves as described by Longuet-Higgins (1963). Capillary waves are characterized by sharp troughs and rounded crests and break when adjacent crests actually pinch off a trough (Crapper 1957). Kolaini et al. 1991 observe that breaking capillary waves generate significant sound and offer this explanation of sound observed in the absence of breaking gravity waves (Knudsen et al. 1948). If this sound gener-ation mechanism is important (even at high wind speeds when gravity waves break), then sound generation could occur on a very small scale governed by the interactions of capillary waves. A n indirect mechanism which may be important to the variations in sound generation could be the variability in wind stress over the long wave phase. Gent and Taylor (1976) have demonstrated that wind stress is modulated by wave form with a maximum occurring on the upwind wave slope and this 80 result is consistent with observations by Zilker et al. (1977). This variability in stress could influence the occurrence of wave breaking (and consequently sound generation) through the mechanism proposed by Banner and Phillips (1974) in which near surface shear in the water destabilizes waves. Alternately, it would be expected that capillary waves would respond quickly to changes in wind stress and so capillary wave generated sounds could be closely tied to wind stress. Comparisons of wind stress with mean ambient sound levels by Vagle et al. (1990), demonstrate a strong correlation following the relation, r oc P 2 5.2 where P is the sound pressure level, and r is the wind stress. This empiri-cal relationship is based on one hour averages and it is not obvious that it should be valid for short time scale variations. However, if it is assumed that Equation 5.2 is applicable over short time scales, then the stress variations over a wave form measured by Gent and Taylor (1976) can be used to estimate the variability of sound generation with Equation 5.2. T h e curves of wind stress variation observed by Gent and Taylor can be approximately modelled as varying as the square of the wave displacement, r oc (a — a m t n ) 2 cos(f? + <f>,) 5.3 where r is the stress, a — amin 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 and u the angular frequency). Combining equations 5.2 and 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 wind stress has on near surface processes, it is particu-larly likely that wind stress variations play some role. Certainly, variations in wind stress would influence the breaking of capillary waves as well as gravity waves and so could indirectly lead to sound level modulations. 5.3 A m o d e l of n e a r 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 this question. This simulation demonstrates that, for appropriate parameter choices, variations in 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. T h e assumption is made that sound sources are confined to be at or near the ocean surface consistent with the mechanisms discussed. T h e sound received by a hydrophone can be determined by integrating over the ocean surface and accounting for spherical spreading and acoustic propagation losses. E v e n acoustic sources far from the hydrophone contribute to the total received signal, but at some point, depending on the instrument geometry, the contri-bution becomes negligible. That radius about the instrument location which contributes 50% of the total acoustic power is a suitable measure of the lis-tening area important to the system: this area is the half power or 3 dB 82 listening area. For the deployment geometry in 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. This configuration is indicated in Figure 5.7 which identifies all components of the model geometry. F i g u r e 5.7: Geometry of modelled dipole sources and receiver. It is desirable to be able to compare model results directly with obser-vations. To do so, it is necessary to recreate the surface wave field occurring above the instrument in an area that is large compared to the 3 dB listen-ing radius of 29 m. A representative surface can be reconstructed for the vicinity of the instrument by phase shifting the wave height spectra observed above the 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, and will not provide good results many wavelengths from the measurement position. For the present application this limitation is acceptable since the dominant wavelength is about 100 m which is already several times the 29 m listening radius. T h e Fourier transform of the ocean surface motion at any point can be expressed as /°° V(x,t)\x=Qe-^dt, 5.5 -oo where r](x,t)\x—o is the observed sea surface variation in time at a position x = 0. T h e Fourier transform at any position x can be determined by phase shifting Equation 5.5 by a distance / according to the linear dispersion rela-tion S(u,l) = 5(w,0)e , ' u ; 2 / / f f . 5.6 T h e sea surface displacements at position / are then recovered from Equation 5.6 by the inverse Fourier transform, 1 r°° »/( ' .*) = 5 - / S(u,l)etutdu. 5.7 It is assumed that this one dimensional wave field is propagating in the x direction and extends infinitely with no surface gradients in the y direction. It is necessary to use finite transforms which distort the reconstructed sea surface. This distortion is minimized by transforming time series twice the required length and then using only the middle half of the adjusted data. The length of these time series was 1024 seconds thus including many cycles of the longest period surface waves (about 12 s). T h e surface reconstructed far from 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 important. Acoustic sources can be placed upon the reconstructed ocean surface ac-cording to several possible schemes. It was decided to describe the acoustic field with a continuous distribution of sources with strengths varying i n propor-tion to some surface characteristics rather than using randomly placed discrete sources. This 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. This 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: observations of near surface ambient sound support this idea (Vagle et al. 1990). Subject to these assumptions, acoustic sources are described by dipole sources distributed evenly over the ocean surface as shown in Figure 5.7. O n the reconstructed surface, dipoles are oriented normal to the surface at all points. In the absence of surface slopes in the y direction (a result of the one dimensional reconstruction of surface waves), dipoles are arranged in rows all tilted at the same angle to the horizontal. The 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 a range R and <j> depends on both position and surface slope. Because the elements are incoherent, the signal strength does not add linearly: instead, signal power 85 must be integrated. T h e contribution to the signal level then received at a hydrophone by any infinite dipole row can be determined by integrating along that row and considering the spherical spreading that would occur, /°° a 2 — cos2 (<f>(x,y))dy, 5.9 where R2 = x2 + y2 + d? is the range from element ds to the receiver, and x, y and d define the hydrophone position as in Figure 5.7. For large ranges or high frequencies, acoustic absorption would become important in Equation 5.9. In the present case however, maximum ranges are about 500 m , and the highest acoustic frequency being considered is 15 k H z : attenuation for such a signal is only 0.7 dB and so can be ignored without significant error. A range dependent effect which could also be important is the scattering of sound by subsurface bubbles observed by Farmer and Lemon (1984). This scattering is not included in the simple model discussed here. Equation 5.9 can be integrated to determine the contribution that an infinite row of dipole sources with a fixed angle of tilt will make to the received intensity: o 1= r c o s 2 U 5.10 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<^ , cos2U(x))dx. 5.11 where <f> depends on both position and surface slope at that position, 86 and a is now position dependent. Because r)(x,t) is determined from observa-tions, Equation 5.11 must be numerically integrated out to a range at which no further contribution is made. In practice this sum converged after integra-tion to 500 m . T h e source strength parameter in Equation 5.11 must be adjusted to rep-resent characteristic signal strength at any point along the wave surface. In particular, the strength must be adjusted in proportion to some wave charac-teristic consistent with the source mechanisms proposed. Rather than creating special functions for each mechanism investigated, a general form with ad-justable parameters was chosen, a2 = AQ + A + (s - sQ)2C s > s r e f 5.13 a 2 = A0 S < Sref, where AQ, A , C , s r e / , and so are adjustable parameters and s is any sea surface dependent parameter such as wave displacement or acceleration. T h e values for parameters i n Equation 5.13 required to best match model sound variations with the observations provide insight into the nature of the source mechanism. Adjustment of sref allows for an intermittent character in the source, the values of Ao and A provide for a background level that does not depend on the wave parameter, and C allows for a quadratic source level dependence. A linear source level dependence was initially included but it provided no improvement in model results and so it was discarded. 5.4 Model Results T h e format of Equation 5.4 was chosen to allow maximal flexibility subject to the explicit constraints of the model. A s part of this generality, no specific 87 wave parameter (5) is imposed upon the system. From the observations it is obvious that the parameter used must be nearly in phase with the wave displacements at the instrument position. Surface wave displacements are one of the direct observations being made and any other wave dependent parameter would be derived from these measurements. Such derivations would inevitably introduce small errors and the result would largely be a value proportional to the wave displacements. For these reasons, only surface wave displacement itself has been explored as a wave parameter in Equation 5.13. Adjustment of parameters in Equation 5.13 was complicated by the non-linear characteristics of the model. Parameters were adjusted to achieve rea-sonable qualitative agreement with observations over a short time series (the 3 minute interval shown in Figure 5.8). Once approximate parameter values had been selected, the correlation between the observed ambient sound fluctu-ations and the model predictions was made using a more extended time series consisting of the 40 minute period beginning at 12:10 27/10/1987 U T C . T h e parameter values were then adjusted to maximize the correlation coefficient between the simulated and observed ambient sound levels for this period. In evaluating these correlations, the low frequency fluctuations present in the data were removed using a filter with a pass band of between 3 s and 20 s. T o avoid difficulties of phase distortion through filtering, both model simulations and data were filtered in both the forward and backward directions. The model was first used to investigate if Equation 5.4 could reproduce fluctuations consistent with the observations. T h e threshold term was disabled in Equation 5.13 (by setting s r e / = —00). For this configuration of the model the fitting procedure was used to determine the values of the three remaining 8 8 / K j - , , , , 12:13:00 12:14:00 12:15:00 12:1B:00 T i n i e F i g u r e 5.8: Comparison of observed and modelled ambient sound fluctuations over a 3 minute period. A ) quadratic dependence on wave displacement, B) intermittent sources located at wave crests, and C) quadratic dependence on wave displacement with sound sources restricted to long wave crests. ( A l l models reproduce mean levels comparable to those observed, but have been displaced to clarify the presentation). 89 parameters; the quadratic scaling (C) was set to 5000 /J,Pa2m~3, the constant term A was set to 50000 / x P o 2 m _ 1 , and the offset displacement so w a s s e t to —2 m (the approximate minimum wave displacement). W i t h s r e / set to —oo, AQ becomes arbitrary. A three minute time series based on these parameter choices is identified as trace " A " in Figure 5.8 and can be compared with the observed modulations. A further visual comparison between observations and model predictions can be presented by a scatter plot between the two time series such as shown in Figure 5.9. Figure 5.9 is based on the 40 minutes period beginning at 12:10 27/10/1987 U T C and demonstrates the agreement of the model with observations (the correlation coefficient for this comparison is 0.55). There however remains substantial scatter throughout the plot with no obvious explanation for the limited correlation. T h e source mechanisms of wave breaking localized to long wave crests suggests the existence of a sound source mechanism localized at wave crests. This mechanism was investigated by adjusting the threshold parameter s r e / so that sound was only generated near wave crests with no variation in signal level in proportion to wave displacement. A t first, trials of this model were made without using the parameter Ao which allows for a background sound source distributed uniformly over the ocean surface. Without this background source, large signal variations occurred in 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 in a downward sense. A n example of such drop-outs can be seen in the example time series identified as trace " B " in Figure 5.8 generated with A = 180000 ^ P a 2 m _ 1 , and sref = —0.95 m. T h e correlation between this model and the observations could not 90 LTJ TJ cn cn U J • D H -H - 3 ' . \ . T . .•£<;... .. i . * « \ ... J'» * . . ' . . . -1 O B S E R V E D S S L CdB] F i g u r e 5.9: Scatter plot of observed ambient sound levels against those mod-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 than 20 seconds. 91 be increased beyond 0.45 without using some form of signal level increase at wave crests. W h e n such additional modulation was used to recover the sharp peaks observed, sref still had to be adjusted to small values to avoid the sudden signal drop-outs. T h e inability of simulations with localized source regions to reproduce the observed sound fluctuations identifies the need for a sound source with a constant component. T h e background source term (AQ) was introduced into Equation 5.13 for this purpose. T h e model parameters were once again recon-figured to optimize the agreement with the observed fluctuations leading to the values; A0 = 100000 fiPa2m~l, A = 0 u.Pa2m~x, sref = 0.2 m , s 0 = —2 m , and C = 10000 fiPa2m-z. T h e time series in Figure 5.8 labelled " C " results from this parameter selection. A comparison of this model 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 The comparisons between simulated and observed sound modulations pro-vide some support for the concept that sound level fluctuations over surface waves can account for the observations. Results from the model configurations presented are summarized in 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 of the small listening area of the instrument: the model assumes line sources arranged parallel to unidirectional waves and for this geometry, the 60 m listening di-ameter is in fact reduced to a line of 36 m length. In the model, if signal 92 Model Ao A C so • S r e / R Comment Pa2m-1 Pa2m-1 Pa2m-Z m m A arb. 50000 5000 -2 —oo 0.55 stress model B 0 180000 0 arb. - . 95 0.45 localized sources C 100000 0 10000 -2 0.2 0.50 all parameters T a b l e 5.1: 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 effec-tive listening area (by changing to a monopole source) reduces this problem but eliminates the ability to simulate the large peaks seen in the observations. For the case of a continuous source term such as used in M o d e l " B " (Table 5.1), the use of the offset term (Ao or A) represents an offset in the signal level of the source term. W h e n applied to a discontinuous source (such as the case of Model " C " in Table 5.1), this term implies the existence of a second source mechanism independent of wave motion. A very likely cause for this term could be the need to account for sound that is reflected back to the surface from the ocean bottom. The ocean depth at the observation site was about 2000 m : 8 kHz sound generated at the surface and reflected off the bottom back to the surface is attenuated by about 3 d B through acoustic ab-sorption and 10 dB due to the bottom interaction. B y applying a simple model of such sound generation it was found that this signal has a 3 dB footprint of 93 about 8000 m diameter and can account for a signal level comparable to that received directly from the surface. A n additional contribution to such a con-stant signal level term could be through the action of sound scattering (from near surface bubbles) or refraction serving to distribute the source location away from the 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 in all cases some means of enhancing signal levels at wave crests was needed to approximate the sharp peaks observed in the sound mod-ulations. Use of a linear term in Equation 5.13 was inadequate for this purpose and in all cases, a quadratic term was needed. Scatter in the comparisons be-tween model and observations (such as shown in Figure 5.9) made it impossible to recognize any improvement in model results when including both linear and quadratic terms. The scatter in comparisons of the model and observations also makes evaluations of model variations difficult. A l l models produced correlations of about 0.5 but no variation of the model could produce correlations greater than 0.55. This 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 represent sound generation terms. O f more concern are those processes not represented by the model. Figure 5.2 demonstrates significant fluctuations in ambient sound not obviously driven by wave motion. Using the spectral character of the modulations as a guide (Figure 5.1), much of this variability can be eliminated by filtering out periods longer than those associated with surface waves. This filtering has been done prior to making 94 correlation comparisons between the model and observations. But , there is no reason to expect the mechanism causing the long period fluctuations to be entirely absent at wave periods and it may be responsible for some of the discrepancies. Based on the correlation coefficients achieved by the various models (Ta-ble 5.1), a best configuration is not obvious. The combination of parameters required in any given case does however provide some insight into the possible source mechanisms. T h e model relying only on variations of wave displace-ment to produce modulations (model " A " in Table 5.1) is attractive i n that it closely models the expected action of wind stress variations and it only requires the adjustment of three parameters. T h e concept of wave breaking localized to wave crests suggest that the localization of sound sources could account for the observed sound modulations. A n attempt to reproduce the observed fluctuations by this means (using model " B " ) clearly demonstrated that such localized sound sources lead to signal drop-outs not seen in the ob-servations. The 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 " and " B " were combined in M o d e l " C " where a background source level acting at all points at the surface is included. A s is demonstrated by the results of model " C " , the introduction of the additional parameter provides little im-provement in the results. In addition, the need for a constant source term is somewhat inconsistent with an intermittent source model: the mechanisms that suggest sources at wave crests (short wave instabihties or parasitic capillary waves), imply that these sources should be absent in troughs. W h e n sound generation is localized only at long wave crests, an additional source term must be introduced in the model to reproduce sound level variations comparable to those observed. 95 5.6 Source Mechanisms T h e model demonstrates that the observed sound modulations can be de-scribed using a continuous distribution of sources. Such a continuous distribu-tion implies that several active sources must be present within the 60 m diam-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 (jQth the length of the listening area). Although the actual sound generating mechanism remains to be identified, sound generation is strongly associated with breaking waves and the injection of air bubbles into the water (Medwin and Beaky 1989). If individual breaking waves are responsible for the sound fluctuations observed, then one breaking wave must be occurring at any time on a scale of about 6 m. Hwang et al. (1989) indicate that for small wind forced waves, the ratio of breaking to non-breaking waves is about 0.1; this ratio provides an upper limit of 0.6 m for the wavelength of breaking waves responsible for sound generation. Having estabhshed a scale for sound sources of 6 m (implying wavelengths of breaking waves of about 0.6 m) lends support to the concept of a small scale continuous source mechanism. It is however quite possible that through statistical variability, randomly placed sources with an increased probability of occurrence at wave crests could produce similar results. One characteristic in the observations which might be used to distinguish wind-stress-regulated variability from that caused by sources at wave crests, is the presence of a phase difference between the wave crests and sound maxima. In general, wave-wave interactions cause short waves to have a maximum steepness at the crests of long waves whereas the location of maximum 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 al. 1976, Gent and Taylor 1976). For the wave fields encountered in 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 in the present data with the laboratory observations by Zilker et al. (1977), phase lags would be expected to be vanishingly small in the absence of wave breaking. In contrast, laboratory observations made by O k u d a et al. (1976), Buckles et al. (1984), and numerical studies by Gent and Taylor (1976) show that relative phase lag is strongly affected by wave breaking so that the lags reported by Zilker et al. (1977) may not be representative of a real ocean. In the present observations, the phase between sound and wave displace-ments was 0 ± 0.1 7r radians when the wind and wave field were crossed at about 4 5 ° but the phase remained positive at 0.1 ± 0.1 7r radians (that is wave displacement leading sound) during observations when wind and wave directions were separated by 3 0 ° . Under these conditions (with large angles between the wind and waves), it is likely that any phase difference would be significantly reduced while the stress would still vary somewhat between crests and troughs. In contrast, the interaction of short waves with long waves at an angle would be reduced approximately as the cosine of the angle between short and long waves (Garrett and Smith 1976), substantially reducing the significance of such interaction. 5.7 S u m m a r y a n d C o n c l u s i o n s Observations of broad band ambient sound levels (2 kHz to 20 kHz) at 30 m depth in the North Pacific Ocean show modulations at surface wave 97 frequencies. Cross-spectral analysis between ambient sound levels and surface wave 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). Two extended periods of data are analyzed. T h e first is a 21 hour period characterized by a growing sea state with the locally generated wind waves at all times 4 5 ° to the 10 second period swell. T h e wind speed increased to a maximum of 13 m s - 1 producing a fully developed sea towards the end of the deployment. During this time, the phase remains fairly constant at 0 ± 0.1 TT radians while the coherence shows some variability and falls off slightly when the sea is fully developed. During the second 44 hour deployment, maximum wind speeds were only about 10 m s - 1 slowly decreasing through the deploy-ment while maintaining a constant direction. During this period when the swell was oriented within 30° of the wind, the coherence remains high and the wave displacements lead the ambient sound fluctuations by about 0.1 ± 0.1 TT radians (that is maximum sound upwind of the wave crests). This phase difference is however just at the limit of the instrument resolution as demonstrated by the 95% confidence bounds. Throughout both these data sets, the slope of scat-ter plots made between wave displacement and ambient sound levels remains constant at 36 ± 8 fiPa m - 1 independent of wind speeds. The strong coherence of ambient sound fluctuations with the wave field suggests that the dominant ambient sound source is modulated by the sur-face waves. For this modulation to occur, the source mechanism must have a scale that is small compared to the dominant wavelength. This conclusion was 98 explored by simulating ambient sound observations using a continuous distri-bution of sources along the surface with source levels adjusted in proportion to surface wave parameters. This model reproduces ambient sound fluctuations similar to those seen in the data however correlations between the model and the observed modulations are limited to about R = 0.5. T h e accuracy of the model is critically dependent on the accurate representation of the ocean sur-face and the model's limited accuracy undoubtedly results from inaccuracies in the ocean surface representation. T h e ability of the model to reproduce ambi-ent sound fluctuations comparable to those observed does provide insight into the possible sound source mechanisms. Based on the model results and the present observations sound generation must occur on 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 on the breaking rates for short gravity waves given by Hwang et al. , 1989). W i n d stress variations and short wave, long wave interactions are offered as a possible causes for the observed sound modulations. There is no strong evidence in 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 wind speeds. This behaviour is consistent with the expected wind stress variation over the wave field as given by Gent and Taylor (1976); stress variations would be purely de-pendent on wave amplitude regardless of wind speed. In addition, wind stress would not be expected to vanish in the long wave troughs, except in the unlikely event that a long wave should break, thus supporting the existence 99 of continuous distribution of sound sources. In contrast, Equation 5.1 demon-strates that just as short waves are steepened at crests, they are flattened in troughs so that this mechanism would suppress short wave breaking and sound generation in wave troughs. T h e model results clearly demonstrate that if regions of no sound generation are present along the surface waves, large drop outs i n sound level would occur; these are not seen in the observations. Finally, Vagle et al. (1990) show that average sound levels are proportional to wind stress and close inspection of their displayed time series suggests that sound levels can respond within 10 minutes to wind speed variations. It is hard to imagine that a sound source dependent on long wave structure could respond so quickly to wind speed changes. Sound generated by wind stress (even when mediated by small waves) is more likely capable of a rapid re-sponse. Visual observations by Donelan et al. (1972), and acoustic observations by Farmer and Vagle (1988) have shown wave breaking to occur in wave groups which would produce modulations at frequencies less than those of the surface waves themselves. T h e observations of Farmer and Vagle were made in a fetch limited sea with no ocean swell. Donelan et al. comment on a variety of sea and laboratory conditions and speculate that the occurrence of crossed waves could affect the observations. Unfortunately, the observations presented here were restricted to a limited variety of wave conditions and it is not possible to investigate the influence of mixed wave states on the ambient sound modulations. A consistent requirement i n model parameterizations was the need for large signal offsets to achieve the signal levels observed. This requirement is 100 likely due to the need to represent sound reflected off the ocean bottom 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 attenua-tion through absorption. T h e observations are consistent with this explanation displaying modulations more clearly at the higher frequencies. This presentation has focused attention on those fluctuations of the am-bient sound field occurring at surface wave periods. There are fluctuations to this signal occurring at much lower frequencies as can be seen in Figure 5.1 but these do not contribute substantially to the signal variance. These lower frequency fluctuations could be due to gusts in the wind, consistent with the speculations presented here, but wave breaking associated with wave groups (as documented by Donelan et al. 1972, and Farmer and Vagle 1988) provides an equally viable explanation. Clearly there is much to be learned about the short term variation in ambient sound levels. 101 C h a p t e r 6 A M o d e l o f L a n g m u i r C i r c u l a t i o n The data presented in Chapter 4 demonstrates that Langmuir circulations are not confined to a fixed scale, but seem to be characterized by a variety of coexisting scales. This observation is not unique; similar distributions of lengths scales have been seen by many researchers as noted in the review paper by Leibovich (1983). What is striking in the present data is the presence of Langmuir cell spacings as small as 1 m while typical scales in 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 in the sonogram images. The presence of many coexisting length scales i n this 2-D flow pattern could be caused by an upscale energy cascade characteristic of 2-D turbulence. This idea is further supported by reports of vortex pairing and the gathering of smaller structures into larger ones (Faller and Auer 1988, and Leibovich 1983). The accurate description of this characteristic of Langmuir circulation has not been demonstrated theoretically although Leibovich and Paollucci (1981) do suggest that such a tendency exists in their numerical models It is my speculation that the multiplicity of scales is not a characteristic of the generation mechanism of Langmuir circulation, but is more likely a con-sequence of the 2-dimensional flow that results. In that case, any mechanism which could introduce 2-D vorticity into the upper region of the mixed layer could result in the flow field that is characterized as Langmuir circulation. 102 To pursue this idea, the next three chapters consider a possible source of near surface vorticity and how interactions i n the flow might produce the mul-tiple scale flows seen in Langmuir circulation. T h e present chapter introduces a vortex generation mechanism based on the interaction of waves with near surface turbulence. Chapter 7 and 8 extend this result by considering the flow field resulting from unidirectional vorticity introduced by any means close to the ocean surface. 6.1 An Alternative Theory for Vorticity Generation To explain the relatively small scales of Langmuir circulation seen in the deep ocean, a mechanism operating on scales small compared to the dominant surface wavelength was considered. It was realized that initially isotropic vor-ticity 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 in 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. Through 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 with wave motion serves to stabilize troughs and desta-bilize crests. Through the act of breaking, turbulence in the water is pref-erentially generated at the wave crests. A s the wave continues to propagate, 103 the patch of turbulence is left behind and is advected by the wave from the crest position to the wave trough. For a wave propagating in the x direction (with z defined as upward), this motion causes the fluid to be stretched in the x direction and contracted in the z direction. Associated with this distortion there will be an intensification of the x vorticity and 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 in 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 from the wind stress, but this vorticity will be shown to not affect the present argument. 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 and 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 in the y direction. However, for a sea with a directional wave field (as is characteristic 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. This argument does not consider how turbulent interactions may act to degrade the vorticity field into an isotropic state, but it does provide an an-swer to the fundamental problem of identifying a source of x directed vorticity. It is clear that once such vorticity exists in the upper ocean it can remain sta-ble for extended periods of time as demonstrated by the existence of Langmuir circulation. 104 T h e mechanism suggested here is independent of, but not incompatible with, the theory of Craik and Leibovich. T h e Craik-Leibovich model suggests that a down wind component of vorticity arises from the interaction between the Stokes drift and vertical vorticity. This interaction leads to an instabil-ity giving rise to Langmuir circulation which under normal oceanic conditions has a characteristic length comparable to the dominant surface wavelength (Leibovich and Paolucci 1981). 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 dis-tortion will lead to an anisotropic mean state. There is no reason that these two mechanisms could not work together with the wave distortion mechanism introducing small scale vorticity while the larger structures are controlled by the Craik-Leibovich instability. 6.2 A n a l y t i c a l F o r m u l a t i o n I wish to demonstrate the viability of the preceding argument and the efficiency of the mechanism described. In order to determine the effect of surface wave distortions on vorticity near the surface of the ocean, the vorticity equation is used: du n — + u • V w = u • V u + vV2u, 6.1 dt ' where u = (£, rj, C) is the vorticity vector and u — (u,v,w) is the velocity vec-tor. Equation 6.1 can be expanded into three component equations to identify which terms are important for the present situation, d£ , d£ d( d£s .^.du du > 3u. * + < " 5 + e 5 + " f l S ) = % + , * + c & ) + , ' v ^ 6 2 105 dri , dri dri dri , dv dv dv , % + lug.+vg + „g.) = « £ + n £ + & ) + »V% 6.4 dt dx dy dz dx dy dz T h e terms of interest are those that cause a change in vorticity through fluid distortions, not through transport: for this reason, the advection terms ( u j § , u | £ , and t o § § ) a x e ignored. Velocities associated with vorticity will be considered small compared to wave motions and vorticity is treated as a pas-sive scalar in the wave motion. In this case, the velocity field can be described by the irrotational wave motion alone which will contribute nothing to the vor-ticity. For the case of a monochromatic, unidirectional wave field, u can then be written as, (u, v, w) = ( 0 7 cos(kx — ~ft)ekz, 0, ay sin(fcx — y t ) e k z ) , 6.5 where a is wave height, 7 is the wave angular frequency, and k is the wavenumber. Using the assumptions identified, Equations 6.2, 6.3, and 6.4 can be re-duced to, 106 Equation 6.6 describes the evolution of £ subject to wave motion; £ dx ex-presses intensification due to stretching, represents the interaction between vertical vorticity and vertical shear in the horizontal velocity, and f V 2 £ is the diffusion due to viscosity. Analogous terms are found in Equations 6.7 and 6.8 but because of the assumption that v = 0, Equation 6.7 has no vorticity or velocity interaction terms. A s a result, Equation 6.7 reduces to a diffusion equation and because the y component of vorticity is not itself of interest in 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 m2s~1 are suggested in the ocean mixed layer (Pond and Pickard, 1983). T h e present objective is to describe the motions which such a large eddy viscosity is intended to represent and so for the present case, a value of viscosity more like that of molecular viscosity {y = 1 0 - 6 m 2 s - 1 ) would be appropriate. In that case, it is reasonable to ignore the viscous terms in equations 6.6 and 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), Equation 6.9 is easily solved by substituting the expression for from Equation 6.5 directly into Equation 6.9 giving; = -£akrf sm(kx - >yt)ekz. 6.11 at Since vorticity is introduced by wave breaking close to the ocean surface, use of the case of z = 0 is adequate. A n additional simplification can be made by considering processes which occur only at the point x = 0. Subject to these further simplifications, Equation 6.11 can be solved to give, _ eak(l-cos(—f*))f 6.12 where £ 0 is the value of £ at t = 0. Equation 6.12 has its maximum at t = ^ when ^ = eak. In breaking waves ak ~ 0.4 (LeBlond and Mysak 1978) so that this maximum in vorticity would be a factor of 1.5 above its initial value. A n average can be similarly arrived at as having a value of about 1.2. T h e degree to which the x component is intensified will oscillate with the passage of each wave, but as more vorticity is introduced selectively at wave crests, a net increase in x vorticity will be realized. Equation 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 t — 0. This equation suggests a decrease on average by a factor of 1/1.2 subject to the same assumptions used for the case of horizontal vorticity. Vorticity originally oriented at some arbitrary angle will 108 have its components subject to the variations predicted by Equations 6.13 and 6.12 but with the added complication of the interaction terms ( C § 7 and £ § 7 ) . It is worth noting that the term £ | j (in Equation 6.9) is a component of the vortex force term identified in the Craik-Leibovich theory (Leibovich, 1980) when the Stokes drift is considered. (The Craik-Leibovich theory also has a term of the form r/|^ because gradients in the y direction are considered.) In their development, they consider u to have some average z dependence. If such a term were considered in the present development, it would contribute to the x component of vorticity. This 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 in this chapter demonstrates that wave motion can serve to selectively intensify the x component of vorticity when vorticity with random orientation is introduced preferentially at wave crests. Although this mechanism would appear to be periodic in character (Equation 6.11), on average, it tends to a net increase in x vorticity because of the phase at which vorticity is introduced. The simplifying steps used in this development ignore several important processes. Viscosity would act to cause an outward diffusion of vorticity involv-ing more fluid in the circulation. The action of (eddy) viscosity would also be essential in acting to diffuse the vorticity down through the mixed layer. In addition, interactions between the vortices will act to merge vortices of com-mon sign, and conversely annihilate vortices of opposite signs. Ultimately the 109 persistence of this organized vorticity (or that of any other origin) will depend on whether or not the rate of vorticity introduction exceeds the rate of de-cay through instabilities and viscous damping. The interactions between the vortices will be highly non-linear and they do not easily lend themselves to analytical considerations. The fate of two dimensional vorticity introduced close to the ocean surface is considered in Chapters 7 and 8. This analysis will be equally valid regardless of the source mechanism of that vorticity and can be considered purely as an investigation into the dynamics of existing Langmuir circulation. C h a p t e r 7 A 2 - D L a g r a n g i a n V o r t i c i t y M o d e l no In Chapter 6 it was demonstrated that through the action of selective vorticity injection at wave crests, it is possible to produce vorticity with a preferred orientation at small scales. A major assumption in that development is that the velocities associated with vorticity are small compared to wave ve-locities. This assumption eliminates the interactions between vortices which is acceptable as long as there are few vortices. As more vortices are introduced through continued wave breaking, a point will eventually be reached when vor-tex interactions must become important. Such interactions are the hallmark of turbulence which acts to destroy any organized flow. Under the present cir-cumstances, 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 from observations that (two dimensional) Langmuir cells can remain stable for long periods in the ocean. If a flow retains a two dimen-sional character, then the vortex interactions will not be destructive but will lead to a cascade to larger scales identified with two dimensional turbulence (Kraichnan 1967). T h e interactions leading to a vorticity cascade are highly non-linear and are most conveniently studied through use of a computer model. This chapter describes the development of a computer model for this purpose and presents I l l some evaluation of that model's capabilities. A discussion of the model results specific to the problem of Langmuir circulation is deferred until Chapter 8. 7.1 Model Requirements There are many numerical models that might be suitable for analyzing a system of two dimensional vorticity. In selecting a model for a particular appli-cation, consideration must be given to computational efficiency and tractability of the problem. For the case of Langmuir circulation, the model must ac-commodate a large range of important scales from the domain size down to resolving the smallest possible structure. T h e domain is normally unlimited in the horizontal, but there is a natural length scale determined by the depth to the bottom or the first significant pycnocline (typically 100 m in a deep ocean environment but 50 m in the observations presented in Chapter 4). T h e smallest scales can be drawn from the sidescan observations of Chapter 4 and so must be approximately 1 m , consistent with the introduction of vorticity by breaking waves since such vorticity will be constrained to have scales bounded by the horizontal extent of these breaking waves (about 1 m based on observa-tions presented in Chapter 5). T h e model domain must then be several times the depth scale limit of 50 m because the largest Langmuir cells have spacings that are 2 to 3 times the mixed layer depth (Weller and Price 1988); a hori-zontal extent of at least 100 m is needed. The time scales that are relevant to such a system are as great as 30 minutes as seen in the observations. A suitable model for this problem is the Lagrangian vorticity model first described by Chorin (1973). In this model, the vorticity of a flow is approx-imated by a distribution of many point vortices. In an inviscid fluid, the evolution of flow is described solely by the subsequent advection of vortices 112 through their mutual interactions. T h e model is suitable for high Reynolds number flows where the neglect of viscosity is acceptable. A great economy of computation is realized with such models because increased resolution is auto-matically provided in areas of high shear by the accumulation of many vortices i n such areas. A form of this model was used by Siggia and Aref (1981) to investigate characteristics of the inverse energy cascade in two-dimensional tur-bulence: their work provides some motivation for this choice of model. For the present application, such a model has the additional intuitive advantage of representing vorticity-dominated flow by a distribution of vorticity. A weak point in the model is the assumption that viscosity is small. This assumption is not an 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 m2s~1 (Pond and Pickard 1983). T h e use of an inviscid model i n this domain 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. T h e position of considering the inviscid results is taken not to fully explain nature, but to provide some greater insight towards a full explanation. Although this model has been developed to extend the idea of vortex in-jection through wave breaking presented in Chapter 6, it makes no restrictions on the source of the vorticity. What is considered is how two-dimensional vor-ticity will interact in the presence of an image surface. For this reason, the results can be considered to model the interactions of Langmuir cells when present, whatever the origin of that circulation might be. In particular, the model results are as applicable to vorticity introduced by the Craik-Leibovich mechanism as to that by the mechanism introduced in Chapter 6. 113 7.2 A 2-D Lagrangian Vorticity Model T h e concept of solving the inviscid Navier-Stokes equations using a L a -grangian vorticity approach is suggested by Chorin (1973) who demonstrates that this simple approach can accurately model the complex turbulent flow past a cylinder. The 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 and 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 = v x u , 7.2 u = V x -<f> can be used in Equations 7.1 to give V24> = 7.3 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 (Equation 7.3) are assigned to each point vortex, then the stream function for the entire flow can be ap-proximated by summing over the stream functions of the constituent vortices 4>{x,z) = ^ 2/(f>i. 7.5 114 Given that the stream function is known, the velocity of each of the point vor-tices can be determined and the motion of those vortices can be approximated to estimate the evolution of the vorticity field. T h e stream function resulting from the new distribution of vortices can again be calculated from Equation 7.5 thereby modelling the evolution of the flow. One difficulty characteristic of this model arises from the infinite veloci-ties encountered at small distances from a point vortex. H a l d and Del Prete (1978) outline a variety of methods that have been developed to deal with 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 finite distribution of vorticity. For the present model, a modification suggested by Chorin (1973) is used in which the stream function of the discrete vortices is described as Mr.\ ( 2 7 r ) _ l l ° g r ( r > a) 7 fi 7.3 Model Implementation The implementation of the Lagrangian vortex model requires consideration of the boundary conditions to be used. Boundary conditions must match the dynamics of the changing vortex locations otherwise the stream function of individual vortices becomes location dependent. A n easy way to do so is by introducing image surfaces. The geometry of the problem at hand is simple under this approach, a single image surface is used at the ocean surface with a second image surface introduced to simulate a bottom or thermocline if desired. These boundaries are realized in the model by introducing images of each vortex introduced into the model. 115 T h e horizontal domain is essentially unbounded and so would be best rep-resented by a periodic boundary condition. Such a boundary is not practical for the present model because vortex interactions must be determined explic-itly for each vortex and image represented in the model. Instead, a periodic boundary condition is approximated by repeating the domain once on each side of the model. W i t h this approach, interactions are considered for the replicates of all vortices within one model domain width of the finite model: the vortices existing beyond this range would contribute only marginally to the resulting stream function. The length scale i n the model is set by the size of vortices and by the periodic domain size so that model results are naturally non-dimensionalized by these and related scalings. Results are however presented in dimensional units because throughout the model development, the observations have been used to gauge the model results. For that purpose, a horizontal domain of 200 m is always considered (consistent with the sidescan sonar range), and a length resolution (as determined by the vortex diameter) of 1 or 2 m is used. T h e model domain is shown schematically in Figure 7.1. Vortices of diameter 2a are introduced into the model in stable pairs with a spacing of 2cr0 at a depth of a. These vortex pairs are introduced at a constant rate at at random locations along the horizontal domain. T h e model is stepped forward in time by advecting each of the point vortices by the existing velocity field. T h e time step is adjusted so that the largest vortex displacement is limited to be small compared to the diameter of the point vortices (typically displacements were restricted to a/10). In this way, time steps in the model are adjusted at all times to accomodate the most closely spaced vortices. N o vortex displacement will exceed this limit of a/10. 116 V | V V V V V V V V V | V \t * • • T ' . •* 1 t V T V V T V T V T V T * » • , t t t tb • t r \ T T T T T T t 1 t '1 * • t t T [ T T T T T T T T T t T 1 T T T T T T 1 T t | f T T f T T T T | T Periodic Boundary Optional Image Surface Image Surface .Test Point Periodic Boundary F i g u r e 7.1: Model domain. Vortices that approach close to the surface acquire large horizontal ve-locities through interactions with their images. To control these motions, any vortex trajectories that pass within cr/2 of the surface are reflected back to a depth of cr/2: a similar procedure is used when required where a bottom boundary is present. 117 Models based on point interactions between vortices have computational requirements that increase as n2 where n is the number of vortices. T h e present configuration uses a constant vortex injection rate and so the number of vortices grows linearly, inexorably reducing the model execution speed. In addition to this computational difficulty, it is not reasonable to expect the enstrophy of the flow to increase indefinitely. This problem is addressed by dif-fusing the vortex diameters with time in a manner that is somewhat analogous to viscous diffusion. T h e rate of vortex growth is given by a2 = 2vt. 7.7 W h e n the vortex diameter increases to some specified value, that vortex is eliminated from the model thereby limiting the number of vortices in the system. T h e method of eliminating vortices after some time removes enstrophy from the model and represents a form of dissipation. T h e interactions rep-resented by the model are essentially inviscid; vorticity cannot be generated or eliminated within the model domain. T h e only method available to hmit the enstrophy is by eliminating vortices and the method being used removes those that have been in the model the longest. Assuming that the action of viscosity will have degraded the strength of these vortices, this method can be considered as a means of representing viscous dissipation. 7.4 Model Subdivision Scheme T h e model stream function at any point is approximated by integrating over all the individual vortex 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 from distant vortices which have little effect on the value of the stream function. This situation has been avoided by determining the vorticity contained within subdivided regions and computing the stream func-tion based on the vorticity of these regions. Model accuracy is recovered by retaining individual vortex interactions for vortices i n close proximity to the point of interest. Nearby vortices are identified as those falling within 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 func-tion close to the model domain boundaries. Close to image surfaces, images of both the individual vortices and the subdivided regions are required. A t hori-zontal 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 and subdivision scheme by identifying the vortices contributing to the stream function computation for an example test point. In Figure 7.1, large arrows represent the collected vorticity of subdivided regions and small arrows represent discrete vortices: arrows are inverted across image surfaces. The computational advantage of this approach critically depends on the number and size of the subdivided regions. T h e relative advantage can be determined by considering the number and type of computational operations required for both the primitive and the subdivided versions of the model. 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 and ra is the number of vortices. In contrast to the "primitive" version of the model, the subdivided ver-sion of the model requires three distinct operations in order to determine the stream function at any point. First, the vorticity contained within each subdi-vided region must be determined and 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 in question must then be deter-mined. Finally, the contribution to the stream function from all those discrete vortices identified as being close to the point of interest must be determined. T h e time required for these calculations can be represented as 9 Tcic = an + Bnm + 6—ra2, 7.9 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 in Equation 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 model domain). What is important is not the actual processing time, but the relative advantage of using the subdividing algorithm; Tcic = an + 8nm + 6±n2 T 8n(n-l) T h e factor a is known to be small and it is linear in 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. Using these two simplifications, Equation 7.10 reduces to ^ = m / n + 9 / m . 7.11 For a given value of n, ^ p - is minimal when m = 3 n - 1 / 2 . Most of the models to be considered incorporate 1500 vortices: the optimal number of subdivdided regions for such cases is 116 for which a computational advantage of = 0.15 is realized. The 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 in this discussion, it will be considered in the follow-ing section on model accuracy through comparisons of models with different operating parameters. 7 . 5 M o d e l A c c u r a c y The question of convergence and ultimate accuracy of vortex models is considered by Hald and Del Prete (1978), and H a l d (1979). Subject to the approximations of the model, they find that the approach converges and has an error proportional to the diameter of the discrete vortices. Another concern with any numerical scheme is the effect of numerical diffusion on the results; errors in the stream function, and the finite time step (displacement step) of the model cause errors in the trajectory of the point vortices. The effect of (random) errors in vortex displacements is to introduce a random component to the vortex motion which acts to diffuse the vortices. This effect can be seen by considering how the model would represent the 121 motion of passive point tracers about a single vortex. This system would be completely stable with the tracers orbiting the vortex, but the random errors in the model would lead to a slow diffusion of tracers outward from the vortex. For the vortex model, this diffusion is analogous to the action of viscosity (as discussed by Chorin, 1973). T h e variance in vortex displacements can be related to viscosity through the relation, x2 = 2ut, 7.12 where x 2 is the variance in position, v is the viscosity, and t is the elapsed time. 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 in vortex displacements occurring in the model since the correct displacements are not actually known. It is however possible to start models with various parameter configurations from a given state, and then compare the vortex displacements predicted by these models. If the models have identical errors, the vortex displacements will be identical and nothing can be learned. However, the errors due to the subdivision scheme can be isolated by comparing against a primitive (non-subdivided) model, and the errors arising from a finite time step can be isolated by comparing models with different time step values. Displacement errors will be different (and it is assumed independent) in these comparisons so that the variance in the distribution of vortex displacements can be related to viscosity through Equation 7.12. The first comparison to be considered is made between two models start-ing from a common state but proceeding with different time steps for 2 s of 122 model time. One model incorporates a time step regulated by a maximum vortex displacement of cr/10, while the second model is constrained to by dis-placements of cr/100 (resulting in time steps ~ t h of the first model). T h e models are identical in all other respects spanning 200 m horizontally, un-bounded vertically, and incorporating 3000 individual vortices. In Figure 7.2a, a visual comparison of differences between these models is obtained by plotting the differences in horizontal and vertical displacement as x and y positions for each of the vortices in the models. If it is assumed that the displacement dif-ferences do not depend on position within the model domain, then Figure 7.2a can be interpreted as portraying the distribution of displacement differences occurring between these models. If the errors occurring i n these models are random, then the variance of displacement errors will add. T h e model based on small time steps makes only a small contribution to this variance and it is assumed that all of the scatter seen in Figure 7.2a is due to errors resulting from the use of a larger time step. At worst, this assumption leads to an over estimation of the variance generated by the model. Subject to this assumption, the amount of scatter seen in Figure 7.2a translates through Equation 7.12 to a viscosity of 1 0 - 6 m 2 5 - 1 . This value is of the order of as that of molecular viscosity and is obviously insignificant in 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 interpre-tation of this scatter i n terms of viscosity. Figure 7.2a is characterized by an apparent isotropic scatter with some anomalous displacements in a downward direction. These anomalous points are not unexpected, they result from the model treatment of vortices interacting with the surface. There is only one 123 .02-nj LD O CL > I cn • CL > o.oo-QJ c t o L X .02-A .02 .01 .01 —I .02 X P O S 1 - X P O S 2 CmD .02n .01-0.00-B X -3.14 -1.05 1.05 A n g l e C r a d J 3.14 F i g u r e 7.2: Comparison of displacement differences between a normal model run, and one with a time step reduced by a factor of 10, (the small time step model will have comparatively small errors and is considered as a refer-ence), a) Scatter plot of displacement differences, b) directional dependence of displacement differences. 124 time step required in the model using a long time step and any escaping vor-tices are arbitrarily replaced at a depth of z = CQ/2. M a n y of these vortices never escape in the model with shorter time steps and they will appear at depths greater than CTQ/2 resulting in anomalously large negative displacement differences in the comparison. To further quantify the degree of isotropy, the displacement variance is plotted as a function of direction in Figure 7.2b. It is seen that the variance is essentially isotropic except for an increase in downward variance related to the surface interacting vortices. From this comparison it is clear that time steps regulated by maximum displacements of O.lcr produce minimal 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 model was executed until a steady state was achieved and that model re-sult was used as the initial condition for both the primitive model and the subdivided model. T h e vortex displacements predicted i n these two models were compared after a two second time step had been completed. Figure 7.3a shows the distribution of displacement differences between the primitive model and a model that has been subdivided into 640 rectangular regions 3.13 m in the horizontal by 5 m in the vertical. A feature of the distribution in Figure 7.3a is the horizontal line of vor-tex displacements. It is caused by vortices interacting with the surface image boundary, but because the time step is the same in both models, (in contrast to the two models compared in Figure 7.2a), many of the same vortices escape the boundary in both models and are returned to the same depth (resulting in a 0 vertical displacement). ru cn • CL >-I CD • CL o.oo-.:'7*-'; 125 .02-A .02--.02 I 1 -.01 .01 XPDS1-XPOS2 Cm] —•i .02 .02-1 B E QJ Dl C CD CE .01-X o.oo--3.14 -1.05 1.05 A n g l e Crad] 3.14 F i g u r e 7.3: Difference in computed displacements between a primitive vortex interaction model and a model accelerated by subdividing it into 640 regions; a) Scatter plot of displacement differences, b) Directional dependence of dis-placement differences. 126 Figure 7.3b shows a plot of variance as a function of direction to quantify the degree of isotropy in the scatter plot of Figure 7.3a. T h e only distortions in this plot are those expected in the horizontal which result from the bound-ary interacting vortices. T h e amount of variance present in this comparison is similar to that seen in Figure 7.2 and so it is concluded that for this subdi-vision scheme, there is neither (significant) increase in displacement scatter or introduction of any undesirable bias. Based on the minimization of Equation 7.11, there is an optimal choice for the number of subdivided regions but this estimate does not account for model accuracy. Comparisons were repeated with a variety of models to determine the sensitivity of the results to the size of the subdivided regions, (always comparing against the same primitive model). Table 7.1 provides a summary of these tests in terms of the horizontal and vertical viscosity implied by the resulting variance. In all cases tested, the viscosities are of the order of molecular viscosity and so the subdivisions should not adversely affect results. Based on the results shown in Table 7.1, models have been subdivided into 64x10 (3.13 m x 5 m) regions. 7.6 Model Scalings It is a worthwhile exercise to consider the scahngs that are present in the model and the implications that these might have on the results. 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, viscosity and maximum vortex size (which controls the vortex life time). It is the results which have some physical meaning which are of interest and not those that are a consequence of the model design. 127 Trial x-dimension y-dimension m m m2s~1 2 — 1 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 10~7 4 2.5 2.5 1 x 10"5 9 x 10~6 Table 7.1: Numerical viscosities resulting from subdivision schemes. T h e vortex life time is determined by the size of injected vortices, the maximum allowed vortex size, and the rate of vortex diffusion. From Equation 7.7, the vortex life time can be found as: (2 2 \ rp _ \°~m ~ ao) j 23 2v where o~m is the maximum vortex radius in meters, cr0 is the initial vortex radius in meters, and v is the viscosity in m2s~l. This time scale is largely a 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 and the rate at which dissipation erodes this enstrophy. T h e values of viscosity used in Equation 7.12 were kept small (less than 1 0 _ 3 m 2 s - 1 ) to be consistent with the concept of an inviscid model. A consequence of this low value was a tendency 128 to extend vortex life times as regulated by Equation 7.13. T h e number of vor-tices active in the model is a direct consequence of the viscosity, the injection rate Vp and the maximum vortex diameter cr m . In order to keep vortex num-bers low i n the model, the value of am was decreased to values of order 2cTo. In this case, the elimination of vortices is a separate non-physical form of vis-cosity. T h e only argument that can be made i n support this approach is that old vortices have a tendency to appear at greater depths in the model where density gradients (not considered by the model) would act to absorb vorticity. Numerical viscosity is also active in the model as discussed previously. Values for this term are however of order 1 0 - 5 as identified in Table 7.1 and so they should have a very small effect on model outcomes. It is possible to increase the viscosity of the model by introducing random motions to the vortices according to Equation 7.12, this approach has not been explored in the model experiments. 7.7 Summary of Lagrangian Vorticity Model Two dimensional flow close to an image boundary is a characteristic fun-damental to Langmuir circulation. A Lagrangian model of vorticity has been developed to improve the understanding of interactions between vortices in this geometry. This model is particularly suited to investigating the presence of multiple scales seen in Langmuir circulation. The model makes no distinction as to the origin of vorticity and so it is equally applicable to any model of Langmuir circulation." It is developed in this instance to determine if vorticity introduced at very small scales can account for the larger structures recognized as Langmuir circulation. 129 The model is based on solving the inviscid equations of fluid motion 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 randomly along the surface image boundary of the model's periodic horizontal domain. There is no explicit need for a bottom boundary because of the Lagrangian nature of the model. In practice, the use of point vortices is difficult since they can introduce infinite velocities in 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 (Hald 1979). There is also a practical limit on the number of vortices used since the execution time of the model increases as the square of the number of vortices. Since the model introduces vortices at a continuous rate, it is necessary to ehminate vortices in some man-ner to avoid excessive computational requirements; the vortex regions diffuse and are removed from the model when they reach some arbitrary diameter. This approach approximates the action of viscous dissipation. T h e number of active vortices in the model eventually reaches a balance between the rate of vortex injection and the life time of vortices. T h e model cannot be relied upon to study the energy budget of a cir-culation pattern because it does not accurately represent energy flow. Rather, the model can be expected to represent the interaction between many point vortices, the effects of a bottom boundary (if included), and the velocity distri-bution within the circulations that are generated. 130 C h a p t e r 8 M o d e l R e s u l t s Evaluation of model results can be carried out at two levels; a qualitative consideration of model characteristics, and a quantitative comparison of model parameters and results. Qualitative characteristics are not strongly dependent on exact parameter choices and these general results will be presented first in this chapter. Progressively, more quantitative results will be considered which offer more information but are more sensitive to the model characteristics. T h e results that are presented are based on nine model runs identified in Table 8.1. In addition to model parameters, Table 8.1 displays some general indicators of the model results: the significance of these indicators will be discussed i n detail as they are encountered through the discussions presented in this chapter. 8.1 Model Streamlines A convenient overview of model characteristics can be obtained by con-sidering the streamlines predicted by the model after it has reached a steady state. Streamlines are constructed by contouring the stream function on a grid of 3 by 3 m over the model domain. Contouring on this grid filters out small scale structures consistent with the model's finite resolution as determined by the discrete vortex dimension (of order ao). A s a first example, typical streamlines produced by the model in the absence of a bottom boundary are displayed in Figure 8.1, these streamlines 131 M o d e l A B . C D E F G H I T (s x 10 3) 3.7 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 K m ^ ^ l O " 3 ) 0.27 0.27 0.27 0.54 0.27 0.27 0.27 0.27 0.27 cr 0(m) 0.5 1.0 2.0 1.0 2.0 1.0 1.0 1.0 1.0 cr m (m) 1.5 1.62 2.37 1.62 2.37 1.62 1.62 1.62 1.62 as-1) 0.005 0.01 0.02 0.01 0.02 0.01 0.01 0.01 0.01 Vortices 3076 1205 1318 1118 2148 1342 1232 1230 1216 D o m a i n (rn) oo oo oo oo oo oo 15 10 20 T0& s(.s) 500 325 326 197 168 264 276 228 216 Tobs/T 0.14 0.11 0.11 0.13 0.06 0.09 0.09 0.07 0.07 Vmax{ms~x) -.02 -.03 -.05 -.03 -.10 -.03 -.05 -.04 -.04 F W H M (m) 37 44 33 48 34 35 14 11 20 T a b l e 8.1: Model run statistics. are drawn from Model C identified in Table 8.1. The contour interval in this figure is 4 m2s~1 with only the values at maxima 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 and 30 m in the vertical. The flow has organized itself into a few well defined cells with the obvious 132 Horizontal Scale (m) Figure 8.1: Contours of stream function occurring when the model has achieved a steady state and there is no bottom present. A contour interval of 4 m2s~1 has been used with values at maxima labelled and all negative areas (characterized by clockwise oriented flow) have been shaded in . presence of several length scales. There is some indication that regions of clockwise flow are pressed towards the right against balancing counter-clockwise flows. The resulting crowding of downward directed streamlines between these regions results in downwelling velocities exceeding those upwelling. For this model, maximum downwelling velocities are about —0.05 m s - 1 compared 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 counter-clockwise 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 obser-vations 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 Vmax-Model C (see Table 8.1) provides downward velocities of —0.05 m s - 1 which is comparable to the values of —0.06 m s - 1 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 in all other respects to that shown in Figure 8.1. T h e streamlines that result from this test are shown in Figure 8.2. A s for Figure 8.1, maxima have been labelled and regions of clockwise flow have been shaded in; a contour interval of 2 m2s~1 has been used. In Figure 8.2, the entire model domain is displayed; 200 m in the horizontal and 10 m in the vertical. Figure 8.2 shows some streamlines crossing the bottom image boundary: this does not result from flow across the model boundary, but is an artifact of the contouring package used in making the figure. In comparing Figure 8.1 with Figure 8.2 it is immediately clear that the presence of the bottom boundary has altered the horizontal length scales (bear in mind the different vertical scales used in producing these figures). The horizontal coherence of the stream function at a fixed depth was 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, x and z are horizontal and vertical spatial coordinates, and ( ) indicates a time average. T h e horizontal coherence is somewhat depth-dependent; for bottom bounded models it is calculated at mid depth, and in the model with no bottom boundary it is computed at 15 ro depth. T h e time average is achieved by repeating the calculation over many (independent) model realizations and the full width at half maximum ( F W H M ) of the autocorrelation function is used as a measure of model horizontal length scale. This value for all model runs is listed in Table 8.1. 135 0 Horizontal Scale (m) Figure 8.2: Contours of stream function occurring when the model has achieved a steady state with a bottom located at 10 m in a 200 m hori-zontal domain. A contour interval of 2 m2s~1 has been used with values at maxima labelled and areas characterized by clockwise oriented flow shaded in . It is not immediately clear what parameters control the F W H M in the unbounded models, but the introduction of the bottom boundary clearly re-stricts length scales in proportion to the boundary depth. Figure 8.3 shows the dependence of length scales on bottom boundary depth for Models G , H and I. These models are identical in 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 or-ganized 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 bottom boundary depth. Length scales are determined from autocorrelations of the stream function and plotted against the bottom boundary depth used in that model. 138 ^ 1 0 0 n S p a c i n g ( m ) 0) o U 0 o o > • H -P i—I (1) l O O - i 1 0 m b o t t o m S p a c i n g ( m ) Figure 8.4: Cell spacing histograms for model results a) 10m bottom bound-ary and b) 20m bottom boundary. Distinct cells are identified on the basis of vertical velocities exceeding —0.01 ms-1. 139 identifiable structures in the sidescan data; about 20 to 30 minutes. A simi-lar sort of measure could be used for the model results based on similarities between successive streamline patterns, but this approach would be extremely time consuming to implement and would not easily be repeatable due to the qualitative nature of the definition. Instead, a more quantitative approach has been used which is based on the coherence between the stream functions of successive model realizations. This approach is not directly comparable to the observations, but since the alternative of visual estimates of streamline struc-ture life time is no better in this regard, the more quantified approach is favoured. For the purpose of estimating structure life times, the coherence is defined as, n r x = (fx<Kx,t)<l>(x,t + T)dx)2  { T ) Jx<f)*(x,t)dxJx<f>*(x,t + T)dx where (f>(x,t) is the model stream function. T h e life time (T0bs) is defined as that time lag beyond which the coherence falls below 0.7 (ie. H(T0b3) = 0.7) This fairly high choice for the coherence threshold results in shorter life times, but the resulting values are more stable than those generated using smaller values where the results are very sensitive to random fluctuations. The results of these calculations are presented in Table 8.1 for all the model variations considered: the model life times are about 200 to 300 seconds depending on the parameter choice. The model life times are much shorter than the 30 minute (or 1800 s) life times observed in the sidescan data but as has already been indicated, the model life times are arbitrarily determined based on the coherence of 0.7. Longer life times could be achieved by using a smaller coherence threshold, 140 but comparisons between model results would then become difficult because of the lack of stability in 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 concern with the model was that the life time of structures might be determined by the vortex life time and not by the vortex interactions themselves. The extent to which this occurs can be evaluated by non-dimensionalizing the observed life times by the vortex life times, T* = T0b3/T. 8.3 T h e values of this indicator are also shown i n Table 8.1 and, while the scaling value remains close to 0.1, significant changes occur with some of the pa-rameters (vortex injection rate Vp in particular). Clearly vortex life times do not dominate the variability in the structure life times, suggesting that vortex interactions are a significant influence. 8.5 Discussion of M o d e l Results 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 in 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 domain. The first notable result of this model is that it reproduces streamlines con-sistent with those expected for Langmuir circulation. In particular, it predicts downwelling speeds in excess of upwelling speeds with the maximum down 141 ward velocity somewhat below the surface. This result is a consequence of the model geometry and the interaction of vortices with their images. T h e response of the model to the presence of a bottom boundary is another geometrical result consistent with observations. T h e maximum length scale is seen to vary linearly with variations in the domain depth. Quantitative comparison of model length scales with observations are difficult, but qualitatively the model his-tograms (Figure 8.4) agree in appearance with those generated from sidescan sonar data (Figure 4.8 page 58). Some inaccuracy of the model scalings is suggested by comparing the life times of structures seen in the model with the predictions of Equation 7.13. These differences can be seen by forming the ratio of observed structure life times with the life time scaling (from Equation 7.13) as shown in Table 8.1. This variation demonstrates that there are mechanisms acting which determine structure stability in addition to the effects of vortex elimination. Comparing the structure life time of M o d e l E with that of Model C is revealing: these models differ in the doubling of the vortex injection rate but the outcome is a halving of the structure life times. Clearly the random injection of vortices in some way acts to disrupt structures already existing and thus reduces the life times of these structures. 8.6 Conclusions In Chapter 6, it was demonstrated that isotropic turbulence introduced selectively at wave crests can result in an enhancement of the vorticity compo-nent oriented parallel to the waves by a factor of 1.2. It is suggested that this mechanism could be responsible for the phenomenon of Langmuir 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 Craik-Leibovich theory is its direct explanation of small scale cells that are seen to coexist with larger structures in the observations presented in Chapter 4. A two dimensional Lagrangian vorticity model described in Chapter 7 was developed to investigate the behaviour of vorticity introduced close to an image surface (the ocean surface). This model does not involve any source mecha-nism 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 Craik and Leibovich, with the provision that it ignores any generation term. T h e experiments performed with this Lagrangian vortex model have been discussed in the present chapter through considerations of model streamlines, velocities, structure life times, and length scales. The form of the streamlines produced by the model are consistent with observations of Langmuir circulation, with pairs of counter rotating vortices occurring at a variety of length scales. 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. The occurrence of down-welling velocities in excess of upwelling velocities is a characteristic that is ob-served in Langmuir circulation and, based on model results, it can be explained by the interaction of vortices with their image pairs. Regions of clockwise vor-ticity are advected towards the right by the corresponding counter-clockwise image vorticity, and conversely, counter-clockwise regions to the left. W h e n a clockwise region encounters a counter-clockwise region, they are pressed to-gether by their images and the observed assymetry results. 143 Spacings between cells in the model have been determined by identifying vertical velocity minima (regions of downwelling) in the model results. His-tograms of spacings estimated i n this way agree in form with comparable histograms made from sidescan sonar observations. T h e introduction of a bot-tom boundary restricts the largest length scales and forces the peak in spacing histograms to smaller scales. T h e characteristic length scale determined from the spatial correlation of the stream function varies linearly with changes in bottom boundary depth. This behaviour is i n agreement with observations that windrow spacings are hmited to 2 or 3 times the water (or mixed layer) depth (Leibovich 1983, Smith et al. 1987). W i t h any modelling simulations, there is the concern that characteristics of the model might influence the flow fields predicted. A particular weakness in the discrete vortex model presented here is the existence of a totally arti-ficial time scale imposed by the life times of individual vortices. Comparisons between model configurations with markedly different vortex life times have demonstrated that the life times do not dominate the persistence of structures in the model. Instead, it is the rate at which vorticity is introduced which controls the persistence of structures: the persistence of model structures varied inversely with the rate of vortex injection. 144 Chapter 9 Summary and Conclusions Near surface processes mediate the exchange of heat, momentum, and matter between the atmosphere and ocean. A n improved understanding of many important processes including ocean circulation, climate, and even the world CO2 budget can only be achieved by understanding the interactions occurring at the ocean surface. Observations of near surface processes are however complicated by the destructive action of surface waves. In addition, many 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 making remote measurements in this hostile environment, and to use those observations to improve the understanding of near surface processes. This thesis reports on the development of instrumentation which combines vertical sonar, sidescan sonar, and ambient sound observations in a freely drift-ing, autonomous package capable of operating in the deep ocean. This system was used to observe the dynamics of near surface processes in the deep ocean as they respond to various wind forcing conditions. The organization of subsur-face bubble clouds into long rows parallel to the wind reveals the occurrence of Langmuir 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 I n s t r u m e n t a t i o n T h e observations presented in this thesis were made possible by an ex-tensive program of instrumentation development. Although much of this devel-opment has involved the application of proven techniques, several components were developed specifically to meet the present requirements. T h e large quantities of data generated by the acoustic systems were recorded using video cassette recorders and a Sony P C M digital interface. T h e 16 bit data recorded by this system can only be recovered at a rate of 44.1 k H z and these data must be analyzed in real time because no com-puter system could (conveniently) store such a large volume of raw data. A Zoran VSP-161 vector signal processing system was employed to allow this real time processing. Software was developed for the Zoran system which allowed spectral analysis of ambient sound data and complete analysis of sidescan and vertical sonar data. Without the high performance digital processing capabili-ties of the Zoran system, the data presentation of this thesis would not have been possible. The need to record phase information with a single digitizing channel led to the use of an implicit clock sampling scheme. Apphcation of this technique was complicated by the need to synthesize specific frequencies to match the (fixed) P C M digitizing rate. This need led to the development (largely by Paul 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 motion and so wave observations were made using a Datawell Waverider buoy. Wave observations are however also possible with 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 de-termined by Waverider data and sonar has demonstrated that the sonar data can provide observations of comparable accuracy to those of the Waverider. Based on the success of this comparison, future acoustic studies can determine surface wave records with confidence using vertical sonar systems. 9.2 Observations Observations were made using the package of acoustic instrumentation in the mid-Pacific Ocean as part of the O C E A N S T O R M S program. These obser-vations provide detailed documentation of a 21-hour period of increasing wind speed (to a maximum of 13 m s - 1 ) . Through these observations, the sea state is observed to build to a fully developed state and the evolution of subsurface bubble plumes is documented. Short period analysis of ambient sound records (2-20 kHz) have been demonstrated to contain signals generated by breaking waves (Farmer and 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 in phase with waves passing over the instrumentation. Sidescan sonar data at 150 k H z provide evidence for Langmuir circulation (through the presence of organized bands of scatterers) throughout the 21 hour 147 deployment presented. These bands had 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 wind speeds below 10 m s - 1 and increased to spacings of 10 to 20 metres at greater wind speeds. Vertical velocity estimates made using an upward looking, 200 k H z echo sounder reveal downward velocities of 0.06 m s - 1 at 8 m depth i n the bubble plumes. T h e maximum velocity was located at 8 m depth in 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. 9.3 Ambient Sound Modulations A simple model of surface sound generation was developed to assist in the understanding of the wave period modulations seen in the ambient sound data. Comparisons between the model predictions and observations suggests that sound sources must be restricted to surface dimensions of 6 m or less (to account for the continuous nature of sound levels in the observations). Two possible source mechanisms are considered: short wave, long wave interactions; and variations in wind stress over the long surface waves. T h e present data are characterized by swell at approximately 9 0 ° to the prevailing wind making it impossible to distinguish between these two mechanisms. 9.4 Langmuir Circulation The sidescan sonar observations of Langmuir circulation demonstrate the occurrence of many coexisting length scales. In this thesis it is speculated that this distribution is caused by a two dimensional vorticity cascade from 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 in the direc-tion of wave propagation can enhance vorticity by about 25%. Once a single component of vorticity is generated at 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 im-age surface (the ocean surface). This 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 model of Langmuir circulation (such as that of Craik and Leibovich). T h e discrete vortex model successfully reproduces many characteristics of Langmuir circulation: a range of vortex length scales is seen, down-welling speeds exceed upwelling speeds, and maximum length scales are restricted in proportion to the domain depth. These results suggest that the concept of a two dimensional up-scale cascade is consistent with the observations of Lang-muir circulation. The model clearly identifies the cause of the asymmetry seen in Langmuir circulation (down welling speeds exceeding upwelling speeds): the circulation across the image surface advects clockwise regions of flow to the right and counter-clockwise regions of flow to the left. Eventually, the 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 and they 149 slowly drift apart. This asymmetrical migration leads to a crowding (and con-sequent intensification) of downwelling streamlines. T h e occurrence of asymmetry in models of Langmuir circulation has been identified as a key requirement for any model of Langmuir circulation (Lei-bovich 1983). T h e present results indicate that the asymmetry (as well as the length scale dependence on bottom boundary depth) is a result of two di-mensional vorticity and the domain geometry germane to Langmuir circulation. A n y model introducing two dimensional vorticity close to an image surface will demonstrate these basic characteristics. T h e main purpose of the vortex interaction model was to investigate the behaviour of small scale vorticity introduced by selective vortex stretching. T h e model results clearly demonstrate that small scale vorticity can lead to flow structures similar to those observed in Langmuir circulation. Near surface flow is however much more complicated than the representation offered by this simple model. T h e presence of vertical shear in the near surface water will ultimately introduce the vortex forcing identified by the Craik Leibovich mech-anism. T h e discrete vortex model cannot represent such interactions and 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 Craik 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 This thesis has touched on only a few of the important and interesting processes occurring at the ocean surface: much work remains to be done. The 150 action of wave breaking, Langmuir circulation, gas exchange, momentum trans-fer and mixing all interact in this complex physical system. It is not possible to provide a complete description of any one component without considering several (if not all) of these processes. Acoustic sampling techniques provide a valuable tool to probe these near surface processes. In this thesis, acoustic analysis has been used to deter-mine vertical velocities, make qualitative estimates of bubble concentrations, display the horizontal extent of subsurface bubble plumes, measure one di-mensional wave spectra, and identify certain characteristics of wave breaking. This is only a partial list of the capabilities of acoustic sampling techniques. Calibrated sonar systems can be used to determine bubble size distributions, passive arrays can track individual sound sources, coded sonars can achieve much improved Doppler speed estimates, and Doppler enabled sidescan sonars can be used to determine directional wave spectra and near surface horizontal currents. A s signal processing capabilities improve, even more advanced acous-tic sampling systems will be developed. There remain many possibilities for further applications of these systems to the study of near surface processes. T h e observations presented indicate the continuous presence of Langmuir circulation over a two week period. These observations, and similar obser-vations by Weller and Price (1988), contribute to the growing evidence that Langmuir circulation is a common phenomenon in the open ocean. A n y model of mixed layer dynamics must therefore account for the enhanced vertical mix-ing 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 Langmuir circulation occurs be gained. 151 T h e evaluation in this thesis demonstrates that many observed characteris-tics of Langmuir circulation can be reproduced by a two dimensional cascade of vorticity. A possible vorticity source is presented as vortex generation by wave breaking and its subsequent intensification by wave action. T h e available data cannot verify or refute this concept: an extended set of observations (preferably under controlled conditions) will be required for such an evaluation. Wave period modulations in ambient sound data have been described by a model with source amplitude variations in proportion to surface wave displace-ment. This model implies that ambient sound is generated preferentially at wave crests. 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A . , A . J . Hal l , A . R . Packwood and A . R . Stubbs, 1985: T h e use of a towed side-scan sonar to investigate processes near the sea surface. Cont. Shelf Res. 4, 597-607. Vagle, Svein, Wil l iam G . Large, and David M . Farmer, 1990: A n evalua-tion of the W O T A N technique of inferring oceanic winds from underwa-ter ambient sound. J . Atmos. Oceanic Tech., 7, 576-595. Walsh, A . L . and P.J . Mulhearn, 1987: Photographic measurements of bub-ble populations from breaking waves at sea. J . Geophys. Res., 92(cl3), 14553-14565. Weller, R . A . and J . F . Price, 1988: Langmuir circulation within the oceanic mixed layer. Deep Sea Res. 35, 711-747. Wenz, G . M . , 1962: Acoustic ambient noise in the ocean: spectra and sources. J . Acoust. Soc. A m . , 34, 1936-1956. W u , J . , 1981: Bubble populations and spectra in near-surface ocean: sum-mary and review of field measurements. J . Geophys. Res. 86, 457-463. Zedel, L . J . and J . Church, 1987: Real-time screening techniques for Doppler current profiler data. J . Atmos. Oceanic Tech., 4, 572-581. Zilker, D . P . , G . W . Cook and T . J . Hanratty, 1977: Influence of the ampli-tude of a wavy wall on a turbulent flow. Part I. Non-separated flows. J . F l u i d Mech. , 82, 29-51. Appendix A Craik-Leibovich Theory 158 This appendix provides a brief outline of the derivation of the vortic-ity equation describing Langmuir circulations after the Craik Leibovich theory. This development is taken from Craik and Leibovich (1976). Consider the total water velocity for the water surface q can be broken into two parts £ = «M u l + « 2 w , A . l where e is the waves slope, euw is the irrotational wave component of motion, and t2v is everything else. It is assumed that the velocity due to wave mo-tion is significantly larger than the non-wave velocity components. W i t h this decomposition, the vorticity equation for a Boussinesq fluid can be written as ut = V x (q x w) + ueV2u A.2 where w = V x q. T h e expression for u> can be expanded by substituting in the expression for q from Equation A . l to give w = e 2 ( V x u ) . A.3 Notice that there is no vorticity introduced from the irrotational wave compo-nent u^,. Both the non-wave velocity component v_ and the vorticity u_ can be ex-panded into a series of the form, n — y_o + ev-i + + -A-4 159 In addition, each of the terms of this expansion can be broken into a mean and fluctuating component of the form Vj — Vj+ < Vj >, A.5 where the overbar refers to a mean value, and the < • • • > refers to the time dependent component. 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. -aV 2 uJ 0 = V x (Fo~ x uTo") + V x (uw x < o; : >) A.6 where the eddy viscosity ue has been assumed to be approximately e2a. This relation can be time averaged over a period short compared to the development time of the Langmuir circulation, but long compared to the wave period to produce a time averaged vorticity equation. -aV2U0 = (u£- V)(^-rMs)-(Ho+Ma)Vwo A.7 where u* is the Stokes drift, us = {judt- V ) u A.8 t Equation A . 7 describes how the vorticity and surface currents (including wave motion) interact. Craik and Leibovich (1976) simplify the problem by assuming that the Stokes drift is unidirectional (implying a directionally symmetric wave spectrum). T h e velocity field and vorticity become, Ms = K(y,*),o,o) UQ" = (u, v, w) A.9 160 W h e n these simplifications are substituted into Equation A.6 the vorticity equation becomes, , du* du3 di d( « v 2 f + ^ + C 1 7 = v ^ + ^ A i d Equation A.10 forms the basis of the Craik-Leibovich theory for Langmuir circulation. In this equation, a V 2 f represents the diffusion of vorticity, r / ^ - + represents the deformation of vortex lines by the Stokes drift, and + u>H represents the convection of vorticity. Appendix B Data Acquisition 161 Storage of acoustic data is made possible by using the Sony P C M system together with the video and H i - F i signal storage available on conventional video cassette recorders ( V C R ' s ) . These systems are designed to record high quality audio frequency signals in a continuous mode for periods as long as 8 hours. T h e y are a convenient medium for many applications but, any signal that is recorded must be conditioned to be compatible with audio frequency band-widths. In addition, the data can only be recovered in a continuous streamed mode so either the data must be transferred to a conventional storage medium 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 5.1 gigabytes of data. But , to implement the alternative, powerful signal process-ing systems which can keep up with the streamed data rate must be used to analyze the data. This Appendix describes the data conditioning required to store the var-ious data types onto the V C R medium. Details of data recovery from the V C R ' s are considered in separate appendices for the various data types; A p -pendix C , D , and E for vertical sonar, sidescan sonar, and ambient sound respectively. Although sidescan sonar is digitized during data playback while ambient sound and vertical sonar are digitized during data storage, the pro-cessing configuration on playback is fundamentally the same in all cases. A general outline of the processing steps and instrumentation used i n data re-162 covery will be given rather than detailing the slight differences between the individual cases. B . l Ambient Sound Signal Condit ioning O f the data recorded, only ambient sound lends itself to storage with a streaming audio frequency system and it consequently required a minimum of signal conditioning. The only consideration in recording these data is that ocean ambient sound levels are known to have a coloured spectrum with a level that decays at about 20 dB per decade at increasing frequencies (Knudsen et al. 1948). This colouring would require system gain levels to be set to accommodate the high power, low frequency signals compromising resolution of higher frequency signals. T o offset this effect, a prewhitening filter with response, where, V ; n is the input voltage, Vout is the output voltage, R = 12414 fi, C = 834 x 1 0 - 1 2 F, and u is the signal angular frequency, was used. Figure B . l displays a typical ambient sound spectrum before and after whitening with this filter. B.2 Sidescan Sonar Condi t ioning The sidescan sonar data is recorded on the two H i - F i channels of the V C R (one channel for each of the two sidescan sonars). These channels are only capable of recording a 20 k H z bandwidth but the sidescan sonar is on a 100 k H z carrier: in order to record this signal some form of demodulation must be used. (R2 + \/u2C2fl2 R B.l 163 F i g u r e B . l : Example of prewhitening filter effect on ambient sound spec-trum. Dashed line is unfiltered ambient sound spectrum, the solid line is filtered. 164 For 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 on bubble distributions. T o isolate this signal from the 100 k H z carrier, the received signal is multiplied with a 137.5 k H z reference producing a signal with information at 17.5 k H z , and 257.5 k H z . This signal is low pass filtered re-taining only the 17.5 k H z signal for recording onto the H i - F i channels. T h e remaining carrier is subsequently removed through the data recovery process-ing. B.3 Vertical Sonar Signal Conditioning T h e vertical sonar systems provide the most challenging recording prob-lems. T h e complexity stems from the desire to make Doppler speed estimates, and so, in addition to the requirement of matching the carrier frequency to the recording bandwidth, the signal phase must also be preserved. W i t h Doppler applications, data recording is normally done by mixing the backscattered sonar signal with a reference oscillator at the sonar frequency to produce a signal with a 0 mean frequency. T o recover the phase from such a "mixed down" signal, the process is repeated using a reference oscillator that is 9 0 ° out of phase with the first. These two signals form a complex 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 and in the present application, both of the digital P C M channels could not be committed to vertical sonar. T o avoid this restriction, a technique 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 the Doppler shifts and any other phase information in the signal, and A(t) is the amplitude envelope of the signal. This received signal is mixed with a reference oscillator of frequency u giving, S{t) - A(t) cos(wi + <f>(t)) cos(wi) = ^2. cos(( w - u)t + m) + cos(^++ B3 T h e high frequency component of this signal is filtered off leaving, c(t) = cos((> - u)t + <f>(t)). BA u can be selected so that (a> — UJ) is exactly 1/4 the digitization rate. c(r) is then sampled whenever i = tj = * J ~s ; = 0 , 1 , 2 , . . . . B.5 Equation B.4 can now be rewritten as A(t) ~ ~ c(tj) = ^ [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 ^ s M ( * i ) ?(<2) = ^ c o s ^ ) =^-sm<f>(t3) ?(*4) = A { i 2 * ] cos^(t4) B.l If (^ (r) and A(t) change slowly in a time of ir/(2(u — UJ)) then the two con-secutive samples from c(r) can be considered as the in 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 in Equation B.7). T h e consequences of assuming a slow rate of phase change compared to the sampling interval can be investigated by considering typical values expected i n the present application. In the case that a radial velocity of 0.2 ms-1 is observed, the value of ^ will be 1.8 x 1 0 - 3 s - 1 (for the 200 k H z sonar). This frequency leads to a speed estimate that is low by 0.01 m s - 1 : this error is small compared to the velocities that are being investigated and so is acceptable. Use of this final assumption is only a convenience in processing the data, if the resulting errors are too large, the values can be recovered completely by accounting for the actual sample times as given in Equation B.7. It was necessary to heterodyne the sonar signals onto carriers of 11.025 k H z to apply the implicit clock scheme to the P C M application. T h i s 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 both the P C M digitizing clock, and the sonar carrier frequencies. Such phase coherence is usu-ally achieved by using a common oscillator and dividing it as appropriate to achieve the various frequencies required. In the present case, such an approach is not possible because of the combination of frequencies used and the inflexi-bility of the digitization clock. T o overcome this problem, a phase locked loop circuit was devised by Paul Johnson (a technologist at the Institute of Ocean Sciences) which allowed the beating up of a reference clock derived from the P C M clock. B y using a reference clock of 787.5 H z , it was possible to gen-erate any frequency required to within 787.5 Hz . T h e choice of 787.5 H z was 167 made because it could generate both the required mix frequencies of 200 k H z ± 11.025 k H z and 50 k H z ± 11.025 k H z . Although this system worked when based on a conventional phase locked loop circuit, a large amount of energy appeared at 787.5 Hz in the mixed signals. T h i s noise was intolerable because it interfered with Doppler frequency shifts. This problem was eliminated by re-placing the conventional phase locked loop with custom made crystal oscillators and assembling phase locked loops based on these oscillators. T h e narrow band characteristic eliminated much of the reference feed through, although some evidence for signal contamination from this source did appear in the data: its removal is discussed in Appendix C . The entire vertical sonar processing scheme was developed specifically for the present application and some means of testing its operation was needed even before building the circuitry. This testing was done using a simple com-puter model of the signal processing steps. T h i s model included two fundamen-tal steps: a backscatter signal was created to simulate the expected signal from a random distribution of acoustic scatterers; and this synthetic signal was then subjected to the processing described for sonar signals. Using this package, tests of various combinations of transmitted pulse lengths and scatterer densi-ties were made and the feasibihty of the processing scheme was demonstrated. For the large scatterer densities expected in subsurface bubble clouds, the pro-cessing provided accurate velocity estimates (for example, velocities estimated for a model with 0.75 m s - 1 came to 0.73 m s - 1 ) B.4 Digi ta l Signal Processing Considerations D a t a once recorded using V C R systems must be recovered in a streaming fashion. It is not convenient to simply transfer the data to a standard record-ing medium because of the enormous volumes of data involved (5 gigabytes on 168 each video cassette). Instead, the data are analyzed as they are recovered from the V C R so that the volume of data can be reduced before storing it on a computer system. A variety of recently developed high speed signal processors offer the capabilities required for this task; for the present application, Zoran corporations VSP-161 was selected. Zoran produces a circuit board compatible with the I B M Personal C o m -puter complete with interfacing software that allows convenient apphcation of their VSP-161 . This board is equipped with a F I F O (first in first out) register that allows buffering of input data on the board 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 Zoran board and conveniently processed. T h e Zoran V S P achieves high speed processing by vectorizing commonly used signal processing operations including: F F T ' s , products, sums, dot prod-ucts, conjugations, and modulations. High speeds are achieved by doing op-erations on arrays of up to 128 complex 16 bit numbers simultaneously. T h e processor does no logical operations explicitly and has very restricted looping capabilities. The limitations in looping and logic were overcome by using a program running in parallel on the host I B M A T , and they have not posed major 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 in subsequent processing. 169 W h e n computing products, numbers being multiplied must be chosen as large as possible since the Zoran retains only the 16 most significant bits of a 32 bit product: if this characteristic is not considered, substantial loss in data resolution can result. B.5 Data Recovery T h e data recovery from video tapes was essentially the same for each of the three data types processed with the Zoran system (sonar, sidescan sonar, and ambient sound). This processing approach will be described here, see Appendix C , D , and E for details of processing vertical sonar, sidescan sonar, and ambient sound respectively. T h e most convenient system for ultimately analyzing the data was a Hewlett-Packard ( H / P ) A900 minicomputer. This system offered convenient data archiving on 6250 B P I 9-track computer tapes and adequate disk stor-age space provided by a 600 Mbyte disk. In addition, the H / P provided fast processing of data with the use of firmware vectorized commands. T h e Zoran V S P operating on the I B M A T must, however, first be used to condense the data from its recorded form before the data could be transferred from the I B M A T to the H / P system. This step was a potential bottleneck because the I B M A T could only store about 1 hour of processed data necessitating transfers for every hour of data recovered. To avoid this problem, a pipelined system was arranged where the data flowed from the Zoran, through the I B M A T , to the H / P A900 in a continuous fashion. T h e Zoran system conditioned and compressed data and passed it onto the I B M A T for logical and higher level operations. D a t a was then passed to the H / P for file organization all in real time (Figure B.2 shows a block diagram of this data aquisition sequence). T y p i c a l P r o c e s s i n g 170 VCH PC Digital Data Interface Data Zoran VSP1B1 Data IBM/AT GPIB HPA900 Serial Data L-out Key Pulse Detector Key Pulse Control Disk Tape F i g u r e B.2 : Typical processing steps used in recovering data from V C R stor-age. 171 T i m e synchronization is critical in all cases to determine target ranges for the active sonars (Equation 3.1), or in the case of ambient sound data, to select data not contaminated by active sonar systems. The necessary 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 much like an oscilloscope trigger: when a key pulse is detected in 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 Zoran F I F O ' s . Accurate absolute time information is critical in coordinating observations from the many instruments being used and between data types recovered from video tapes. T i m e data was recorded onto the low grade audio channel of the V C R ' s every 500 ms and it was necessary to recover these times while pro-cessing sonar data. 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 seconds can be consumed while waiting to read the latest time stamp. This 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. Using this method, each data record transferred to the H / P is labelled with a time stamp providing 100 ms precision (but only ± 2 5 0 ms can be claimed because of the time 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 to recover normal echo sounder data, vertical velocities from acoustic Doppler estimates, and range to surface for wave measurements and data alignment. This appendix deals with three as-pects of vertical sonar signal processing; general Doppler velocity estimation, implementation of the required processing through the data acquisition system, and velocity data conditioning. Estimates of Doppler frequency shift can in principle be made through a Fourier analysis. Such processing is extremely in-efficient, and the complex covariance spectral estimation technique used instead will be described. Details of signal pre-conditioning and the actual imple-mentation of the complex covariance technique will be presented. Also, those processing steps required to provide accurate final velocity estimates will be explained. C l Complex Covariance Method Accurate estimates of Doppler shifts in 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 in the present application, spatial res-olution (crx) is ultimately determined by the length of the acoustic pulse; where C is the speed of sound in water and t is the acoustic pulse length. In contrast, the accuracy of speed determination is optimized by having a narrow 174 peak in 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 observa-tion requirements and the restrictions imposed by Equations C . l and C.2. A detailed discussion of these competing terms is presented by Theriault (1986). For the practical computation of Doppler velocities, it is desirable not to restrict the range resolution beyond that given by Equation C . l by limitations in the signal processing. In particular, if mean frequency shifts were deter-mined by considering frequency spectra, then the length of Fourier transform used would become a restriction to the range resolution. This complication is completely avoided by estimating mean frequency shifts through consideration of the derivatives of the signal autocorrelation which can be related to spec-tral moments. This approach is known as the complex covariance method for Doppler speed estimation (Miller and Rochwarger 1972). For a power spectrum P ( / ) , the mean frequency based on the first mo-ment is, " ~ fp(f)df c z If the corresponding autocorrelation function is R(h), then it is easily shown that dR(h) fi = - ^ h r CA R(h) v ' h=Q. T h e autocorrelation function can be expressed as R(h) = A(ft )e '* ( f t ) C.5 175 where A(h) expresses the amplitude and (j>(h) the phase at lag h. Using the expression for R(h) given by Equation C.5, becomes, ® . a f f i l e + A ( h ) i ? m e ^ . CM dt dt K ' dt Equation C.6 is simplified by using first difference approximations for the derivatives and assuming that (for any autocorrelation function) A(h) is even and <j>(h) is odd. Equation C.4 can then be used to estimate the frequency as; d<f> Cl 1 x(ImR{T)\ ~ 2irh \ReR(T) J ' where R(T) is the autocorrelation function determined at some small time lag (as discussed by Miller and Rochwarger 1972). The complex covariance method makes velocity estimates possible for each estimation of the autocorrelation function. This technique is computationally very simple and can be applied to data windows as small as the time lag chosen, thereby imposing no artificial restriction on the range resolution. C . 2 Z o r a n P r o c e s s i n g Signal amplitude and 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. This pro-cessing is done as the data are recovered from the V C R with the Zoran V S P controlled by the I B M A T . T h e processing steps and computer timing rela-tionships are identified in the flow chart of Figure C l : notice that while the Zoran system is waiting for and processing data from one sonar return, the 176 I B M A T is computing data products for the previous return. T h e processing steps outlined in Figure C . l will be discussed in the order in which they are executed. T h e Zoran system loads the 2816 data points (corresponding to 63 ms or 48 m of range) received immediately after the sonar transmission. Since the instrument is known to be at about 30 m depth, this block of data necessarily includes the surface return. A first problem is encountered with this step due to a hardware fault on the Zoran board: the F I F O register will generate a duplicate data point when a read request is issued to an empty F I F O . For most of the applications, a single duplicate data point 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 from 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 and by monitoring this status word, data is requested only when there is data in the F I F O . This 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 data are loaded, D C offsets introduced by a bias voltage in the P C M digitizer must be eliminated. These offsets are observed to be as large as 200 digitizer counts while good data signals can be recovered with amplitudes as low as 5 counts: if such offsets are not removed, the Doppler phase estimations become meaningless. T h e implicit clock sampling scheme provides a convenient means of correcting for these data offsets. Equation B.7 demonstrates that the data are received as a sequence; Re(i), Im(i), -Re(i + 1), -Im(i + 1), Re(i + 2), Im(i + 2),... . C.8 177 IBM/AT Set Up Initialize Zoran ZORAN Grab Data Walt for Interupt Read Data Find Surface Disable Data Start Enable Zoran Data Velocity Magnitude Xfer to HP Record Time if needed Sign Change Remove Offset Find Surface Issue Interupt Compute Correlations Magnitude F i g u r e C l : Data acquisition processing steps used for recovering vertical sonar data. 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;, . . . . This offset can be estimated by adding successive (real or imaginary) values. For 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) and 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 in this manner eliminating any offsets that may be present. T h e data of interest are located at and just below the sea surface: data occurring appreciably beyond the sea surface in the sonar record is not mean-ingful. For this reason it is necessary to identify the surface location in the sonar return and adjust the data 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 maximum return which will identify the sur-face. In the present application however, an acoustic pulse of 2.4 ms is being used to allow acoustic Doppler processing and this technique would introduce a ± 0 . 9 8 m uncertainty in surface location. This uncertainty is eliminated by using the rising edge of the surface return as a surface indicator (this approach is described in detail in Appendix F ) . The Zoran processor is not capable of 179 the logic required to find the surface in the signal by any method, but the I B M A T could not possibly do the processing required in real time. These problems are circumvented by conditioning the signal return into an amplitude record, smoothing it and determining a subsampled first difference (slope) on the Zoran system. The resulting (reduced) data is scanned by the I B M A T to find the peak slope locating the surface to within 0.1 m accuracy. T h i s posi-tion in the data is then related back to the Zoran program which can continue processing relative to that point. W i t h the data aligned to the surface, a profile of backscatter amplitudes can be directly determined. There is no need to retain all of the data avail-able since the 2.6 ms pulse creates a backscatter profile with only a 1.95 m range resolution. The data are blocked into 10 bins of 1.95 m length with the base of the topmost bin coincident with the surface location. T h e surface bin is retained because it records the backscatter strength of the surface and also identifies the vertical velocity of the surface. W i t h this system, the max-imum depth from which data are recorded is arbitrarily set to 18 m since no significant backscatter is received below this depth. Velocity estimates from the vertical sonar data are made using the com-plex covariance technique to avoid the computational requirements of power spectral analysis. To apply this method to the sonar data on the Zoran sys-tem requires the computation only of the signal autocorrelation at some lag. Although simple in principle, these computations require multiplications which can introduce underflow conditions in the Zoran processor. This problem was reduced by amplifying data values (through multiple self additions) before any correlation analysis being careful not to create overflow conditions in the pro-cess. 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 the surface and decay exponentially with depth. T h e amplification required at each depth was determined by trial; Table C l indicates the factors chosen. B i n # Depth Gain Factor m 9 0 1 8 2 1 7 4 16 6 6 32 5 8 32 4 10 32 3 12 32 2 14 64 1 16 64 0 18 64 T a b l e C . l : B i n gain factors. W i t h the data so amplified, autocorrelations were computed directly from the data. For each of the 10, 2.6 ms range bin, 64 estimates of the auto-correlation function are made (not all independent). 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 Zoran is used to compute the average autocorelation slope for each bin 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 on data quality indicators such as low am-plitudes or large velocity anomalies as described in Zedel and Church (1986). 181 These screened values are then transferred to the H / P for subsequent data analysis. T h e velocity processing contains several operations that required testing before they could be relied upon for data recovery. In particular, the combi-nation of the implicit clock sampling scheme and the mean removal technique required testing before data analysis could proceed with confidence. As a test of all the velocity processing operations, a function generator was used to pro-vide a reference signal which was digitized by the P C M and analyzed using the velocity analysis processing package. A variety of frequency offsets from the sonar carrier were analyzed with this system and the hardware and software provided accurate measurements of these frequency offsets. Results of these tests are summarized in Table C.2 demonstrating the accuracy of the package. C.3 Velocity Processing T h e velocity data as processed and stored are in a relatively crude form. They have not been corrected for the vertical motion of the instrument plat-form and they are subject to several potential biasing errors. This section will discuss the accuracy of the Doppler measurements, the significance of the potential biasing terms, and corrections applied to the data. T h e 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. Although these bubbles will have a vertical velocity due to buoyancy, their rise speed is only about 0.0006 m s - 1 (after Thorpe 1984b) and so for the present application they make excellent 182 Reference Zoran Difference % Error Input Estimate (ref. - est.) Hz H z Hz -1000 -994.8 ± 2.3 - 5 . 2 ± 2.3 0.5 -800 -795.7 ± 1.6 - 4 . 3 ± 1.6 0.5 -600 -597.0 ± .3 - 3 . 0 ± 0.3 0.5 -400 -398.4 ± - 1 . 0 - 1 . 6 ± 1.0 0.4 -200 -199.2 ± 0.5 - 0 . 8 ± 0.5 0.4 0 0.45 ± 0.01 -0 .45 ± 0.01 oo 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 will be from larger bub-bles (with greater rise speeds). However, at 200 kHz, a bubble diameter of greater than 800 fim is required to scatter energy comparable to that scattered by resonant bubbles and populations of such bubbles are typically l /1000 t ; i that of the 32 fj,m bubbles (Walsh and Mulhearn 1987). Doppler systems do not make point measurements, but rather an average over the volume of water ensonified by the acoustical beam. For the data being considered, this volume 183 is a 2 m long cylinder with a diameter of 3 m or less. This volume places a fundamental limitation on the spatial resolution of the velocity estimates. Velocities are determined by frequency shifts occurring on the backscat-tered signal and the accuracy 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 with a transmit pulse length (r) of 2.4 ms. For pulse-to-pulse incoherent Doppler, the speed uncertainty (a) for a single sample is given by C a = C.12 (47TT/)' where, C is the speed of sound and / is the operating frequency (Theriault 1986). For the present example a — .25 ms~x. In addition to the uncertainty due to the Doppler speed estimation, the mean 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 and estimating vertical velocities from knowledge of the swell period and the wave height (approximately 10 second period with a 1.5 m amplitude). Using this approach, the uncertainty in speed estimates for a single sample due to wave action alone is about 1.2 m s - 1 at the surface. Platform motion along the beam 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. This error can only be removed by recording platform motion along the direction of the beam axis. In the present applica-tion, a vertical accelerometer was used to measure these vertical motions (see Figure 3.4), and these data are used to correct profile velocities for package motion. 184 Ti l t ing motions of the platform cause changes in the acoustic beam direc-tion and consequently change the component of speed being measured. This error cannot be eliminated since no measurement of other velocity components is made; all that can be done is to minimize the effect by minimizing in-strument tilts. This requirement was considered when designing the mooring package by maximizing the instruments righting moment. E v e n so, a record of instrument tilt was made so that the degree of data contamination could be estimated from geometrical considerations. Figure 3.4d and e (page 27) show an example of observed instrument tilts about two orthogonal axes. From these records it is known that the package can have a mean tilt of 3 ° or 4 ° with wave coupled oscillations of 3 ° about that mean. T h e average tilt will allow a portion of any horizontal surface current to be resolved onto the acoustic beam; this contribution will be Vz = V sin(0) where V is the horizontal velocity, and 8 is the tilt angle. T h e actual horizontal velocities at the surface were not measured, but from the S4 current meter positioned at 41 m depth, the mean velocity of the mixed layer relative to the instrument package was about 0.3 ms-1. Such a mean current resolved along the acoustic beam axis could introduce a 0.02 m s - 1 bias in the vertical velocity estimates. Although this bias could be of any sign, the geometry of the instrument would most likely result in a positive velocity: drag on the surface float will tilt the package in the surface current direction and the echo sounder beams will detect a velocity component away from the package (a net positive velocity). This bias would however be a consistent value for periods of the response time of the surface wave field, and since variations occurring on time scales much smaller than that are of interest, any such contamination would be obvious in the data. 185 T h e tilt oscillations coupled with wave motion could also introduce velocity biases by selectively sampling the velocity field. T o place an estimate on the magnitude of this error, sampled velocities were computed for an ideal linear wave and idealized sinusoidal instrument motion. A linear estimate of the velocity fluctuations close to the surface is given by u = A cos(fcx — u>t)ekz w = Asin(fcx — ut)ekz , C.13 v = 0. Where A is the maximum surface velocity, k is the wave number for a wave of frequency OJ, and x is the horizontal component in the direction of wave propagation. T h e tilt angle 6 must vary periodically with frequency and so can be expressed as 6 = 7 s i n ( - w i + <£), C.14 where 7 is the magnitude of tilt, and <j> is the phase of tilt relative to the wave field. Doppler sonar systems measure the component of velocity resolved onto the acoustical beam axis. Taking x = 0 as a point on 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)ekz sin0 + Asin(ks6 - ut)ekz cos6. C.15 Since 9 is small (typically less than 5 ° , see Figure 3.4d, and e), Equation C.15 can be simplified and an average over time will give 6 = + 1 } sin(^)e*' . C.16 If we assume in the worst case that the phase term is a maximum (sin(<^ >) = ± 1 ) and use representative values for the other parameters (k = 0.04 r n - 1 , 186 s = 30 ra, 7 = 2 . 5 ° = 0.04 radians, A = 1.6 m s - 1 , and z = 0 m) , then 6 = ± 0 . 0 8 m s - 1 . The observations indicate that the phase is actually close to 1 8 0 ° (see Figure 3.4c and d); thus any such bias will be much smaller than this worst case estimate. C.4 Low Amplitude Bias Preliminary plots of vertical velocity revealed a negative bias correlated with low signal levels: when signal levels became low, wave period oscillations were still clearly seen in profile time series, but they were biased to negative values. T o investigate this signal contamination, velocities were averaged ac-cording to their signal amplitudes (for example, all velocity estimates for which the signal amplitude fell between 10 and 15 binary counts would be averaged). T h e periodic wave velocities will average to zero and, because signal amplitudes and velocities should not be correlated, these velocity averages at selected am-plitudes should also converge to zero. A n y departure from a zero average is indicative of a systematic bias in the data. A n example of how this bias de-pends on the amplitude is presented in Figure C.2 where the average velocities based on 12 hours of data- are plotted against the amplitudes at which they occurred. 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 in the electronics. To 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 and the output was observed on a spectrum analyzer. This analysis revealed many peaks spaced at constant intervals of about 800 H z . Considering the details of the receiver electronics, the only possible cause 187 - 1 -1D.D A m p l i t u d e [ c o u n t s ] F i g u r e C .2 : 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 in heterodyning the received signal (see Appendix B) . T h e presence of this signal contamination can also be seen in power spec-tra made from 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 Hz Doppler shift, but the broadband background noise shows a peak that occurs at 785 H z . This analysis of receiver processing clearly demonstrates the occurrence of data contamination by the 787.5 kHz oscillator. B y knowing the character of this contamination, and 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. For 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 can be seen by considering the first moment of a power spectrum P(f) : u _ S f P ( M C 1 7 fP(fW a i 7 If the power spectrum (P ( / ) ) is made up of a noise spectrum and a true sig-nal spectrum, these constituent spectra can be approximated by two gaussian spectra with different means and variances: S(f) = s e ^ r 1 -a C.18 where, S(f) is the signal spectrum with mean frequency F distributed with variance a and B(f) is the noise spectrum with mean frequency p and vari-ance a. (These spectra can be expressed equivalently in frequency or velocity because of the linear relationship between velocity and frequency.) T h e first moment of this composite spectrum is then _ ff(S(f) + B(f))df f(S(f) + B(f))df • 189 1D-i F r e q u e n c y H F i g u r e C . 3 : Example of the background spectral content of the received sonar signal. This 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 up of the carrier frequency by the receiver, of more concern is the presence of a broadband noise floor with a peak at about 785 H z . 190 Expanding these terms and integrating, the first moment becomes = Fas + pab C 2 Q as + ab The biasing effect of noise in the first moment estimation given by Equa-tion C.20 depends on the ratio of power in the noise compared to that in the signal (as regulated by the products ab, and as). A broad noise spectrum with a low peak will have the same effect as noise with a high peak power but narrow spectrum. To demonstrate the behaviour of this bias, values of the parameters in Equation C.20 are set to typical values expected based on the observed character of Figure C.3. Choosing a = 1000 Hz2, a = 100 Hz2, b = .01, p = 750 Hz, and F = 0, the dependence of the first moment on signal amplitude ( 5 ) is shown in Figure C.4. Figure C.4 is plotted in the same format as Figure C.2 except that the results are scaled as frequency rather than veloc-ity; 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 in the data (Figure C.2). The noise model presented behaves very similarly to that of the data supporting this interpretation. This model can now be used to provide a means for removing the bias from the low amplitude data. If it is assumed that the noise power remains constant irrespective of the signal level, and that the signal mean frequency remains at zero (which is expected on average) then equation C.20 can be used with the data to calibrate the biasing effects of the noise. Equation C.20 is rearranged to a form that is linear in signal amplitude; 1 as 1 + -Pab P C.21 = Ms + I 191 F i g u r e C . 4 : Bias in mean frequency estimates associated with low amplitude signals when a spectrum is contaminated by coloured noise. This 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. where, M = and I = K For the assumptions made, the signal peak is at 0 frequency so that fi given by Equation C.21 represents the expected bias for this situation. The data of Figure C .2 were re-plotted against 1/v recovering a 192 straight line as expected from Equation C.21 (Figure C.5). Using linear regres-sion, these data determine values of M and I as —1089.5 Hz-1 ( c o u n t s ) - 1 , and 1236.9 Hz"1: the hne defined by these parameters is indicated in Figure C.5 . -4DH 1 1 O.D 5.0 10.0 A m p l i t u d e ( c o u n t s ) F i g u r e C . 5 : Plot of inverse velocity bias ( 1 / V ) against average signal ampli-tude. Using the same data as shown in Figure C.2. T h e straight line is a linear regression fit to the data. 193 Assuming that these correction coefficients remain constant irrespective of signal mean frequency F (an assumption implicitly used in the computation of M and I), Equation C.20 can be modified for the case of non-zero F giving /z( l + -J—) - ^ - = F. C.22 M — s Ms Knowing that the observed mean frequency is given by p, the true signal frequency F can be recovered with knowledge of the signal amplitude using equation C.22. T o evaluate the effects of Equation C.22, the processing used to generate Figure C.2 was repeated with corrected data producing Figure C.6. T h e cor-rection term effectively removes the observed bias for amplitudes greater than about 3 digital counts: data received at amplitudes less than this level cannot be corrected and such data must be rejected. To demonstrate the final result of correcting for the velocity bias (and rejecting data with amplitudes below 3 counts), two minutes of velocity data before and after corrections are displayed in Figure C.7. T o provide a refer-ence, Figure C.7a displays the surface vertical velocities and Figure C.7b shows the signal amplitudes in bin 5 (at a depth of 8 m below the surface): this particular data interval was selected because it shows a progression from high to low signal amplitudes. Uncorrected vertical velocities (Figure C.7c) clearly demonstrate an increasing bias to negative values as the signal amplitude de-creases. After applying the velocity corrections (Figure C.7d), the tendency to negative bias is absent although some gaps now appear at those intervals where the signal amplitude persists below the threshold of 3 counts. 194 + 1 + + + + + + + + + + + + + + + + + + + + + -+ + + + + + + • + + + + + + + •• 0.0 5.0 10 .0 A m p l i t u d e [ c o u n t s ] Figure C.6: Observed bias in velocity data after correcting for the biasing effects using Equation C.22. As in Figure C.2, 6 hours of velocity data were averaged according to the observed velocities and 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 17:32:10 T i m e ( U T C ) 17:32:30 Figure C.7: T ime series of velocity observations before and after correcting for the amplitude bias effect; a) ocean surface vertical velocity, b) backscatter amplitude observed at 10 m depth, c) raw (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. A p p e n d i x D S i d e s c a n S o n a r P r o c e s s i n g 196 Sidescan sonar data were collected with the intention of determining the horizontal distribution of subsurface bubble clouds. T o meet this objective, the backscattered signals must be reconstructed into sonogram images. This appendix describes the data processing and conditioning necessary to recover backscatter signal strength from the recorded data and how that information is used to produce meaningful sonogram images. D . l Z o r a n Processing T h r o u g h analog processing during data recording, the sidescan data are placed onto a 17.5 k H z carrier and stored in 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 into a Sony P C M system and the resulting 44.1 kHz, 16 bit data stream is captured using the Zoran V S P . Processing this data requires selection of the data interval of interest, removal of offsets (substantially introduced by the antialiasing filters of the P C M digitizer), extraction of the signal from the carrier, and subsampling the resulting amplitude series. These processing steps are outlined schematically in Figure D . l . T h e sidescan data, by its nature, contains no useful information until after the return from the surface. Since the instrument is located at 32 m depth, the first 43 ms (1888 data points) of data after transmission are discarded. No 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 S i d e S c a n P r o c e s s i n g IBM/AT Zoran DSP 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 : Data acquisition processing steps used for recovering sidescan sonar data from V C R storage. 198 200 m data window being considered. Following the discarded 43 ms interval, 232 ms of data (10240 data points) are captured into Zoran memory. W i t h the vertical sonar data, implicit clock sampling allowed data to be adjusted to have a zero mean value over successive data points. Although this method is not possible for the sidescan data, these data are still on a carrier and so averages can be used to remove any D C offsets. For these data, averages are accumulated for blocks of 128 data points (representing 2.89 ms or 2 meters of range) and the calculated offset is removed from that block. Since all that is needed from the sidescan data is signal amplitude, the data are rectified and smoothed with a running average. T h e recorded carrier has a frequency of 17.5 k H z so that the rectified signal still has significant ripple over successive data points. This ripple is eliminated by filtering the data with an 8 point running mean. T h e smoothing of this filter is consistent with the 0.1 ms transmit pulse used which would span 4 data points. Each block of sidescan data constitutes 10240 data points and these are received at a rate of 4 H z (between the two operating sidescan systems). If all the data are retained, each hour would generate 150 Mbyte of data and so, in the interest of storage economy, subsampling is necessary. Based on inspection of the processed data, retention of only 1 in 16 data points retains most variability seen in 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 and stored directly on the H / P A900 system. D.2 Sidescan Image Processing T h e sidescan data format is very simple and is most easily viewed as a conventional sonogram image. Even these basic acoustic data can benefit sub-stantially from the signal conditioning made possible by computer processing. 199 In particular, it is the spatial distribution of subsurface bubble clouds that are of interest and so it is desirable to clarify their representation in the fi-nal data display. T h e bubble clouds are best demarked by changes in acoustic backscatter strength, not by the overall signal level so it is useful to eliminate signal level variations with range (such as result from geometrical spreading and acoustic absorption). In addition, sidescan sonar data do not have a naturally linear spatial scale as do conventional backscatter systems and this non-linearity must be corrected. This 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 plotting echo return strength against range as an image density or colour and plotting these progressively in time. A first requirement is to transform the acoustic backscatter time series into a spatial representation of acoustic cross section along the ocean surface. This 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 Equation 3.1; the range along the surface is then, D.l Using Equation 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 data can be determined from Equation D . l and is p==-LC(d2 + D2)1'2. D.2 200 r 1 Sur face 3 dB Beam Figure D.2: Geometry of sidescan sonar deployment. A t large ranges this approaches p = Cl/2 (about 0.25 m for data as recorded), but as the range approaches 0, p approaches infinity. Clearly, the ability of sidescan sonar to resolve structures at short ranges is very poor and this characteristic is obvious in the data (see Figure 4.5page 50). Sonogram images can be produced directly by plotting received signal level as a function of range. Such plots suffer from the changes in backscatter level due to acoustic propagation losses and transducer beam 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. In princi-ple, range dependence can be determined analytically by considering acoustic absorption, spherical spreading and the transducer beam pattern, but accurate 201 calibration in such a manner is extremely difficult. A dynamic and more accu-rate 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: Typical calibration curve used to correct sidescan sonar data for range dependent signal variations. A p p e n d i x E A m b i e n t S o u n d P r o c e s s i n g 203 The ambient sound data are the most convenient to record because of their natural suitability to the P C M system but, they are also the most sen-sitive to contamination. A n y variation in signal amplitude must be quantified and remain consistent to allow calibration of the ambient sound levels. Pro-cessing these data from V C R storage to computer files involves: selection of those data intervals not contaminated by active sonar transmissions, removal of offsets from the data, tapering the data with a cosine window, application of a Fourier transform, and averaging several transforms to increase data stability. These steps, and the division of processing between the Zoran V S P , and the I B M A T are identified schematically in Figure E . l . Even though the operating frequencies of the active sonars fall well beyond the receiving bandwidth of the hydrophone, the transmit pulses (and in some cases the surface returns) contain significant energy within that bandwidth so that contamination of the ambient sound data occurs. Selection of those inter-vals that could be considered free of contamination was done by observation of the ambient sound data on an oscilloscope. Based on this evaluation, 7 windows of 5.8 ms duration (corresponding to 7, 256 point F F T ' s ) could be extracted from each 160 ms sonar system cycle. Figure E.2 identifies the data windows accepted and their placement in the sonar cycle. As with all data processed through the P C M system, signal offsets must be eliminated prior to Fourier analysis. For the ambient sound records, this 204 A m b i e n t S o u n d P r o c e s s i n g I B M / A T Zoran DSP Disable Data Flow Read Data Start Zoran Enable Data Flow Record Time Load 644 pts =15 ms to Clear 50 kHz Transmit Load 256 pts Remove Mean Window, FFT Load 3128 pts =70.8 ms to Clear 200 kHz Transmit Load 256 pts Remove Mean Window, FFT Load 256 pts =17.4 ms to Clear 200 kHz Surface Return Load 256 pts Remove Mean Window. FFT Scale FFT 's Compute Magnitude Average X 3 X 3 X1 Issue Interupt D Figure E . l : Data acquisition processing steps used for recovering ambient sound data from V C R storage. 205 Key Pulse 50 kHz xmit 50 kHz Surface Return Key Pulse 200 kHz xmit 200 kHz Surface Return / / 1 ' i N t ' J 3, 256 pt FFT's 3, 25B pt FFT's 1, 25B pt FFT 1 80. T i m e Cms) o. 40. 120. 160. Figure E.2: Ambient sound data can only be recovered during intervals when data are not contaminated by sidescan and vertical sonar transmissions and surface returns. This figure indicates the time intervals during which the 7, 256 point F F T ' s are drawn during the data collection cycle. problem is complicated because system gains had been selected too low during the data acquisition: under some conditions good data are limited to data counts as low as 10 or 20. Under these conditions, extreme care is needed to avoid underflow conditions on the Zoran while at the same time not applying excessive amplification. To deal with this special case, a cumbersome but safe mean determination scheme was used. Each 256 point data block was divided by 2 and then successive data points were added together halving the number of data points but preserving the mean. This 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 in one pass of the Zoran V S P . T h e data were windowed with a cosine taper, and then directly transformed. Through this process, the Zoran system generates a scaling factor which applies to the entire transform. This scaling factor is retained to preserve data calibration through the 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 ac-curacy by losing the 16 least significant bits of the 32 bit product. W i t h the present data, often characterized by low bit counts, such a loss in accuracy is unacceptable. To avoid this problem, an iterative scheme to determine vector magnitudes is incorporated which is based on the fact that when the absolute values of both components of a complex number are taken, the phase of the re-sulting complex number is restricted to between 0° and 9 0 ° . B y rotating such a vector by 4 5 ° clockwise (easily done on the Zoran 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 ° and 4 5 ° . This procedure can be repeated using successively smaller rotation angles (90, 45, 22.5, 11.25, 5.125 etc.) constraining the phase of the vector to progressively smaller values. Even-tually, when the phase angle is suitably bounded (to 5 . 1 2 5 ° for these data), the vector magnitude is effectively represented by the real component. A s with 207 many Zoran algorithms, the sequence of operations appears cumbersome, but the processor's speed makes it an acceptable approach and in this case, it completely eliminates the need for multiplications. After the Zoran V S P has completed the magnitude estimates for each transform, they are converted to a common scaling factor and averaged. T h e I B M A T takes the averaged spectra based on 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 in ambient sound processing was possible during the 10 minutes out of every hour when no active sonar was operating. At.these times, there is no contamination of data and 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 A m b i e n t Sound Calibrat ion 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 in ambient sound power, but calibrations are needed for cross comparisons with other data sets. The various considerations in ambient sound calibration will be identified in this section and the scalings that they apply will be noted. T h e signal processing steps affecting ambient sound signal levels are iden-tified in Table E . l . Starting with 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-TS + W-G + R + PCM-Z-B, E.l 208 where SSL = Sound Signal Level in d B re 1 (iPa2/Hz, S = dB re 0 VU (0 VU = 32768 counts), Ts = Transducer sensitivity = -157 dB re IV/pPa (for the I T C 5298), W = whitening filter response, G = amplifier gain = 37.7 d B , R = resistor bridge loss = 6 d B , PCM = Digitization gain = 6.6 dB re 0 VU/V, Z = gain through Zoran processing = 30.5 d B , B = gain due to bandwidth in the F F T = 22.4 d B . T h e pre-whitening filter response is, by definition, frequency dependent: knowing the resistance R, capacitance C , and frequency, the relationship between input and output voltage (Vi„, and V0) is given by, v^ = (jp + i / t d ' c 2 ) 1 / ^ E 2 V0ut R T h e gain through both the Zoran and P C M conversions were determined ex-perimentally. In the absence of a standard sound source, no complete end to end test could be made of the instrument calibration. What was possible was a com-parison of ambient sound levels observed with those expected for the wind conditions encountered. Vagle et al. (1990) provide a relationship between wind speed and S S L (Equation 4.1 in the text); for a 5 m s - 1 wind, the S S L at 8 k H z is expected to be 45 dB relfiPa2 / Hz and the value expected at 15 ms~l is 57 d B . In the present data, the observed values of SSL for these wind conditions were observed to be 45 and 55 d B . These values are in very good agreement supporting the accuracy of the calibration. 209 T a b l e E . l : Steps affecting ambient sound calibration. Component G a i n (dB) Hydrophone Sensitivity -157.7 Prewhitening Filter -10 @ 8 k H z Amplifier 37.7 Resistor Bridge -6 P C M -6 Zoran Processing 30 F F T Total 22.4 -90.2 210 A p p e n d i x F W a v e M e a s u r e m e n t D e t a i l s M a n y of the parameters investigated in 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 option may appear redundant with the availability of the Waverider data, but for any analysis requiring pre-cise relative timing between wave observations and other acoustic observations, it is a great convenience to have both data types referenced to a common clock. A n additional benefit exists since if this method can be demonstrated to be accurate, it will be possible to free future acoustic studies of the need for independent wave height measurements. This appendix will outline the tech-niques used to determined wave heights (and spectra) from the vertical sonar systems and compare those to the more accepted records of the Waverider buoy. F . l Surface F i n d i n g and Veloci ty Determinat ion T h e sonar data provide two somewhat independent measures of wave en-ergy; first there is the time series of range to the surface, and 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 and this pulse length makes any simple method of surface finding inaccurate (as is discussed in Appendix 211 C ) . Figure F . l a displays a typical acoustic return from the ocean surface using the 200 k H z sonar system. Based on the location of the peak signal return, the resolution of the range to the surface is no better than about ± l m . A n alternative means of identifying the surface is provided by the large relative signal strength of the surface (about 20 d B above near surface vol-ume scattering). B y identifying the characteristically steep leading edge of the surface return (see Figure F . l a ) , a much more accurate surface detection is possible. T h e first difference of the signal amplitude is computed (ie. dA/dt) to identify the leading edge. In using this approach, some smoothing of the am-plitude return is required to reject large slopes associated with low amplitude noise. Figure 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 in surface location do occur. These errors 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 from the surface (see Figure F . l a ) . For wave spectra determined from wave height, such errors do cause difficulty and they require filtering to remove spikes reducing the data accuracy in time. Sonar surface estimates are made at a rate of 6 Hz which is far in excess of that needed for meaningful wave measurements, averages over 3 samples providing 0.5 s time resolution and have been used for the wave analysis which follows. 212 1800-cu TD D •U - 500-a £ < a] Amplitude b] Amplitude Slope c] Complex Signal 8192 B256 8319 Data Element F i g u r e F . l : Example of an acoustic return from the ocean surface: a) is the amplitude return, b) is the slope of the surface return, and c) is the complex demodulated signal. 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 from 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 mod-ulation of the transmitted acoustic pulse. M u c h greater accuracy is however achieved from velocity estimates off the surface. Figure F . l c shows an exam-ple of the complex (real and imaginary) return from the surface: the smooth sinusoidal form of data through the surface return testifies to the small band-width of this acoustic return. This small bandwidth occurs because there are no incoherent returns from any object other than the surface, the signal is essentially coherent. T h e high estimate accuracy possible because of the co-herent surface return and the high vertical velocities of wave action (of order 1 m s - 1 ) combine to provide a signal that requires no more averaging than that of the surface range data. 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 techniques. It is important to note that the errors which occur in determining the range to the surface do not introduce comparable errors in the velocity es-timates. T h e velocity estimates are restricted to a range resolution of 1 m (determined by the acoustic pulse length used). Errors in 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 ve-locities associated with the waves being measured (those with wavelengths of 12 m and greater) do not vary significantly over a depth of 1 m. 214 Figure F.2: Comparison of 1 minute of surface wave observations: a) is based on Waverider data, b) is based on sonar range, and c) is the Doppler derived vertical velocity of the surface. 215 F.2 System Limitations Measurements of both range to the surface and surface velocity are rela-tive to a freely moving package in the present deployment configuration. This motion must be accounted for if accurate wave measurements are to be made and this correction has been done by using a vertical accelerometer and two tilt meters (measuring orthogonal tilt components) mounted on the instrumen-tation package. The 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 and displacements. In Figure F.3, 5 minutes of surface wave data, instrument tilt and instrument vertical motion are displayed along with surface wave height. T h e strong wave period oscil-lations seen in these data clearly demonstrated the need to correct for these motions in the final data. T h e high frequency (high wavenumber) cutoff for sonar based wave mea-surements is determined either by the sampling rate (2 Hz for these data), or by the surface footprint of the acoustic beam. Based on a 3 dB beam pat-tern, the 200 kHz system would sample a 3 rn diameter disk on the ocean surface. T h e scattering cross section of the surface is however about 20 dB greater than 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. For this reason, it is more appropriate to consider the sonar as having an omnidirectional radiation pattern as shown in Figure F.4 and to consider the consequences of such sampling. In this case, the system resolution is de-termined by the region of intersection of a sphere centered on the transducer depth with the wave covered ocean surface. 216 I * -54 124-M 116-108-w 100-Heading „ / \ 11:45:00 11:46:40 11:48:20 t i m e ( U T C ) 11:50:00 Figure F.3: 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 : \< Effective Footprint • | I 3 dB Footprint i X Transducer F i g u r e F.4: Schematic diagram of sonar sampling in the presence of surface waves. 218 A s depicted in Figure F.4, at any time t after sonar transmission, the sonar receives acoustic backscatter from a spherical surface with a radius of R = Ct/2, where C is the speed of sound i n water. Considering a two di-mensional projection of this backscatter region, the locus of points sampled is determined by, R = (x2 + (z - d ) 2 ) * , F . l where d is the instrument depth, and x and z are horizontal and vertical spa-tial coordinates relative to a point at the surface directly above the instrument location. ( A two dimensional projection is adequate in this case because the ocean surface is being characterized by a unidirectional surface wave). T h e ocean surface can be defined by a single representative 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 wavenum-ber. T h e range to the ocean surface will be detected by the sonar at the minimum value of R which intersects the ocean surface. Combining Equations F . l and F.2, gives the minimum value of R as R = (x2 + (asm(kx - ut) - d)2)^. F.3 A t this point, a worst case estimate of the surface footprint is of interest and from inspection of Figure F.4, the larges footprint will occur when the wave phase (kx — ut) is j evaluated at x — 0 (ie. the wave crest is centered over the sonar system). For this situation, the minimum value of Equation F.3 occurs when x = (d — a cos kx)ak sin kx. FA 219 For most applications, a « d and Equation F.4 can be simplified to x = akd sin kx, F.5 and the sonar footprint can be determined from this expression by the value of x required to satisfy Equation F.5. T h e footprint (2x) identified by Equation F.5 is dependent on frequency and wave slope: as the waves become longer and less steep, the footprint becomes smaller. A t the smallest wavelengths, the 3 dB footprint limits the system resolution to about 3 m . A t longer wavelengths, wave slopes in the data set being considered are bounded by about ak < 0.1: Table F . l pro-vides a comparison of detection ranges based on Equation F.5 for various wave lengths assuming a fixed wave slope of 0.1. T h e maximum error is seen for waves of 2.8 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 ad-dition, for a beam angle of 2 0 ° , the beam pattern provides 20 d B of side lobe suppression and will bound the sonar footprint to 22 m . For the present data set, these resolution constraints are not restrictive since there is little wave energy seen at periods shorter than 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. This placement makes comparisons between the wave measurement systems convenient, but introduces the possibility of interference of the sonar system by the Waverider and rubber cord. T h e rubber cord itself has not introduced any significant problems when considering profile data from the sonar systems and so is not expected to cause problems at the 220 period wavelength wavenumber wave slope footprint s m m " 1 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 T a b l e F . l : Sonar effective footprints for various surface wavelengths. surface. T h e buoy itself could present a strong single target at the surface which serves as a proxy surface return. If this interferance occurred, it would not affect the present application of wave measurements since the surface buoy itself follows the wave motions. There remains the question of how the sonar systems might respond in the absence of a surface float. The present data set cannot be used to investigate this problem, but previous applications of upward looking sonar have not had difficulties identifying the surface and it is unlikely that the absence of a surface float would greatly reduce the surface finding ability. F .3 W a v e r i d e r A c c u r a c y T h e Datawell 0.9 m diameter waverider buoy is used as a reference in this comparison. This buoy is a heave measuring buoy which determines wave height by integrating vertical accelerations. The manufacturer indicates that 221 this instrument has a high frequency cutoff of about 0.5 Hz 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 .., 1 . ,„ , F.6 l-y/2pi-p2 ( l - ? 0 3 where p = ~ , g = ^ - , T i s the wave period, i is \f—l, and T\ and T 2 are time constants of 30.8 s and 460 s respectively. Correction for this effect has been applied to all of the data presented. F.4 Wave Spectral Analysis T h e time series shown in Figure F.2 demonstrate the potential of using sonar to determine wave characteristics, but because of the inevitable timing difficulties, a quantified comparison is difficult. Ultimately some form of wave spectrum is required, and because spectra are not as sensitive to timing errors as direct correlations, comparisons of measurements are made using spectra of wave energy density. From 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, and a is the wave amplitude. Spectra of wave energy can be directly generated from 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 displace-ments (essentially the same approach used to convert package acceleration to velocity and displacement). 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), F.8 where n is surface displacement, 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). F.9 at Comparing Equations F.8 and F.9, it is seen that power spectra of velocity will be scaled by a factor of u2 over displacement spectra. A l l that is required is to divide through by u2 to convert a velocity power spectrum to a displace-ment spectrum. Notice that as frequencies approach zero, this scaling tends to infinity and so this scaling becomes unstable at low frequencies. For all the data types, the same basic spectral analysis technique was used and these steps are identified in Figure F.5. D a t a were averaged into .5 second samples and 10, 512 point F F T ' s were computed using a cosine taper and an overlap of 50 %. The power spectra from these F F T ' s were averaged together and scaled depending on the data type (wave height or velocity). T h e spectra that result from this processing are representative of 20 minutes of data. F.5 Comparison of Spectra 60 hours of observations were suitable for comparisons between the sonar and Waverider spectra. During a 20 hour period of increasing wind speeds, a Spectral Analysis 223 Haw Data Loop X 10 Scale A average Corret Package : t for Motion Final Power S p e c t r u m 512, 0 Sam .5 sec pies Cosine Taper FFT Add Power to Aver age Back Space File 256 points C5Q°/o Overlap] F i g u r e F.5 : Flow chart of processing steps used in spectral analysis of wave data. 224 complete range of sea states occurred varying from ocean swell with no winds, to a fully developed sea in the presence of a crossed swell. T w o examples will be considered; one sea dominated by ocean swell, and the second during the period of developing seas. Figure F.6 shows wave spectra based on 20 minutes of data starting at 00:20 U T C on October 27, 1987 when wind speeds had been calm for some time and were just increasing to about 5 m s - 1 . Figure F.6a is determined from Waverider data, Figure F.6b is determined from the sonar range to the surface, and Figure F.6c is determined from surface vertical velocity data. No-tice that although the spectra are normalized (by peak energy), the scales have been adjusted so that absolute comparisons are possible. The total energy den-sity for these spectra are 4.6 kJm~2, 4.7 kJm~2, and 5.2 kJm~2 for Figure F.6a, b and c respectively. Figure F.6c shows some anomalous increased energy at long period waves. This energy is a result of the scaling to convert from velocity to amplitude spectra which tends to infinity at infinite periods. Aside from this one fault, comparison between these spectra demonstrates incredibly good agreement especially the velocity and range to surface spectra. A more complicated sea state was encountered when the wind speed in-creased to 13 ms~l and added a developing sea to the existing swell. D a t a collected under these conditions are shown in Figure F.7 with wave spectra based on 20 minutes of data starting at 12:20 U T C on October 27, 1987. A s in Figure F.6, Figure F.7a displays data from the Waverider buoy, Figure F.7b displays data based on the sonar surface range record, and Figure F.7c is based on sonar surface velocities. In these spectra, the total observed energy densities are 9.4 kJm~2, 9.9 kJm~2 and 8.8 kJm~2 for the spectra of Figure 225 Figure F .6: Wave observations for the 20 minute period starting at 27/10/1987, 00:10 U T C . Low wind speeds have prevailed for several hours and the wave field is dominated by ocean swell, a) Waverider observations, b) sonar range observations, c) sonar vertical velocity observations. 226 F.7a, b and c respectively. Again, 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 wind waves. In the present comparison, this problem is almost completely eliminated by the sampling method itself: the two sonar systems sample exactly the same area which is directly underneath the Waverider buoy within about 3 or 4 m (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. The three systems have markedly different errors associated with the sam-pling they use. The 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 filtering necessary to integrate measured accelerations. A short period 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; all that is required is to identify the location of the surface in the sonar backscatter. In the present study, range determination has been somewhat complicated by 227 TIME: 27/10 12:20 P e r i o d ( s ) Figure F . 7 : Wave observations for the 20 minute period starting at 27/10/1987, 12:10 U T C . W i n d speeds have increased from the earlier calm conditions to about l O m s - 1 at this time and in addition to the ocean swell, there is now a developing sea. a) Waverider observations, b) sonar range obser-vations, c) sonar vertical velocity observations. 228 the use of long sonar pulses for Doppler velocity processing but it remains a fairly robust measurement. The method does not measure the range to the surface at a fixed point, but rather the minimum range from the sonar to the surface (as described by Equation F.3). In the present application this imposes a wavelength restriction on the waves being measured of about 12 m (or a period of 3 s). 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 in these data. T h e two methods of estimating wave spectra using the vertical sonar sys-tem are largely independent techniques even though they are made with the same sonar system. They do share the common difficulty of having a poorly defined sampling position caused by the finite sonar characteristics: both mea-surements are made at some point within a 6 m diameter disk centered above the instrument location. This limitation restricts both methods to the measure-ment of wavelengths greater than 12 m . For measurements based on the range to the surface, errors identifying the surface result in high frequency noise; this noise has been reduced in the present data by averaging the successive range estimates. Velocity based wave spectra depend on the range to surface data to identify the location of the ocean surface. T h e errors in the range deter-mination do not however translate to errors in the velocity estimates because surface range errors are normally less than 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 ve-locity estimates) provides adequate accuracy for the determination of wave 229 spectra presented here. Some error is introduced i n the velocity based wave spectra at long periods because the velocity power spectrum must be scaled by the ( f requency) - 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 and contaminates the spectra: this characteristic is obvious in the examples presented. One potential problem with both 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 conceiv-able 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 did the surface detection algorithm fail. T h e maximum wind speeds encountered were however no greater than 15 m s - 1 and this blocking effect may become a difficulty at greater wind speeds. The overall agreement in peak locations between the wave spectra pro-vides strong evidence for the individual accuracy of each of these systems. The agreement between sonar range and velocity estimates is particularly striking; even small details are reproduced in these two spectra. Such strong agree-ment does not demonstrate that these two methods are both correct since they clearly suffer from some common errors. What it does demonstrate is that the errors not common to both of these techniques (Doppler velocity estimation, surface identification, and conversion from velocity to amplitude representa-tions) are not introducing significant errors. 230 There is quite a bit of variance in peak energy levels, but it is to be ex-pected since slight changes in frequency can split the power between two adja-cent frequency bins. The total energy density represented by the three methods provides a convenient benchmark for comparison avoiding this difficulty. For the two sea states considered, the observed energy densities are summarized in Table F.2. In both cases, the three observation techniques agree within 10% of each other in total energy density. This accuracy is comparable to that reported for the Waverider in the comprehensive comparison by Allender et al. (1989). Wave condition Waverider Sonar Range Sonar Velocity swell mixed 4.6 x 1 0 3 J m " 2 9.4 x 10 3 J m ~ 2 4.7 x 103 Jm~2 9.9 x 103 Jm~2 5.2 X 10 3 Jm~2 8.8 x 10 3 Jm~2 T a b l e F . 2 : Wave energy densities determined by sonar and Waverider. F . 7 S u m m a r y a n d C o n c l u s i o n s Wave measurements have been made using an upward looking sonar sys-tem positioned at 30 m depth in a deep ocean environment. Wave spectra are generated using both wave heights (sonar range to surface), and the vertical velocity of the surface using the same sonar. To provide a reference for com-parison, wave spectra determined using a Datawell Waverider buoy are used. A l l data are sampled at essentially the same location due to the deployment geometry: the waverider is located above the upward looking sonar on the 231 same drifting instrumentation array. This 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 remark-able similarities (Figure F.6 and Figure F.7). T h e total wave energy density estimated from these spectra agrees within 10 % in each case (Table F.2). T h e only error terms common to all three techniques are those associated with motion of the sampling platform (ie. the tendency of the observations to be Doppler shifted by instrument motion in the long waves). A l l other error sources are absent in at least one of the techniques: based on these results, the collective effect of those errors is less than 10% in wave energy density. These results demonstrate that vertical sonar can provide excellent esti-mates of surface wave motion even from a moving platform in 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 ap-plications of interest in this study, the accuracy of sonar wave measurements eliminates the need for independent wave observations. More generally, sonar techniques could provide a method of making wave observations where buoy observations are not suitable such as in areas of heavy shipping, or areas prone to icing. Name and loc a t i o n Attendance dates F i e l d Degree Grade date % University of 9/77- Physics 1982 81 V i c t o r i a , 4/82 (honors) V i c t o r i a , B.C. University of 9/82- Physics 1985 94 V i c t o r i a , 2/85 (acoustics) V i c t o r i a , B.C. University of 9/86- Oceanography 1991 89 B r i t i s h Columbia Vancouver, B.C. M.Sc. Degree- 1985 University of V i c t o r i a V i c t o r i a , B.C. Canada Thesis Topic Evaluation 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 in a Fjord Ph.D. Degree- 1991 University of B r i t i s h Columbia Vancouver, B.C. Canada CSIRO Marine Labs GPO 1538 Hobart Tasmania, 7001 A u s t r a l i a Phone: (002) 206-666 From 3/85 u n t i l 6/86 Seakem Oceanography Ltd. 2045 M i l l s Rd., Sidney, B.C. Canada Phone: (604) 656-0881 Defense Research Establishment P a c i f i c C.F.B. Esquimalt Esquimalt, B.C. Canada Phone: (604) 388-1921 from 1/80 u n t i l 5/80 from 5/82 u n t i l 9/82 Seakem Oceanography Ltd. 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 Ministry of Transportation and Highways Geotechnical and Materials Testing Branch 324 Kingston Street 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 PUBLICATIONS Zedel, L . J . , D.M. Farmer, (accepted Dec. 1990), Organised s t r u c t u r e s i n subsurface bubble clouds: Langmuir c i r c u l a t i o n i n the open ocean, J o u r n a l of Geophysical Research. Zedel, L . J . , J.A. Church, 1987, Real-Time screening techniques f o r Doppler c u r r e n t p r o f i l e r data, J o u r n a l of Atmospheric and Oceanic Technology. 4, 572-581. Stacey M.W. , L . J . Zedel, 1986, The time dependent, h y d r a u l i c flow over the s i l l of Observatory I n l e t , J o u r n a l of P h y s i c a l Oceanography. 16, 1062-1076. Zedel, L . J . , 1985, E v a l u a t i o n of an A c o u s t i c Doppler P r o f i l e r with 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 t h e s i s . Z e d e l , L . J . , 1982, Development of a Prototype Inexpensive A c o u s t i c Release, C o n t r a c t e r s Report to Department of F i s h e r i e s and Oceans Canada, (DSS F i l e no. 06SB.FP941-2-0452). J . Ozard, L . J . Zedel, 1981, D e t e c t i o n of an A c o u s t i c Target i n Shallow Water by a B a r r i e r of O m n i d i r e c t i o n a l Sensors, D.R.E.P. T e c h n i c a l Manual 81-18. 

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