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Velocity microstructure measurements in the western and central equatorial Pacific Moum, James Norman 1984

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VELOCITY MICROSTRUCTURE MEASUREMENTS  IN THE WESTERN AND CENTRAL  EQUATORIAL PACIFIC by  JAMES NORMAN MOUM B.A.Sc.,  University  Of T o r o n t o , 1978  M.A.Sc.,  University  Of T o r o n t o , 1979  A THESIS SUBMITTED  IN PARTIAL  THE REQUIREMENTS DOCTOR OF  FULFILMENT OF  FOR THE DEGREE OF PHILOSOPHY in  THE FACULTY OF GRADUATE STUDIES P h y s i c s And O c e a n o g r a p h y D e p a r t m e n t s  We a c c e p t  this  to the  t h e s i s as c o n f o r m i n g  required standard  THE UNIVERSITY OF BRITISH COLUMBIA May 1984  ©  James Norman Mourn, 1984  DE-6  In p r e s e n t i n g requirements  this thesis f o r an  B r i t i s h Columbia,  it  freely available  Library  shall  for reference  and  study.  I  understood that for  f o r extensive copying of  h i s or  be  her  g r a n t e d by  f i n a n c i a l gain  shall  not  be  of  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3 Date  (3/81)  ^fuL)  ?  /ftf  of  Columbia  make  further this  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  permission.  Department  the  representatives.  copying or p u b l i c a t i o n  the  University  the  s c h o l a r l y p u r p o s e s may by  the  I agree that  agree that p e r m i s s i o n department o r  f u l f i l m e n t of  advanced degree a t  of  for  in partial  written  i i  Abstract Measurements quite  different  Camel  III.  of  velocity  oceanic  In  microstructure  regimes u s i n g the  conjunction  with the  were  made  free-falling  Pacific  (PEQUOD) e x p e d i t i o n , p r o f i l e s  were made a t  equator  between  Estimates  dissipation velocity  of  turbulent  r e g i o n of  undercurrent) previously no  less  than  between  reported.  10% of  t h e work  42°N,  of  maximum  34°N in  subsurface indicates  It  than  zonal  of  of  the  the  smaller  the  than  those  from t h e  level core  done by t h e  the proposed gradient  places  in  equatorial  undercurrent  work  of the  (in  integrated  all  from  meters  measurements was made a l o n g  south  of  the  between  manifested  maximum  turbulent  made  rate  110  pressure  does not h o l d a t  the  the  small  times  the  near  surprisingly  the c o r e  to  of  e,  possible that  at  all  is  zonal balance  and  the  times  for  e scales  patches  500 and  frequency, in  in  as N,  800 a  meters secondary  which  averaged d i s s i p a t i o n . with N  152°E  between  Kuroshio Extension current.  itself  model was d e v e l o p e d t o e x p l a i n of  ten  made of  is  done by the  buoyancy  that  above  (=* 70 m e t e r s )  s t r o n g main t h e r m o c l i n e south  90 and  or  Ocean  undercurrent.  A second set and  70,  just  an e s t i m a t e  friction  equatorial  at  The d i s s i p a t i o n  gradient.  turbulent  27°N  more  zonal v e l o c i t y  pressure  the  mean s h e a r are  energy,  measurements a r e  Averaged values large  153°W.  kinetic  microstructure  magnitude.  of  and  two  profiler,  Equatorial  Dynamics  138°W  in  rather the  than  relatively  t h e main t h e r m o c l i n e  depth  depth. greater  and  subsurface  concurred A plot  A  with  a  of  e vs N  A  simple  occurrence  w h i c h assumes  that  the  turbulence  of  the  is  generated  probability  of  by  internal  occurrence  of  waves.  The  prediction  small Richardson  number  is  -1/N  proportional distribution  to of  e  which  the  turbulence  predicts relatively  the  shape  successfully.  of  the  i v  Table Abstract L i s t of T a b l e s L i s t of F i g u r e s Acknowledgement Chapter  of  Contents ii vi viii xii  ....  I  INTRODUCTION  "  1  Chapter II BACKGROUND THEORY 2.1 Mean K i n e t i c E n e r g y E q u a t i o n 2.2 T u r b u l e n t K i n e t i c E n e r g y E q u a t i o n 2.3 The E s t i m a t e Of e 2.4 S t r a t i f i e d Flow P a r a m e t e r s  7 7 9 11 13  Chapter III EXPERIMENTAL CONSIDERATIONS 3.1 A B r i e f D e s c r i p t i o n Of Camel III 3.2 S i g n a l P r o c e s s i n g 3.3 The S t u d y A r e a s 3.3.1 PEQUOD 3 . 3 . 2 WESPAC  15 17 18 21 21 25  C h a p t e r IV RESULTS FROM WESPAC 4.1 The D r o p s S o u t h Of The R i n g 4.2 e And Eddy K i n e t i c E n e r g y 4.3 e And N  28 35 39 42  Chapter V A MODEL OF TURBULENCE IN AN INTERNAL WAVE F I E L D 5.1 I n t e r n a l Wave E n e r g y P r o f i l e s 5.2 I n t e r n a l Wave S h e a r s 5.3 The D i s t r i b u t i o n Of Shear And R i c h a r d s o n Number 5.4 C o m p a r i s o n W i t h The D a t a 5.5 D i s c u s s i o n  51 52 55 ...58 61 68  C h a p t e r VI RESULTS FROM PEQUOD ..72 6.1 C u r r e n t s And H y d r o g r a p h y 72 6.2 P r e v i o u s E q u a t o r i a l M i c r o s t r u c t u r e M e a s u r e m e n t s . . . 7 5 6.3 PEQUOD M i c r o s t r u c t u r e 76 6.4 The O n - e q u a t o r P r o f i l e s ...82 6.5 e And The Z o n a l P r e s s u r e G r a d i e n t 90 6 . 6 e And N, S, R i • 95 6.7 S t a t i s t i c s Of R i And e 101 Chapter VII ESTIMATES OF EDDY COEFFICIENTS 7.1 V a r i o u s E s t i m a t o r s 7.2 C o m p a r i s o n Of E s t i m a t e s  107 108 111  V  7.3 Deep Ocean E s t i m a t e s  7.4 C o m p a r i s o n W i t h E q u a t o r i a l M o d e l V a l u e s  Chapter VIII COMPARISON OF DATA SETS AND PATCH S I Z E STATISTICS 8.1 L o g n o r m a l P r o p e r t i e s Of e 8.2 P a t c h S i z e S t a t i s t i c s Chapter  117  118 123 126 133  IX  DISCUSSION AND CONCLUSIONS  148  BIBLIOGRAPHY  152  APPENDIX A - HYDRODYNAMICS  157  APPENDIX B - PRESSURE  160  APPENDIX C - FALL RATE  163  APPENDIX D - TEMPERATURE  166  APPENDIX E - VELOCITY SHEAR  169  APPENDIX F - CALCULATION OF SPECTRA  184  APPENDIX G - RESOLUTION OF THE DISSIPATION MEASUREMENT APPENDIX H - ERRORS IN THE DISSIPATION CALCULATION APPENDIX I APPENDIX J  ..196 203  - UNITS OF e 214 - TREATMENT OF WHITE HORSE VELOCITY AND CTD DATA 215  APPENDIX K - PEQUOD DROPS  219  APPENDIX L - WESPAC DROPS  248  vi  List  of  Tables  Table  1 -  Scaling  Table  2 -  Correlation  Table  3 -  Depth, t h i c k n e s s and p a t c h - a v e r a g e d d i s s i p a t i o n s f o r t h e p a t c h e s l o c a t e d n e a r 500 m e t e r s d e p t h f o r t h e d r o p s w i t h i n 1/2° o f the equator at 145°W 79  Table  4 -  Comparison of e a v e r a g e d 1982 and 1979 d r o p s  Table  5 -  C o m p a r i s o n of v e r t i c a l eddy c o e f f i c i e n t s d i f f e r e n t e q u a t o r i a l data sets  Table  6 -  A v e r a g e v a l u e s of e f r o m PEQUOD and WESPAC data sets compared to Vancouver I s l a n d slope v a l u e s from L u e c k , C r a w f o r d and O s b o r n ( l 9 8 3 ) 124  Table  7 -  Patch s i z e s t a t i s t i c s over the depth  for the range  PEQUOD data set 20-300 meters 135  Table  8 -  Patch s i z e s t a t i s t i c s over the depth  for the range  PEQUOD data set 300-1000 meters 136  Table  9 -  Patch s i z e s t a t i s t i c s for the WESPAC o v e r the d e p t h range 20-300 m e t e r s  Table  10 -  Patch size statistics for t h e WESPAC d a t a o v e r t h e d e p t h range 300-1000 m e t e r s  set 138  Table  11 -  Patch s i z e s t a t i s t i c s for d e p t h s > 1 000 m e t e r s  for 139  Table  B.1  -  Camel III  pressure  T a b l e D.1  -  Camel III  temperature  T a b l e F.1  -  The spectral routine used vertical shear spectrum  T a b l e F.2  -  Comparison of cumulative variances calculated using the spectral routine with the expected values ( u n i t s are b i t s ) 193  given  to the  defined  of  factors  cubic  for  data  normalization  sets  coefficients  in Table  1  polynomial  for  over  the  titles  65  data  .  sets  66  20-140 m e t e r s  fit  to and  five 112  data set ......137  data  calibration  from 89  for  t h e WESPAC d a t a  calibration  2  and  set  162  data  and  result  168  estimate the sample output 186  vii  T a b l e F.3  -  Comparison of cumulative, variances calculated using the spectral routine with the expected values ( u n i t s are s e c " ) ' 195 2  T a b l e G.1  -  Integration of the noise spectral density function and calculation of equivalent d i s s i p a t i o n due t o the inherent noise of the shear probe 199  T a b l e G.2  -  Comparison of noise levels due t o FM and t a p e r e c o r d i n g s y s t e m s on a l l of the shear channels 202  Table  K.1  -  PEQUOD d r o p l o g  220  Table  L.1  -  WESPAC d r o p l o g  249  viii  List  of  Figures  Figure  1 -  Schematic  of  Camel III  16  Figure  2 -  Schematic  of  signal processing  19  Figure  3 -  Map of Pacific Ocean PEQUOD s t u d y r e g i o n s  Figure  4 -  PEQUOD c r u i s e  track  (February,  1982)  23  Figure  5 -  WESPAC c r u i s e  track  (May/June,  1982)  26  Figure  6 -  T o t a l l e n g t h s of d a t a and t o t a l WESPAC d a t a  Figure  7 -  Temperature s e c t i o n along  152°E  Figure  8 -  Salinity  152°E  Figure  9 -  Turbulent kinetic energy dissipation vertically o v e r 100 meter i n t e r v a l s f o r made a l o n g 1 5 2 ° E i n M a y / J u n e , 1982  Figure  10 -  Vertical estimates 2,4,5,6,8  Figure  11 -  Vertical profile of averages of 25 meter e s t i m a t e s of t u r b u l e n t k i n e t i c energy d i s s i p a t i o n o v e r WESPAC d r o p s 2 , 4 , 5 , 6 , 8 38  Figure  12 -  a) Eddy k i n e t i c e n e r g y . b) t u r b u l e n t k i n e t i c e n e r g y over depth  Figure  13 -  Scatter  Figure  14 -  a) 100 meter vertical averages of buoyancy f r e q u e n c y a v e r a g e d o v e r a l l of t h e WESPAC d r o p s . b) l00 meter vertical averages of turbulent kinetic energy d i s s i p a t i o n averaged over a l l of t h e WESPAC d r o p s 45  Figure  15 ^  Log-log p l o t s  of  Figure  16 -  Log-log p l o t s  of 7 vs N  Figure  17 -  Plots of internal wave potential energy(PE), k i n e t i c e n e r g y ( K E ) and t o t a l e n e r g y ( T E ) 54  section  of  record for sets  along  profile of of b u o y a n c y  plots  showing  the  the  WESPAC and ....22  total  PEQUOD 27  i n May/June  1982 30  i n May/June  1982 32  averaged 10 d r o p s 33  averages of 25 meter f r e q u e n c y o v e r WESPAC d r o p s ...36  buoyancy  dissipation  averaged 41  f r e q u e n c y and e  e v s N from F i g u r e s  14a,b  43  ....46 49  ix  Figure  18 -  Plot of the d e p e n d e n c e of cutoff, X , on the upper v e r t i c a l mode number  the s h o r t limit, j  +  profiles  of  Figure  19 -  Vertical  Figure  20 -  Vertical profiles column (PCT)  Figure  21 -  Vertical 20 and  Figure  22 -  V e r t i c a l p r o f i l e s of 50 meter v e r t i c a l l y v a l u e s of l o g e f r o m PEQUOD  Figure  23 -  Averaged dissipations observed during the P a r i z e a u c r u i s e i n 1979, t h e A t l a n t i s II cruise in 1974 and t h e Thomas G.Thompson c r u i s e i n 1982 81  Figure  24 -  Eight v e r t i c a l profiles of vertical estimated from W h i t e H o r s e h o r i z o n t a l t a k e n w i t h i n 1/2° of the equator in 1 982  Figure  25 -  Eight vertical profiles of Brunt-Vaisala f r e q u e n c y measured s i m u l t a n e o u s l y as the shears of F i g u r e 24 85  Figure  26 -  Vertical profiles of turbulent k i n e t i c energy d i s s i p a t i o n averaged over 25 m e t e r s depth and which are nearly synoptic with the data of F i g u r e s 24 £ 25 86  Figure  27 -  Time v a r i a t i o n s of e a v e r a g e d over m e t e r s a n d cube o f d a i l y wind s p e e d  Figure  28 -  Scatter plots f r o m PEQUOD  Figure  29 -  Plot  of  log  e vs  l o g S f r o m PEQUOD  .99  Figure  30 -  Plot  of  log  e vs  l o g Ri  100  Figure  31 -  Scatter  Figure  32 -  Relative estimated February,  of  Pr(Ri<l)  fraction  of  and  +  wavelength , of the 57 Pr(Ri<l/4) 62  turbulent  water 63  profiles of n o r m a l i z e d PCT f r o m F i g u r e n o r m a l i z e d Pr(Ri<1/4) from Figure 19 67  plots  of  log  of  frequency from the 1982  e vs  log  l o g N,  averaged 80  shear as velocities February, . .84  20  to  l o g S and l o g  from PEQUOD N  vs  140 91 Ri 96  l o g S f r o m PEQUOD 102  of occurrence of White Horse data  log taken  Ri in 104  Figure  33 -  Normalized frequency h a l f decade i n t e r v a l  Figure  34 -  Vertical  profiles  (equation  7.5)  Figure  35 -  Vertical  for  profiles  of of  the of  data Figure  36 -  Vertical K  Figure  37 -  rPP  (equation  Vertical K  vPP  profiles  7.11)  profiles  (equation  of  of  7.10)  occurrence  of  K  (equation 0 PEQUOD d a t a  K and 0  K  G  for  log  e  7.4)  and K  the  WESPAC  G 115  116  25 metre a v e r a g e s  of  K  from PEQUOD 25 metre a v e r a g e s from PEQUOD  per 105  of  K  V  0  and 120 and 121  Figure  38 -  Cumulative distribution of dissipation values  of t h e from  b a s e 10 l o g a r i t h m PEQUOD 20-300m 128  Figure  39 -  Cumulative distribution of dissipation values  of t h e b a s e 10 l o g a r i t h m from PEQUOD 300-1000m 129  Figure  40 -  Cumulative distribution of dissipation values  of t h e b a s e 10 l o g a r i t h m from WESPAC 20-300m 130  Figure  41 -  Cumulative distribution of dissipation values  of t h e b a s e 10 l o g a r i t h m from WESPAC 300-1000m 131  Figure  42 -  Cumulative distribution of dissipation values  of  Figure  43 -  Log-log plot of average patch-averaged d i s s i p a t i o n s vs average p a t c h t h i c k n e s s for the PEQUOD d a t a below 300 m e t e r s 141  Figure  44 -  Log-log plot of average patch-averaged d i s s i p a t i o n s vs average p a t c h t h i c k n e s s for the WESPAC d a t a below 300 m e t e r s 142  Figure  45 -  Log-log p l o t of a v e r a g e b u o y a n c y l e n g t h s c a l e vs a v e r a g e p a t c h t h i c k n e s s f o r t h e PEQUOD d a t a below 300 m e t e r s . 1 45  t h e b a s e 10 l o g a r i t h m from WESPAC >l000m 1 32  xi  Figure  46 -  Log-log p l o t  of  a v e r a g e buoyancy  average patch 300 m e t e r s  thickness  for  Figure  B.1  -  Camel III amplifier  preamplifier  Figure  C.1  -  Camel  fall  III  length  scale  t h e WESPAC d a t a and  rate  lowpass  vs  below .146 filter161  circuit  (pressure  differentiator) Figure  C.2  -  Camel  III  164  Pressure  derivative  transfer  function 165  Figure  D.1  -  Thermistor  preamplifier  and  temperature  circuit 167  Figure  E. 1 -  The a i r f o i l  Figure  E. 2 -  Typical  Figure  E. 3 -  Camel  Figure  E. 4 -  Veloc i t y  Figure  E. 5 -  Velocity  Figure  E. 6 -  Velocity  Figure  E. 7 -  Complete shear  Figure  E. 8 -  Veloc i t y  Figure  E. 9 -  Velocity f u n r t i on  Figure  G. 1 -  Noise  Figure  H. 1 -  Four  Figure  H. 2 -  P e r c e n t a g e of  Figure  H. 3 -  Figure  H.4  -  probe showing  airfoil  flow  components  probe c a l i b r a t i o n  III v e l o c i t y  shear  signal  curve  . . . . 170  ...  , , 1 72  processing . ..174 . . . 175  shear  preamplifier  transfer  function 177 , , 178  circuit  transfer  function  ..  , , 179 ...181  shear  spectral shear  high density spectra  the  gain  amplifier  measured w i t h from  variance  p o t t e d shear 1 98  Quatsino  resolved  transfer 182  by  Sound the  on  shear ...207 , . .210  Spectra from t h e the time  four  adjacent  blocks  (57- 60) o f ...211  xii  Acknowledgement I would like to express my gratitude to Professor T.R.Osborn for h i s g u i d a n c e and f o r h i s s u p p o r t of my p r o j e c t . As w e l l , I w o u l d l i k e t o t h a n k Professor P.H.LeBlond for his freely-given time and t h o u g h t s . I have b e n e f i t t e d from t i m e t o t i m e by b e i n g a b l e t o t a l k w i t h P r o f e s s o r s S . P o n d , L . A . M y s a k and R.W.Burling. I am a l s o indebted to Dr.R.G.Lueck for many valuable discussions and m u c h - a p p r e c i a t e d t e c h n i c a l a d v i c e and to Dr.W.R.Crawford for his input to the analysis of the equatorial data. I would like to t h a n k D r . J . G . R i c h m a n f o r a l l o w i n g me t o participate in the PEQUOD expedition. Drs.P.P.Niiler and W.J.Schmitz p e r m i t t e d me t o t a k e measurements d u r i n g t h e WESPAC cruise. Dr.J.R.Luyten supplied the White Horse data and Dr.P.Niiler the CTD d a t a f r o m WESPAC. The c a p t a i n and crew of t h e R/V Thomas G.Thompson p r o v i d e d e x p e r t h e l p i n d e p l o y i n g and successfully r e c o v e r i n g Camel I I I . V a r i o u s members of t h e Woods H o l e Buoy G r o u p l e n t c o n s i d e r a b l e time and expertise to the s e a g o i n g o p e r a t i o n d u r i n g both c r u i s e s . R.Noel a s s i s t e d w i t h the o p e r a t i o n on t h e PEQUOD c r u i s e and R . M . N i n n i s p l a y e d t h e r o l e of t e c h n i c a l a s s i s t a n t and d e v i l ' s a d v o c a t e on t h e WESPAC t r i p . S.Milaire made the shear probes and, with B.Anderson, p r o v i d e d s u b s t a n t i a l t e c h n i c a l a s s i s t a n c e d u r i n g the development s t a g e of Camel I I I . H . H e c k l d i d most of t h e m a c h i n i n g . F i n a l l y , I would l i k e t o t h a n k t h e many graduate students and postdoctoral fellows with whom I have been f o r t u n a t e t o a s s o c i a t e w i t h and l e a r n f r o m d u r i n g my tenure as a graduate s t u d e n t a t UBC. The Natural Sciences and E n g i n e e r i n g R e s e a r c h Canada s u p p o r t e d me w i t h a p o s t g r a d u a t e scholarship studies.  C o u n c i l of during my  1  I. The  study  of  essentially  a study  responsible  for  momentum motions  and in  nature  these  small  treatment  the  of  first  in  experiments  provide  the  inertial  s u b r a n g e of  first  until,  Scripps  capable  of  describe scales  the  in the  the  turbulence  what  is  nonlinear of  the  the  study  of  empirical  Defence by a  turbulence  conditions  of  Narrows), of  ranging  fundamental From  sufficiently  they the  were  to  of  the  scales  of  the  from ^ 1 meter (a  couple  a  ocean  C.S.Cox  instrumentation  temperature came down t o of  For  measuring by  high  able  existence  o n l y workers  microstructure  ocean  Research  itself.  1960's a group headed  small  Stewart  p r o p o s e d by K o l m o g o r o f f .  were t h e late  by G r a n t ,  were m o t i v a t e d  evidence  term  in the  scale  t o d e s c r i b e how  of O c e a n o g r a p h y d e v e l o p e d  the  larger  and  in order  are salt,  extent  Instead,  is  heat,  highly  the  Canadian  the  under  these  scales  which e x i s t  of  turbulence  Institute  time,  the  solid  resolving  Around t h i s  oceanic  i n Seymour  8  years,  turbulence at  (10  the  processes,  (DREP)  conducted  number  of  of  nature  which  understand  Due t o  parameters  ocean  dynamics.  at  Reynolds  number  flow  Pacific the  to  been l i m i t e d .  scale  Moilliet(1962)  Establishment,  mechanisms  experimentation  studies  the  To u n d e r s t a n d t h e  necessary  scale  the  in  d i s p e r s i n g , d i f f u s i n g of  has  large  turbulence  scale  scales.  involves  affect  interest  small  is  small  parameterization  and  it  the  turbulence  The  the  quantities.  sea  at  they  of  other  happening  analytical  three-dimensional  the m i x i n g ,  the  of  INTRODUCTION  into the  field. use  to  smallest  centimeters  for  2  velocity, for  one  centimeter  for  temperature  ocean  was  for  measuring v e l o c i t y  d e v e l o p e d by T . R . O s b o r n a t  Osborn(1974).  made  shear)  u s i n g an a i r f o i l  smallest  scales  (except  in  of  the  r e g i o n s of  mounted on a v e r t i c a l vertical which  shear  an  of  New  rapid  undercurrent thereby  of  the  the  in  showed  the  agreement  techniques.  temperature  gradient  within a factor  of  From t h e  o b t a i n e d of  the  kinetic  providing  with  the  valuable  made of  shear  who were  gradient  (in  the  equatorial  energy  dissipation,  large the  given  scale  dynamics.  dissipation by  h i g h wavenumber  cutoff  t h e d i s s i p a t i o n was  of  the  probe  with  Oakey(l982)  d i s s i p a t i o n estimates  shear  in  the  (1979b)  spectrum, two t o  description  variation.  kinetic  recently  from energy  microstructure  drives  w i t h the  p r o b e measurements was  was  zonal pressure  which  estimate  The p r o b e  in o b t a i n i n g a  velocity  turbulent  the  fluctuations  turbulent  t h e measurements made  turbulence  the  resolving  fluctuations  p r o f i l i n g techniques are  Atlantic)  confidence  different  agree  of  t h e work done by t h e  with  linking  shear  who  the  t e m p o r a l and h o r i z o n t a l  equatorial  Added  of  British  of  turbulence).  was d e m o n s t r a t e d by C r a w f o r d and O s b o r n  to balance  the  made  of  the  was  velocity  velocity  in  measurement  and a measure was  horizontal  was  The s i g n i f i c a n c e  able  intense  profiler  variability  i n f o r m a t i o n on t h e  probes  probe capable  The p r o b e p r o v e d u s e f u l  the v e r t i c a l  The  cross-stream  very  the  estimate  dissipation.  ocean.  (or  microstructure  the U n i v e r s i t y  C o l u m b i a and d e s c r i b e d i n  the  millimeters  salt) The t e c h n i q u e  of  and a few  using  two  of  the  estimated  estimates  to  when  3  the  temperature  gradient  c o n s i d e r e d t o be a t e s t from  temperature  that  made by t h e  of  data, shear  The s o u r c e s of  turbulence  differential  h e a t i n g and  large  mean  equatorial Other  well  turbulence. the  In  the  wave  is  difficult  processes the It  lack is  not  vertical  on of  thought  horizontal  the  buoyancy  flux  temperature  tilted  Recently, relative of  show  the  ocean,  the  of  producing (as  upper  greater the  l o s s of  effects  of  temperature  the  to  role  of  levels  primary  salt  signature  of  from t h e h o r i z o n t a l  i m p o r t a n c e of  source  from  double  diffusive  double  the  diffusive  fingers salt  1979). in  finestructure  their  to  with  a  fingers  is  However,  if  some way  turbulence  due  measurements.  they  may  able  to  p r o d u c e d by  the  measurements  of  Gregg(l983)  double d i f f u s i o n using  and s a l i n i t y  of  energy  and s a l i n i t y  detect  and  have  some p l a c e s .  ( S c h m i t t and E v a n s ,  Larson  in  layers.  measured d i s s i p a t i o n s d i s c u s s e d h e r e ,  since  estimate  to  in  wave,  relatively  turbulence the  the  o c e a n b o t t o m and s i d e s  t o be t h e  to assess  profiler  are  of  a strong role  possible  be d e t e c t e d .  the  a  capable  c o n f i n e d to  a l t h o u g h the  simultaneous  fingers  at  interior  generally  essentially the  the  with  near  (wind,  create  generate  generally  field,  m i x i n g may a l s o p l a y It  may  effects  is  consistent  processes  often  s t u d i e d but appear  turbulence  internal  are  Surface  Strong currents  which  layer  dissipation  mostly concentrated  cooling)  layer.  regions)  are  ocean.  shears  boundary  been l e s s  for  the  computing  Although  p r o b e was p r o v i d e d .  of  upper  t h e method of  an i n d e p e n d e n t e s t i m a t e  boundaries  well-mixed  s p e c t r u m was w e l l - r e s o l v e d .  were  coincident  with  velocity  4  microstructure were  diffusion.  characteristic Here,  responsible relation  the  the  for  buoyancy  production  of  Reynolds  the  of  remarkably  level  Munk(1979)  result  quickly,  will  internal  locally  wave  some the  as we s h a l l  see,  relation  the  energy  of  the  buoyancy  for  the  turbulent  thesis,  I  in the  will  5 to  10 t h a n  than  working  the the  against  have  special oceans.  shown  the  do  thereby  in  Garrett  and  universality  not  dissipate  The t e m p o r a l  in  internal  kinetic  constancy  wave f i e l d one  energy  d e s c r i b e a set  the  increased  turbulence.  frequency,  energy  saturating  locally  the  may be a  diffusing  levels  be  cases)  constancy  they  resulting into  the  i n t h e d e e p ocean t o  region.  wave e n e r g y  fingering,  suggested that  The s p a t i a l  enhanced s p e c t r a l  internal  value  this  a large  be T-s  20 y e a r s  quite  if  to  responsible.  world's  which,  double  large  greater  was  last  long d i s t a n c e s  spectrum,  of  In  in  of  the  of  mean s h e a r  partly  wave s p e c t r u m .  propagate  dissipation  similar  It  maxima  temperature  Where  salt  much  wave e n e r g y  throughout  source over  may be due t o  local  were  waves i n t h e  l o n g - l a s t i n g waves,  from a l o c a l  the  least  in  regime  by a f a c t o r  by t h e  T-s  sufficiently  for  energy  (except  steps  d i s c u s s a c o n c e p t w h i c h may e x p l a i n  internal of  form  well.  internal  local  dissipation.  as  was a t  constant  and  the  flux,  internal of  was  were g r e a t e r  turbulent  spectrum  shape  necessary  stress  Studies  flux  r e g i m e c a s e and  estimated  of  above  the d i f f u s i v e  measured  dissipations  diffusive  of  buoyancy  the  showed t h e  measured  the  Regions  f o u n d w h i c h e x h i b i t e d the d i s t i n c t i v e  and s a l i n i t y  in  measurements.  Since,  scales  as  suspects  a  dissipation.  of measurements  of  5  velocity  microstructure  discussed) and  I  which  will  I  (made u s i n g  conducted in  attempt  to put  these  profiles  were made i n t h e c e n t r a l already  microstructure these.  In  Western  May and June o f  c o l l e c t e d at virtually these  Ocean  depths  all  of  the  equatorial  and  it  is  already  Pacific  into  velocity  relatively  their  a  microstructure  Pacific.  large  For  data  interesting  greater  significant than  velocity  1000  meters  this  bank to  amount of  microstructure  Ocean proper  of  compare  1982, measurements were made  and  the  of  probes  in  the  data  was  (representing  data  anywhere  at  depths). In  Chapter  developed Chapter  2 the  and 3  the  there  equations which govern appropriate  is  a  procedures,  the  and  measurements  other  by  the  descriptions  of  the  handling are  found.  turbulent  kinetic  velocities  are  from  western  the  Chapter  4.  set  energy  is  made d u r i n g t h e in  instrumentation, As w e l l ,  energy  of  balance  two c r u i s e  cruises.  (WESPAC)  result  arising between  maximum  and  cruise from t h e the  frequency in  tracks  Chapter  more  vertical  In  experimental  lab c a l i b r a t i o n s  the  are  discussed.  seagoing  which  in Appendices K  strong r e l a t i o n  subsurface  turbulence  d i s s i p a t i o n , CTD d a t a  Pacific  The n o t a b l e  all  d i s s i p a t i o n and t h e b u o y a n c y  well-defined  of  the  p r o c e s s i n g , the  Appendices  presented  the  oceanic  discussion  on-deck s i g n a l  supplemented  data  a  measurements  Pacific  r e g i o n s of  1982 a s e t  exists  shear  measurements  In  there  of  two  context.  region  February  the  3  is  detailed and d a t a  profiles  of  and h o r i z o n t a l  L.  The  are  discussed  analysis  turbulent  results  of  in  this  kinetic  in a region with a  buoyancy  frequency.  An  6  attempt shear results  to e x p l a i n  this  instability from t h e  PEQUOD d a t a horizontal  set  is  velocity  and  comparison  mean  of ,  turbulent  Chapter  8.  comparing  nearly  It  is  other  d i s c u s s i o n and t h e  vertical  values  properties  data  wave  Chapter  6 the  presented.  profiles  Various  estimates estimates  d i s c u s s e d and compared i n  hoped t h a t  internal In  5.  (PEQUOD) a r e  synoptic  lognormal s t a t i s t i c s patch  on  by CTD d a t a made w i t h  number were o b t a i n e d . are  of  Pacific  as w e l l as  based  in Chapter  e n h a n c e d by t h e  eddy c o e f f i c i e n t s  dissipation  .model  developed  equatorial  instrumentation, Richardson  is  with a  this  sets.  conclusions.  of  turbulent  of  Chapter  9  mean  of  shear  and  of  turbulent  Chapter  7.  kinetic  energy  and d i s t r i b u t i o n s provide  of  independent  d i s s i p a t i o n and  may  The  a  A  estimates  are  given  format  contains  a  in for  short  7  II. 2.1  Mean K i n e t i c In  the  tensor  x  are  =  y  respective density = M/P  of the  gravity,  Energy  Equation  following discussion  Cartesian 2  BACKGROUND THEORY  notation  horizontal,  velocities the  fluid  kinematic  K the  is  thermal  are is  of  used  .  and x U,  p,  M is  governing  Spatial = z is  3  = U,  the  U  =  2  the  coordinates  positive V  and  U  coefficient  viscosity,  g  the  diffusivity  and 6  equations, x,  = x,  upwards.  The  =  3  of  W.  The  viscosity,  v  acceleration  due  the  delta.  Kronecker  to  ij The  conservation  of momentum i s  equations  for  an  stratified  fluid  (Phillips, 1 9 7 7 )  p(9U / d t i  incompressible,-  non-rotating,  2  of mass i s  d p / d t  are  Navier-Stokes  + U 9U /dx ) = - 9p/9x - pg6 + M 9 U /dx dx j i j i i3 i j j  The c o n s e r v a t i o n  which,  e x p r e s s e d by t h e  if  small,  the  fluid  reduces  + 9(pU  is  viscous,  ( 2 . 1 )  e x p r e s s e d by  i  ) / d x  = n.d p/dx 2  i  i  dx  i  i n c o m p r e s s i b l e and t h e  diffusion  terms  to  dp/dt  + U 9p/9x = 0 i i  and  9U /9x = 0 i i  (2.2)  8  It  is  usually  common t o  plus  fluctuating  components  after  Osborne Reynolds  separate (referred  who f i r s t  measurements made u s i n g t h e  shear  of  is  about  motion is  1-50  is  shear  than  al.(l98l),  the  1  scale  field.  with et  For  fluctuating  in  believed  the  than  ocean,  the  will  scales  implies  that  scales  of  will  be  this  t h e mean m o t i o n  waves down t o  expansion of  the v a r i a b l e s  expressed b y U  = u i  describing  the  i  t o as  + u ' , p = p + p ' ,  derived.  hypothesis  averages  =  fluctuating  The  is  motion  at  least velocity  scales  of  and  eddies  et  dominate  scales  probe)  of the all This  and  all  waves.  Reynolds'  fluctuating  components  p = p + p ' .  components of  overbar  Equations  ensemble  averages. are  approximation  is  used  so  importance  the  gravity  term i n  the  to  zero. ratio  (2.1).  u,  spatial  Averages  equal that  the  d e n o t e s an a v e r a g e  a s s u m e d , whereby  components  to  the  t h e mean motion..  h e n c e f o r t h be d r o p p e d from t h e mean q u a n t i t i e s ergodic  the  the  i  t h e mean and f l u c t u a t i n g  separately  scales  (Gargett  the  shear  The  scales  processes  as  internal  i n t o mean p l u s  to  s p e c t r u m of  includes currents, smallest  expansion  (or  thesis,  be t a k e n  referred  (i.e., cm  and o t h e r  t h e p u r p o s e s of  these  parameters  ( t h o s e s c a l e s m e a s u r e d by t h e  larger  at  50  mean  separation).  for mixing  al.(1984))  into  sensitive  that  turbulence  components  field  t o as R e y n o l d s '  probe are  greater  meter)  flow  suggested the  responsible  scales  Gargett  turbulence  is  At  d o e s not  flow  and i t  random and i s  turbulent).  greater  the  cm  the  flow  are  and  will  p and p. averages  The = time  of  individual  The  Boussinesq  p'/p  is  only  of  9  To o b t a i n mean f i e l d ,  the equation d e s c r i b i n g the k i n e t i c  ( 2 . 1 ) i s m u l t i p l i e d by u  and averaged  i  energy of the so t h a t  J_p{3(u u )/9t + u 3(u u )/9x } = - u 9p/9x - pgu 6 2 i i j i i j i i i i 3  + nu 9 u /9x 9x - p9(u u'u*)/9x i i j j i i j j  + pu'u'9u /9x i j i j  2  The mean k i n e t i c  energy  i s J_(u u ) a n d , from ( 2 . 3 ) , 2  on  the  vertical term  (under  the  the d i v e r g e n c e  and t h e R e y n o l d s  This  last  term  transferred  stresses  provides  the  of  turbulent  Energy kinetic  energy  i  + u 9/9x ( u ' u ' ) } j j i i  (I)  viscous  by  gravity diffusion  Reynolds  stresses  t h e mean  which  the energy  equation  is  derived  a n d d i v i d i n g by p t o g i v e  = - J_9/9x {u p i i  1  (p +u'u'/2)} j j f  (II)  (IV)  is  field.  - g p ' w ' - u'u'9u /9x + *>9/9x {u'(9u'/9x +3u'/9x )} p i j i j j i i j j i (III)  shear,  Equation  ( 2 . 1 ) by u ' , a v e r a g i n g  J_{9/9t(u'u') 2 i i  f o r the  working against means  since the  f o r t h e mean m o t i o n ) ,  the  from t h e mean t o t h e t u r b u l e n t  2.2 T u r b u l e n t K i n e t i c  multiplying  accounts  c o n s i d e r e d t o be s m a l l  u'u', i j  gradient  approximation),  o f t h e mean a d v e c t i o n  depends  i  pressure gradient  Boussinesq  (which i s g e n e r a l l y  The  i  work done by t h e h o r i z o n t a l p r e s s u r e hydrostatic  (2.3)  (V)  by  10  -  J ^ O u ' / B x +3u'/3x )(3u'/9x +9u'/9x ). 2 i j j i i j j i  (2.4)  (VI) I  represents  energy  the  J_(u'u'). 2 i i  pressure  of  divergence plus  done  of  that  by t h e  energy  by  the  the  r a t e of  the  transport  of  the  viscous  derivatives  then  turbulence  the  two  stresses  of  a by  energy  of  the  time  balance the  turbulent  by  is  are  is  work  motion.  if  zero,  of  done VI  is  e.  energy.  then  equal  mechanical  stresses  Reynolds  responsible  the  total  Further,  the  work  redistribution  homogeneous,  zero.  the  the  term  energy,  change t h e  between  buoyancy  V is  spatial  the  correlation  Ill  and i s  (2.3)  change a r e  Reynolds  is  redistributing  in  r a t e s of  to  the  of If  spatial z e r o and flow  as w e l l .  is This  production  of  and t h e mean s h e a r ,  the  f l u x and t h e d i s s i p a t i o n o f  by v i s c o s i t y ,  - £p'w' P  is  in  This  kinetic  be  dynamic  energy  shear.  the  a local  and do not  term I  total  work done by t h e  fields.  turbulent  kinetic  this  components.  term  c o n s i d e r e d to  part  p r o d u c t i o n by t h e kinetic  essential  o f mean t u r b u l e n c e q u a n t i t i e s  advective  in  is  by t h e  turbulent  mean  the  and V r e p r e s e n t energy  is  is  identical  shear  of  flow  the  d i s s i p a t i o n of  turbulence  results  the  done  turbulent  the p r e s s u r e - v e l o c i t y  IV  exchange between  turbulence  steady,  of  flux.  the  Alternatively,  transport  buoyancy  of  work  e n e r g y among t h e  Terms II  the  the  turbulence.  sign to  for  the  is  working a g a i n s t  opposite  the  derivative  The p-u c o r r e l a t i o n  turbulent  stresses  II  the  turbulence. the  total  turbulent  or  - u'u'9u /3x - e = 0 i j i j  (2.5)  11  Osborn(l980) in  light  buoyancy  d i s c u s s e s the  of  laboratory  flux  is  representing stratified usually  the  at  most  turbulent  The E s t i m a t e With  the  full  the  of  each of  with  retain  of  the  this  this  is  expected  term i n the  = aJT^/(u "u 3u 7  f  p  /3x  r  i  an e s t i m a t e  is  j  i .  j  form,  e is  +  to  the  written  e,  f o r m of  the  is flux  2  + 2(3v'/3y)  be  2  +  is  fluctuations,  and a h o t  isotropic.  turbulence.  In  2  2(3w'/3z)  2  2  al.(l984).  film  probe  dissipation  scales  if  we make t h e  assumption  T h i s may be a good a s s u m p t i o n From a s u b m e r s i b l e the  to  measurements made o v e r  i s o t r o p y at  major  2  probes to detect  fluctuations  the  a  (3v'/3z+3w*/3y) }.  mounted  shear  velocity  provided  (3u'/3z+3w'/3x)  et  with  +  2  simplified considerably  turbulence  the  as  according to Gargett  that  it  In  ).  o b t a i n e d of  + (3u'/3y+3v'/3x)  the  terms.  f o r m of  the  (2.5),  ratio,  probe sensors used to d e t e c t  = f{2(3u'/3x)  that  that  in  two  (2.5)  Of e  made p e r t a i n i n g  component  can  out  terms  other  e = _ M 3 u ' / 3 x +3u'/3x ) 2 i j j i  This  two t e r m s of  significant  flows  shear  microstructure, assumption  first  number,  R  2.3  the  pointing  20%  to  of  measurements,  least  convenient  Richardson  ratio  platform  cross-stream  measure  the  a wide range o f  may  be  limit  of  a  turbulent streamwise e  indicate  relatively  safe  JL  a s s u m p t i o n t o make down t o a l o w e r  e  = (75)*t>N , where 2  1  1  N is =  the  local  0.001  buoyancy  rad/sec  2  frequency.  and  =*  v  In  0.01  the  deep o c e a n where N  cm /sec,  this  2  results  in  is  e  ^ 1  3x10" as  W/m ,  7  the  the  which  3  instrumental  western  is  is  noise  Pacific  0.005  precisely  the  level  (see  thermocline  rad/sec  and  e  level  w h i c h has been  defined  Mourn and L u e c k ( 1 9 8 4 ) ) .  (discussed  =* 8 X 1 0 ~  in Chapter  W/m  6  this  3  4)  In  where N  may d e g r a d e  the  1  reliability affect of  the  e near  of  the  small  averages or  estimates  which are  greater  than  of  e but  d o m i n a t e d by  s h o u l d not individual  seriously estimates  e . 1  Hinze(l975,  p219)  gives  (9u'/9x) (9u'/9y)  2  (9u'/9y) (9v'/9x)  following  = (9v'/3y)  2  = (9u'/9z)  the  = (9v'/9x)  2  =  2  2  isotropic  (9w'/9z)  2  = 2(9u'/9x)  = ( 9 u ' / 9 z ) (9w'/9x)  relations:  2  = ...  = - J_(9u'/9x)  2  =  2 The s h e a r p r o b e s measure turbulent  velocity  derivatives obtained  (henceforth of  these  the  (as  is,  profiles  vertical  derivatives  the primes w i l l  be d r o p p e d ) .  ,  of  yield  the  vertical  an e s t i m a t e  3u'/9z  Rewriting  and e  of  course, The u n i t s  be w r i t t e n  as  3  the  in  terms (2.6)  2  kinematic  used in  this  form  for  e  thesis  are  W/m  e = YSpv ( 9 u + 9 v ) 2  4  is  9v'/9z  two components y i e l d s e = V5v(9u +9v ). 4 3z 9z  [L /T ]. 2  Vertical  components  d i s c u s s e d i n A p p e n d i x E)  2  This  cross-stream  field.  so t h a t  of  the  9z  2  9z  with 3  units  requiring  of e to  13  or e = JJ5M(9U 4 9z  2.4  Stratified  The  Flow  (g/c)  9V ) 9z  .  2  Parameters  Brunt-Vaisala  -c[9p/9z -  2 +  or buoyancy  frequency  where p i s t h e i n s i t u  2  i s defined  density  and  by N  =  2  i s a measure  P  of  the  may  local  be  thought  oscillation its  static  of  of  as  l e s s than  wide  of sources  the  upper  ocean. scales  frequency On  the  natural  do  other  greater  propagate  The  hand,  N  The  wave  N  length  scale L  N  with =  are while by  a•  represents  spectrum  i s associated  from  waves  parameter  to the internal  of the turbulence.  than  as  N  vertical  a s waves and a r e g e n e r a t e d  i n the ocean.  limit  of  w h i c h has been d i s t u r b e d  not  N travel  Alternatively,  frequency  Frequencies  or  frequencies  i n the f l u i d .  of f l u i d  position.  attenuated  range  the  a parcel  equilibrium  rapidly  stability  of  the  the largest  (e/N )^  which  3  b is  discussed  effects  are  turbulence  or  Richardson the  stability  Richardson potential kinetic  o f t h e same o r d e r  another  dynamic  8 represents  at larger scales  Various way  i n Chapter  number, energy  energy  are  as the n o n l i n e a r  i s supressed  numbers which relative  by r a i s i n g  above, mass  by t h e b u o y a n c y .  roughly  in  describe  to accomplish  the  text.  i s the ratio  (the  buoyancy  e f f e c t s and t h e  e f f e c t s of the l o c a l  discussed  defined  required  the scale at which  buoyancy  this  in  one  static  and  The  flux  of the gain i n flux)  (the shear  to  the  production  1 4  term).  The  gradient  Richardson  number  is  R  = N /(9u) . 2  2  g the made  PEQUOD W h i t e H o r s e d a t a over  number, R  9  .  Ri  25 meter  depth i n t e r v a l s  = g_ApAz/(Au) i s P Unfortunately, this estimate  difference smaller  = N /S  estimates  2  2  estimates  scales.  2  of  of N and  9z S  =  and a d i f f e r e n c e calculated is  From  Au/Az  Richardson  as an e s t i m a t e  only  as  p and u and c o n c e a l s  the  are  good  as  information  of the at  15  III.  EXPERIMENTAL CONSIDERATIONS  D e t a i l e d d i s c u s s i o n s of III  are  i n c l u d e d in  be r e f e r r e d  to here.  deployment  and  instrumentation  the a p p e n d i c e s to t h i s In  this  recovery  p r o c e s s i n g are  discussed.  cruise  and o t h e r  tracks  the  chapter,  of  the  As  thesis  Camel  and w i l l  only  shipboard procedures  for  instrument  well,  aboard  I  and  will  the  signal  briefly  measurements made d u r i n g t h e  discuss  PEQUOD and  WESPAC c r u i s e s . A general  point  to  made  such  experimental  conditions distinguishes  a  laboratory  being able small  this.  setup.  to adjust  time  scales  A  concerns  experiments  from  as  be  certain  In  the  parameters  and  until  satisfied  oceanic With  an  extended  lab,  this  time  s u c h as  in  mind,  it  various  would be  to  provide turbulent  and s h o r t  time  the  a  that  the  basis  quantities,  scales,  experiment  this to  thesis,  I  limitation  hope  that  I  in  which are scales  of  synoptic  i n d i s c u s s i n g the  make  results  of  meantime. sets  in  Especially spatial grave  proper the  reference  experiments.  are in  scales  and  finding mission processes.  of  space  t h e measurements  w h i c h have s m a l l  on r e l a t i n g  and  d o i n g so and  the  comparison.  of  over  time  t o make c o h e r e n t  resemble a f a c t  shall  luxury  Certainly,  due t o  p r o b l e m c a n be q u i t e  than a study which c o n c e n t r a t e s  experiment  results.  before  changed  for  of  over  experiments  often  lapse  ideal  parameters  and t o e n s u r e  measuring  cause  may  of  control  one has t h e  repeat  but  'design'  of  type  w i t h the  c o n d i t i o n s may be r a d i c a l l y  measurements o f and  period  lack  this  o c e a n i c measurements may be r e p e a t e d , expense,  the  may  rather  In to  this this  16  LAUNCHER XBT WIRE LINK LIGHT STROBE  MAIN PRESSURE HOUSING AND ELECTRONICS  BALLAST RELEASE MECHANISM  LEAD BALLAST  PRE-AMP 2 SHEAR PROBES  THERMISTOR  CAMEL HI  Figure  1 -  S c h e m a t i c o f Camel III a s i t was t h e WESPAC a n d PEQUOD c r u i s e s .  configured  for  1.7  3.1  A Brief  D e s c r i p t i o n Of Camel  A schematic shear  which  contains  preamplifying  multiconductor electronics affixed  in  These  the  recovery  aids  was  method u s e d f o r  on t h e  fitted  over  the  has  been  a  trips  side  speed  is  meters  since  trip of  for  is  housing.  Two  by p r e s s u r e also  circuitry  signals  to  the  ballast  is  cone by  activated  shows t h e  and u n d e r w a t e r  wire  ballast  launcher  pinger).  used t o a t t a c h a  nose  Underwater  Lead  d e p l o y i n g Camel III  the up  water. by  about  only  A new  Thomas G.  lifting  instrument.  meters  to  into  taken  the  rising  chosen  signal.  preamplified  equipment a v a i l a b l e . on the R/V  the P a c i f i c  release  and t h e  - main body t r a n s i t i o n  radio,  1.  snap  and  The  ring  hook  and  recovery.  The extent  probe  The s c h e m a t i c  t o p of Camel III  Figure  transducer  pressure  released  (flasher,  shown i n  mounted on a s t r e a m l i n e d  the  preamplifier  mechanisms.  for  link  are  are  shear  main  links  is  pressure  the  release  around the  the  cables  to the  links.  line  Camel III  probes plus a thermistor  piece for  view of  III  t h e Camel out Once t h e  a fall  slightly  slows  c o i n c i d e w i t h the  w h i l e we g e n e r a l l y  trip.  launcher  faster,  retrieval to  about  the over  large  picker  cradle  the is  crane  was u s e d on  its  w e i g h t of  with depth.  attempted  of  s p e e d of  a White Horse drop (which l a s t e d  t h e PEQUOD  the  45 m i n u t e s and a l i t t l e  Camel III  cherry  Thompson and t h i s  t h e water At  depends to a  instrument  activated  80 cm/sec  return  trip  90 m i n u t e s  to to  to and  1000 2000  The s u r f a c i n g t i m e of  and  was  t h e CTD on t h e WESPAC  s q u e e z e a Camel d r o p approximately  inside  2-3 h o u r s )  on  18  Surfacing  of  the  instrument  s i g n a l p i c k e d up by t h e pretuned  to  launch.  At  the  substantially of  the  by two  glitter  was  just  and t h e We  The  under  longest  no  Camel III  of  the  flashers  r e q u i r e d to  failures  zeroed in of  surfaced  instrument  snap hook c o u l d be a t t a c h e d  from  With the  s n a p hook  in p l a c e ,  the  towards  the  of  capstan  line  instrument  batteries 3.2  stern  the  was for  then  the  describe the  ship,  disassembly  in  the  the  surfaced  eyes  straining  of  about  45°.  transmitters  on  was  so t h a t  the  was  the  to  platform.  was a l l o w e d recovered  to  drift  using  the  s h i p ' s A-frame.  cradle  order  ship  hydrographic  where i t in  the  instrument,  instrument  secured to the  The  and moved i n s i d e  replace  the  the  gel-cell  tapes.  Processing  The i n s t r u m e n t a t i o n in  surface  instrument  t o an a r c or  end  the  had been l o c a t e d ,  through a snatch block  and c a s s e t t e  Signal  of  OAR f l a s h e r s  manouvered a l o n g s i d e and downwind of  lab  aided  recovery  the  spot  with a dozen p a i r s  finder  was  to  drops.  Once t h e  ship's  spot  was  prior  h o u r s , however, to  radio  which  transmitter  mounted on t h e  difficult time  unit  instrument  daylight  quite  radio direction  the  the  During  two h o u r s ,  experienced  any of  strobe  c o u l d make i t  instrument.  of  sighting  instrument.  i n d i c a t e d by t h e  s h i p b o a r d OAR r e c e i v e r  frequency  night,  was  appendices the  basic  to  and e l e c t r o n i c s  are  d i s c u s s e d in  detail  this  In  this  I  thesis.  p r o c e s s i n g of  block diagram F i g u r e  2.  the  FM s i g n a l  section  will  with reference  to  19  PRESSURE TRANSDUCER  I  ACCELEROKETERS  THERMISTOR  d/dt  t  d/dt  SHEAR PROBES  T  r  t  2  T  r  .d/dt  d/dt  amp  imp  DP  VCOI 400Hz  VC02 560Hz  VC03 730Hz  DT  Al  VC08 3000Hz  VC04 960Hz  A2  I  SA1  amp  SI  VC05 VC06 1300Hz 1700Hz  SA2  S2  VC09 VCO 7 VCOI 3900Hz 2300Hz 5400Hz  CHART RECORDER (REAL TIME) INTERNAL CASSETTE RECORDER  FM DISCRIMINATOR  *»CHART RECORDER  DIGITIZER  MAGNETIC  TAPE  AUTOMATIC DEGLITCHER  CLEANED SHEAR SIGNALS  HIGHPASS F I L T E R S  FURTHER EDITING  CALCULATE D I S S I P A T I O N  igure 2 -  Schematic of s i g n a l  processing  20  In  all,  oscillators frequency  ten  signals  (VCOs)  modulated  which (FM)  FM m u l t i p l e x e d s i g n a l .  tape  inside XBT  where  Camel I I I .  wire  it  is  link  and  real  viewing  successfully when  the  there  is  using this  is  XBT  tool  signal  (the  frequency  a chart peace  limit  and v i e w e d on a c h a r t  of  link.  was  is  of  produce  r e c o r d e d on  cassette  However,  the  signal  real  time,  to the  ship, to  a  A b i g advantage  of  which  due t o  finite  goes  l e n g t h of  900  meters  Since  the m a j o r i t y recorder  with  impedance  about  cassette  in  c o n v e r t e d back  mind  to  to  the is  voltages  summed  recorder.  e x t e n d e d and t h e  signal  cassette  These are  This  system.  wire  signal  transmit  were d e e p e r , for  the  used to  the  a practical  project  The  is  voltage-controlled  t h e measurements  on  operating  wire  the  primary  viewed  convert  to  To view  discriminated  voltage) time  is  input  signals.  the  an  are  in of  a  losses  the  wire,  depth  when  the d r o p s  system  in  was  the  c o p i e d once a b o a r d t h e  ship  recording. immediately  recorder.  Back  in  the  lab,  the  signals  were d i g i t i z e d u s i n g an LSI—11 c o m p u t e r and r e c o r d e d on m a g n e t i c tape.  The  forms of Lueck, be  high frequency  glitches  (bad  shear  data  points)  C r a w f o r d and O s b o r n ( 1 9 8 3 ) .  1-100 d a t a p o i n t s  long)  bad d a t a  percent  of  and a g r e e s the  were p r o c e s s e d as  time.  with  in Appendix  F.  subject are  To e r a d i c a t e  to  several  discussed  these  for data  the  was  determination  better  d a t a were s u i t a b l y  in  ( w h i c h may  deglitching routine  criterion  'eyeballed'  Once t h e  are  which  an a u t o m a t i c  u s e d w h i c h p r o v i d e s an o b j e c t i v e of  signals  than  'clean'  90 they  21  3.3  The S t u d y Figure  Areas  3 is  WESPAC c r u i s e region  was  profiles  a map of  occupied in February,  were made.  Two  145°W.  i n May and J u n e of  of  profiles  transects Five  equator.  current for  of  the  the  additional  J.Richman  J . L u y t e n was  were  III  made  in  1982.  equator  stations  responsible for  in  were made a l o n g were  occupied  Figure  138°W and  along  the  meter d a t a ,  I  will  Since  not  I  discuss  further.  The W h i t e H o r s e positioning  of  shown  the White Horse p r o f i l e s .  any  profiles  are  nets  and C . E r i k s e n m a i n t a i n e d t h e m o o r i n g s w h i l e  these  is  dropsonde  of  three  freely-falling,  which  is  t r a n s p o n d e r s moored t o  instrument  as  it  used  are  salinity  the White Horse  falls  at  acoustically  to It  determine is  about  1  vertical  m/sec. net.  25 meter  at  intervals.  2 meter  g i v e n by L u y t e n ,  intervals  and  by  a  interrogate The b o t t o m The  Brown m i c r o - p r o f i l i n g CTD mounted on  computed a t  is  self-  positioned  the bottom which  r e f e r r e d to as a transponder  a l s o has a N e i l  Velocities  a  h o r i z o n t a l ocean c u r r e n t s .  transponders are  and  profiles  PEQUOD t r i p  not worked w i t h t h e c u r r e n t  Horse  The PEQUOD  meter m o o r i n g s , W h i t e H o r s e  have  the  boxes.  and  1982 where n i n e t e e n Camel  T h i r t e e n Camel III  location  and Camel III  set  Ocean w i t h t h e PEQUOD  PEQUOD The  4.  Pacific  r e g i o n s e n c l o s e d by r e c t a n g u l a r  t h e WESPAC r e g i o n 3.3.1  the  White it.  temperature  A d e t a i l e d d e s c r i p t i o n of  N e e d e l l and Thomson  (1982).  22  120* E  H0° E  Figure 3 -  160 E  180" E  160" W  HO H  120 H  LONGITUDE Map of P a c i f i c Ocean PEQUOD study regions  showing  the WESPAC and  100 W  80  H  23  » # A 2 <  .16(930a)  UJ Q  1500B)  °#A*^,iS(900a>  3  Al9(92Sa)  or  •ooo  P#0A  D0A  «§OOQ-J  3(1300a)  K #OA  4I900B)•-  r#As<920a)  - r t . # A l 3 ( 9 0 0 a >  G#A6(900a)  "OAl2<900a>  in  ««ooo  o U7 A I 0 ( 8 t 0 a A  1«(920»)M  83Sa> (82to)  A ! 7 < 9 3 0 « » ;  0  WHITE HORSE  O  MOORIMG  A  CAMEL 111  in o  o.  157 H  152 W  147  W  142  W  137° W  132° H  LONGITUDE  Figure 4 -  PEQUOD c r u i s e track (February, 1982). The s o l i d dots with accompanying l e t t e r s represent White Horse n e t s . Open c i r c l e s a r e a t l o c a t i o n s of current meter moorings. Open t r i a n g l e s and a s s o c i a t e d Camel I I I drop numbers a r e f o l l o w e d by the depth of the drop i n parentheses, The large concentration of drops near 0 ° , 145°W n e c e s s i t a t e d the lower l e f t hand blowup.  24  For used of  the  to  determine  (where  2  measure  of  the  a measure of values the  given  of  this  the  two p a r a m e t e r s .  (g/c) )^  of  p u r p o s e of  stability  The b u o y a n c y c  is  static  the  treatment  of  i n Appendix  frequency,  of  PEQUOD  cruise.  Sixteen  12,335  meters  The  profiles  of  Camel III of  data.  case,  these Due  profiles yielded to  a  d r o p s were l i m i t e d  time  to drop  l a g of A  spacing four  immediately  on b o a r d b e f o r e  White  Prior  was a b o u t  deployed  only drop Horse  frequency  terms  (-gAp/pAz ,  is  S = AU/Az of N and  water c o l u m n .  a is  large  A discussion  and  CTD  data  is  were made d u r i n g  the  useful  data,  pressure  leak  to  900 m e t e r s  13 Camel  between  hours.  after  Camel  From d r o p  was  13 o n ,  surfaced,  the drop  w i t h White deployed  aboard  ship.  and W h i t e the  t h e W h i t e H o r s e and was  the White Horse  in  not  safely III  totalling  after  synoptic  III  t h e W h i t e H o r s e had been b r o u g h t back maximum  in  seawater)  values  E l e v e n d r o p s were made w h i c h were n e a r l y  until  =  was  J.  nineteen  Horse p r o f i l e s .  data  fluid  f l u i d while  Small  the  N  sound i n  the  stability.  Horse  the White Horse v e l o c i t y  of  preamplifier  White  a stratified  s p e e d of  stability  t h e dynamic  the  of  S tend to d e s t a b i l i z e  A total  3.  study,  Horse  Camel  was  brought  back  resulting  in  a  time  minutes. log  for  velocity,  profiles  are  PEQUOD,  Camel III  temperature,  dissipation  salinity  i n c l u d e d in Appendix  K.  and  profiles, buoyancy  25  3.3.2  WESPAC The  locations  stations Figure  5.  of  Having  solved  the  make  equator.  drops  2300 m e t e r s .  amounts  broke  to  For  surface  data  dissipation  depths  5805 m e t e r s  the  WESPAC were  shortly  after  includes  profiles  frequency  profiles  treatment  of  and  from  CTD d a t a  a  is  data  III  given  was  but  III  log  data  possible  made a l o n g  below  the  Nearly  of  brought for  (a  in Appendix  are 2300  so t h a t  it  ship. Camel  and  discussion J).  total  to  aboard  salinity  from  data'  ranges  WESPAC,  of  nearly  data  PEQUOD  was d e p l o y e d  the  depth  equivalent  the  temperature, CTD  good d a t a .  d r o p s were made t o  CTD was  drop  the  it  were  were  w h i l e WESPAC d a t a  the  of  in  P.Niiler  profiles  depth d i s t r i b u t i o n  Camel  marked  while  meters  than of  obtained  900 m e t e r s  are  problem,  trips.  t h e WESPAC t r i p ,  Appendix L  13,070  o b t a i n e d and t h r e e  and  above  Camel  preamplifier  6 shows  41°N  moorings  Thirteen  greater  Figure  of  the  yielded  leaking  were  PEQUOD  concentrated meters.  which  Consequently,  meters  both the  deployed  CTD d a t a .  eleven  m o o r i n g s and t w e n t y - t h r e e CTD  1 5 2 ° E from 2 7 ° N t o  W.Schmitz  made,  1000  ten c u r r e n t  occupied along  commissioned the  to  of  III  buoyancy of  the  26  45° N  25. 21. 23 A . O ^ I 3 ( 2 J 4 0 B )  40° N  «-a> 2 1 A. O 20  4 ^ 1 2 ( 2 2 7 0 n )  1 9 ^ 0 / ^ . 1 I (2240a)  1 7 * 0  35" N  I 5 * 0 ^ l 0 ( i 5 i 0 a ) 14.A. U * 0 / ^ 9 < 1 « 5 a )  Q ZD  1 2 *  f-> cn  9 * 0 B  30" N-  A ^ 6 ( 9 7 5 m )  7 * O . £ t 5 ( 6 7 0 a ) ---  £ •  5AA4(H00a)  • AO  3^iaO/^.2(M70a>  2 5 °  N  A l ( B « 0 a )  .aV  CTD  O  MOORING CAMEL I I I  2 0 °  N  142° Z  147 €  152 E LONGITUDE  Figure  5 -  157" E  162" E  WESPAC c r u i s e track (May/June, 1982). Solid triangles and numbers t o l e f t o f 152° m e r i d i o n r e p r e s e n t CTD c a s t s , open c i r c l e s are locations of c u r r e n t meter m o o r i n g s and open t r i a n g l e s a r e Camel III profiles. The d r o p number accompanies the Camel III p o s i t i o n and the d r o p depth (dbar) i s in parentheses.  27  GOOD DATA 500  Figure  6 -  dbar 1000  1500  T o t a l l e n g t h s of d a t a r e c o r d from the 100 d b a r d e p t h i n t e r v a l s f o r t h e t o t a l t o t a l WESPAC d a t a s e t s .  specified PEQUOD and  28  IV. Camel III  profiles  Western N o r t h P a c i f i c single  profile  w i t h the which  final  at  were made i n May and June of  Ocean a l o n g  23°N,  recovery  were  Preliminary  RESULTS FROM WESPAC  148°W). of  are  from 2 8 ° N t o  array  deployed  presented  in  Extension,  site  when compared t o Atlantic as  an  exploratory of  distribution  to  of  low  array  array the  low  p e r i o d s of  these  the  analogous  to  frequency  frequency  was not  Stream).  or  longer.  intended to  Niiler)  salinity Because T,  S  fields of  at  their  and  profiles  give  N  a  spatial  the  time of  importance  profiles  resolve  array  the 152°E  the  North planned  geographical and  frequency  temperatures  the  the m i c r o s t r u c t u r e  refer  out  that  scales.  (kindly  I  which  al.(l982)  spatial  of  study,  sampled  was  e d d i e s and p o i n t  snapshot  this  Kuroshio  Western  Schmitz et as  the  The  supplied  by  temperature  and  measurements.  have  included  in Appendix L a l o n g w i t h the  the  dissipation  f r o m WESPAC.  T h e r e have been  no  microstructure  in  measurements  velocity  1000  in  and  1980.  sparsely  averages  currents  fluctuations  of  the  The WP1  time  The CTD measurements made a l o n g P.  of  characterize  basic  two days  segment  region  of  al.(l982).  has been r e l a t i v e l y  (bounding the G u l f  variability  have  the  (and a  instruments  mid-summer et  the  conjunction  moored  Schmitz  bounds t h e most e n e r g e t i c which  of  in  region roughly a  42°N  T h e s e were made i n  t h e WP1  originally results  152°E  1982 i n  meters  of  this  anywhere.  previously region.  reported As  microstructure In  these  well, at  measurements there  depths  respects  of  have been no greater  alone,  the  than  ensuing  29  pages d e s c r i b e A large column in  scale  along  terms  of  cruise. about  152°E  A  34°N  large (I  is  profiles  structure  of  42°N in May/June,  are,  section  the  water  1982 i s  respectively,  (Figure  features  cold  will  the  given  sections  of  and e p r o f i l e s .  scale  core  henceforth  with only a s i n g l e This  7-9 w h i c h  salinity  large  results.  from 2 8 ° N t o  temperature  interesting  new  d e s c r i p t i o n of  Figures  temperature, The  completely  section  at  the  7) time  ring-like refer  an  important  feature  into  different  regions.  a  of  1982  as a  be s u r e  in  the  feature  to t h i s  one c a n n o t  shows  WESPAC  was c e n t r e d ring  that  separating  Drops  number of  at  although  this  is  so).  the  Camel  III  1-8 were made  south  of  the middle of  the  #  the  ring  while  r i n g and d r o p s  drop 10-13  instrument  problems  fraction  good d a t a  of  Kuroshio  Extension  location  of  occurs at  1980 the  the  the  r i n g and of  deep,  of  is  500  defined  in e a r l y  i s o t h e r m s n o r t h of  the  Sea  and  of Sea  considerable  the of  Oyashio,  which  Okhotsk.  interleaving  200  2°  The  due  only a axis  1982, w h i c h  small  of  al.(l982) depth,  to  the  as  and  the this  represents  from i t s  position  of WP1.  The s i g n a t u r e s  d e e p as  front  are  1800 m e t e r s .  Kuroshio Extension flows  (but  contain  meters  summer of  As w e l l , of  ring  meters).  Extension as  front  the  drops  deployment  Kuroshio  in  by S c h m i t z e t  approximately  least  the  at  of  latter  above  original  the  apparent  sloping  north  these  37.5°N  shift  during  were  15°C isotherm at  about  a northward  9 was made d i r e c t l y  southward n o r t h of  w a t e r masses as  July, of  both  quite  The  upward  front  from the  the  in  ring,  s e e n by t h e  indicate Bering there  is  closed  30  Figure  7 -  Temperature section f r o m CTD measurements t a k e n a l o n g 152°E i n May/June 1982. Isotherms are plotted every 1°C. A c o l d core ring i s centred a t 34°N, t h e K u r o s h i o E x t e n s i o n f r o n t a t 38°N and the O y a s h i o f r o n t a t 42°N.  31  contours  i n b o t h t h e T and S  South of and  800 m e t e r s  6°C across the  of  main  rad/sec  and t h e  Figure  8 shows t h e  in  The the  these.  then  s o u t h of  slightly  upward t i l t profiles meters  upward  of  the  south  above  averages  parallel  isotherms  of  the  profiles  follow. of  Here e  south.  downwards  to the  I  frontal  the  the  the  e will  will  be  are  early  readily  deep s i g n a t u r e s  generally  ring.  In  refer  100  discussed  to Figure  meter  Figure  to emphasize d i f f e r e n c e s  from  all  of  34.1  sloping  ring  and  of  maximum i n N l i e s  numbered  The s c a l e  0.006-0.008  r i n g c o r r e s p o n d i n g to the  of  frequency  c o n t o r t e d by t h e  50 i n d e p e n d e n t e s t i m a t e s  i n A p p e n d i x L.  south  152°E  features the  The  the the  about  200  detail  in  S.  of  9 for  8).  north.  along  section,  approximately on  of  800  minimum bounded by t h e  s o u t h of  ring  over  section  of  and  The b u o y a n c y values  front,  south  t h e minimum i n  Individual pages t o  nearly  across  the O y a s h i o  600  are  salinity  stretches  by  (Figure  s e c t i o n as a r e  A coherent  somewhat  offset  maximum  and  to  depth  salinity  salinity  isohalines  downward  has  ring  is  350  f-rom 1 5 ° C  with  the  maximum s h i f t s  1982.  e a c h of  to  thermocline  between  t o a minimum between  increasing  upwards  lies  decreases  The s t r a t i f i c a t i o n  t h e main t h e r m o c l i n e  i n .the  apparent  temperature  which d e c r e a s e s  r i n g and t i l t  summer,  t h e main t h e r m o c l i n e  range.  thereafter  isotherms  ppt  ring,  d e p t h and t h e  this  salinity  meters,  the  the  sections.  9 which  vertical of  e).  in  represents  intervals  (or  The p r o f i l e s  are  comparison w i t h the d e t a i l e d of  the  e bar  in adjacent  graphs  values  is  linear  w h i c h may be  profiles in  order  reduced  32  45N  Figure  8 -  Salinity section from CTD measurements taken along 152°E in May/June 1982. Isohalines are p l o t t e d e v e r y 0.1 p p t . Note the shaded salinity minimum bounded by t h e 34.1 p p t i s o h a l i n e s .  33  XSN  Figure  SON  9 -  SSN  40N  Turbulent kinetic energy dissipation averaged v e r t i c a l l y o v e r 100 m e t e r i n t e r v a l s f o r 10 drops made along 152°E i n May/June, 1982. The h i s t o g r a m s c a l e i s l i n e a r and p r o p o r t i o n a l t o t h e s i z e i n d i c a t e d i n t h e l o w e r l e f t hand c o r n e r .  4SN  34  by t h e  heavy  represent  averaging.  for  local  constant  the  fraction  value  the  the  prior drop.  of  the  near and  of  individual  record  wind to  input  surface likely  but  drop,  I  profiles  do  wind  rising  was  the  slowly  smallest  near-  input  a  speeds at  the  time  stationary.  4 knots at  at  complete  These  s h i p dropped to  to  a  dissipated  The s m a l l  have  d i d r e c o r d wind  to  is  that  reduced energy  not  ship  dissipations  showed  mixed l a y e r .  I  speed r e l a t i v e  T h e s e were t h e  averaged  by t h e  due t o  when t h e  d r o p 8,  surface  Elliott(1982)  energy  Unfortunately,  e a c h Camel III  days  Oakey  in drop 8 is  surface.  show t h a t  the  m i x i n g i n the  meteorological of  d r o p 8,  maxima.  by t u r b u l e n t surface  sections  bad d a t a .  Except are  Blank  nil  the  two  time  wind s p e e d s r e c o r d e d  on  of the  WESPAC c r u i s e . Drop  2  throughout All  of  is  the  notable  entire  the p r o f i l e s  subsurface  drop,  6 and 8.  tendency  is  towards  the  for  of  although  the  Recall  down t o w a r d s  that  high  ring  e.  turbulence  apparent  e to  encompasses t h e  t h e n o r t h between  drop  4  have  distinct  drop  in depth  d e p t h range of  levels  100 m e t e r s .  quite in  increase  the  over  except  These are  less  t h e maximum i n  ring.  the  when a v e r a g e d  maxima i n  i n t h e main t h e r m o c l i n e slope  to  even  south  secondary  d r o p s 2,  due  the  5.  in The  northwards isotherms  e maxima and t h a t  2 7 . 5 ° N and 3 2 . 5 ° N ,  these (Figure  7). D r o p 9 made i n s i d e except n o r t h of  for the  a  small  r i n g are  the c o l d c o r e maximum  in  interesting  ring  e near in  that  is  relatively  400 m e t e r s . they  quiet  The d r o p s  represent  the  35  first They of  measurements o f show s i g n a l  the d a t a  not  (<  thick  5  the  2050 m e t e r s  d i s s i p a t i o n of  1,2,4,5,6  r i n g which  152°E.  Drop  is  1 was  CTD p r o f i l e s a  the  thermocline  is  10.  depths  a test  over  than  minimum i n N i s  in  are  11.  This  has  30 a  3  the  T  and  d r o p made w e l l  of  S  south  sections  s o u t h of  the  d r o p s s o u t h of  thermocline  the  main  10 r e p r e s e n t s five  drops  along  ring  thermocline. in N which  averages south  the  v a l u e of  of  of  N  the  and  ring  salinity The  main  evident  over  10 a t  to N at  is  ring  t h e minimum a t  equal  the  and a s t r o n g  The maximum i n F i g u r e  approximately  which N g r a d u a l l y Individual  6  d i s t i n g u i s h e d by a peak  twice  patches  3x10" W/m .  seasonal  bottom  the  the  12%  e x c e p t i o n b e i n g the  drop  c o i n c i d i n g with these  Figure  o c c u r r i n g over  3  Most o f  from  depths.  available.  a s s o c i a t e d CTD d a t a . more  6  these  Ring  evident  shallow  minimum a t  Figure  10~ W/m  at  and 8 shown i n A p p e n d i x L were made  t h e CTD d a t a were n o t  indicate  than  with a notable  The D r o p s S o u t h Of The Drops  of  greater  meters)  p a t c h at  patch-averaged 4.1  levels  microstructure  from d e p t h s > 1000 m e t e r s .  thick  meter  velocity  25  meter  that  have  500 m e t e r s  is  300 m e t e r s .  900  in  meters,  The below  decreases. profiles  exhibit  size  from < 2 meters  to n e a r l y  over  the  sampled (the  was  drop  2  energetic  of  d e p t h range which  was  the p r o f i l e s  to at  turbulent  50 m e t e r s deepest  thick  ranging  and t h e s e  drop south of  1450 m e t e r s ) . depth,  patches  D r o p 2 was  in  extend the  ring  the  most  from b o t h PEQUOD and WESPAC  36  1400H—  Figure  10 -  r  Vertical profile of e s t i m a t e s of buoyancy 2,4,5,6,8.  averages of 25 meter f r e q u e n c y o v e r WESPAC d r o p s  37  trips,  bearing  'patchiness' it  most  little  t o any of  closely  Microstructure Osborn(l98l)  objective  other  which  was  about  the  lO" W/m ) 6  the  the  within  water column i s  8  by  turbulent  v a l u e of  In  fact and  Gargett  and  2000  Bermuda. to  or  Fine  the  of  Chapter  compared t o an a v e r a g e  3  from  island  magnitude  from WESPAC.  reported  made  in  either  13  (FAME)  method d e s c r i b e d 38% of  in  profiles  drop  Experiment  contour  thickness, >  the  resembles  and  bathymetric  resemblance  meter  Using  the  determine  patch  in drop 2  (i.e.,  19% o v e r  all  of  the  d r o p s made s o u t h  of  WESPAC d r o p s . There are the  ring.  two d i s t i n c t  Firstly,  and 450 m e t e r s ,  there  meters)  intervals  level  3xlO" W/m .  of  minima  7  in  the  Figure  are  profiles  11  d e p t h r e g i o n bounded r o u g h l y  are  at  of  N contain  a  levels  plot  of  The minimum i n  activity  range depth  distinctly.  range  done d e e p e r at  turbulent  200-400 m e t e r s  least  points).  of than  three  and near  extensive the  are  drops  of  to  e is  N.  noise  subsurface  Secondly,  occurring  s o u t h of  200  and  values  the  400 points  over  the  (averaging  into  the  remainder  500 m e t e r s  and i t  of  e  ring. meters in  the  entire was  o n l y d r o p 2 was d e e p e r  at  the  averages  seven a d j a c e n t  were a v e r a g e d  The maximum v a l u e of  the  vertical  1350 m e t e r s  since  (50-200  instrument  frequently  between  smallest  by 200  e.  25 meter  fact,  the averages 1350 m e t e r s  more  drops 2 , 4 , 5 , 6 , 8  In the  frequency,  both  over  out  or  buoyancy  w h i c h were t h e n a v e r a g e d  stands  the  consistent  and h i g h e r is  of  These r e g i o n s concur w i t h  3  patches  the  which  s u b s u r f a c e maxima of turbulent  in  features  not  while of is  the  Figure  11  -  Vertical profile of averages of 25 meter e s t i m a t e s of t u r b u l e n t k i n e t i c energy d i s s i p a t i o n o v e r WESPAC d r o p s 2,4,5,6,8.  39  larger 500  than  the  meters'  meter  there  averages  variability averaged 4.2  averaged value nearest is  in  e profile  the  show t h a t  over  to  support  this  internal  ocean  in  of  the  form  contribution local  to  the  to the  the  in the  a  factor  e,  six.  25  This  smoothly  As t h i s for  next c h a p t e r , south  and p r o v i d e  set  of  I  of  varying  measurements  boundary  energy,  K ,  ring  was  to is to  made  source  exists  whose  energy  current  results  try  some r e a s o n s  which a s t r o n g energy  western  will  the  s u r r o u n d i n g s may be e s t i m a t e d  eddy k i n e t i c  adjacent  of  relatively  drops  wave f i e l d ,  contention. the  the  to  of  Below  Energy  turbulence  the  surface.  200-450 m e t e r s .  i n a r e g i o n of the  up  e n s u i n g pages and i n  the  related  by  contrast  e And Eddy K i n e t i c In  the  considerable v a r i a b i l i t y  differing  is  to  by  from  determining Schmitz  et  E al.(1982)  are  lack  correlation  of  presented to attempt between  to convince  e and K .  K  E t h e mean v a l u e s  of  the  variances  of  in  mid-summer,  Averaging  is  hopefully,  1980  done  over  describes  and  the  climate  of  calculated  horizontal  in  eleven  reader  of  the  using  E  meters  recovered  about  is  the  components m e a s u r e d by moored c u r r e n t  the  which  early  months K  were d e p l o y e d summer,  of  in  velocity  this  data  1981. which,  part  of  the  E ocean.  Schmitz  et  al.(l982)  discuss  the d a t a  handling  in  more  detail. Schmitz first  setting  et of  al.(l982)  describe  t h e WP1 m o o r i n g a r r a y  selected  results  from mid-summer  from  the  1980  to  40  mid-summer Schmitz the a  1981.  et  A  CTD s e c t i o n  al.(l982))  front  of  southward  the  indicates  of  2°  for  when  compared  to  (this  is  an e n t i r e l y  the  the  and  8  energies at  depth  c o v e r e d by t h e from  the  Extension  drops  to  fronts  The  current  data  dissipation  meter  profiles  turbulence,  There are K  E  . .  First  the  In  Figure  relative are  A  averaging  heavily  w h i c h does  itself  trends  all  three  to  at  the  meters)  the  position,  p o s i t i o n of vertically  substantially  lower  meters) the  or  ring.  adjacent  values  are  eddy  of  K . E  the  the  intervals  dissipations  of  respect  limitation  the  two d a t a  over  of  to  to  sets.  time w h i l e  snapshots  the  through  the the  considerably.  latitudinal  ten,  (for at  deeper  Vertically  K  with  n o r t h of  Secondly, and  kinetic  r i n g s and K u r o s h i o  severe  vary  just  5  deployment,  depth i n t e r v a l s ,  from 2 8 ° N by a b o u t a f a c t o r  With  from F i g u r e s  1°.. w i t h  averaged  spatial  deeper  1982).  the c o r r e s p o n d i n g depth  p o s i t i o n s of 1982.  ring  -  WP1  12b a r e  over  northward (for  the  Figures 7"and 8  derived  have been s h i f t e d  the  for  for  from  initial  represent  all,  of  and  represents  which c o r r e s p o n d t o depth  two d i s t i n c t  of  for  from 1980 and the  is  1°  2 from  33.5°N  which  These data  averaged  align  comparison i s  of  152°E  Camel d r o p s .  this  field  al.(l982).  The two p l o t s  other  35.5°N,  ring  12a w h i c h  intervals  Camel  intervals. each  et  estimated along  three  r i n g at  and a b o u t  different  i n mind c o n s i d e r F i g u r e Schmitz  front  1980 ( F i g u r e  1982 T and S s e c t i o n s  this  of  a c o l d core  Kuroshio E x t e n s i o n at  shift  likely  from J u l y  section  of  increases  E  peak  values  the  shallow  each  mooring  meters  adjacent  record  values  41  Figure  12 -  a)Eddy k i n e t i c energy estimated by Schmitz et al(l982) for current meters located at depth i n t e r v a l s 250-300m(dots), 5 0 0 - 7 0 0 m ( t r i a n g l e s ) and 1000-1500m(squares) a l o n g 152°E. Longitude is marked above the plots. b)turbulent kinetic energy d i s s i p a t i o n averaged over depth intervals corresponding to a) one y e a r a f t e r t h e r e c o v e r y o f t h e m o o r i n g s by S c h m i t z e t - a l ( l 9 8 2 ) . The p l o t i s s h i f t e d 1° t o t h e s o u t h f o r r e a s o n s discussed in the text. Note t h a t ( i n c o n t r a s t t o F i g u r e s 7-9) s o u t h i s t o t h e r i g h t .  42  differ  by up t o a f a c t o r  contrast  to  the  depth)  averaged  south  of  2°  the  s o u t h of  e  of  ten.  section.  values  of  the  Indeed,  e are  r i n g and t h e s e r i n g where  These  the  two  the  traits  500-700 meter  greatest  for  r e a c h a peak w h i c h  t h e peak  in K  are  is  occurs.  in  (mid-  every  drop  located  about  There  is  no  E apparent  peak  in  the average  meter  or  1000-1500  inside  the  ring,  averaged there  e.  is  turbulence 4.3  actually  levels  of  e in e i t h e r  segments.  has  these  apparent  some of  albeit  reason  to  and k i n e t i c  Drop the  available  be compared i s N  were  intervals. were  the  t h e 250-300  9 ,which  smallest  was made  values  of  r o u g h and q u a l i t a t i v e  results  suggest  between  energy  a  in the  information  CTD d a t a .  calculated For  relation  eddy  field.  over  set  to which the  the  the d a t a  T,  2 5  .  Subsets  25 meter  of  these  water  column c o u l d be c o n s i d e r e d s e p a r a t e l y  more  crucial fields  From t h e distinguish values  of  lowest  are  the  generally  scatter any  N are  PEQUOD  plots  trends.  data  of  Figure  However,  a s s o c i a t e d w i t h the  values  it  13 is  of N c o i n c i d e w i t h lower  the  is  grouping effects 300  values values  of  is the  meters).  difficult  noted that  highest  to  p o r t i o n s of  upper  it  intervals  so  the  c o n f i n e d to the  e  chosen  (this  where  depth of  were  (300m-bottom)  may  values  25 meter  depth  data  the  for  and l o w e r  over  independent values  that  current  upper(20-300m)  S data  sets,  corresponding  (e,N)  turbulence  As d i s c u s s e d i n A p p e n d i x L,  from  e a c h of  averaged  produce the  the  of  e And N The o t h e r  of  meter  From  no  value  the of  of  e,  to  highest e  while  except  43  io-  WESPAC 20-300m  10"  a) ,e  io-»'  8 •4 10-']  10"  *"1  1  1—'  I ' I Ml  io-  •  1 • I I I • l|  " • "  WESPAC  <  '  1  1—I  •  I I I ' I  <••••'  300m-bottom  10"  b)  ^ io- s  :  10-«i  io-= 7  io-»-  I* • ••• -<—i—i  111111  LOG N  i ' i ><i  •—i—i i 111  (rad/sec)  i i S c a t t e r p l o t s o f b u o y a n c y f r e q u e n c y and t u r b u l e n t k i n e t i c e n e r g y d i s s i p a t i o n , e a c h e s t i m a t e d f o r 25 meter depth intervals. A v e r a g e s were made o v e r 1/3 d e c a d e i n t e r v a l s i n N ( s o l i d d o t s ) .  44  for  the  low  N,  near  surface  turbulent  due t o wind m i x i n g .  averages  of  e made o v e r  intervals  of  N.  precluded there  is  between the in  A paucity  meaningful  of  in  13a i s  the  vertically  in  the  the  decade of  three  plots,  averaged  the  13b  values  averaged value  form of  is  in  drawn  are  e  and  N  presented  were  p r o f i l e s are  14a,b.  the c o l d core  apparent  e value at  (cf.  2100 m e t e r s  the  made all  by  of  Even  in  Figures is  in  the  though  r i n g have now been  t h e maxima and minima  still  11 due t o  of  averaging  and 10 and  dominated  s m a l l amount of  above 11).  by  the  data a v a i l a b l e  at  depth. The  show decade data  vertical  the a v e r a g i n g ,  drop  upper N b i n  100 m e t e r s and t h e n o v e r  d r o p s made i n and n o r t h of  event this  over  The r e s u l t a n t  The h i g h a v e r a g e d  half  1.  These averages  thermocline  represent  The l i n e  14 and  in  of  strongly  representative).  different  included the  not  dots  e a c h of  wind m i x i n g ,  distinctly 15.  black  lying within  In  e  N bin  13a w h i c h a r e  in the  correlation  averaging drops.  values  averaging.  13c has a s l o p e of  Figures  the v a l u e s  of  and N ( b e c a u s e  in  The l a r g e  a strong positive  lowest  A  all  values  a  e and N p r o f i l e s relatively  in  the d a t a about  averaged over  order  of  all  e of  combined in F i g u r e of  e with N over  B a r s were drawn a b o u t  the  t o p r o v i d e an i n d i c a t i o n of  t h e mean.  25 meter v a l u e s  14a,b are  strong c o r r e l a t i o n  i n each parameter. point  of  were  For  each data p o i n t ,  averaged  the d r o p s .  For  for the  each  three  one  850  the  15  to full  meter  spread of  consecutive  drop  850 meter d a t a  and  then  point,  45  LOG  2200 ' i I I  Figure 14 -  '  '  '  1  1  —' ' —*** 1  '—  "  t (W/m ) 1  '—•—'—• • i • i  a)100 meter v e r t i c a l averages of buoyancy frequency averaged over a l l of the WESPAC drops. b)100 meter v e r t i c a l averages of t u r b u l e n t k i n e t i c energy d i s s i p a t i o n averaged over a l l of the WESPAC drops.  46  47  there  were  average the  20 p o i n t s  value  was  mean was  1.7xl0" W/m 6  1.0xl0~ W/m 6  1.8x10" W/m . 6  t h e d a t a ,~~"tTTen,  A  the  is  A l t h o u g h the  to  note  averaging  noted  at  any  by  that  location  of  energy  7  drawn  in Figure  differences  not much d i f f e r e n t Lueck,  Crawford  lost  by t h e  over  15.  in  averaging. intervals a  strong  1.  Osborn(1983),  f o r midocean However,  wave d y n a m i c s w h i c h internal  wave f i e l d  These  3  depth  from  and  not w e l l e s t a b l i s h e d .  e <  W/m .  6  13, b o t h e x h i b i t  e/N may be a c o n s t a n t is  in Figure  15 i s  of  The m i d d l e 80% of  3  2x 1 0" <e< 1 . 7x 1 0"  done i n F i g u r e  a r g u m e n t s b a s e d on i n t e r n a l rate  7  the  The about  p o i n t s had v a l u e s  > 2x10" W/m .  concerns  is  825<z<875 m e t e r s .  standard d e v i a t i o n  the  spread bars are  s l o p e which  observation  and t h e  by  a s compared t o N - i n t e r v a l s  As  3  90% of  3  bounded  or data  point  positive  depth range  and 90% had v a l u e s  3  uncertainty  in  measurements there  suggest to  the  the  exist  that  the  turbulence  7 scales  with  indicates is  N  that  linearly  decay  time  As w e l l ,  scale  a  recent 7 is  accounts,  positive  the  in the  to  N  internal  discussion 1 or  1.5  velocity then,  wave f i e l d .  chapter.  between  energy  1  and  2.  internal  wave f i e l d , Gargett  WKB  and,  if  r  the  of  the  that,  source of  This w i l l  is  the  e = TE/T a N .  and  Holloway(1984)  1  internal  when the  (TE)  then  d e p e n d i n g on t h e a p p r o p r i a t e variance  scaling  wave f i e l d  (Munk(l98l))  by  suggest  d e p e n d e n c e on N,  internal  following  total  of  the v e r t i c a l  Various  the  the  is  y  proportional  suggests that for  where  e  wave  has  turbulent  be p u r s u e d  further  a  scaling field. strong  energy in  is the  48  To  complete  comparison  is  the  presentation  made w i t h o t h e r  Osborn(l983)  made a, s e r i e s  data  of  Island  averaged  depth i n t e r v a l s  bottom. in  These c l u s t e r  Figure  and t h e s e lower  the  16. are  the  circles  which  lies  true  v a l u e of  the  data  in  below  300m i s  been drawn w i t h a s l o p e of  16.  triangles  e for The  circles squares  the  N  2cph  upper  and  range  within  are  WESPAC  values  are  from  PEQUOD  shown from PEQUOD). same  cluster-  solid  indicating  1 and t h e  and  continental  were  averaged  Figure  solid  the  a  200-500m, and 500m-  p l o t t e d as  Solid  Crawford  The d a t a  l00-200m,  are  e.  15 and  e-N s t a t i s t i c s ,  Lueck,  1980.  j o i n e d by a b a r  r e p r o d u c e d from F i g u r e (only  sets.  and O s b o r n ( l 9 8 l )  open c i r c l e s  are  the  i n May,  averages  Gargett  the  measurements o v e r  s l o p e of V a n c o u v e r over  of  A line  intercept  as  has  Figure  15. A  comparison  c o n s i d e r i n g the from  e  =  result  a best  Crawford  in  the  data  of  fit  sets  line  following  for  of  their  values  of  each  of  and G a r g e t t  respective a  0  (in  PEQUOD - 1 . 4 x 1 0 "  estimated  c r u d e manner  and O s b o r n ( l 9 8 l )  -  and  data  units  sets).  of  2  1.8X10'  4.0X10  - 7  .  set  These  m /sec •sec): 3  7  -  by  Osborn(l98l)  7  C r a w f o r d and O s b o r n ( l 9 8 3 )  Gargett  a c c o m p l i s h e d by  s l o p e = 1 through each data  WESPAC - 2 . 2 x 1 0 "  Lueck,  best  in a r e l a t i v e l y  and O s b o r n ( l 9 8 3 )  done t h i s  is  proportionality  T h i s was done  0  have a l r e a d y  the  constant  a N.  'eyeballing' (Lueck,  of  7  49  LOG  N (rad/sec)  Log-log p l o t s of e vs N f o r the four data sets i n the l e g e n d and f u r t h e r d i s c u s s e d i n the t e x t . The WESPAC a n d S a r g a s s o Sea v a l u e s a r e g r e a t e r t h a n t h o s e from PEQUOD a n d t h e V a n c o u v e r Island slope.  50  The  Gargett  additional plot.  and O s b o r n ( l 9 8 l )  data  point  Although  large,  it  is  from e a c h WESPAC  the  region.  Island slope  are  and  the  of  the  relative  this  16,  it  is  than both of the  the  plot.  then,  the of  a  present is  0  quite  levels  apparent  of  e  that  the  PEQUOD and V a n c o u v e r  PEQUOD d a t a  present  w i t h which  quite  u s i n g an  In  set the  Figure  includes  spirit  16 i s  t o compare o t h e r  of  the  Lueck,  o f f e r e d as  values  of  an  e/N  in  determine  an  ocean. Although  indisputable the  it  data,  that  relating  the  'mean'  state  stable  estimate field  criterion  is  relationship  on t h e  the data rapidly  of  e.  of  is  of  behave  the With  the  few  internal  An o m n i p r e s e n t  problem  parameters  process  with  from the  further  field.  internal the  the a  of  the  numerous l o c a t i o n s ,  this  s h o u l d not  Figures  to  r e q u i r e d to get snapshots  to a minimal degree.  examine wave  at  with  perhaps  spatial  turbulence  e and N  e n c o u r a g i n g and  so w e l l .  averaging a  to  t h e d e p e n d e n c e of  changing turbulence  inferred  to  impossible  nonetheless  t r e n d s and t h e s e  agreement  encouraged  it  met o n l y  distinct  apparent  clearly  involves  vertical  exist  is  parameterization  available  surprising in  indicative  Osborn(1983),  appended g u i d e l i n e  of  estimate  and t h a t  of  range  the  greater  levels  the  in  From F i g u r e  averages  Crawford  outside  was c a l c u l a t e d  uncertainty  certainly  levels  smallest  lying  intercept  13,  However,  there  do  With  the  16, and  the  be i g n o r e d . 15  wave  and  scaling,  d e p e n d e n c e of  the  one  is  turbulence  51  V.  A MODEL OF TURBULENCE  In  this  distribution  chapter, of  shear  an  attempt  instability  An o f t - q u o t e d c o n d i t i o n f o r requires  that  everywhere results  the  in  flow  stratified  shear).  For  vertical Locally than  the  due  one may i n f e r  evidence  occurrence  following  over  < 1/4  wave  is  of  that  provided  which  this  =  an  is,  flat  indicator  is  at  measurements  b r e a k i n g does o c c u r . a  scales the  waves,  an  1/4  Eriksen(l978  cutoff  at  of  order  the  effect  of  estimate  a field for  used i s  the p r o f i l e  in  provocative  in  an  the  internal  1).  Eriksen  frequency  be  of  down t o R i = makes  the  interpreted  as  experimental 1/4  randomly shear  of  less  exists  meters'.  of  the  shear).  instability  a R i c h a r d s o n number of a few  the  and  The r e m a r k a b l e  of  to  wave s h e a r s  Eriksen  may  mean  value  arctan(Ri)  t h e R i c h a r d s o n number f r o m a g i v e n  distribution  a  for a  a  refers  ,Table  of  > 1/4  2  t h e mean to  flow  experimental  u'  of  an a b r u p t c u t o f f .  'The  2  Indeed,  distribution  shear  N /(u') ,  internal  (breaking).  by  waves.  experiences  (that  the  derivation  chapter,  R i c h a r d s o n number v e r s u s  that  vertical  evaluate  is  field  almost  To s i m u l a t e  (the  Ri  remarks:  is  internal  Ri  discusses  s u p e r p o s i t i o n of  below w h i c h t h e r e  result  of  internal  initial  of a R i c h a r d s o n number c u t o f f  field  evidence  the  t h e mean f l o w  the  that  d e s c r i b e s an  1/4,  to  internal  wave  of  number,  column  model  in a s t r a t i f i e d  t h e R i c h a r d s o n number may be r e d u c e d  1/4  the  water  to  i n a f i e l d of  makes  purposes  derivative  made  (Turner(1973)  Miles(l961)  variably  is  stability  Richardson  the  and  IN AN INTERNAL WAVE F I E L D  is  superposed required  distribution Figure  10).  of  With  to N the  52  a i d of  the G a r r e t t  dynamics,  the  and Munk e x p r e s s i o n s f o r  shear,  u',  is  calculated  the p r e d i c t e d shear  spectrum.  to  likelihood  estimate  sufficient  the  magnitude to c r e a t e  for  instability.  5.1  I n t e r n a l Wave E n e r g y On  This  the  is  basis  observations, a  a Richardson  t h e n compared t o  of  linear  of  and  model  the  of  the  e x p e r i m e n t a l and t h e o r e t i c a l  waves.  N,  and t h e GM s p e c t r a l  Munk(l98l) small are  scale  calculated  gives  a recent  processes.  p r e s e n t e d as  for  the  test its  c o m p a r i s o n of  new  of  the  energy  from t h e m e a s u r e d b u o y a n c y  d i s c u s s i o n of  with  the  levels.  The most  follows,  have  since  b e g i n w i t h an e s t i m a t e  study w i l l wave f i e l d  1979)  investigation  results.  frequency,  enough  available  T h i s model has w i t h s t o o d  a standard  internal  of  frequency-wavenumber  c o n c e p t i o n and now p r o v i d e s  the  used  shear  the  1975,  complete  of  in  a  of  data.  and  Munk(l972,  internal  This  is  number s m a l l  theory  s p e c t r u m of vigorous  mean.square  distribution  occurrence  wave  Profiles  Garrett  synthesized  internal  from t h e  A Rayleigh of  the  recent F  the  internal  forms of spectrum  waves  and  t h e GM s p e c t r a of  vertical  S displacements,  F  the  energy;  total  wave F  5  u  (u,j)  F F •(«, j) e  that  of  horizontal velocities  and F  e  = that  of  = b N (g) -f )E(o),j) N <P~  (5.1)  = b N N(gj + f ) E ( g j , i )  (5.2)  2  2  2  0  2  0  2  2  = M F +N F ) = b N N E ( c o , j ) 2 u $ 2  2  0  (5.3)  53  where j i s N(z) is  the v e r t i c a l  and i s  the  taken  t o be  mode number,  b is  1300 m e t e r s ,  N  surface-extrapolated  = 7.3X10" E(CJ,J)  sec'  5  is  the  is  1  buoyancy  the C o r i o l i s  the e - f o l d i n g  = 5.2X10~  0  frequency  frequency  d i m e n s i o n l e s s energy d e n s i t y E(CJ,J) B(w)  sec"  3  scale (3  1  of  cphl  u s e d by GM, and f  at  30°  latitude.  d e f i n e d by  ~~  = B(u)H(j)E,  = 2f/U7T(cj -f )^) , 2  2  N J" B(o))da> = 1 , f  H(j) = ( j + J o ) - V ( 2 ( j 2  2  2  + j  2 0  )- ), 1  1  00  L H ( j ) = 1, 1  where j  = 3 is  0  a mode s c a l e  is  the  dimensionless  and  is  set  at  wave  Extensive  measurements have p r o v e n E t o be r e m a r k a b l y  within  a  factor  parameter'  E  internal  (to  'energy  number.  of  two).  The c o n t r i b u t i o n  6.3X10' . 5  universal  to F  of  the  negligible  by  e vertical  velocity  spectrum i s  M u n k ( l 9 8 l ) compared t o 14 o f  those  considered of F  The mean-square q u a n t i t i e s <$ > = JdcoIF 2  calculated  the  Figures  7 and  , then, 0  (for  = 53N N  f<<N) [m ] 2  0  fl  0  2  2  0  potential(PE)  as a f u n c t i o n . o f  (compare  = 3b EN N = 44x10" N [ m / s ] • 2 N 2  U  which  are  (w,j) = J _ b E N 2 N  2  be  u  2  $  <u > = /dcjZF from  and F $  Eriksen(1978)).  to  and  depth,  z;  kinetic(KE)  energies  are  54  Figure  17 -  Plots of kinetic calculated the t e x t F i g u r e 10.  i n t e r n a l wave p o t e n t i a l energy(PE), energy(KE) and total energy(TE) from the equations i n s e c t i o n 5.1 of and) the buoyancy frequency p r o f i l e of 4 /  55  PE  = J_N ( z ) < $ 2 2  2  (z)>  KE = J_<u (z)> 2 2  TE = PE+KE Using  the  N  s o u t h of  given  above,  5.2  to  o  profile  drops  referred  = {53N /2+22X10-*/N }N  the PE,  O  in Figure  ring,  of  t h e WESPAC  <u >  and  2  in Figure  <$ > 2  17 and w i l l  be  Shears  The mean-square v a l u e wave f i e l d  the  = <(3u) > 3z  2  dispersion  of  vertical  shear  due  to  the  waves  is  is:  <(u') > The  represents  calculation plotted  (5.4)  2  later.  I n t e r n a l Wave  internal  2  10, w h i c h  and t h e  KE and TE a r e  [m /sec ]  + < ( 3 v ) > = m <u :j3z  2  relation  2  for  2  linear  2  internal  (Olbers,1983): m  2  = k (N -g; ) , u -f 2  2  where  m is  vertical constant bottom, When  N  the  vertical  velocities value H,  of  yields  is  2  and k t h e  may  N the  (5.5)  2  2  be  horizontal  e x p r e s s e d as w = a s i n ( m z ) .  requirement  mH = jit, j  a f u n c t i o n of  c o n d i t i o n mH = J7r becomes  wavenumber.  that  w = 0  at  For  the  = 1,2,...  z,  a WKB  solution  is  r e q u i r e d and  0  This the  f o r m of  the  waveguide.  form f o r  m,  the  (5.6)  2  boundary c o n d i t i o n a s s u r e s a t t e n u a t i o n  Because  of  the  (Munk,l98l) 2  2  a  ocean  m = J7r/(N -cj ). b v/N -w 2  The  the  l i m i t i n g case  relative of  intractability  co«H i s t a k e n so t h a t  outside of  this  56  m = JTTN.  bN  This  simplification  c o n t r i b u t i o n of However,  (Gargett  and t h a t  is  is  made  evidence  relatively  (McComas  wave s h e a r the  with  in  is  indicate the  it  and  some  slopes  that  simplification  in  implying low  <(u' ) >  = Jdcj2m F  2  shear  shear domain  from low t o  high  that  the  f r e q u e n c y modes,  s u g g e s t e d h e r e may be  t h e mean-square  thermocline.  wavenumber  the  the  a l t h o u g h the  downward  Muller(1981))  about  in the  vertical  concentrated  The e x p r e s s i o n f o r  concern  waves t r a p p e d  to  flat  al.(l98l)),  et  frequencies internal  0  high frequency  there  spectrum i s  (5.7)  justified.  becomes  (CJ, j )  2  u which,  with  (5.2)  and ( 5 . 7 )  is N  < ( u ' ) > = 2 7r f EN Z j H ( j ) J* o r 2  3  N The i n t e g r a l  is  37r/4f and the  2.13 and i t  is  estimate  2j H(j),  of  r e q u i r e d that 2  <(u'  The upper critical  f  0  ) > 2  limit  parameter  0  2  2  /(co -f ) z  z  summation L j H ( j )  = j  2  j  be >> j  (co + f ) d c j .  3  2  +  , the  = 3.  upper  limit  +  J , where  to  the  finite  Thus,  = 3TT N EJ J. 2  2  +  0  to the which  (5.8)  3  N  J =  vertical is  related  mode  number,  j  to the  vertical  wavelength  +  ,  is  a  by m  +  = 27r/X  +  = j + 7TN. bN  A parameter of  study  realistic  showing the  N values  must c o n c u r w i t h t h e  is  0  d e p e n d e n c e of  shown i n F i g u r e  upper wavenumber  X  +  18.  cutoff  of  on j  +  for  a  The c h o i c e the  range of  internal  j  +  57  0  400  800  P l o t of t h e dependence of the upper wavelength cutoff, X , on the upper limit, of the v e r t i c a l mode number f o r f o u r d i f f e r e n t v a l u e s o f b u o y a n c y f r e q u e n c y , N. A h o r i z o n t a l l i n e a t X, = 10 m e t e r s i s drawn f o r c o m p a r i s o n to the * 10 meter break i n the v e r t i c a l shear spectrum found "by G a r g e t t e t a l ( l 9 8 1 ) . +  58  wave s p e c t r u m . ocean  measured n e a r l y  profilers Gargett  et  spectral  al.(l98l). break  which  that  the  break  horizontal  meters. at  at  +  with  the  line  at  wavelengths > 600, the  10(j  and this  order in  +  superposed shear  wavelengths  range  ocean  field.  of  j  +  distribution  function  shear  measurements  test.  of  show no d e p a r t u r e However,  d i s t r i b u t i o n and t h e r e  the is  there  by is  a  from  Gregg(l977) gradient 10  drawn  spectra  for  meters.  A  in Figure  greater  vertical = 400)  Further  18.  than  N = 2-4 c p h  +  found  10  converge  wavelength and a t  2 cph  calculations  are  . And R i c h a r d s o n Number  the  likelihood  known fashion  and  for R i .  from  compiled  wave p a r a m e t e r s  and 5 m e t e r s ( j  Desaubies  for  Atlantic  for  velocity  the  near is  the  separating  become many t i m e s  +  statistics  shear  also  10 m e t e r s ( j = 4 0 0 ) .  in a r e a l i s t i c  i n the  temperature  10 m e t e r s  = 200)  to c a l c u l a t e  an  was  meters  internal  was  The D i s t r i b u t i o n Of Shear  number  2  scales  10  +  +  In  X  about  bandwidth  4 c p h of  to  spectra presented,  the  in  separate  For  Choosing 200^j ^400 allows  20(j =200)  restricted 5.3  j  shear  bandwidths  s l o p e of  reference  < 5 meters.  cutoffs of  in wave  For  by t h r e e  w i t h buoyancy p a r a m e t e r s .  < 100, t h e  +  vertical  spatial  slope at  which  scales  internal  j  in  range  that  For  simultaneously  with d i f f e r i n g  consistent  the  A c o m p o s i t e s p e c t r u m of  the  N,  the  in order and  of  small  internal  to estimate use  stratification  main  waves must  Smith(l982)  Indeed,  Richardson  to  Evans(l982)  thermocline  were  no r e a s o n ,  not a  priori,  Gaussian  suggests in  tested to  total  develop  the  from a n o r m a l d i s t r i b u t i o n data  the  be  a  that North  b a s e d on a  for  any o t h e r •  reject  the  59  hypothesis example, is  that  the  that,  shear way  is  data  Rayleigh  easily  available  obtained  an e s t i m a t e  data.  the  statistics  of  useful  of  surface  a m p l i t u d e s of vectors  a  having  probability  values  only  the  large  that number  random  p(x)  the  a  = x~ "/2 and x"  2  2  7  for  the  value  for  grounds  (Maisel(1971)).  the for  of  the  vectors.  s u p e r p o s i t i o n of  independent  The  u s e d by a  field  distribution  of  two-dimensional The form of  the  is 2  is  the  ( w h i c h was  ],  2  2  7  = 0, where a  from  descriptor shear  the  obvious  shear  solid  d e s c r i b e s the  = x exp[-j_x /a ~a  no  required  some as  of  phase  function  the  distribution  it  is  mean-square  also  to d e s c r i b e  consideration  there  are  independent  Rayleigh  is  density  see),  t h e mean v a l u e of  number of  the  waves)  we s h a l l  these  (for  t h e mean-square v a l u e of  distribution  a large  distribution  A practical  for  There are  Longuet-Higgins(1952) of  for  but  latter  property  (as  B o t h of  distribution.  assuming  another  distribution).  distribution  Rayleigh  follow  a l t h o u g h an e s t i m a t e  to get  normal  the  for  x > 0  for  x < 0  t h e mean s q u a r e v a l u e .  The  cumulative  x density  function  is  J* p ( x ) d x ,  p'(x) In  terms  of  internal  upper  the  limit  = 1 -  wave  p'(u') describes  the  exp[-lx /a ]. 2  2  2  shear,  = 1 -  probability to  or  — 00  exp[-(u') /<(u') >]  that  2  the  shear  corresponding  2  is  less  Richardson  than  u'.  number,  The Ri  =  60  N /(u')  2  p'(u')  so  2  requires  u'  a maximum v a l u e  describes  the  = 1-p'(u')  probability  some v a l u e ,  2  =. exp[  the  0  squared shear 1  1  is  less  = N /(u') 2  Richardson  number  -2NQ(U' ) 3ir N Ej J  ]  2  3  (5.9)  t  c o r r e s p o n d i n g t o an a r b i t r a r y  is  2  2  (5.8),  2  c -  by  = exp[-(u') /<(u') >]  that  With  RfH  Pr(Ri) The  described  that Pr(Ri)  than  t o have  (u')  Pr(Ri<c - )  0  = exp[  1  0  = c N  2  2  so  constant  Ri  that  -2N c 0  ].  0  (5.10)  3ir NEj J 2  +  -1/N The e x p r e s s i o n  (5.10)  gives  intuitively  acceptable  of  shear  local  formulated regions  in  of  s m a l l N.  'layers  also  layers  Carried  N,  one  of of  chapter.  to  the  dependence  This in  implies the  small Richardson  s u c h as takes  a  type  if  breaking of  which  that  the  internal number,  thermocline,  different  shear  further, the  the  gravitational  largest  step  find  choice.  largest  wave b r e a k i n g and expects  of  Munk(l98l)  that  e  instability  terms  large  an  than  approach  regions  to  stability(largest  shear  causes  e-N d e p e n d e n c e  of  N)  are  u'/N)'.  instability  results  turbulence, found i n  in  determine  instability(largest the  regime,  greater in  an  likelihood  wave is  is  the  then  in one  previous  61  5.4  C o m p a r i s o n W i t h The D a t a In  Figure  calculated 400.  19 v e r t i c a l  values  WESPAC r e g i o n dependence  of  south  on  j  +  N used are of  curves  of  hand a x i s  curves,  however,  To  compare  an e s t i m a t e was  percent  The c r i t e r i o n  at  makes  except  h i g h N and  indicate  the  almost  strong  over  for  used  level  = 200,  +  10 t o  The  On  +  .  The  the  actually  this  indistinguishable j  and  critical  impossible to  shape  distribution  of  the  of  water  scale, from  the  of  the  (call  the p r o f i l e s  2,4,5,6,8  s o u t h of  turbulence  detection e .  small  column  intervals  dissipation,  300  simulate  depth  for of  Pr(Ri<l/4)  N-dependence.  fraction  50 meter  and  ring.'  it  w i t h the p r o b a b i l i t y the  j  any p o s i t i o n .  are  for  for  core  Pr(Ri<l/4)  turbulent)  threshold  Pr(Ri<l)  from F i g u r e  cold  Pr(Ri)  was made of  turbulent  the  unfortunately  d e t e r m i n e a number f o r  right  of  f r o m ( 5 . 1 0 ) . h a v e been p l o t t e d  The  the  profiles  this  was  The t h i c k n e s s  that  PCT  the  a  Ri,  for  ring.  critical of  patches  c with successive  independent  estimates  of  e w h i c h were > e  were  c added the  to 50  calculate meter  interval  thicknesses)/50. same as  the  in Figure  The 19.  thickness the  of  individual  turbulent  scale  used  The c h o i c e  of  fraction  in Figure e  patches.  is  is  20 f o r  subjective  Over Z(patch  PCT i s and i s ,  the at  c the  low  end,  limited  instrumentation.Although m a g n i t u d e s of the  vertical  Figure profiles  by it  20 (as appear  is  the  noise  not c l e a r  w e l l as F i g u r e not  level  how t o 19),  t o be a f f e c t e d  of  interpret  the  shapes  by t h e c h o i c e  the the of of  62  Pr(small 0.15 l  200  200  0.30 l 300  200  H  Ri) 0.45  0.60  400  300  J.-400  u  (0  JD TJ  «  II / 600H I 1 / M / /•/ //  W C/J KJ (X CU  ii 1/ •1.000 Hi  Pr(Bi<1) Pr(»i<l/4)  1400  Figure  19 -  Vertical profiles of Pr(Ri<1) and Pr(Ri<1/4) calculated from e q u a t i o n (5.10) and t h e buoyancy f r e q u e n c y p r o f i l e o f F i g u r e 10 f o r j = 200, 300, 400. t  63  PCT 0.60  1400  Figure  20  -  V e r t i c a l p r o f i l e s of f r a c t i o n of turbulent water column (PCT) estimated for two different threshold levels of turbulent kinetic energy dissipation. The horizontal scale i s identical t o t h a t i n F i g u r e 19.  64  e . c  Two  values  3x(instrumental I0x(noise  level). levels  indicate  that  a  factor  than  in  of  are  c  level The  varies the  the  e  noise  threshold  (by  of  by  in  = 3X10"  factors  the  Presumably,  20.  while  3  in of  column i s  PCT  itself other  2-6.  3X10'  But  significantly  and t h i s  c h o i c e s of  10"  using  low N r e g i o n above  thermocline  thermocline.  W/m )  7  difference  water  4-5)  used in F i g u r e  W/m W/m  6  3  both less  the  is is  3  these  two  curves  turbulent  thermocline  decreases  e  6  below  would g i v e  the  similar  c shapes  (until  s u c h a low v a l u e  noise-saturated  or  exist  of  in  the  Figure 25  meter  depth  measured  intervals  indicative  that  chosen that  for  of  Figure  the  11(the  drops s o u t h of  either  relative  patch  R e g i o n s where t h e  greater  than  interpreted  thin is  and/or  strongly  smaller,  the  are  turbulent  patches  the  e and v i c e - v e r s a .  turbulence magnitude. levels  it  would  be  would  not  averaged  relative  normal  it  values).  PCT c o n c u r s w i t h low  trend are  chosen  a high value  20 may be compared t o  general,low this  set  such  were  thicker  over  ring).  In  Anomalies  to  thickness ratio  as h a v i n g  p a t c h e s and where t h e  are  e  and/or  or  e/PCT  is  relatively ratio  more  e/PCT weakly  turbulent. A the  rough  shape o f  plotted averaging  in  test the  was d e v i s e d t o  model  Figure  (5.10)  20.  problem e x i s t s  was d e c i d e d t h a t  it  Since  indicate  agrees it  with the  was a c c e p t a b l e  with  the  degree  the  to  which  measured  data  has been a c k n o w l e d g e d t h a t limited available to  smooth  the  data  set,  profiles  an it in  65  Figure  20  with  compare t h e s e Pr(Ri<1/4), nearest given  a  three-point  directly each  with each other  profile  factor,  each data  In o r d e r  and w i t h the p r o f i l e s  The s c a l i n g  set are given  one may r e c o v e r  average.  was n o r m a l i z e d u s i n g t h e peak  to the t h e r m o c l i n e . to  running  factors  in Table  the o r i g i n a l  values  1.  to of  values  and the  titles  With the s c a l i n g  of  Pr(Ri<1/4)  and  PCT. Data  Set T i t l e  e c  = 3X10"  e c  = I0"  j j j Table  +  +  +  PCT1  6  PCT2  e  Pr(Ri<!/4)  from  .  . 0 8 7 @ 500m  (5.10) 6.9x10"  7  @ 500m  = 300  PR300  1.7X10"  5  @ 500m  = 400  PR400  8.3X10"  Scaling  Profiles 21.  to data  700  for  @ 500m  5  normalization  and  titles  sets.  600 m e t e r s ,  t h e agreement  about  correlation  factors  o f n o r m a l i z e d PCT  Above  thermocline,  r  . 3 8 @ 700m  PR200  given  below  Factor  = 200  1 -  Figure  Scaling  and  Pr(Ri<l/4)  a depth which  with the data  meters  the  coefficients  is s t i l l  i s very  agreement  were  are  shown  i n t h e main  good.  is  in  However,  poor.  calculated  Sample as  = Z(x -x)(y -y)/(/(Z(x - x ) ) / ( Z ( y - y ) ) ) i i i i i i i  and t h e s e  2  are l i s t e d  100-1250 m e t e r s , interval  in Table  the  100-600 m e t e r s  2  2.  Over  correlations  the e n t i r e  are  the c a l c u l a t e d  poor.  correlation  depth But  interval over  the  coefficient  66  SETS  DEPTH RANGES  PCT1,PR200  100-1250m  .34  PCT1,PR200  100-600  .89  PCT2,PR200  100-1250  PCT2,PR200  100-600  .94  PCT1,PR300  100-1250  .37  PCT1,PR300  100-600  .90  PCT2,PR300  100-1250  . 12  PCT2,PR300  100-600  .94  PCT1,PR400  100-1250  .37;  PCT1,PR400  100-600  .89  PCT2,PR400  100-1250  .11  PCT2,PR400  100-600  .94  Table 2 -  ;  .  Correlation coefficient, r, calculated f o r the pairs of data s e t s d e f i n e d i n T a b l e 1 and over the depth ranges s p e c i f i e d .  67  V e r t i c a l p r o f i l e s o f n o r m a l i z e d PCT from Figure 20 a n d n o r m a l i z e d P r ( R i < l / 4 ) f r o m F i g u r e 19. The profiles were normalized by t h e maximum v a l u e s nearest the thermocline. The normalization f a c t o r s a r e l i s t e d i n T a b l e 1.  68  is  better  W/m )  . 8 9 and i s  and e a c h of  3  5.5  than  the  . 9 4 between  family  PR200,  the  set  PCT2  = 3xl0~  (e c  6  PR300 and PR40.0.  Discussion A number o f  (5.10) which  should this  theory, N(z)  a s s u m p t i o n s w h i c h were made i n o r d e r be  emphasized.  model r e l i e s  requiring  i n the  a  was  is  varying  slowly  it  components  (u> - N ) do n o t c o n t r i b u t e Thirdly,  t h e model t o this  was assumed t h a t  a major  j . and t h e  parameter.  The  the  N(z).  other  the  use  open t o  high frequency  the  choice  to  WKB  to  which  question.  internal  significantly  t o make  of  The d e g r e e  is  derive  t h e GM model upon  with  problem i s  inability  all,  varying  Secondly,  variance.  of  developed  slowly  thermocline  First  to  to  wave  the  shear  high s e n s i t i v i t y  a  clear  choice  be made i s  that  of for  of  e c  which, data  although to  which  correlate measure  does not  it  two q u i t e of  greater  it  the  is  affect  compared.  different  fraction  than a d e t e c t o r  the  of  model,  Finally,  parameters. the water  threshold,  does it PCT  affect  was a t t e m p t e d is  an  column w h i c h has This  e .  is  the to  actual e  levels  compared t o  the  point  the  c probability condition  for  that shear  superposition requires scales  of  water  column  instability internal  instability  the  model  is  waves.  The  to manifest  uncertainty  unable in  the  at  any  (Pr(Ri<l/4))  to p r e d i c t choice  of  due  implicit  itself  w h i c h may be m e a s u r e d by Camel  The fact,  the  the  as  to  meets the  local  a s s u m p t i o n made turbulence  at  III. the magnitude of j  +  alone  PCT.  results  in  In a  69  scaling well, PCT  factor  below or  may be  difference  about  agree.  due t o  the  exhibited  in drop 2 which  (Perhaps  a  greater  reduced the since drops  2  4,5,6,8  averaging  scheme  averages.  This  ethical  the  averaging  pertinent  d i s c u s s e d in of  to  drops  be q u i t e  to  is  not  comments  magnitudes  chapter.  Conversely,  in character  from  c o u l d be d r o p p e d from the  set,  behaviour  the  of  the  be a c c e p t e d on live  with the  with  the  understanding  'correct').  inadequacies  may  levels  r e g i o n would have  was d e c i d e d t o  likely  this  previous  different  data  though,  averaging.  it  of  e  t a m p e r i n g c o u l d not  and i t  the  the  As  intense  i n the  improve  limited  W i t h due r e g a r d t o of  is  order  the  nor  unrepresentative  subjective  of  = 200 and 4 0 0 .  +  As has been m e n t i o n e d ,  may be a r g u e d t h a t in  j  shape  d r o p 2 on t h e  g r o u n d s , however,  shortcomings that  of  appears it  neither  number  influence  drop  >100 between  700 m e t e r s ,  Pr(Ri<l/4) in part  of  be  made  stated above, in  light  of  a  number  the  limited  -1/N s u c c e s s of model  is  the model.  f o l l o w e d by PCT i n a t  This positive the  Apparently  relation The  d e p e n d e n c e of e a N  fact  so g r e a t l y  is  the  least  that  part  of  due t o  the  of  of  j  with  chapter.  PCT and P r ( R i < 1 / 4 )  the c h o i c e s  the  water column.  qualitatively  previous  t h e m a g n i t u d e s of  in part  behaviour  PCT on N a g r e e s  suggested in the  1  e  +  and e .  differ  However,  c it  seems c l e a r  (the  scaling  PCT2). either  that  the  shear  instabilities  factor  for  PR400  is  To a t t e m p t a larger  j  +  1000 t i m e s  occur  only  smaller  than  t o match PCT and P r ( R i < l / 4 ) , (for  w h i c h we have a l r e a d y  rarely that  one might  determined  of  infer would  70  give  an  Gargett  unrealistically et  al.(l98l))  high  wavenumber  or a d e t e c t o r  cutoff  in  threshold l e v e l ,  light  e ,  of  which  c is  greater  the  by some f a c t o r s  actual  breaking  event  converted However, which  amount  to it  data  is  satisfy  in  of  the  estimated PCT i n  the  an  explain  energy  why  internal  the  are  WESPAC  of  data, of  e,  In  it  than  set,  is  not  100 m e t e r s , to  a  < 1%  a  20).  lot  Hence,  required  appears  l e a d i n g to a  i s much s m a l l e r  given.  data  there  levels  short,  is  representing  s u c h as F i g u r e  dissipation  instability  sideline wave  in  involves  last'. long  the  oceans level  wave e n e r g y  used to e s t i m a t e internal  answers  of  single  energy  (which t r a n s l a t e s  3  If  to  that  the  breaking  event  the measured  levels  the  time  question  t h e waves a r e  internal  are  the  distances,  s u g g e s t e d by G a r r e t t  equilibrium spectral the  no  by a  the  a n d , below  profile  the  t h e n e n e r g y may p r o p a g a t e  s o u r c e a n d , as  W/m  released  entire  3  the q u e s t i o n  ocean.  internal  dispersing  5  argument.  (5.10)  An i n t e r e s t i n g does  of  a shear  from  the  to  which  this,  e > 1 0 " " W/m  vertical  above of  by  meters  e > 10"  no e v i d e n c e  probability  of  a  from  is  independent e s t i m a t e s  indicates  zeroes  leads  which  For  13,070  7,000  This  mechanism  noted that,  occurrence  the  there  the  constitutes  single  of  and  10.  energy  turbulence.  is  approximately  of  of  of  far  and M u n k ( l 9 7 9 ) , to  effectively from a  almost  The e s t i m a t e  (5.4)  relation  scale  representing  wave s p e c t r u m , p r o v i d e d t h a t  e,  the  which  is  local  may h e l p  everywhere'. and t h e  long  long-lasting,  thereby  wave f i e l d  'filled  'how  the  to same  made  for  e = a N may be 0  decay  of  a parameter  the of  71  the  turbulence,  internal  is  representative  wave f i e l d .  Defining  T = Lueck, for  Crawford  N .  Figure  0  is  .0055 r a d / s e c .  Osborn(l98l)  show  .0055 rad/sec-. these  yield  to  r  frequency, (McComas which  of  less  than  basin  the  value  from PEQUOD  the  thermocline  (Figure  25).  which  indicate  N  appropriate  via  36 d a y s  The f a c t o r equation  of  (5.4)  smaller  the  scale.  then  they  than  the  range  to  If  Gargett  for  that  the  and 16  these  the  large  waves t r a v e l will  at  propagate  scale  400-1000  extrapolated  N  values  limits  use a p r o p a g a t i o n  maximum)  of  km,  «  a , 0  days  for  in  the  estimates scale, 10  low  cm/sec  200-500 km, basin.  20 c m / s e c ,  which  is  0  Vancouver  an o c e a n  s p e e d of  and  of  two v a r i a b i l i t y  of - two u n c e r t a i n t y . internal  rad/sec  extrapolated  0  the  t h e WESPAC d a t a  and Munk(1979) increases  from  .0045  avoid  for  considerably  only  N  of  29 d a y s  energy-containing  this  a value  PEQUOD,  data.  a factor  of  for  E,  lost  o  used a v a l u e  rad/sec  and M u l l e r ( 1 9 8 1 ) )  is  Garrett  .005  o  46 days  Sea  parameter,  within  A suitable  Together with  Sargasso  energy  that  profiles  Island slope data, the  4  o  from WESPAC ( t o  is  energy  {53N /2+22x10- /N }/a .  14a i n d i c a t e s  from > 300 m e t e r s  the  r = TE/e,  and O s b o r n ( l 9 8 3 )  from > 900 m e t e r s  of  is  but still  72  VI. 6.1  RESULTS FROM PEQUOD  C u r r e n t s And H y d r o g r a p h y The  large  parameters Many  scale  structure  in equatorial  standard  of  regions  oceanographic  is  c o n t a i n d i s c u s s i o n s of  dynamics.  Preliminary  review  is  JISAO,  given  series order  of 10  6  Prevailing  theoretical  University  by L e e t m a a ,  The e q u a t o r i a l  meters  and  20°N. are  and In  the  winds  the  North  considerably  resulting  North E q u a t o r i a l  Ocean-Atmosphere  is  of  in  the  occurs at east  the western  pressure  at  Current  wind s h e a r  of  latitudes (NEC)  still  results  s t r o n g enough t o d o m i n a t e ,  the  deep.  the  westward  of  10°S  between  winds  and  i n an e a s t w a r d  to  1 0 ° N and  1 0 ° N , the  easterly)  to  this  Undercurrent  b o u n d a r y of Near  of  a  the  flowing  (NECC).  transport  gradient.  is  A recent  meters  2  tropics drive  (SEC)  (although  Equatorial  p r e d o m i n a n t l y westward  work  comprised  t h e d o l d r u m s from 4 ° N t o  Countercurrent  the  and  Newsletter  editor).  basically  More r e m a r k a b l e and more p e r t i n e n t existence  observations  m e t e r s wide and 1 0  Current  weaker  meridional  5  Equatorial  r e g i o n of  Pickard(1983),  experimental  of W a s h i n g t o n ,  regime  10  f l o w i n g South E q u a t o r i a l 4°N,  and  known.  s u b s u r f a c e z o n a l j e t s which are  l o n g by  easterly  and  well  M c C r e a r y and M o o r e ( 1 9 8 l ) .  current  surface  (Pond  equatorial  r e p o r t e d i n the T r o p i c a l  (D.Halpern,  and h y d r o g r a p h i c  now r e l a t i v e l y  texts  Gill(l982))  regularly  the c u r r e n t s  near the the  resulting  the  study  (EUC). equator,  ocean r e s u l t i n g surface, in  the  the  is  the  Due t o a  buildup  in a  west-  wind s t r e s s  westward  the  is  flowing  73  SEC,  but  with  increasing  diminished and,  i n the  pressure gradient  depth  the  effect  t h e r m o c l i n e below  dominates.  the  The r e s u l t  is  of  t h e winds  mixed  layer,  the eastward  is the  flowing  EUC. Included PEQUOD a r e salinity  in  Appendix  vertical  and t h e  FCwith  profiles  of  calculated  is  buoyancy  d i s c u s s e d in Appendix  The  basic  parameters are  features  seen  w i t h t h e Camel III net  D  the of  maximum  eastward  is quite  p o s s i b l e that  missed  the  due  meters  or  decreases  EUC i s  about  .01  4  resolution  measurements.  sec  zero.  in  138°W  about  This  (see  were  the White Horse  about  and  D which (see  is  about  75 cm/sec  maximum  of  is  75 cm/sec and  At while  has  a  (unfortunately,  it  the  is  150  EUC  core  the White Horse cm/sec  B e n e a t h t h e EUC c o r e  the  120  velocity is  f i e l d w h i c h c a n be d e t e c t e d above  the  structure  is  J)  of  evident  in  n e t K on 20/02/82 and n e t Q)  meters  in  there  Appendix  700  associated  Appendix K).  d e p t h r e s o l u t i o n of  .  hydrographic  120 m e t e r s  Between 600 and  the  White  some of but  the  Horse other  s h o u l d not  be  indicate  a  typical.  The t e m p e r a t u r e d a t a shallow  - 1  the v e l o c i t y  (notably  considered  net  westward a t  real  25 meter  structure  profiles  of  the  of  The r e s u l t i n g mean s h e a r  to near  cm/sec  currents  1/2°N,  s i t u a t e d at  velocity  to the  velocities).  the  SEC f l o w s  the c o r e  These  J.  in the p r o f i l e s  surface  of  from  temperature,  frequency.  The t r e a t m e n t  of  drop 3 at  profiles  horizontal current,  measured w i t h the White H o r s e . data  t h e Camel III  wind mixed l a y e r  (Appendix (the  winds  K)  generally  in mid-winter  are  typically  74  slacker the  than a v e r a g e ) .  very  depth.  A low g r a d i e n t  strong thermocline  The n e a r - s u r f a c e  mixing.  The t y p i c a l  is  situated  salinity  thermocline  is  seen  L and F i n A p p e n d i x K,  in nets  salinity  profiles  r e g i o n s near the  exhibit  and i n  thermocline  is  .005  meters  d e p t h , which  rad/sec  constant  consistently A many of shear  r e g i o n of  temperature the a  strong  is  the  just  below of  above  SEC-EUC  and  thermocline.  due  to  local  the  example).  finestructure  vertical  the  All  main  can of  the the  The maximum v a l u e of N  in  A s e c o n d maximum of to p r o f i l e  d e p t h of  about  features  be  in  the  12°C  is  near  350  thermostad  which  the  thermocline  interface.  has  in  of  other  in the  (a  been  in nets  salinity  and t h e  gradient.  interesting  t o compare t h e m i c r o s t r u c t u r e  data  in  D and E  constant  gradient  communication)  temperature  mean  t h e minimum  locally  temporal v a r i a t i o n s density  minimum i n large  profiles, of  the  (personal  local  Evident  combination  c o r r e s p o n d i n g minimum i n t h e  wind  (but  the p r o f i l e s  feature  weakening  M.McPhaden  of  CTD p r o f i l e s ) .  extent a  effects  of for  and  100-140 m e t e r s  i n the  from p r o f i l e  interesting  and t o a l e s s e r be  the  .016-.024 r a d / s e c .  temperature  and  about  this  maximum l o c a t e d  thermocline.  persists  the N p r o f i l e s  to  in a l l  found in e q u a t o r i a l  unique  especially appears  the about  about  r e g i o n of  evident  at  shows  strong s a l i n i t y  not  in T u n d e r l i e s  of It  this  has  above found  potential will region.  be  75  6.2  Previous Equatorial The  Microstructure  previous  notable  microstructure  are  reported  Osborn(1979a,  1979b,  Measurements  equatorial in  1981),  measurements  Gregg(l976),  Osborn  and  of  Crawford  and  Bilodeau(1980)  and  Crawford(1982). Gregg(1976) at  155°W on t h e  to  the  those the  upper  of  the  core  turbulence  made s i x equator  in J u l y ,  500 m e t e r s large  profiles  characteristics  r e g i o n of  EUC and t h e  was  f o u n d t o be e x c e p t i o n a l l y weak  in  the  EUC  thermostad.  Osborn  microstructure  and  data  i n the  June  and  July,  microstructure  data  temperature velocity  microstructure extend  is  consistently over  collected  one  least  the  below  the  temperature  between 24°W  and  velocity  following  points;  found c o n c u r r e n t l y  with  temperature  gradient  turbulent  patches  sign; some  and f i n e s t r u c t u r e  Atlantic  SEC-EUC in  coincident  the  the  measurements  tens are  of more  than  in  meters; intense the  the in  Gregg  measurements.  Velocity Atlantic  of  at  microstructure  unless  of  the  weak  Atlantic  generally  interface,  moderate  and v e r y  them t o make t h e is  e m p h a s i z e d were  in  core,  limited  intensity  high  Nearly  fluctuations  t h e O s b o r n and B i l o d e a u Pacific  1974.  allowed  horizontally  temperature  equatorial  microstructure  turbulence  The  Bilodeau(1980)  were  SEC-EUC  thermostad.  t h e r m o s t a d between 300 and 400 m e t e r s  in  the  the  quite  microstructure  The d r o p s  of  interface,  33°W  temperature  1972.  and t h e  mean s h e a r  of  microstructure  i n J u n e and  Osborn(1979a,b)  and  July, in  the  measurements 1974  were  equatorial  made  in  the by  Pacific  equatorial  Crawford  and  in January  and  76  February, Again,  1979 ( C r a w f o r d  indicate  interface  and  large  low  Atlantic,  high turbulent  EUC  but were n o t  core  The r e m a r k a b l e between of  the  result  is  of  these  upper  in  were a l s o  In  the  below  the  Pacific.  scale  made  dynamics  indicated that  energy  in the  r a t e at  as a s i n k  SEC-  connection  zonal pressure gradient, friction  the  in the  large  data  kinetic  in  found  t h e EUC c o r e  The A t l a n t i c  500 m e t e r s .  t h e EUC c o r e .  s t u d i e s was t h e  turbulent  turbulent  of  the  EUC above  which the  thereby  EUC  defining  kinetic  energy  in  currents.  PEQUOD M i c r o s t r u c t u i r e Profiles  of  turbulent-  calculated  from  the c e n t r a l  equatorial  in  intensities  currents.  from the  of  equatorial 6.3  Crawford(1982)).  intensities  comparable i n magnitude to the  gains energy role  intensities  f o u n d below  r a t e of d i s s i p a t i o n of the core  turbulent  t u r b u l e n c e measurements and t h e  equatorial  the  Osborn(1981 a ) ,  t h e measurements were c o n f i n e d t o t h e  These r e s u l t s EUC  and  Appendix  K.  the  velocity Pacific  kinetic  energy  dissipation,  e,  microstructure data obtained  from  in February,  Thirteen p r o f i l e s  1982  were made a t  are  contained  or w i t h i n  of 2  the  equator  other  (these w i l l  three  referred  t o as  Without display r e g i o n of much  were  made  within  t o as  2°  of  on-equator)  the  equator  and  (and w i l l  the be  off-equator).  e x c e p t i o n , the on-equator p r o f i l e s  high  levels  the  SEC-EUC  smaller  be r e f e r r e d  in  the  of  dissipation  interface. velocity  The  in  the  estimated  c o r e of  in large e  Appendix  K  mean s h e a r is  usually  t h e EUC .where t h e mean  77  shear  is  a minimum.  only  occasionally  Below t h e c o r e , is  the  e very  by C r a w f o r d and O s b o r n ( 1 9 8 1 b ) contrary  to  the  results  a l t h o u g h d r o p 3 has t h e 20  to  140  b a s e of  meters  the  However,  EUC,  large  for  the  from  the  in the  individual  t h e maximum e v a l u e s  in t h i s  Pacific  is high  region  data  v a l u e of  large  For  of  at  is  example, over  r e g i o n at  e are  from d r o p 5 a r e  found  e averaged  mean s h e a r  estimates  (as  but  but w h i c h  Atlantic).  second l a r g e s t  depth,  the  t h e mean s h e a r  quite  the  the  small.  base of  the  EUC. The s t r o n g t h e r m o c l i n e to  the  deeper  exchange waters.  profiles degrees which at  In  is of  the  is  the  frequent  and t h e  of  briefly at  of  in  level  the  level.  levels  of  interesting  feature,  of  low  the p r e v i o u s  d r o p s of  least of  above  much  one and up t o turbulence  below  of  e are  equatorial  is  much  less  in in  light the  is  (100  strong evidence  activity meters),  immediately  smaller above  the  drop  show r e d u c e d e i n  two d e c a d e s  in  of  region  t h e EUC c o r e and w h i c h  low m i c r o s t r u c t u r e  all  the  lower.  activity  section,  Drop 2  the  varying  so,  the  especially  finestructure  stability  in  patches  are  with  or  to of  estimates  depths  turbulent  turbulence  t h e EUC c o r e .  patches  greater  many  turbulence  150 m e t e r s  barrier  surface  in  and i n d i v i d u a l  At  and d r o p 6 (80 m e t e r s )  N r e g i o n ; at  upper  of  static  three  r e g i o n above  thick  high  mentioned in  least  meters)  very  estimate  minimum  from t h e  feature  occurrence  Another  energy  effective  a recurrent  noise  the  t o be an  fact,  a sharp c u t o f f  profiles  McPhaden's  turbulent  intermittency  there  or n e a r  of  appears  was in  low N 3  (65  t h e minimum compared t o  and b e l o w .  In  78  other  d r o p s t h e minimum i n N i s . e i t h e r  and t h e r e Of  is  drops  four  (12,14,15,17)  500  meters  1/2°  show s t r i k i n g l y  depth.  patch,  made w i t h i n  Drop  10  d r o p s 7 and  drop  13 has  shows 8  and  patches  s e p a r a t e d by - 25 m e t e r s and summarized i n T a b l e  Figure Independent  22  compares  2 meter  latitude averaged  range. e greater  drops.  dissipation  is W/m  6  the  of  of  for  only a factor  fourteen)  of  equator  W/m  5  off-equator  averages.  900  e is  W/m  meters 3  for  3  As a c o m p a r i s o n Osborn(1979a,b) over  and  t h e d e p t h range  Crawford(1982)  which  patches  equidistant  at  500  5 meter  at  500  thick  meters.  profiles.  (50,  the  respective  100 m e t e r s )  by a f a c t o r  of  over  indicate  4-5 o v e r  the  over  the  u p p e r 200 m e t e r s ,  the  for  the  on-equator  and  Below  on-equator  drops. the  200  At  EUC c o r e , meters,  data  150 the  only  meters,  difference three  (of  averages  of  e are  smaller  than  When a v e r a g e d o v e r  the  depth  range  200-  5.6x10"  off-equator  a 500 meter  centred  off-equator  two.  separate  sign  of  at  c were a v e r a g e d v e r t i c a l l y  c o r r e s p o n d i n g t o a d e p t h j u s t , below is  patches  the drops w i t h i n  Averaged  1.6x10"  3  nearly  145°W,  turbulent  o n - e q u a t o r and o f f - e q u a t o r  all  near  equator at  thinner  The two upper v a l u e s  off-equator  3.3xl0"  nonexistent  3.  estimates  50 m e t e r s and t h e n o v e r  the  no  have  three  of  similar  meters  These are  weak or  no o b v i o u s minimum e r e g i o n .  eight  turbulent  very  7  W/m  3  for  o n - e q u a t o r d r o p s and 3 . 3 x 1 0 "  7  drops. with  the  measurements  Crawford(1982),  of  d i s s i p a t i o n s were  20-140 m e t e r s and p l o t t e d on is  shown h e r e  Crawford  as F i g u r e  23.  and  averaged  Figure The two  3  of  single  79  DROP  PATCH CENTRE  THICKNESS  e(W/m xlQ ) 3  7  weak  8  weak  10  no  12  483  13  3 p a t c h e s each  14  510  15  10  540  15  30  492  10  40  518  27  20  492  35  40  15  17  Table  3 -  7  sign meters  35  meters  5 meters  50 10-20  Depth, t h i c k n e s s and p a t c h - a v e r a g e d dissipations f o r t h e p a t c h e s l o c a t e d n e a r 500 m e t e r s d e p t h f o r t h e d r o p s w i t h i n 1/2° o f t h e e q u a t o r a t - 1 4 5 ° W .  80  LOG 10-  /  e (W/m ) 3  10"  10  6  J  - 5  -1.1  200  u  m x>  pa  oi Ul cn 04  600  -i  Figure  22  -  i :—IT.I  r  n t  i  1 — i — i  i i i i  V e r t i c a l p r o f i l e s o f 50 m e t e r v e r t i c a l l y a v e r a g e d values of log e a v e r a g e d o v e r a l l o f t h e Camel III profiles taken within 1/2° of the e q u a t o r ( d o t s ) a n d o v e r t h e p r o f i l e s o u t s i d e o f 1° of t h e e q u a t o r ( t r i a n g l e s ) .  81  AVERAGE DISSIPATION  •  P a c i f i c , 1979 20 to 140 meters depth  O  A t l a n t i c , 1974 20 meters t o undercurrent  /V  P a c i f i c , 1982 20 to 140 meters depth  core  „  3  3 *  2 O  NORTH  O  I 15  I M  13  Figure  I 12  11  23 -  I to  9  I  1  8  7  6  5  4  •  Jo*  SOUTH  I 3  Averaged dissipations observed during the P a r i z e a u c r u i s e i n 1979, t h e A t l a n t i s II cruise i n 1974 and t h e Thomas G.Thompson c r u i s e i n 1982. The 1982 d a t a were added to Figure 3 from Crawford(1982).  82  largest three  values  f r o m 1982 a r e  off-equator  general  agreement  on-equator  not  so  for  6.4 The O n - e q u a t o r  from  145°W  White 1/2° these  the  onset  profiles  one  equator  W/m ,  in  3  thirteen  mentioned  of  1982 E l  is  Nino  The  for  both  clearly  w h i c h were t a k e n , the  are  drops.  data  stations  from  the p r o f i l e s 153°W.  or n e a r  The  145°W but  occupied listed  it  should  event.  are  from 138°W,  four  other  five  were n o t  profiles  a c c o m p a n i e d by o v e r - t h e - s i d e  current  over  the  depth range  20 t o  equatorial  synoptic  150°W,  shear  1979, a l l  joint 4 and  C r a w f o r d made n i n e t e e n  in e a r l y  where in Table  at  from w h i c h t h e  6  the  the  off-equator  were made a r e  T h r e e of  profiles.  were  of  drops  1979 e q u a t o r i a l  on-equator  were made a t  Horse of  of  26.  and  two  1982 d a t a ,  to the  Horse  in Figure  the  7x10~  and  Profiles  The l o n g i t u d e  shown  than  equator  f o u n d by C r a w f o r d ( 1 9 8 2 )  1974 and P a c i f i c ,  be n o t e d , w e l l p r i o r  profiles  0°  the  However,  from t h e  peak a t  of  less  the  in magnitude  dominant  Camel-White  all  only  and r e c u r r e n t  the A t l a n t i c ,  are  1/2°  with Crawford(1982).  drops,  distinguishable large  values  within  and  within  nine  meter  140  with  of  profiles  meters  was  estimated. White Horse v e l o c i t y running  mean  m a g n i t u d e of Vaisala  the  are  represents  to  over  the  the  calculated in Figures  average  were smoothed u s i n g a  first-differenced  was c a l c u l a t e d  shown the  and t h e n  shear  frequency  correspond profiles  filter  profiles  25 over  meter  range.  The  at  The  eight  24 and 2 5 , where  value  to estimate  approximately  shear.  each  depth  3-point  the of  the  Brunt-  25 m e t e r s  to  individual thick the  line eight  83  profiles.  Figure  26 i n c l u d e s t h e  The mean s h e a r the  profile  South E q u a t o r i a l  v a l u e of about  (SEC)  i n the  1  Undercurrent(EUC)  interface.  above  from .008 t o  t h e EUC c o r e  shears  generally  found in  be d e t e r m i n e d , g i v e n Horse  velocity  deep at  138°W,  meters  deep  the of  shear  at  value  maximum  deepens  approximately  Vaisala  .018  350  persistent.  profiles  indicate  one o n l y above t h e o c c u r r e n c e s of Vertical estimates  of  Individual W/m  3  thick  Ri<l/4  e 25  were meter  is  the  shows  A  145°W  is  e are  averaged  a  averages  in  fact  the  150  maximum  of  located  shear  are  25  range over 3x10"  many  W/m  3  the e i g h t  but  Brunt-  less  than  individual  Individual  and  at  at  intervals.  26.  4 decades 8  and  (Ri)  25 meter  meters  of This  considerably smaller  there  over  maximum  EUC c o r e .  shown i n F i g u r e  average  130 m e t e r s about  subsurface  is  over  White  one.  comparison  where i n  the  the  can  a s e c o n d s h e a r maximum  second  meters  larger  As w e l l a s  and  b u l k R i c h a r d s o n numbers  of  the  of 3  i n d i c a t e d by t h e minimum i n  upper  EUC c o r e on d r o p 3 t o  represents  at  when c a l c u l a t e d o v e r  profiles  above t h e line  core,  profiles.  located  A  SEC-Equatorial  with  1  EUC c o r e  rad/sec  420  sec" ,  in  t o a maximum  t h e E U C . c o r e was a b o u t  profile  to  the  surface  d e p t h r e s o l u t i o n of  The c o r e  westward.  the  diagrams.  span a l m o s t a f a c t o r  eastern  t h e m a g n i t u d e of  average  these  increases of  .022  deeper  Below t h e  The B r u n t - V a i s a l a  historically  the  slightly  profile.  region  25 meter  153°W.  which  Values  measurements, only  about h a l f  the  for  shows a minimum n e a r  Current  .014 s e c "  symbol key  plotted. from 2 x 1 0 "  depth.  Camel  4  The  profiles  w h i c h were a s s o c i a t e d w i t h W h i t e H o r s e p r o f i l e s and shows a  near  84  Eight v e r t i c a l profiles of vertical shear as estimated from White Horse h o r i z o n t a l v e l o c i t i e s t a k e n w i t h i n 1/2° o f the equator in February, 1982. Longitudes of individual profiles are l i s t e d i n t h e key t o F i g u r e 26. The thick line i s the average of the e i g h t p r o f i l e s .  85 i  I  BRUNT VAISALA FREQUENCy (RAD/SEC) 0"J  0  1000 n  I  1  .01 I  n  I  1  .02 l _  L  r  Eight vertical profiles of Brunt-Vaisala f r e q u e n c y measured s i m u l t a n e o u s l y as the shears of Figure 24. The symbols a r e k e y e d i n F i g u r e 26. The t h i c k l i n e i s t h e a v e r a g e o f the eight profiles.  86  Vertical profiles of turbulent k i n e t i c energy d i s s i p a t i o n averaged over 25 m e t e r s depth and which are nearly synoptic with the data of F i g u r e s 24 & 25. The t h i c k l i n e i s t h e average of the eight p r o f i l e s . L a r g e s o l i d d o t s a r e 20 meter averages o v e r n i n e t e e n profiles taken at 150°W and within 1/2° o f the equator by Wm.Crawford i n J a n u a r y / F e b r u a r y , 1979. The l a r g e diamonds a r e 20 meter averages over thirteen e q u a t o r i a l p r o f i l e s from F e b r u a r y , 1982.  87  s u r f a c e maximum of  4x10"  depth,  exception  with  indicates  averaged  vertically directly  the  independently diamonds  the  were  Crawford(1982)), enhanced w h i l e In  150°W  are  averaging 'to  reduce the  to  be  purpose,  with  Osborn(1981 a ) .  the  1982 d a t a  measurements  The  averaged at  February,  1982,  peak  and  500  of  due  With  the  large  compare  to  peaks  to  the  are  nineteen  The  a  slightly  data  profiles are  were much  different  1982  smaller  the  present  for  direct  two  large  profiles  show  d e p t h - a v e r a g e d f r o m 20 t o  the  13  (to  160 m e t e r s  i n the  the  profiles  shallower  by more t h a n a  fact,  days  f r o m C r a w f o r d and  a g r e e m e n t below  However,  In  For  at  somewhat  individual  intensity'.  us c o n f i d e n c e t h a t  the  profiles  These d i f f e r  individual  comparable).  1979 p r o f i l e s  t e n d e n c y of m u l t i p l e  1 979 p r o f i l e s  meters!  lies  the  meter  1982 d a t a a r e  solid dots.  data.  which a r e  e  145°W w h i c h were made  Crawford averaged over  core  than  in  frequency.  at  20  averages  gives  110  meter  to  (this  values  7 0 , 90 and  500  meters  quantitative  r e g i o n above t h e EUC  greater  over  show  are  times  are  high turbulent  our  which  d e s c r i p t i o n remains unchanged.  we have a v e r a g e d o v e r  and  three  b i a s c a u s e d by t h e of  500 m e t e r s  (these  the  by l a r g e  used.  near  profiles  Crawford(1982)  days  comparison  meters)  to  The 20 meter  scheme  with  peak  surface  the q u a l i t a t i v e  5 of  on  Horse  contrast  e  in Brunt-Vaisala  near  denoted  from F i g u r e  a  The  averaged  the  marked  Crawford.  of  f i v e Camel p r o f i l e s  of W h i t e  and  and a g e n e r a l d e c r e a s e o f  3  values.  b e n e a t h t h e peak of  W/m  dissipations  adjacent  inclusion  of  5  with  sets  of  mean s h e a r 20  factor profiles  140 m e t e r s  300  meter of  ten from  g i v e 7 of  88  0.28x10"' from  W/m  1979  while averaging  3  gives  1.2x10""  over  the  W/m ,  19  more  3  equatorial  profiles  than  a factor  profiles  nor  of  four  difference. Unfortunately, profiles the  have  neither  completely  from w h i c h  1982 p r o f i l e s dissipation absolute  over  values  20  to  but  times  a l o n g w i t h the  shear  and R i  differencing  between  the p r o f i l e s  were f o u r  than  in February  less  and R i  that  the  and l a r g e r  This  on  values  drop  considering only in February from  20  surprisingly paragraph.  the  140  well  of  greater.  indicate  from  those  1979 e q u a t o r i a l  This  from 20 t o  Averaged  data  50 p e r c e n t  is  shown  140 m e t e r s  the  drops  in Table 4  estimated  by over  times  in  1979  greater  greater.  of  of  by  e are  shear,  with  the  was  considerably  1979 d a t a  a c c o m p a n i e d by s m a l l e r  or of  an  the  is  for  the  values  basis.  noted  in  3  drops  which the  set,  However, made  3 3 , 36 and 38 i n T a b l e W/m  of  expect.  1982 d a t a  equatorial  0.29x10""  figure  indicate  reasonably  averaged  four  which are  meters  shear  as one m i g h t  drop  of  January/February  Crawford's  t o be so c l e a r  average  1979, t h r e e to  from t h e  1982 w h i l e t h e a v e r a g e d  values  a  by a b o u t  these  meter  D i s s i p a t i o n s averaged  t r e n d does not appear  either  for  of  those depths.  considerably  larger  meters  e estimated  four  1982  Nine  w i t h White Horse p r o f i l e s .  smaller  about  shear measurements.  was e s t i m a t e d w h i l e e i g h t  140  which are  the  were a s s o c i a t e d w i t h c u r r e n t  shear  were s y n o p t i c  mentioned above, remains  the  1979  synoptic  1979 d i s s i p a t i o n p r o f i l e s  profiles  Ri  the  4,  7  agrees  preceding  JANUARY t FEBRUARY, 1979  FEBRUARY, 19B2  ttW/m'xIC")  Drop  AU/Az  Ri'NV(AU/Az)  3(13B W)  .66  .011  1.3  4(13B°W)  .16  .0090  2.2  5( 13B°W)  .071  .015  0  10(145°W)  .61  ]  Drop  13-14  t(W/m'»l0«)  AO/Az  1.5  .0094  Ri-N'/(AU/Az)  .53  .66  .0096  1.3  22-24  .71  .0083  2.0  21  .011  1.5  33  .42  .0051.  1.2  13(14S W)  .17  .0070  2.0  36  .58  .0047  4.3  14(145°W)  .082  .0048  3.9  38  .12  .0035  3.3  C  ]  CO  10 17(U5°W)  .16  .0089  1 .8 7 - .77x10-*H/m*  19(153 W) D  .036  .0069  1.0 AU/Az - .0074 s e c "  1  T • . 19x10" *W/oi* RT • 2.5 AOTAZ • .0093. sec"'  RT -  1.8  Table 4 -  Comparison of e averaged over 20-140 meters from 1982 and 1979 drops. The v e l o c i t y and depth a r e differenced over 20-140 meters by Crawford(1982) for the 1979 data and over 12.5-137.5 meters f o r the 1982 d a t a . At the bottom are averages over the l i s t e d drops.  •'I i• -j.  90  The  effect  in F i g u r e . 2 7 . is  plotted  of  against  and  winds on t h e  Averaged over  s p e e d and d i r e c t i o n steady  the  20 t o  time.  The  Wind  measurements and t h e cube o f  1200  hours of  the  data of  Figure  particular  Crawford(1982)  27  is  Crawford's  values  The  winds  comparable  w i t h somewhat large two  three  less  are  of  t h e d r o p i n wind s p e e d .  with the  Crawford  upper  of  of  the  terms.  (2.3)  premise,  proposed.  If  From t h e  surface  at  is  no  from  1982.  two d a t a  aside 20 t o  other  between  of  emphasized  sets  from  the  22.  The  e o c c u r d u r i n g and j u s t  after  indication  wind s p e e d and  e,  Crawford(1982).  suggested energy  term  of  the  to the  in  that  equation the  holds t r u e ,  dissipation  balance  plotted  is  the  from F e b r u a r y  between  production  from the a  is  this  six  Gradient  kinetic  waters  the  abscissa  others  1982 d a t a  there  Osborn(1979b)  turbulent  turbulence  equation basic  the  and  equatorial  dissipation  the  relatively over  The  between  wind  For comparison,  distinction  relation  f i n d i n g of  € And The Z o n a l P r e s s u r e  balance  for  averaged  any  was  27.  plotted.  strength  However,  one c o n f i d e n c e of  i n agreement 6.5  in  shown  dissipation  speed  from 1979 and t h e  variability  values  wind  in Figure  day d r o p i n wind s p e e d s  smallest  to give  the  also  is  s i x measurements of  direction  d a y s and t h e  that  are  day  are  calendar  the  s p e e d s were a v e r a g e d  daily  the  e values  140 m e t e r s ,  Each day,  were made.  easterly.  estimated  a (2.4)  production  an e s t i m a t e  in  the  and  the  may be  t h e mean k i n e t i c  measurements. mean  level  reasonable  of  kinetic no z o n a l  made energy  With  this  energy  was  velocity,  91  Time v a r i a t i o n s of turbulent kinetic energy d i s s i p a t i o n a v e r a g e d o v e r 20 t o 140 m e t e r s . Dots r e p r e s e n t s t a t i o n s w i t h i n 1/2° o f t h e e q u a t o r and c r o s s e s a r e o u t s i d e o f 1° o f t h e e q u a t o r . Small d o t s and c r o s s e s a r e f r o m 1979 and l a r g e d o t s and c r o s s e s f r o m 1982. The s o l i d l i n e i s t h e c u b e o f the average daily w i n d s p e e d from 1979 and t h e dotted line i s that from 1982 (revised from F i g u r e 4 of Crawford(1982)).  92  it  was  found t h a t  surface  was  on t h e  approximately  zonal pressure  towards  the  west  u'w'du/dx . the  zonal  same t i m e ,  plus  was  level  losses of  other  terms  suggested that  for  stress  sum of in  the  piling  to t u r b u l e n t  in to  driving  turbulent  the  balance  accuracy  w h i c h no e s t i m a t e  of  the  work  done  up  the  water  work  the  done was  At  t e r m s was  the  e =  EUC  friction.  of  could  at  friction,  no z o n a l v e l o c i t y ,  gradient  t h a n c o u l d be e x p e c t e d f r o m t h e that  wind  udP/dx,  b a l a n c e d by l o s s e s  it  by t h e  b a l a n c e d by t h e  the  pressure  approximately  input  gradient,  Below t h e  3  by  the energy  the  better  observations be  made  and  may  be  signi f icant. Five for  W h i t e H o r s e CTD p r o f i l e s  c o m p u t i n g dynamic h e i g h t s .  E at  138°W on 0 2 / 0 9 / 8 2 ,  02/21/82  and  net  computed from t h e (0/1000  dbar  17.8 m / s  2  2  in  at  at  Wyrtki(l983)  of  close  at  CTD d a t a the  net  The v a r i a t i o n  Q  net  K at  on  at  surface  the  K is  f r o m 16.0 t o  2  2  due t o  look  at  the  data  depression  of  the  thermocline  The a  t  = 24,  meters  25 and 26 s u r f a c e s  and t h e  p o s i t i o n of  EUC d e e p e n e d by 25 m e t e r s . velocity  measurement  (at  2  16.7 m / s 2  that  internal  indicates  that  occurred at were  a  20 net  1000 at  2  at  dbar net  net  E, K.  suggested  by  the  to  30  A  meter  K on 0 2 / 2 0 / 8 2 . by  t h e measured v e l o c i t y  12.5 m e t e r s )  2  heights  waves and t i d e s .  depressed  Coincidentally,  to  15.7 m / s  than  net  02/20/82 and  Dynamic  relative  are  available  were made a t  02/24/82.  much g r e a t e r  ±0.2 m / s  are  145°W on 0 2 / 1 5 / 8 2 ,  153°W  range  equator  These p r o f i l e s  standard notation)  Q but net  on t h e  20  to  30  maximum i n  the  nearest  surface  indicated a reversal  from  93  s t r o n g westward flow  between  (-53  cm/sec)  02/15/82  westward f l o w  to  and  on 0 2 / 2 1 / 8 2 .  strong  eastward  02/20/82 Also,  and  (+57  back  to  on 0 2 / 2 1 / 8 2 , t h e  cm/sec) 10 cm/sec  depressed  a t  surfaces the it  as  w e l l as t h e EUC c o r e  original was  d e p t h s of  impossible  pressure  gradient  However, may be  of  a  140°W  Piton(l968) al.d977) 7  April  good  show  of  historical  at  2  along  and May,  coincident  104°W  dynamic  of  reported  estimate  of  dynamic h e i g h t s  pressure gradient A reasonable  the  surface  EUC  core.  7  is  of  at  at  salinities.  2.8xl0" m/s  105°W.  estimate, 5xl0" m/s 7  Following  2  dbar  These  at  100/270 d b a r .  then,  of  the  and i s the  the  turbulent  7  method  2  of  AXBT in  A  of  number  5.4x10" I  m/s  7  150°W  2  the  a  and zonal  gradient depth of  Crawford  integrated  to  have made an  at  zonal pressure is  and  information  near  et  110°W made  zonal pressure  3xl0" m/s  dissipation  An  indicate  2  7  and  50/700 d b a r  AXBT s e c t i o n  100/270  t h e work done by t h e  the  at  2  0/270 d b a r o f  From t h e  EUC  from which Katz  in Halpern(1980).  Osborn(1979b), l o s s to  section  the  Lemasson  p r o v i d e d H a l p e r n w i t h the  and 1 3 3 ° W .  the  1958.  4.8x10" m/s  equator  estimates  t h e d e p t h of  from 1 7 2 ° E t o  Pacific  inferred  zonal  Knauss(l966)  the  153°W  at  at  2  May,  height  between  using  the  from w h i c h  gradient.  m/s  7  in  compute a z o n a l p r e s s u r e g r a d i e n t  130°W  data  1 6 0 ° E and  1979 i s  of  variability,  of  100/700 d b a r between  CTD p r o f i l e s  the  estimate  pressure  2.6x10"  and a  a  large  1 meter  PEQUOD d a t a .  computed a g r a d i e n t  3.3xl0" m/s section  obtain  zonal  gradient  c o r e between  Due t o t h i s  exists  the  to w i t h i n  02/25/82.  from t h e  there  made  computed  to  returned  and  gradient  and  over  two  the  94  regions.  Between t h e  70 m e t e r s ) the  average  the  the average  kg/m )  equatorial  in  balance  net  input  of  wind a t  the  Unfortunately,  Below  I  is  level  = 110 t o  gradient  is  eastward  and  the  1xl0~ W/m 3  gradient. meters then, of  the  Since  the  Recall  there  dissipation in  is  26)  the  yields  the  estimates, February,  of  the 3  3  this  indicates  a  which  is  2  Atlantic  their  If  2  quoted  measurements.  estimate  of  wind  PEQUOD d a t a .  the  and t o  average  average  is  is  historical to  was  is  zonal  70,  90  the  that  about pressure and  estimate  zonal  smaller.  110  made  gradient.  reliability the  is  Presumably,  pressure  the  much  to  The  3  gradient  1979 v a l u e s .  doubt  one may s u s p e c t  - 45 cm/sec  dissipation  zonal  pressure  5  pressure  balance  core  1xl0~ W/m .  work done by t h e  the  t h e EUC  zonal  velocity  zonal  a closer  1982  over  4xl0~ W/m .  equatorial time  2  5  3  reliable  10% of  reason  done by  6xl0" W/m ,  14xl0~ W/m ,  1982 d i s s i p a t i o n s a t  were  no  a  the  10% of  done by t h e is  the  holds,  of  and  7  dissipation  by  westward  m/s)(4.5x10" m/s )(70  meters  depth-integrated  that  1979 d a t a  work  gradient  done the  at  the  2  average  about  (Figure the  70  i n the  meters),  7  or  2  (.3  velocity  The work  2  no z o n a l v e l o c i t y  3.5x10" m/s ,  and  2  is  surface  w i t h the of  140  work  3  7  know of  synoptic  (which i s  11x10" W/m  4.5x10" m/s .  and  wind s t r e s s  do not  the  resulting  no z o n a l  = 30 cm/sec  C r a w f o r d and O s b o r n ( l 9 7 9 )  to  which  of  The d i s s i p a t i o n a v e r a g e d  20  by C r a w f o r d and O s b o r n ( 1 9 7 9 b )  stress  is  then,  2  between  level  a d e p t h - i n t e g r a t e d d i s s i p a t i o n of  by t h e  identical  is  gradient, 3  drops  the  velocity  = I0xl0~ w/m .  3  resulting  and t h e  pressure gradient  zonal pressure  m)(l028  surface  of  the  pressure  Although  the  95  estimates  of  dynamic  representative zonal  pressure  then, sink  of  there for  pressure  rather  good r e a s o n  energy  which  gradient.  the  some i n d i c a t i o n the  strength  data  from the of  the  is  input  of 6.6  kinetic  terms  in  S,  available  data  of  possible  to  trends.  PEQUOD d a t a  Ri  errors  involved  = N /S , 2  must be  EUC  by  the  is  not  time  the  be  estimated  data  steady  there  sets  either of  in the  is  that  due t o  change  role  zonal  suggested  As w e l l ,  r a t e of  another  have  not  a role.  a significant  the d a t a  in  cruise  compared  in order  the  balance  shear,  S,  as  and t h e  the  calculating  data  difference  buoyancy  Ri,  to  the  to determine  With the White Horse v e l o c i t y  as w e l l  2  from PEQUOD a r e  from the  28 shows s c a t t e r  calculated over of  over 25  e over  approximately and t h r e e  the  Apparently,  the  it  is  Richardson  frequency.  S and N a r e  The  discussed  in  J.  Figure  averages  there  and o t h e r  undercurrent  estimate  number,  averaged  one.  larger  Ri 4,  existence  Ri  to  a much  not  (2.3).  As i n C h a p t e r  Appendix  that  may p l a y  e n e r g y may p l a y  e And N,  other  do i n d i c a t e  terms which c o u l d  set  certainly  and O s b o r n ( 1 9 7 9 b )  m e a n d e r i n g or p u l s i n g and hence mean  they  are  than a s m a l l e r  Crawford  Atlantic  PEQUOD  to b e l i e v e  that meridional divergence from  from  t h e mean s t a t e ,  gradient  is  the  height  one  decades  25 meter  plots  respective  in R i .  The N,  one h a l f In  the  three  depth i n t e r v a l s  meters.  and  of  large S,  e a c h of  the  plotted  black  and R i  decades  parameters  dots  bins. i n N,  three  N,  S,  against  e  represent  The d a t a  span  two d e c a d e s  in S  plots  the  scatter  96  io-»  ftOUOO 20K-8OTTDH  E  3 "  1 o-  »1  § j 10 *  LOG N ( r a d / s e c )  1 0  io-» •tBUQD 2 0 H - B 0 T T 0 *  E  3 — 1 0 - •]  10-'i  10  io-»  LOG S ( 1 / s e c )  1 0  "'  PWUOD 20K-BOTTOT  E  \ 3  io-»  io-  10°  10'  10  J  LOG RI  Figure  28 -  Scatter plots of l o g ( t u r b u l e n t k i n e t i c energy dissipation averaged over 25 meter vertical intervals) vs log(buoyancy frequency(N)), log(vertical shear(S)) and log(difference Richardson number(Ri) c a l c u l a t e d from N and S ) . The data represent the entire water column sampled synoptically by both Camel I I I a n d by White Horse. Large b l a c k dots a r e averages over 1/3 decade i n t e r v a l s i n N, 1/2 d e c a d e i n t e r v a l s i n S and o v e r t h e r a n g e s <1, 1-4, a n d 4-40 i n R i .  97  is  considerable.  are  associated with large  smallest  values  For  >  are  Ri  of  e are  2 there  Ri  > 10.  w i t h Ri  <  trends.  The  compared t o  A cursory of  the  patch  smaller  than  average  from  which  at  of Ri  is  Hence,  averaged Figure  which  in Figure  support the  wave s c a l i n g . of  the  it  would  are  the  below  these other are  thin hand,  as  is  solid  patches  this  these  type  of N,  obscuring  that  many  are  much  of  full  25 meter large  made o n l y  done i n F i g u r e s  for  represent  16.  As d i s c u s s e d i n C h a p t e r  type  of  the data  below  relation  large  e a N  mean s h e a r  300  1  meters  are in  4,  100  inappropriate.  the  meter  the  upper  The p l o t t e d d a t a  over been  arguments internal  surface  would seem t o d o m i n a t e the  have  b a s e d on  the  the  16, 29 and 3 0 .  e and N w h i c h have t h e n been a v e r a g e d data  25  S and N  locally  the  of  S and  dominate the  the e s t i m a t e s  squares  those  associated  meters,  best  e  e measurements.  200  is  the  of  support  d i f f e r e n c e d over  comparison  e  N.  from  not  resolution  r e s o l u t i o n of  was d e c i d e d t h a t p l o t t i n g be  values  Only  Since  equatorial  generation, values  of  smaller  in Appendix K i n d i c a t e s  But  the  small  making  spatial  especially  the  S and  e values  in  of  Similarly,  dissipations  substantially  16,  the d r o p s .  included  data  parameters  averages  small  25 meter  calculated  gradients.  of  the  On t h e  e.  thereby  vertical  the  sizes,  intervals,  In  the  values  indistinguishable  limitation  25 m e t e r s .  meter  heavily  > 2 but are  t h e much f i n e r  glance  largest  no t r e n d a l t h o u g h t h e  bin-averaged  due t o  the  associated with small  significant is  however,  S and N and s m a l l R i .  Certainly,  1.  A  comparison  all  is  a s s o c i a t e d w i t h Ri  for  Ri  Generally,  layers  turbulence 300  meter  do not  differ  98  substantially slope  =  1  f r o m t h o s e of gives  previously  a  noted,  the  reasonable  the  PEQUOD  averaged  d a t a measured to d a t e ,  activity  in  the  29 nor or  the  shear  values  of  to  the  are  the In  e,  the  intervals  quite  a s do t h e  of  e  upper  w a t e r s due  shear  due t o  over  are  internal  the d a t a .  As  the  smallest  of  turbulent  equatorial  Pacific.  Neither  trends  high levels  at  is  (in  15 and  of  the  apparent.  Figures of  Ri  u p p e r 300 The  upper  and s u b s t a n t i a l l y  larger  values  it  there  100  of  not  Ri.  Of c o u r s e ,  s u r p r i s i n g that  But  at  is  to the In  calculated  greater that  due  these  is  over  a  strong  25 meter  depth.  The  depths the  of  from the  scaling  internal  there  be  depth  vertical  measurement situation  t h e mechanism by w h i c h  distinct  the  to  by t h e W h i t e H o r s e  isolation  fact,  due t o  waves,  is  appears  meters  resolved  generated  in part  turbulence  on S,  and we b e l i e v e  strong thermocline. the  Ri  300 m e t e r s .  is  of  e plots.  quite  three  e on b o t h S and R i  different,  turbulence  central  and h i g h s h e a r  are  300 m e t e r s ,  and a v e r a g e d the  represent  successively  lower  of  of  line  values.  upper of  vs for  low R i  exhibit  dependence same  the  S and R i  for  description  A  as was done t o p r o d u c e F i g u r e s  expected trends values  dependence  i n the  but  sets.  indicating a dearth  strong evidence  shear,  meters),  scales  generate  30 o f f e r  low  three  averaging  data  data  d e e p e r w a t e r s of  Identical 16 was done t o  other  waves.  little  deep e a N If  chance  r e s o l v e d by t h e W h i t e H o r s e m e a s u r e m e n t .  that  1  in  water  the  is the  upper  by  the  has h i n t e d  that  the that  turbulence  is  the  is  shear  As was m e n t i o n e d  in  99  LOG S  Figure  29 -  (1/sec)  P l o t of l o g e v s l o g S, where e and S have been vertically a v e r a g e d o v e r 100 m e t e r i n t e r v a l s and t h e n o v e r a l l of t h e PEQUOD d r o p s with synoptic Camel I l l - W h i t e H o r s e d a t a .  100  io-  PEQUOD  CD  10  "  5-  o  -  8 3  10"«  CD <  o 10  ' T  10 - 1  1  1  1  1  I  l •  10° LOG  Figure  30  -  I  I  !  1  1  1  • 1 l"T  10  RI  P l o t o f l o g e v s l o g R i , where e a n d R i h a v e been vertically a v e r a g e d o v e r TOO m e t e r i n t e r v a l s and t h e n o v e r a l l o f t h e PEQUOD d r o p s with synoptic Camel I l l - W h i t e H o r s e d a t a .  101  Chapter  5,  wavenumber spectrum  Gargett limit  to  et the  internal  corresponding  Eriksen(1978)  indicate  al.(l98l)  to  provide evidence  for  an u p p e r  wave h o r i z o n t a l v e l o c i t y  ten meters while  breaking at  shear  t h e measurements of  vertical  scales  of  several  meters. One  may s p e c u l a t e a l i t t l e  on S and R i . 2/7 e  on t h e  relative  7 a B e a N, e a S and e a R i ,  If  then  d e p e n d e n c e of  e  Ri  =  N /S  2  a  But  it  has  been  implying  that  2/a .  A  This  requires  \/B  2/7 - 2 / a .  =  proposed that  7 = 1 and a p p a r e n t l y ,  0 < a <  e has a s t r o n g e r d e p e n d e n c e on N t h a n  1,  or  Two f a c t o r s depths  greater  dynamic  range  huge e r r o r 6.7  intervals 1/4,  1,  Of Ri  are  large  31  N  intervals,  The c h a r a c t e r  larger  dynamic  vertical  exist  data  (especially  for  more f r e q u e n t l y  One  of  And t h e  values  of  S.  b o t h S and R i these  other  is  is  the  due  at  small  to  the  Ri.  And e and  4 have been p l o t t e d  there  thereby  t r e n d s of  meters.  S  plotted against  waters,  lines  300  in estimating  depth  drop.  than  Figure  B < 0,  t e n d t o o b s c u r e any  in both parameters.  Statistics In  by  2  calculated each o t h e r .  for  reference.  The  25 meter diagonals'  The d a t a a r e  20 - 300 m e t e r s and 300 m e t e r s of  each  is  quite  ranges points Ri>l)  of  at  least  have  been  that,  in  of S  joined  the  by i n c r e a s e d S r a t h e r  N if  and  than  In  grouped  upper  S  and  also  Successive  Ri  reduced N  h o r i z o n t a l than v e r t i c a l .  =  the  these  upper w a t e r s ,  Ri  In  not N.  and  depth  - bottom of  distinctive.  both higher values  a r e more n e a r l y  over  indicate is  reduced  since the  deep  the  102 i  F i g u r e 31 -  S c a t t e r p l o t s of l o g N v s l o g S e s t i m a t e d over 25 meter i n t e r v a l s f o r the depth ranges noted i n the p l o t s . Adjacent v e r t i c a l p o i n t s a r e j o i n e d .  103  waters,  no  indicates  pattern  many v a l u e s  r a n g e most v a l u e s  of  are  the  plotted  on  is  obvious.  of  l/4<Ri<1.  Ri  are  The In  greater  same p l o t  20  the  than  -  300  4.  labelled  300  meter  meter  -  plot  bottom  T h e s e two d a t a  20 m e t e r s  sets  - bottom  for  comparison. The c o m p l e t e Figure to  the  32.  range  regimes  wave  array.  3<Ri<l0.  Very  calculation,  These Ri the  counted. that  to  averaged  create  available 3<Ri<lO. less  Ri  by  the  PEQUOD d a t a  was  data  values  the a l t o g e t h e r  to  data  are  <0.25  these (30.5%)  partly  1000 when S  25 meter  depth  in  similar  from  his  different  should  not  be  lies  the  bin  in  artificial,  since  in  approached  zero  to  intervals.  w h i c h had e g r e a t e r  each  of  e less  e < noise  curve  smoothly v a r y i n g  errors  differ  from  and t h e  percentage  data  than curve  As one m i g h t e x p e c t ,  in  the  is  10"  8  noise  In  W/m  each Ri  3  level  33 d i f f e r s .  were  (again,  note  are  obtained  data than  in  the  30% was why t h e  others.  Also,  bin,  value  Less  likely  to curve  associated  The amount o f  w h i l e more t h a n  of  error  the  level).  in Figure  0.1<Ri<0.3 lack  than  the  than a g i v e n  were t h e n n o r m a l i z e d a t  values  This  due t o taken,  be  were t h e n g r o u p e d a c c o r d i n g t o  e = 0 if  for  set  Ri  remarkably  to  the  of  is  shown  found  were of  This  is  zero.  These  by s e t t i n g  Most  respective  number of  data  high values  avoid d i v i s i o n  the  However,  from w h i c h t h e further.  e over  for  Eriksen(1978)  compared  the  Ri  About 2.7% has R i < 0 . 3 .  2.5% t h a t  internal  of  used 3%  was  range  upper c u r v e the  due t o b o t h t h e  relative  sample  size  Ri.  relatively  more v a l u e s  of  is  e above a  104  t-  !  Hi-t/4  Ri«1  i  Ri»4  LOG R i  Relative frequency of occurrence of log Ri e s t i m a t e d from the White Horse data taken in February, 1982 over the depth ranges c o i n c i d e n t w i t h Camel III data.  i  i  105  \  -7  -6 LOG  F i g u r e 33  -5 e  -4  (»/•»);  Normalized frequency of occurrence of l o g e per half decade i n t e r v a l f o r the ranges of R i noted i n the key.  106  given value  exist  the  relative  of  Figure  lower ~oThTe r.  two  for  levels  33.  At  curves  the  lower  values  and r o l l o f f s larger are  Ri,  of  the  of  Ri,  as  is  constant  Ri  the d i s t i n c t i o n  virtually  is  e x p r e s s e d by bin  curves  b l u r r e d and  indistinguishable  from  the each  1 07  VII. A  serious  dynamics  is  temporal grid  ESTIMATES OF EDDY COEFFICIENTS problem  the p a r a m e t e r i z a t i o n  and/or  s i z e of  oceanic  spatial  the model.  flows  modellers  are  require  can  be i n c l u d e d i n  (for  the  values  of  the  circulation mass  (momentum  be  greater  relative  fine  of  due  must  coefficients  (for  the  time  be  grid  requiring  surface  the  scales  have  step  of  to  the  In  a  the  size  is  reduced  effects  turbulence. from  effects this  and  fashion  molecular  fluid  itself,  field.  scale  As the  ocean  of momentum and  horizontal),  waves  vertical  least  or a t  coefficients In  models  o c e a n and w h i c h model of  mixing  is  In  chapter,  this  is  eddy  reduced the e d d i e s  equatorial  vertical  the  large  eddy  the  of the  considered in  turbulence. of  the  flow  carefully  (mostly  the  to  or  smaller  Generally,  contrast  (mostly  layers  estimated  at  momentum)  peculiar  turbulence  the  which  u s e d i n an a n a l o g o u s  In  eddies  g r i d such as  to  fluid  Essentially,  motion.  properties  As t h e  and P h i l a n d e r ( 1 9 8 1 ) , entirely  which are  d e p e n d e n c e on t h e  on t h e  vertical  to  and  resolved  concentrate  are  due  of  and a means by w h i c h t h e s e  model one must c o n s i d e r  only)  than  sinks  t o be m o d e l l e d .  isopycnals).  well  eddy  energy  equations  used  flow  transport  across  of  and K , w h i c h a r e  v  motions  smaller  counterparts.  eddy c o e f f i c i e n t s  context  a  the  mass),  molecular  coefficients,  such,  those  i n t r o d u c i n g an eddy v i s c o s i t y  their  modellers  The p r o b l e m s p r e s e n t e d t o m o d e l l e r s  m o d e l s can r e s o l v e  diffusivity  the  scales  estimates  their  to  of  by  d i s c u s s e d by G a r r e t t ( 1 9 7 9 ) .  than  done by  encountered  and a which  require  Pacanowski  expected  microstructure  may  to  be  a number of data  are  108  compared  using  Gregg(1976) averaged to  that  7.1  the  and  of  (as  production, written  j  of  for in  /9x  f  = -  as  e -  the  involves  done a g a i n s t  the  energy turbulent  buoyancy,  and  p'w'g/p.  (7.1)  ratio  of  into the  the  flux  buoyancy  Richardson flux  to  g'p^T /(pu u 9u /9x ) i j i j r  = -K 9 p / 9 z  = K  P  the  r  P  With  T  above  pN /g, 2  P  r  the  (7.1),  (7.3)  2  coefficient (7.2),  for  the  and ( 7 . 3 )  the  energy  vertical  the  relation  diffusion for  K  P  is  (7.4) 7  recommends an u p p e r bound of which  (7.2)  r  = gJ V /(pH ),  represents  density.  ,  work  2)  kinetic  J  =  Osborn(l980) f  turbulent  Chapter  K = R / ( 1 - R ) e p f f N  R  the  t e r m s may be i n c o r p o r a t e d  K  P  p r e s e n t e d and compared  production,  p'w'  where K  heavily  set.  balance  i  defined  R  Since  is  A  as  these  turbulent  Osborn(l980)  measurements.  eddy d i f f u s i v i t y  d i s s i p a t i o n and t h e  i  number,  PEQUOD  discussed  u'u'9u Two of  Crawford(1982),  Estimators  An a c c e p t a b l e  is  1982  t h e WESPAC d a t a  Various  equation  of  the  profile of  results  going  0.15  into  for  the  value  the buoyancy  flux  of is  109  sufficient  to  requires estimate  K of  suppress <  P K  0.2e/N .  turbulence. Oakey(l982)  2  from t e m p e r a t u r e  P  t o be d e f i n e d s h o r t l y ) to  the  be 0 . 2 6 ± 0 . 2 1 .  to  differ  significantly,  two e r r o r  e,  factor  study.  The  the  estimated  K /(e/N ) P  0.2  given  will  p will  an  estimates the  = 0.15  on  of  factor  R /(1-R f  T  ,  of this  ) = 0.2) f  h e n c e f o r t h be d e n o t e d as K . 0 A smoothed e s t i m a t e  which  was  originally  discussed  To with the  G  of  K  is 0  o b t a i n e d by  in Chapter  s u g g e s t e d by K  4.  invoking  Calling this  K  G  e = (as  =  0.2a /N  the  turbulent  eddy v i s c o s i t y  velocity  case, and  viscosity.  K  u  eddy  viscosity,  V  With  represents is  (7.1)  0  was  (7.5)  o  estimate  this  it  a N,  Gargett(1984)),  defined  K , V  (7.1)  is  again  then and  used  as  K = u'w'/Ou/3z). V In  (K  O s b o r n and  through for  (or  f  estimates  estimated  f  R  independent  measurements  be c a r r i e d  K , with R  limit  w h i c h he  2  independent  Oakey do n o t in  makes  microstructure  estimate  S i n c e the  This  (7.6) the  the  m a g n i t u d e of  vertical  the  coefficient  horizontal of  eddy  (7.2),  K = e/(.1-R ) S V f  2  (7.7)  110  Using  the  u p p e r bound of  R  = 0.15,  K  f The a v a i l a b l e  < 1.2e/S . 2  V  measurements a l l o w  estimates  t o be made o f K 0  and K  G  from t h e WESPAC d a t a  With estimate heat,  measurements  of  c a n be made o f  the  K . T  r e p o r t e d here to  estimates  and K  and K  G  coefficient  temperature  but  the  K  , K  temperature  No  of  0  V  microstructure,  of  vertical  microstructure  coefficients  f r o m PEQUOD.  in  the  d i f f u s i o n of  measurements  d i s c u s s e d above  made by G r e g g ( l 9 7 6 )  an  are  are  compared  equatorial  Pacific  T and  Osborn  Originally  and  Bilodeau(1980)  derived  on  a  form  of  the  p r o d u c t i o n of  the  destruction  in  the  equatorial  Atlantic.  by O s b o r n and C O X ( 1 9 7 2 ) , t h e model  the  temperature  temperature  variance  variance  is  e q u a t i o n which  by t h e  buoyancy  based  balances flux  and  by m o l e c u l a r d i f f u s i o n , w~ T 9T/9z r  The eddy c o e f f i c i e n t  r  for  = -K( 9T'/9Z) . 2  vertical  d i f f u s i o n of  heat  is  defined  by K so  = -w~ T /(9T/9z) r  T  „  T  (7.8)  that K  Having conditions  = K(9T'/9Z) /(9T/9Z) z  T  derived of  the  estimates  applicability  for  (7.9)  2  K ,  K ,  K ,  0  G  T  each  must  be  and  K  the V  stated.  The  111  balance  equations  temperature  variance  advection. small  for  the  equations  turbulence  the  upper  turbulent  have  These c o e f f i c i e n t s  scale  Further,  used  must o n l y  of  energy  and  effects  of  be a s s o c i a t e d w i t h  the  excluded  causing l o c a l bound  kinetic the  cross-isopycnal diffusion.  R  has  been  inferred  from  f measurements  of  instabilities. account K . V  for  In  turbulence  As O s b o r n ( l 9 8 0 )  double d i f f u s i v e  estimating  arguments  in  shear  f l o w s and  notes,  the  Kelvin-Helmholtz  estimate  relegating  cannot  O  mixing.  The same must be t r u e  K , an a p p r o x i m a t i o n b a s e d on G  has been made,  K  the  use of  for  internal K  wave  t o deep o c e a n  G environments thought  surface  C o m p a r i s o n Of A  and K  V  where t h e  t o be i n t e r n a l  equatorial 7.2  only,  Table  5.  For  from  averages  was  estimates  of  of  vertical  equatorial  Atlantic  1982 d a t a ,  over  dissipation  K  from  the  eddy c o e f f i c i e n t s and  ranges  those e q u a t o r i a l  Pacific shown a r e  of  is  such  as  of  by the  Crawford(1982) turbulent  are  0  is  G  T  shown  in  estimates  it  from  a  energy  does  made White  drop  thermostad.  used  kinetic  1/(1 —R ) a p p e a r s as f  K , K , K  drops with concurrent  The t h e r m o s t a d e s t i m a t e s  made  V  source  regions  only drop with a well-developed  balance  h e n c e no f a c t o r  away  the  the  the  and  energy  Estimates  Horse measurements. which  waves,  turbulent  waters.  comparison from t h e  dominant  in  14 The  productionequation  (7.7).  and  Pacific.1982  Pacific,1979 Crawford*1982)  K  above  core  .003-.09  core  below  core  thermostad  below  1 .-5.  300m  .05-.07  .007-.2  1 .-100.  .1-10.  .03-.2  .0007-.2  .02-.07  .02-.3  1.  .1  1.  .002-.9  .05-.5  Table  5 -  .8-40.  Atlantic,1974  Atlantic.1974  Pacific.1972  Crawford(1982)  Osborn(1980)  Gregg(1976)  K  1 .-100.  .2-1.  1 .-10.  .02-.6  .8  8.-40.  .1-4.  1.  4.  .015  .3-3.  (2x1)xU9  (2±1)x.0l  >5.  <50xmolecular  (2±1)x(.04-.2)  .15  .02-100.  Comparison of vertical eddy coefficients (in u n i t s of c m / s e c ) f o r f i v e different equatorial data sets. The m o l e c u l a r v a l u e f o r t h e t h e r a m l d i f f u s i v i t y of water i s = 0.0015 c m / s e c . 2  2  value  113  Crawford's  estimates  would be 20% l a r g e r  w i t h the  buoyancy  term  included. Osborn(l980)  finds  good agreement  between  K  and K  in  and  these  also  0 above agree  the  EUC c o r e  w i t h the  from t h e A t l a n t i c .  estimates  of  K  made  T  Furthermore, by  Gregg(l976)  in  the  one t o a g r e e  with  T Pacific  i n and above  Munk(l966) properties  that are  t h e EUC c o r e .  the  the  eddy  leads  coefficients  same.  It  a s s u m p t i o n s made t o d e r i v e  This  for  also  gives  and  (7.9).  (7.4)  different  confidence  scalar in  The e s t i m a t e s  the given  for the r a n g e s of  Pacific, 1982 d a t a and f r o m C r a w f o r d ( 1 9 8 2 ) represent K and K . R e f l e c t i n g t h e l o w e r v a l u e s of e f o u n d in 0 V Pacific i n 1982, K i s s i g n i f i c a n t l y l o w e r t h a n . a n y of t h e  the  0  other  estimates  of  K  and K . 0  core, for  the  lower  when m o l e c u l a r The  at  heat,  effects  derivation  fact,  in  and  below  the  EUC  T  bound i s  t h e d i f f u s i o n of  In  or  smaller  implying that  may r i v a l of  K  the  relies  than  the m o l e c u l a r  there  may be  turbulent  value  occasions  fluxes.  on an a s s u m p t i o n of  internal  G wave d e p e n d e n c e w h i c h c a n n o t upper  equatorial  than K below than  0  except the  those  at  core  waters  and,  d e p t h s below from the  smaller  as  values  hold  expected, K  300 m e t e r s .  Pacific,  from the A t l a n t i c ,  considerably  be e x p e c t e d t o  1982 a r e  G The  is  much  values  considerably  1974 a n d , as has of  true  been  e were f o u n d below  in  the  smaller of  K  V  smaller  discussed, the c o r e  in  1 14  the In  Pacific  i n b o t h 1979 and  and above t h e EUC c o r e ,  sets  is  quite  Figure  1982 t h a n  i n the A t l a n t i c  t h e agreement  between  the  in  1974.  three  data  good. 36  shows t h e  25 meter a v e r a g e d e s t i m a t e s  of  K  for 0  the  eight  upper  equatorial  values  (20-70 m e t e r s )  minimum  values  smaller  or a b o u t  associated local  in  minimum i n (see  the  10K.  with  500 m e t e r s  profiles  of  are  PEQUOD (open c i r c l e s ) . between  c o r e of  Figures  just  the  above t h e  25 and 2 6 ) .  Below  two  cm /sec.  The  2  of  ten  400 m e t e r s  is  t h e r m o s t a d and  the  minimum a t  maximum i n N below  e which o c c u r s  2  t h e EUC a r e . t w o  The d i s t i n c t i v e  the  1 and  The  factors  local  maximum  500 m e t e r s ,  K  at  ranges 0  from 0.06 t o In  0.1  Figure  cm /sec. 2  34  the  were u s e d t o g e n e r a t e K  G  is,  from t h e of  The l a c k  c o u r s e , due t o t h e  this  resolved.  profile  The deep v a l u e s  e and N p l o t t e d  of  of  0 400 m e t e r s  Figure  agreement above  K  t h e agreement  the of  K  16  averaged estimates  surface and K  0 900 m e t e r s .  in Figure  d i f f e r i n g assumptions i n v o l v e d  Below 400 m e t e r s  averaged  of  more h e a v i l y  PEQUOD d a t a .  two e s t i m a t e s . In  values  is  are  about  in  quite  currents 0.1  and  the  good.  are  poorly  cm /sec 2  at  G  35 i n c l u d e s s i m i l a r l y  derived p r o f i l e s  from  WESPAC c a l c u l a t e d from t h e e and N v a l u e s of F i g u r e s 1 4 a , b . At 900 m e t e r s , K and K a r e s l i g h t l y g r e a t e r than 0.1 cm /sec. 0 G The greater values of K and K a r e e x p e c t e d i n l i g h t of t h e 2  0  greater  turbulence  levels  from the  G  d e e p e r w a t e r s of WESPAC and  115  V e r t i c a l p r o f i l e s of K  0  (equation  7.4)  and  K  G (equation 7.5) f o r the PEQUOD d a t a , e and N were averaged v e r t i c a l l y over 100 meters and then over a l l of the p r o f i l e s .  t/1  w  117  incorporated Below  into  900 m e t e r s ,  below  2000  K  coefficient steadily  0  meters,  representation 7.3  the  Deep Ocean  of  a  estimated  0  increases  assuming  that  K  from F i g u r e ,  and i s is  G  about  0.5  truly  a  16.  cm /sec 2  smoothed  K . 0  Estimates  The deep e s t i m a t e s  of  K  approach that  of  Munk(l966)  who  P  estimated  a  constant  value  of  K  t o be a b o u t  1 cm /sec 2  in  the  P  d e e p o c e a n from a b a l a n c e upward  advection  downwards  of  of  lighter  dense water. wp  where  the  subscript  the  vertical  Gargett(1984)  z  the  assumed  z  and t h e  - (K  between  turbulent  the  diffusion  can be e x p r e s s e d as  p ) = 0, p z z differentiation  z.  This  may  be  with respect rewritten  to (and  as  (w-(K  K  equation  The b a l a n c e  coordinate does t h i s )  density  water  z represents  p Munk(l966)  of  ) ) - K p =0. p z p zz  t o be a c o n s t a n t  value  i n the  deep  ocean  P  between  1 and 4 k i l o m e t e r s  With the By  estimates  estimating  and  assuming  of  the a  of  averaged  upwelling  (K  ) is p z  Figure r a t e of  uniform  remainder  the w o r l d ' s  estimated  in order  to  35 t h i s  simplify  f o r m a t i o n of  Antarctic  (rising)  o c e a n s , Munk(1966) w,  of  1x10"  from t h e v a l u e s  at  analysis.  a s s u m p t i o n may be c h e c k e d .  spreading  speed,  the  5  rate  Bottom Water over  estimated a  cm/sec.  the  globally  From F r g u r e  500 and 2000 m e t e r s  to  35, be  118  0.3  cm /sec  in  Munk's value  for  2  estimate  1500  meters  or  w and d o e s n o t  made f o r  K .  2X10~  affect  A point  to  cm/sec.  6  the  note  This  order  is  that  of  is  20% o f  magnitude  a constant  (K  P = 2X10~  cm/sec  6  ) P z  gives  a value  of  K  =1  cm /sec  at  2  5000  meters.  P The  indication  is  that  K  increases  with  depth.  A  quick  P calculation,  though,  mean t h a t  mass  the  shows  flux  that  this  increases  with depth.  p "* " = -K 7  t r e n d does not  necessarily  The mass  flux  is  p .  7  P z W i t h the  estimate  K  for  K ,  G  p p'w'  but  N  2  = -gp /p so z  T  7.4  o  authors  a  o  d e c r e a s e d mass  recent  express  vertical model o f viscosity  the  paper  the  mixing,  need  K  vPP  rPP  a  + K  Values and P h i l a n d e r ( 1 9 8 1 )  proper  as  it  The  parameterization  applies forms  to  used  their for  the of  numerical the  eddy  are  = 1 + 50/(l+5Ri)  = 0.1  with depth.  Model  for  ocean.  and d i f f u s i v i t y  flux  by P a c a n o w s k i  especially  tropical  K  /N  = 0.2a pN/g  T  Comparison With E q u a t o r i a l In  z  that  p w which, i n d i c a t e s  = -0.2a p  vPP  2  /(1+5Ri)  (7.10) (7.11)  119  In  Figures  K  and K  6  to  V  36 and 37 t h e v a l u e s  of  estimated  and  evaluate  profiles  K  and  rPP  of F i g u r e s  The  from  nearest  K  (7.4) is  vPP  K  rPP  and K  (7.7).  by a b o u t  compared t o  The v a l u e of  calculated  from  the  Ri  N  used  and  S  24 and 2 5 . surface  values  of  K  and K rPP  low  are  vPP  a factor  of  4-5,  likely  are  each  too  vPP  due t o t h e  inability  of  the  R i - d e p e n d e n c e t o a c c o u n t f o r t h e wind mixed l a y e r . The v a l u e of K i n t h e l a r g e s h e a r r e g i o n above t h e EUC c o r e i s more n e a r l y rPP equal  to K  than K In  factor be  beneath t h i s , least  r e g i o n of of  in  but,  by a t  rPP  the  0  six.  the  and t o  300 m e t e r s ,  a factor  of  EUC c o r e  itself,  The a s y m p t o t i c  good a g r e e m e n t  is  0  smaller  two and up t o a f a c t o r the d i f f e r e n c e  v a l u e of  with K  K  0.1  cm /sec  is  of  ten.  about a  appears  2  but a s d i s c u s s e d a b o v e ,  to  we e x p e c t  0 K  0  to  increase  minimum  at  with depth.  400 m e t e r s  K and K agree 0 rPP Richardson  i n the  number  The c o n s i s t e n t l y  It  is  is  known w h e t h e r  anomalous.  upper water  dependence  greater  not  In  of  the  the  K  right  sense  compared  to  1982  be  of  which  Certainly,  great may the  c o n c e r n due t o represent  values  of  K  an are  rPP  shapes  the  for K K  rPP not  strong  column i n d i c a t i n g t h a t  gives  values  general,  the  of the  rPP  should 0  lower  anomalously in better  estimates low  of  data  agreement  with  e from set. the  120  EDDY D I F F U S I V I T Y 10 -2 •'  r  IO'  '  '  •  1  I  ( c m / s e c ) '} 2  10  10<  I I I  I I I III  200-  Vs (0  400  TJ tx D tn in  ca cu 6 0 0  K  -  0.2*/**  o  K  rPP  - 0.1*K  /(»*5Ri)  vPP.  800  1000-  Figure  36 -  -i—i  Vertical K  i i 11 i n  profiles  (equation rPP  i  i i i i 11 II  i  i i i Ii n  o f 25 m e t r e a v e r a g e s o f K  7 . 1 1 ) f r o m PEQUOD.  0  and  121  EDDY VISCOSITY 10" 0  10"  2  . -  j  i  .  (cm /sec) 2  10°  1  i . i..i  i — i  10  1 1 1 1 1 i i — i — i  i i . i i  2004  u to  4>  400  ca  «  R  in  R  LO Ed  a.  v  vPP  -  1.2f/S*  • i+50/( 1+5RD*  600  8001  1000  Figure  37 -  Vertical  i  profiles  i 111  1  1—i i  i  i  i  11  1  r-  o f 25 m e t r e a v e r a g e s  of K  and V  K  (equation . . n n  vPP  7.10)  from  PEQUOD.  122  other  estimates  upper  equatorial  of  Table  ocean,  reasonably w e l l .  5.  then,  However,  In  the  the Ri  large  shear  r e g i o n of  dependence appears to  we e x p e c t K  to  increase  with  the  agree  depth.  0 In K  vPP  .  Figure But,  than  K  vPP.  37, the c u r v a t u r e  b e s i d e s the very  )  at  75 m e t e r s ,  two agreement  (this  estimate  of  K V  itself,  the  core the  data.  is  of  R'  V  low v a l u e  actually of  the e s t i m a t e s  better  than t h e  Below t h e c o r e ,  of  K V  (factor  are  within  5e/e  to  Perhaps,  the A t l a n t i c  different  eddy c o e f f i c i e n t s . t o be t o o  low.  that ten  of less  a factor for  1 ) .  In  K  the  2  i s much g r e a t e r  than K  estimate  but  EUC of is  V of  Crawford(1982)  oceans r e q u i r e d i f f e r e n t The a s y m p t o t i c  of the  1-2 c m / s e c a g r e e w e l l w i t h a l l  vPP closer  of  estimated error  when one c o n s i d e r s t h a t estimates  mirrors  value  of  in Table  parameterizations K V  at  depth  5. of  appears  123  VIII.  COMPARISON OF DATA SETS AND PATCH S I Z E  Some s t a t i s t i c s are  presented  for  o f e and t h e d i s t r i b u t i o n  in  this  chapter.  c o m p a r i s o n o f t h e two d a t a  w e l l as to other  data  sets  of the  These p r o v i d e  sets  already  involved  STATISTICS  in  in existence  turbulence  a common g r o u n d this  study  as  and t o t h o s e y e t  t o be c o m p i l e d . Table ranges  heavily  averaged  f o r PEQUOD,  WESPAC,  slope data  the r e l a t i v e l y  1000 For  meters  7  is,  range of d a t a 3  range  from  current  W/m  3  greater  The  four  due t o t h e  times  near  range  also  of  eight  averaged greater  over  (20-300  times  larger  eight  the  Vancouver  enormous the  the  Because than  range.  meters), than  This  influence equator.  of While  7  25-500  large the  almost  28%  turbulent  column  that,  being  turbulent  . 3 9 f o r WESPAC 2 0 - 3 0 0 ,  50%  e are > 1 0 "  6  from  a s w e l l as a  turbulent,  portion  value  surface  of  are  is  e from the  estimates  7/PCT i n d i c a t e  water  for that  (compare 7/PCT = 1.7 f o r PEQUOD  PEQUOD 300-1000,  the depth  times 7 from  Island slope data.  ratios  the  e over  from d e p t h s g r e a t e r  from PEQUOD  from PEQUOD, o n l y  relative  portion  dissipation  and  are given  o r PCT) o f t h e i n d e p e n d e n t  from t h i s  WESPAC.  no r e s u l t s  from WESPAC and a l s o  structure  (%turbulent  of  Crawford and O s b o r n ( 1 9 8 3 ) .  i s about  the Vancouver  of c o u r s e ,  values  s m a l l amount o f d a t a  W/m , w h i c h  comparable meters  of L u e c k ,  from PEQUOD,  the upper  85x10"  for  lists  indicated  Island of  6  the  i s more  than  20-300,  .47  .42 f o r WESPAC 300-  124  20-300m  300-1000m  >1000m  20m-bottom  PEQUOD quantity of data (dbar)  37B0  8015  *(W/m') xlO  85.  %turbulent (>10-*W/m')  49  10  2180  5085  540  4.7  12335  35.  7  21  WESPAC quantity of data (dbar) e(W/m») xlO  11.  %turbulent  28  5805  9.2  3.8  13070 6.5  7  VANCOUVER e(W/m») xlO'  Table  6 -  ISLAND SLOPE  22  12  25-500m  19  >500m  10.  Average values of e f r o m PEQUOD a n d WESPAC d a t a s e t s compared t o V a n c o u v e r Island slope values from Lueck, Crawford and Osborn(1983). These v a l u e s may s l i g h t l y u n d e r e s t i m a t e t r u e v a l u e s of e s i n c e n o i s e l e v e l s were s e t = 0 . T h e q u a n t i t y o f d a t a r e f e r s t o t h e t o t a l amount o f d a t a taken i n each depth range.  1 25  1000,  and  .32 f o r WESPAC >1000  More  interesting  is  f r o m WESPAC i s  twice that  Island  data  slope  for  the  meters). range  from PEQUOD and a l s o o f the  a s > 500 m e t e r s  1100  The  because the  reason  t w i c e a s much of  relative  values  (these  for  include  the  large  t h e water column  of  of  the  set).  e  =  This  e/PCT a r e  about  of  range  second  maximum  are  column i s  turbulent  estimates the of  turbulence  of  vertical In  N)  substantially  made  still  meters  is  meters  from t h e  Vancouver  the  but  drops  of 7 h e r e  to is  (since  f r o m PEQUOD and  Vancouver  interesting  Chapter  4.  appears  that  higher,  Crawford  turbulent  f r o m WESPAC ( i n  higher  thw WESPAC  Island in  light  From the  the  the  values  range  not b e c a u s e  of  individual  b e c a u s e more of  data  show  (3.8x10" W/m ,  which  noise  However,  3  level).  exists  at  than  depth  indicating  a slightly  turbulent  it  which e  the  water  .  profiling), fact,  are  6  instrumental  quiet.  in  1000 m e t e r s , yet  follow,  300-1000 m e t e r s  estimates  Below  6 and t o  in  value  equal  particularly posed  0  in Table  the  is  a N— r e l a t i o n  information e i n the  fact  the  three  is  WESPAC, a l t h o u g h PCT was not computed f o r slope data  for  range d e s i g n a t e d by L u e c k ,  and O s b o r n ( l 9 8 3 ) meters).  300-1000 m e t e r s ,  that  greater  i n the  equatorial  (^  data.  is  the  only  marginally  a considerable  12% of  almost  the deep  fraction  shallower  smallest  7  above amount  6000 m e t e r s  ocean  is  not  f r o m WESPAC > 1000  depth  range  300-1000  1 26  8.1 L o q n o r m a l P r o p e r t i e s It  has been p r o p o s e d by G u r v i c h and Yaglom(1967)  others  that  random  variables  Stewart,  small  atmosphere spatial  and  over  used  of  Lueck  properties indicate  the  values  of  of  e  quarter  than  line  paper  indicates  that  l o g a r i t h m of the follows  a  Similarly, variable  function P(y)  over a  above  the  the  values. lognormal  and t h e i r  data  lognormally.  The c u m u l a t i v e  in  6  were  frequency  Figures  of o b s e r v a t i o n s  on  with  normal  variable  values  a straight  line  that  distribution.  = exp[ - ( l n ( y ) - ) / 2 a 2  a normal fit  the  of the random  The form o f t h e  (from S t e w a r t ,  M  probability  follows  indicates  is  38-42  i n d i c a t e d on t h e h o r i z o n t a l  data  random  lognormal  distribution  B u r l i n g d 970))  to that  of the  the  random  squares  e behaves  point  percentage  fit  their  d e c a d e was computed a n d p l o t t e d on Each  equal  distribution.  which  the  both the  expected  presented  intervals.  paper.  or  of  from e a c h s u b g r o u p i n T a b l e  decade  A straight  probability  the l a r g e s t  and  that  sufficiently  are ranges over  axis.  variable  is  b u t below  the cumulative  probability  and  t h e wind-mixed l a y e r  there  layer  indicates  e i n and below  probability  less  work  briefly  that  represents  boundary  Stegen  e ) have l o g n o r m a l p r o p e r t i e s  o c c u r r e n c e of each q u a r t e r  normal  distribution.  Gibson,  velocities  which  level  and  as w e l l as  s u c h as e a r e  lognormal  Osborn(l982)  of  in  a  Their  of t u r b u l e n t  The d i s s i p a t i o n v a l u e s grouped  properties  turbulent  to c a l c u l a t e  noise  and  follow  the ocean.  their  instrumental  turbulent  Burling(1970)  studied  derivatives  are  range  scale which  Wilson  Williams(1970)  (as  Of e  2  Wilson ]/(2v)*oy  and  1 27  where u = l n ( y ) is  given  38-42  and a  are  plotted  as  (log(y)  u and a a r e  estimated e  mean  estimated  value  included.  that  e  is  is  n.  At  small values  of  is a d i s t i n c t of  the  occurrence plot  is  the  noise  data of  small  too s m a l l . . level  _7  of  the  fact,  the  was  Gibson, which found  is  discussed  Stegen  is  that  straight  line  fit  the data  of  the  the  follows  behaviour  of  6  level)  data  from  frequency  of  lognormal  truncated  that  is  each  noise the  the  are  they  at not  do not  high values  of  e and  and Lueck and O s b o r n ( l 9 8 2 )  and  3 8 , 40 and 4 1 .  e generally  very  few e x p e c t e d l a r g e  deviation  38-42 e x h i b i t line  and  and B u r l i n g ( 1 9 7 0 )  this  a straight  lines  and s m a l l v a l u e s  and  Figures  38-  in Table  the  is  to b e l i e v e  in F i g u r e s of  Figures  from the  problem e x i s t s at  values  to  natural  construct  The  the d i s t r i b u t i o n  Stewart, Wilson  apparent  the h i g h e s t  u n d e r s a m p l i n g of Each  by  is  e predicted  and W i l l i a m s ( 1 9 7 0 )  especially  which  3  Figures  from  In  y  For comparison,  level.  no r e a s o n  A somewhat d i f f e r e n t  which  of  necessary  y.  e used to  instrumentation  measured a l t h o u g h t h e r e exist.  the  noise  values  In  of  e (<3xl0 W/m  above  is  d a t a and l i s t e d  estimates  of  e in  straight  from t h e s e .  of  of  10 l o g a r i t h m s  plotted  from t h e  deviation  it  to c a l c u l a t e  from t h e  estimated  The number o f  values  10 l o g a r i t h m s ,  = 2.3031n(y))  0  the  u and a t o b a s e  t h e mean v a l u e ,  there  Since  base  The mean v a l u e  2  2  logarithms  plot  - ln(y) .  2  by y = exp[u + o /2].  change t h e p a r a m e t e r s  42,  = ln(y)  2  deviated  was  was  from  the  attributed  to  values.  ranges of  reasonably  It  well.  e over One  which  estimate  99.95 99.8 99.5 99 98 95  1  1 1 1 11 1 1  |  T  1 1 1 11 1  —1  I |  1  1—r  T  T  I  1|  1  — i — i — t » i i  1—  :  PEQUOD 20-300m  -  90 80 70 60 50 40 30 20 10  5 2 1  0.5 0.2  -  -  0. 05 10"  •  8  •  I  l  • • •  11 1 AJ 10  1  7  1  U  =  -6.05  a  =  .90  e  =  85x10" W/m  =  76x10" W/m  7  7  —  3  3  n = 1855  1  1—1 1 1 1  1  10•  .A.  1  1J.1  10 -  6  i  i_  i  i  l i l t .  5  LOG e (W/m ) 3  Figure  38 -  C u m u l a t i v e d i s t r i b u t i o n of the base 10 l o g a r i t h m of dissipation values from PEQUOD 20-300m p l o t t e d a g a i n s t n o r m a l p r o b a b i l i t y co-ordinates. The p a r a m e t e r s u and a a r e the mean and standard deviation of the natural logarithm of e, e s t i m a t e d from t h e straight line. e i s e s t i m a t e d from n and a. 7 i s the o b s e r v e d mean from T a b l e 6. The number of i n d e p e n d e n t 2 meter estimates of e i s n. 0  10 - o  M CO  Figure  39 -  Cumulative d i s t r i b u t i o n of t h e base 10 l o g a r i t h m of d i s s i p a t i o n v a l u e s f r o m PEQUOD 300-1000m.  Figure  40 -  C u m u l a t i v e d i s t r i b u t i o n of the b a s e 10 logarithm of d i s s i p a t i o n v a l u e s f r o m WESPAC 20-300m.  10-  10"  8  7  10"  10"  6  5  LOG e (W/m ) 3  Figure  41 -  Cumulative d i s t r i b u t i o n of the b a s e 10 l o g a r i t h m of d i s s i p a t i o n v a l u e s from WESPAC 300-1000m.  10"  4  Figure  42 -  133  of  the  degree  to which the  representative  of  made  line  the  from t h e  20-300m d a t a  dynamic of  the  sets  get  defined. have a t  the  This  statistics  stretches for  quite  instability  this  it  while  within  the p o i n t s  is  estimate  e  the  t h e mean v a l u e s  the  the  of  0  of  extended  PEQUOD d a t a .  a factor  distribution  contribution  patch  above, this  to  two  All  of  a  of  the  does p r o v i d e  spatially  turbulent  the  e > 10"  definition  is  an o b j e c t i v e  to d i s c u s s i n g the  for  of  single  a much l a r g e r  d u r i n g the  shear  some i n t e r e s t i n g  I n s i d e of  at  certainly criterion  e may change  2 meter The  of  Kelvin-  which  appear  initial  the  the  patch.  studies  Van D y k e d 9 8 2 ) ) ,  centre  large  (thereby  3  does not a c t u a l l y  lab  was  p a t c h must  independent estimates  occur within  the  averaged  W/m  6  patch  patch  a turbulent  but does a l l o w  (Turner(1 973), in  both turbulent  the  study,  second c r i t e r i o n  to  of  s i z e to ^ 2 meters).  successive  While t h i s  used to d e r i v e Prior  are  to  due t o  of  came f r o m l o o k i n g a t  stable  turbulence. rigorous  the case  considerably  Helmholtz b i l l o w s be  in  of of  likely  independent estimate  no two 3  motivation  best,  discussed  smallest  W/m .  quiet  The e s t i m a t e s  the  relative  one  itself, 6  t h e agreement  the purposes of  least  be < 1 0 "  i d e a of  values  the  fitted  Statistics  -For  limiting  line  values.  an  dissipation  to  are  however,  s i z e s and t h e i r  thick  e.  estimates,  To  the  with  is  especially  Patch Size  patch  the data  range,  o b s e r v e d mean 8.2  straight  edges  stages  suggests  not meant which  of  to  can  be be  comparisons.  contents  of  Tables  7-11,  the  means  134  of  deriving  turbulent their of  these are patches  vertical  patches  meters)  shown.  (as  scale  which  From  half  (t fell  in  each  Their  the  total  t h i c k n e s s of  data  subset,  relative  and t h e  each  (<3  , 3-10,  #Patches. order  The  number  These  of m a g n i t u d e  e a c h r a n g e by t h e  average  patch,  the over  multiplied  by  dissipation  over  the  Table  This  statistic,  and  size,  patch-averaged  summed t  patch  all  of  divided  entire  the by  data  ranges ranges.  t,  Total  dividing  data  (H)  was  computed.  dissipation,  in  e , t  the  was  patches  in  the  range,  where  e is  the  average  He  subset  lOOtle  total  to  10-30, >30  i m p o r t a n c e was e s t i m a t e d by  calculated,  5).  were s o r t e d a c c o r d i n g  Range  under  sets,  i n e a c h r a n g e were summed and l i s t e d u n d e r  Thickness.  Within  data  = t h i c k n e s s or p a t c h s i z e ) .  d e c a d e and t h e r e f o r e  The p a t c h s i z e s  respective  d e f i n e d above)  were c o u n t e d and l i s t e d  represent  the  (and  is  included  indicates  /(He),  the  in  relative  t contribution  of  dissipation. in a s i n g l e  each  The range  range  to  the  vertically  d i s s i p a t i o n averaged over is  and t h i s  e  isolates  all  the  integrated  of  the  actual  patches  magnitude  t of  values  e  (which i s which  is As  (Table  also  within  the  a f u n c t i o n of  range the  from t h e fraction  relative of  the  contribution water  column  turbulent). expected,  7),  large  in  the  upper 300 m e t e r s  p a t c h e s due t o t h e  t h e w a t e r c o l u m n ; 34% of  the  entire  large  of  mean  the  PEQUOD d a t a  shear  u p p e r 300 m e t e r s  has  dominate  Zt Range  •Patches  Total  Thickness  <3  33  76  3-10  32  10-30 >30  %Total  tZe t  t  I00t£e /(Hi) t  t  0.4%  1.6x10"*  50  1.6  2.4  6.4  106  3.3  4.0  40.  2570  80.  20.  2.0%  2.3  5.4x10'  211  5.6  6.6  7.6  16  266  7.0  17.  20  1290  34.  65.  1  12x10"  5  85%  49%  total  d a t a •* 3780  t =tZe /Zt t t  H "  meters  total  data LO  t « 85.x10-  7  t = drop averaged  W/m  1  = individual  €  He «  32.xIO"'  Table  7 -  20-300 m e t e r s  patch  average  t  W/m' e  PEQUOD  dissipation  •  b i n averaged  dissipation  t t  = patch thickness  t  <* b i n a v e r a g e d  patch thickness  cn  ^Patches  .  Total  Thickness  100t£e /{Hi) t  tZt  Le Range  %Total  6. 1%  1.6x10"'  52  14.  2.4  5.1  75  20.  2.6  1.3  58  15.  4.3  <3  64  139.  1.7%  2.2  11 .xlO"  3-10  43  218  2.7  5.1  10.  10-30  20  293  3.7  15.  >30  3  134  1.7  45.  5  23x10"  5  55%  10%  total  data  t  H = total  =• 8 0 ) 5 m e t e r s  » 4.7x10"'  W/m  He * 3.8x10''  W/m  c «= d r o p  1  <  Table  8 -  data  CT\  averaged  = individual  dissipation  patch  average  t  J  ( PEQUOD  t -tl« / E t t t  300-1000 m e t e r s  » b i n averaged  dissipation  t t  " patch  thickness  t  •= b i n a v e r a g e d  Patch s i z e s t a t i s t i c s f o r the PEQUOD o v e r t h e d e p t h range 300-1000 m e t e r s .  patch  data  thickness  set  Ee Ranqe  #Patches  Total  %Total  Thickness  t  2.9%  2.2  4.4xl0"  109  5.0  5.5  12  254  12.  4  191  8.8  <3  29  64  3-10  20  10-30 >30  tie t  t  I00t£e / ( H e ) t  10x10"*  4.1%  4.2  23  9.5  2.1  21 .  4.8  100  42.  4.0  48.  1.3  64  27^  3.3  s  H « total  d a t a <* 2180 m e t e r s  7 » 11.xlO"  7  H7 * 2 . 4 x 1 0 '  = individual  Table  9 -  dissipation  patch  average  t  W/m  2  7 WESPAC  data  e = drop averaged  W/m' e  1  1.5x10"'  82%  28%  total  e =tLe / E t t t  20-300  meters  ° b i n averaged  dissipation  t t  * patch t h i c k n e s s  t  • b i n averaged  patch thickness  Patch size statistics f o r t h e WESPAC d a t a s e t o v e r t h e d e p t h range 20-300 m e t e r s .  Ranqe  tZt  Zt ((Patches  Total  Thickness  %Total  t  I00t£« /(Ht) t  t  t  7 -tZt /Zt t t  <3  73  159  3.1%  2.2  12.X10-'  26x10 - 5  5.6%  1.7xl0-«  3-10  62  387  7.6  6.2  14.  86  18.  2.2  10-30  27  401  7.9  15.  8.7  130  28.  3.2  >30  5  181  3.6  36.  2.7  98  21 •  5.4  -  22%  total  data • < *  H7 »  73%  H -  5085 m e t e r s 9.2x10"  7  4.7x10-'  < - drop  W/m* c  V/m  2  300-1000 m e t e r s  data averaged  = individual  patch  - b i n averaged • patch  dissipation  thickness  t - b i n averaged  10 -  average  t t  Table  dissipation  t  t WESPAC  total  Patch s i z e s t a t i s t i c s for the WESPAC o v e r the d e p t h range 300-1000 m e t e r s .  patch  data  thickness  set  CO CO  Ranqe  #Patches  Total  Thickness  %Total  t  2e  100tE« /(Ht) t •  tZe t  <3  51  107  1.8%  2.1  8.8x10"  3-10  47  280  4.8  6.0  8.7  10-30  17  257  4.4  15.  >30  1  33  0.6  33.  t  8.4%  1.7x10"'  52  24.  1.9  3.8  58  26.  2.2  .33  11  4_j9  3.3  s  19x10  s  12%  total  t =tZe / E t t t  63%  d a t a =• 5805 m e t e r s  H = total  data, LO  7 =• 3 . 8 x 1 0 "  7  H7 » 2.2x10-'  WESPAC  Table  11 -  W/m  1  W/m  J  > 1000 m e t e r s  7 <  7  t  t  » drop  averaged  >• i n d i v i d u a l  dissipation  patch  • b i n averaged  t  • patch  t  •= b i n a v e r a g e d  average  dissipation  thickness  patch  thickness  1 40  turbulent  p a t c h e s > 30 m e t e r s  vertically 34% of  integrated  the  300 m e t e r s  were  Indicative  found,  of  the  dissipation  is  indicating  that  r e g i o n s where  e , t  in  trend  is  be  (other  55% in  larger  of  of  e -t t  with  the  the  in  this  level  of  range  the  turbulence  but  Successively  patches.  10"  <  larger  3  meters  W/m  6  3  = 0).  The  dissipations, In  fact, a  this minor  the  have  relative  integrated dissipation is waters)  from  patch s i z e s  But  is  W/m ,  6  10"  subsets with  dissipations.  10-30  10%  integrated  e < n o i s e were s e t  larger  30  data.  c o n t r i b u t i o n must be  the other data  averaged  >  e  >  only  vertically with  t  total  patch-averaged  i n the  in  all  concentrated  in  simply because a  i n the water column e x i s t s  greater in  this  sizes. dependence i s  p l o t t e d on l o g - l o g s c a l e are  80% o f  concentrated  of  the  large  than the upper e q u a t o r i a l  range o f p a t c h  bins)  of  greater  to the v e r t i c a l l y  patches  2%  patches  values  the  in a l l  <  above the n o i s e  i n T a b l e 9.  p r o p o r t i o n of  are  just  concentrated  contribution  The  is  (He)  onryT"" patches  relatively  for  evident  successively  the  a  is  8),  only  averaging,  contradiction  cases  = 65 m e t e r s ) .  q u i e s c e n t deep w a t e r s ,  contained  e is  trend  to  (Table  relatively  Further,  notable  dissipation  representing  turbulent.  (since,  (t  data.  Below meters  thick  equally  shown i n F i g u r e s  so  that  spaced (although  half  43 and 4 4 .  decade  These  ranges  successive estimates  of  (or t  are  141  •  •  I  I  I  I  1  ]  I  I  1_  PEQUOD >300 METERS  E  10"  1 I I IM 10°  10'  -i—I'M'  10  J  LOG t ( m e t e r s )  Log-log plot of average patch-averaged d i s s i p a t i o n s vs a v e r a g e p a t c h t h i c k n e s s for the PEQUOD d a t a below 300 m e t e r s .  142  _J  10"  i  i  i  i  -i  11  i  i  •  •  • I  |  i  i  VESPflC >300 METERS  9  I* 8•J  1 0"  '-)  1  ( — i — | — i  |  i  10°  44 -  1 — | — i — | — i  10  10' LOG  Figure  i |  t  J  (meters)  Log-log plot of average patch-averaged d i s s i p a t i o n s vs average p a t c h t h i c k n e s s for the WESPAC d a t a below 300 m e t e r s .  143  not  necessarily  meters Table The  is 8)  shown  in Figure  while Figure  plots  sizes  equally  show  spaced). 43  (the  The numbers  44 c o m b i n e s t h e  quite  clearly  have s u c c e s s i v e l y  larger  PEQUOD d a t a  d a t a of  that  values  are  Tables  e .  300  directly  successively of  below  from  10 and 1 1 . larger  Similar  patch  plots  were  t made u s i n g s m a l l e r , and  the  linearly  t r e n d was e q u a l l y  n o i s e due t o  the  of  Figures  the  estimates  However,  small  spaced bins evident  sample  sizes  43 and 44 shows t h a t  of  half  t  differ  of  compared t o none  in  with, in  neither  between  f r o m WESPAC a r e  this  range  f r o m PEQUOD.  scale  buoyancy  length  the below  t o which these from t h e  scale,  A  ...) more  comparison  estimates  data  be compared and w h i c h c a n be e s t i m a t e d the  the  6-9,  somewhat  some b i n s .  significantly  length  3-6,  however,  the  The a p p r o p r i a t e  is  (0-3,  of  data  e  t  sets.  1000 m e t e r s  patch  s i z e s may  available  defined  by  nor  L  data  =(e/N )^ 3  b (Turner(1973),  p143),  which  represents  the  scale  of  m o t i o n where  b u o y a n c y f o r c e s become of t h e same o r d e r as t h e i n e r t i a l f o r c e s . L , t h e n , i s an a p p r o p r i a t e s c a l e f o r t h e l a r g e s t eddies which b are  able  to  overturn,  stratification. of  L  b  subrange  and of  Gargett  describes high  buoyancy p a r a m e t e r s ,  given et  the  al.(198l)  the  discuss  successful  wavenumber e and N.  background  oceanic  turbulence  the  s c a l i n g of energy  and  significance the  spectra  buoyancy using  144  L  was e s t i m a t e d by d e t e r m i n i n g p a t c h a v e r a g e s  b  the d a t a  below  calculate  300 m e t e r s  N.  into half  For  each p a t c h ,  are  From PEQUOD, L 40  which t h e r e e  d e c a d e b i n s and f u r t h e r  These v a r i a b l e s  and  for  cm  from  plotted  patches  for  v a l u e of  L  evidence  of  a  is  average. higher  for  b  to  grouped  each  t.  for  the  between  upper b i n were  A l t h o u g h the  than the  from t h e s e p l o t s .  of  45 and 4 6 .  The e s t i m a t e  comparable  a trend  L  not p l o t t e d b e c a u s e t h e r e  from PEQUOD i s  b  averaged to get  f r o m 25 t o 40 cm and i s  WESPAC.  PEQUOD (> 30 m e t e r s )  t  all  were a l s o CTD d a t a  and N were e s t i m a t e d ,  in Figures  ranges  b  over  In  other  fact,  from  too  few  10-30 meter  two t h e r e  L  30  is  is  no  remarkably  b constant.  Individual  but  fall  most  v a l u e of  estimates  in the  113 cm i s  range  actually  range  from 9 t o  113  20-40 cm, a s do t h e a v e r a g e s .  f r o m 2030 m e t e r s  of WESPAC d r o p 11 where  cm (The e  = t  3x10"  6  W/m  3  and N was e s t i m a t e d  drop 12 to v a l u e o f L ). b  spatial  concealed  i n the from  representing  nearest  CTD s t a t i o n  at  be ^ 0.0013 r a d / s e c . T h i s i s by f a r t h e l a r g e s t U n f o r t u n a t e l y , these s c a l e s are smaller than the  vertical  counted  from the  resolution lower  both 46% of  bin  data all  of  of  the  (< 3 m e t e r s ) . sets  below  e  measurements  and  114  patches  of  311  are  300 m e t e r s were < 3 m e t e r s ,  the p a t c h e s .  However,  these  only  1 45  _i  10  i—i  -i—i—i—r  i i  i  T-r-  10"  c  LOG  Log-log plot average patch 300 m e t e r s .  t  •  1  I  I  I  i i i  1—I—i—r-i-r  10  J  (meters)  of a v e r a g e b u o y a n c y l e n g t h s c a l e v s t h i c k n e s s f o r t h e PEQUOD d a t a below  146  •  10°  •  i  i  i i • i •  i — i  i  i  • i  8 -i  10" 10  r  io  C  LOG  Figure  46 -  t  -I 1  r—|—I  | • •  10  J  (meters)  L o g - l o g p l o t of a v e r a g e average patch t h i c k n e s s 300 m e t e r s .  buoyancy l e n g t h s c a l e vs f o r the WESPAC d a t a below  147  represent about  310 o f  15%,  dissipation.  and  2079 m e t e r s contribute  of  data  only  The dominant p a t c h e s ,  with  e  6% t o t h e then,  are  >  10"  6  W/m ,  vertically many t i m e s  3  averaged L  in b  thickness.  or  148  IX.  DISCUSSION AND CONCLUSIONS  The main c o n t r i b u t i o n global the  data  this  thesis  set  of  ocean t u r b u l e n c e  measurements  of  this  plot  7-N  of  of  Figure  t o make b e t t e r further  use  meaningful is  made h e r e  in Chapter  discrete  But,  large  of  thicknesses;  various  8  of  sets.  water  but  contribution  of  integrated  are  ranges  over  of  the  turbulent; sizes  and  for  made  made  patch  dissipation;  data  standards  are  is  of  exist,  Certainly,  averages  estimates which  order  c o m p a r i s o n of of  the  the  In  now  established.  only  column  workers,  which  number  Not  to  comparing  standard.  statistical a  In  other  sets  be  provides  intervals,  the  vertically  those  data  the  addition  measurements.  must  also,  data  vertical  fraction  the  formats  averaging  comparing  to  the  16 p r o v i d e d a c o n v e n i e n t of  one.  thesis  is  patch to  the  patch-averaged  dissipations. The d a t a  from  relationship Further,  it  occurring  depths  between is  seen t h a t  turbulence  trend  rather  than  e.  Scaling  of  in  the  internal  constant  sets  and r a n g e s  of =  the  time  TE/e,  frequency  and ,  of  scale  for  N ,  the on  and a . 0  is  for  to  4)X10~  decay the  7  of  values to  much energy  of  a e  is  higher  individual  and r a t e  m /sec «sec. the  3  internal  for An  range  of  of  loss  e a  N .  four  estimates  1  data  estimate  wave f i e l d  surface-extrapolated  The b e s t  and N.  frequently  estimated  2  strong  more  suggest a r e l a t i o n  a , 0  indicate  due  to  wave f i e l d  (1.4  depends 0  arguments  proportionality, from  meters  averaged  this  of  The  300  heavily  estimates energy  >  is  r  buoyancy from  the  149  data  sets  made  are  10-100 d a y s ,  independently  impediment t o t h e  factor  of  better of  turbulent  of  the  in  time  kinetic  in  of  the  scale  energy  the  range  and G a r r e t t  reliability  uncertainty  estimate  is  by 0 1 b e r s ( l 9 8 3 )  A major  two  which  of  and  the  Munk(l979).  estimate  GM s p e c t r a l  must a w a i t  and  is  the  estimates.  joint  dissipation  estimates  A  measurements internal  wave  spectra. A very described manner. local  s i m p l e model i s dependence  The p r e d i c t i o n turbulent  waves and t h a t  probability  to  value  internal  distribution  is  based  in  on  at  the  least  occurrence  of  breaking events  that  the R i c h a r d s o n  than  1/4  the  A  due  the  is  the  qualitative that  b r e a k i n g of  number  is  the  internal  determined  locally  reduced  t o a random s u p e r p o s i t i o n of  reasonable  turbulence  a  for  assumption  due t o  shears. of  N  accounts  is  less  wave  and  e  which  dissipation  the  by t h e a  of  presented  in  fit  the  is  made  to  the  water column t h r o u g h  the  -1/N e  dependence- of  relate  the  turbulence) Nearly the  magnitudes  synoptic  of  permit  estimates  correlation  to  between  however,  and  and R i  and  individual  e  estimates  it  is  data  a  local  e-S  < 10). not  be  of  shear  25 m e t e r  both  should  how  PCT  to  (percent  Pr(Ri<1/4).  comparison  the  Ri  clear  parameter  the and  estimates  and  a s t r o n g dependence  (for  not  and W h i t e H o r s e measurements  Independent  averaged b a s i s , S  the  Camel III  Pacific  R i c h a r d s o n numbers. poor  although  and t h e model p a r a m e t e r  equatorial  dissipation  Pr(Ri),  e-Ri. exists  turbulent difference indicate  On a  between  surprising  a  heavily  The p o o r c o r r e l a t i o n s too  from  if  e for one  150  considers  that  turbulence  may,  overturning in  a  in  In  slightly  reason  synoptic  with  is  have  the  the  fact  the  state  large  quite  White  Ri)  which  (increase)  turbulence  from  shear  that  low  decrease  case,  decayed  may  (and  locally  this  r e g i o n s of  overturned  simpler  shears  fact,  event.  Conversely, yet  large  the  low R i )  low  values  the  due t o  the  measured may be  original  (or  the  cause  event.  which  have  of  Perhaps  e.  not  Camel measurements were  H o r s e measurements  in e i t h e r  a  not  time  or  space. The s u b s t a n t i a l l y equatorial  Pacific  Crawford(1982)) and  region.  Apparently as  sets.  not of  is  variability  e,  in  Ri  light  of  balance,  turbulent  the  kinetic  dominant energy  by  of  the  of (on  the  the  requires  a measure of  as  well  as of  t h e mean s h e a r .  In  of  the  mean  kinetic  equation,  .measured  to  the v a r i a b i l i t y  in  of  turbulence is  of the  in  the  not  as  from  a c o m p a r i s o n of  1979  and  the  basis  1.982  of  data  individual  The f i n d i n g s  may  relate of  not  stresses  the  the  terms of  1982 a r e  1981b).  In  e and t h e p r o d u c t i o n of  Reynolds  t h e mean s h e a r  dissipations  1979 r e s u l t s  Osborn(1979b,  against  energy  the  p r o d u c t i o n - d i s s i p a t i o n model  terms are  and hence  from  indicative  o r wind s p e e d .  t h e EUC p r o p o s e d by C r a w f o r d and  this  be  either  relationship  shear,  to  the  i n t h e mean s h e a r  from a c o m p a r i s o n  a direct  surprising  in  dissipations  opposed to  considered  the v a r i a t i o n  f o u n d between  be  averaged  1982 (as  variation  d r o p s or  Nor  drops)  temporal  the  individual  in  must be  spatial  great  smaller  variability  Reynolds the the  large  working  balance much enough t o  of  e  stresses of  terms  smaller balance  151  the  work done by t h e  of  zero zonal v e l o c i t y  terms  in  compare  in  .003-.5  the  equatorial  300  the  K  made  for  a  the the  Pacific  data  mass,  K , P  EUC  agree  very  from  1-40  and  from depths  both  the  closely.  The  with  2  imply  sources  At  from  1 cm /sec at  w i t h d e p t h does not  of  itself.  increases  v a l u e of  other  important.  core  made  level  Hence,  ranging  core  estimates  the  number  here  above  the  to Munk's(l966) of  from  r e g i o n of  western  coefficient  increase  mean s h e a r  core.  e q u a i t o n must be  those  meters,  and t h e  extrapolating The  in  between  undercurrent  energy  with  large  2  than  gradient  eddy c o e f f i c i e n t s  cm /sec  greater  eddy  of  favourably  2  and t h e  t h e mean k i n e t i c  Estimates  cm /sec  zonal pressure  depth,  5000 m e t e r s .  greater  turbulent  P fluxes with depth. An values  analysis of  of  patch  statistics  d i s s i p a t i o n averaged  over  a  -indicates single  that  patch,  i)average e ,  are  t larger  for  buoyancy  thicker  length  scale  patches L  is  than  for  thinner  virtually  patches  constant,  and  ii)the  regardless  of  b patch  size,  thickness.  t,  implying  The p a r a m e t e r  that L  patches  indicates  the  are  many t i m e s  largest  L  b  in  overturning  b scales, of  and  a number o f  hence,  a single  adjacent  turbulent  overturning  p a t c h would be c o m p r i s e d  events.  152  BIBLIOGRAPHY Crawford,W.R.(1976): T u r b u l e n t energy d i s s i p a t i o n in the Atlantic equatorial undercurrent. Ph.D. thesis, Institute o f O c e a n o g r a p h y , U n i v e r s i t y of B r i t i s h C o l u m b i a , 150pp. Crawford,W.R.(1982): Pacific equatorial J . P h y s . O c e a n o g r . , J_2 , 1137-1149.  turbulence.  Crawford,W.R. and T . R . O s b o r n ( 1 9 7 9 a ) : M i c r o s t r u c t u r e measurements i n t h e A t l a n t i c e q u a t o r i a l u n d e r c u r r e n t d u r i n g GATE. Deep Sea R e s . ( G A T E s u p p l e m e n t I I ) , 26 , 285-308. Crawford,W.R. and T . R . O s b o r n ( 1 9 7 9 b ) : E n e r g e t i c s of t h e A t l a n t i c equatorial undercurrent. Deep Sea R e s . ( G A T E s u p p l e m e n t II ) , 26 , 3 0 9 - 3 2 3 . Crawford,W.R. and T . R . O s b o r n ( 1 9 8 1 a ) : T u r b u l e n c e i n t h e . e q u a t o r i a l P a c i f i c Ocean. Ms.Rep. 81-1, I n s t i t u t e Ocean S c i e n c e s , S i d n e y , B . C . , 63pp.  of  Crawford,W.R. and T . R . O s b o r n ( 1 9 8 1 b ) : C o n t r o l of e q u a t o r i a l o c e a n c u r r e n t s by t u r b u l e n t d i s s i p a t i o n . S c i e n c e , 212 , 539-540. D e l , G r o s s o , V . A . ( 1 9 7 4 ) : New e q u a t i o n of s t a t e f o r t h e s p e e d of sound i n n a t u r a l w a t e r s ( w i t h c o m p a r i s o n t o o t h e r equations). J . A c o u s t i c . S o c . A m . , 56 , 1084-1091. Desaubies,Y. and W . K . S m i t h ( 1 9 8 2 ) : S t a t i s t i c s of R i c h a r d s o n number and i n s t a b i l i t y i n o c e a n i c i n t e r n a l w a v e s . J . P h y s . O c e a n o g r . , J_2 , 1245-1 2 5 9 . E r i k s e n , C . C . ( 1 9 7 8 ) : Measurements and m o d e l s of f i n e s t r u c t u r e , i n t e r n a l g r a v i t y waves and wave b r e a k i n g i n t h e d e e p o c e a n . J . G e o p h y s . R e s . , 83 , 2 9 8 9 - 3 0 0 9 . E v a n s , D . L . ( 1 9 8 2 ) : O b s e r v a t i o n s of s m a l l - s c a l e s h e a r and d e n s i t y s t r u c t u r e i n the o c e a n . Deep Sea R e s . , 29 , 5 8 1 - 5 9 5 . G a r g e t t , A . E . ( 1 9 8 4 ) : V e r t i c a l eddy d i f f u s i v i t y interior. J . M a r i n e R e s . , in p r e s s .  in  the  ocean  G a r g e t t , A . E . , P . J . H e n d r i c k s , T . B . S a n f o r d , T . R . O s b o r n and A . J . W i l l i a m s I I I ( 1 9 8 1 ) : A c o m p o s i t e s p e c t r u m of v e r t i c a l shear in the upper o c e a n . J . P h y s . O c e a n o g r . , V\_ , 12581271. Gargett,A.E. internal  and G . H o l l o w a y ( 1 9 8 4 ) : D i s s i p a t i o n and d i f f u s i o n by wave b r e a k i n g . J.Marine Res., in p r e s s .  153  G a r g e t t , A . E . , T . R . O s b o r n and P . W . N a s m y t h ( 1 9 8 4 ) : L o c a l i s o t r o p y and t h e d e c a y o f t u r b u l e n c e i n a s t r a t i f i e d f l u i d , submitted to J . F l u i d . M e c h . Gargett,A.E. and T . R . O s b o r n ( 1 9 8 1 ) : Small s c a l e shear measurements d u r i n g t h e f i n e and m i c r o s t r u c t u r e e x p e r i m e n t (FAME). J . G e o p h y s . R e s . , 86 , 1929-1944. G a r r e t t , C . J . R . ( 1 9 7 9 ) : M i x i n g i n the ocean D y n . A t m o s . O c e a n s , 3 , 239-265.  interior.  Garrett,C.J.R. and W . H . M u n k ( 1 9 7 2 ) : S p a c e - t i m e s c a l e s o f i n t e r n a l waves. G e o p h y s . F l u i d . D y n . , 2 , 225-264. Garrett,C.J.R. and W . H . M u n k ( 1 9 7 5 ) : S p a c e - t i m e s c a l e s of i n t e r n a l waves: a p r o g r e s s r e p o r t . J.Geophys.Res., 291-297.  8_0 ,  Garrett,C.J.R. and W . H . M u n k ( 1 9 7 9 ) : I n t e r n a l waves i n t h e o c e a n . A n n . R e v . F l u i d . M e c h . , JJ_ , 3 3 9 - 3 6 9 . G i b s o n , C . H . , G . R . S t e g e n and R . B . W i 1 1 i a m s ( 1 9 7 0 ) : S t a t i s t i c s of t h e f i n e s t r u c t u r e of t u r b u l e n t v e l o c i t y and t e m p e r a t u r e f i e l d s measured a t h i g h R e y n o l d s numbers. J . F l u i d . M e c h . , 4j_ , 153-167. G i l l , A . E . ( 1 9 8 2 ) : A t m o s p h e r e - O c e a n Dynamics Y o r k , 662pp.  , A c a d e m i c P r e s s , New  G r a n t , H . L . , R . W . S t e w a r t and A . M o i l l i e t ( 1 9 6 2 ) : T u r b u l e n c e from a t i d a l c h a n n e l . J . F l u i d . M e c h . , j_2 , 2 4 1 - 2 6 3 .  spectra  G r e g g , M . C . ( 1 9 7 6 ) : T e m p e r a t u r e and s a l i n i t y m i c r o s t r u c t u r e i n t h e Pacific equatorial undercurrent. J . G e o p h y s . R e s . , 8J_ , 1180-1196. G r e g g , M . C . ( 1 9 7 7 ) : V a r i a t i o n s i n the i n t e n s i t y of s m a l l s c a l e m i x i n g i n t h e main t h e r m o c l i n e . J . P h y s . O c e a n o g r . , 7 , 436454. G r e g g , M . C . ( 1 9 7 9 ) : The e f f e c t s o f b i a s e r r o r s a n d s y s t e m n o i s e on p a r a m e t e r s computed f r o m C , T , P and V p r o f i l e s . J . P h y s . O c e a n o g r . , 9 , 199-217. Gurvich,A.S. a n d A . M . Y a g l o m ( 1 9 6 7 ) : Breakdown o f e d d i e s a n d probability distributions for small-scale turbulence. P h y s . F l u i d s , s u p p l e m e n t , U) , S 5 9 - S 6 7 . H a l p e r n , D . ( 1 9 8 0 ) : A P a c i f i c e q u a t o r i a l t e m p e r a t u r e s e c t i o n from 1 7 2 ° E t o 110°W d u r i n g w i n t e r and s p r i n g 1979. Deep Sea R e s . , 27 , 9 3 1 - 9 4 0 . Hinze,J.O.(1975): Turbulence Y o r k , 790 p p .  , 2nd e d i t i o n , M c G r a w - H i l l , New  154  Hoerner,S.F.(1965): by t h e a u t h o r ,  F l u i d Dynamic D r a g Washington, D.C.  ,  2nd e d i t i o n ,  published  K a t z , E . J . , R . B e l e v i t s c h , J . B r u c e , V.Bubnov, W.Duing, P . H i s a r d , H.-U.Lass, J.Meincke, A.DeMesquita, L . M i l l e r , and A . R y b n i k o v ( 1 9 7 7 ) : Zonal p r e s s u r e g r a d i e n t a l o n g the equatorial Atlantic. J . M a r i n e R e s . , 3_5 , 2 9 3 - 3 0 7 . K n a u s s , J . A . ( 1 9 6 6 ) : F u r t h e r measurements and o b s e r v a t i o n s Cromwell C u r r e n t . J . M a r i n e R e s . , 24 2 0 5 - 2 4 0 .  in  the  L a m b e c k , K . K . ( 1 9 7 7 ) : T i d a l d i s s i p a t i o n i n the o c e a n s : a s t r o n o m i c a l , g e o p h y s i c a l and o c e a n o g r a p h i c c o n s e q u e n c e s . P h i l . T r a n s . R o y . S o c . L o n d o n , S e r i e s A , 287 , 5 4 5 - 5 9 4 . Larson,N.G. and M . C . G r e g g ( 1 9 8 3 ) : T u r b u l e n t d i s s i p a t i o n and shear in thermohaline i n t r u s i o n s . N a t u r e , 306 , n o . 5 6 3 8 , 26-38. L e e t m a , A . , J . P . M c C r e a r y and D . W . M o o r e ( 1 9 8 1 ) : Equatorial c u r r e n t s : o b s e r v a t i o n s and t h e o r y . i n E v o l u t i o n of P h y s i c a l O c e a n o g r a p h y , Warren and Wunsch, e d s . , 184-196. Lemasson,L. and B . P i t o n ( 1 9 6 8 ) : A n o m a l i e dynamique de l a s u r f a c e de l a mer l e l o n g de l ' e q u a t e u r d a n s 1'Ocean P a c i f i q u e . Cah.ORSTOM, S e r . O c e a n o g . , 6 , 3 9 - 4 5 . L o n g u e t - H i g g i n s , M . S . ( 1 9 5 2 ) : On t h e s t a t i s t i c a l t h e h e i g h t s of s e a waves. J.Marine Res.,  d i s t r i b u t i o n of jj_ , 2 4 5 - 2 6 6 .  L u e c k , R . G . , W . R . C r a w f o r d and T . R . O s b o r n ( 1 9 8 3 ) : T u r b u l e n t d i s s i p a t i o n over the c o n t i n e n t a l s l o p e o f f Vancouver Island. J . P h y s . O c e a n o g r . , J_3 , 1809-1818. Lueck,R.G. and T . R . O s b o r n ( 1 9 8 2 ) : D i s s i p a t i o n measurements from t h e F r o n t s 80 e x p e d i t i o n . D e p a r t m e n t of O c e a n o g r a p h y , U n i v e r s i t y of B r i t i s h C o l u m b i a m a n u s c r i p t r e p o r t n o . 3 8 , 183pp. L u y t e n , J . R . , G . N e e d e l l and J . T h o m s o n ( 1 9 8 2 ) : An a c o u s t i c d r o p s o n d e - d e s i g n , p e r f o r m a n c e and e v a l u a t i o n . Deep Sea R e s . , 23 , 4 9 9 - 5 2 4 . M a i s e l , ( 1 9 7 1 ) : P r o b a b i l i t y , S t a t i s t i c s and Random Simon and S c h u s t e r , New Y o r k , 2 8 0 p p . McComas,C.H.. internal  Processes  and P . M u l l e r (1 981 ): The dynamic b a l a n c e waves. J . P h y s . O c e a n o g r . , JJ_ , 9 7 0 - 9 8 6 .  M i l e s , J . W . ( 1 9 6 1 ) : On t h e s t a b i l i t y J . F l u i d . M e c h . , 10 , 4 9 6 - 5 0 8 .  of  heterogeneous  of  shear  flows.  155  Mourn,J.N. and R . G . L u e c k ( 1 9 8 4 ) : C a u s e s and i m p l i c a t i o n s of n o i s e i n o c e a n i c d i s s i p a t i o n measurements, s u b m i t t e d t o Deep Sea Res. Mourn,J.N. and R . G . L u e c k ( 1 9 8 3 ) : N o i s e i n o c e a n i c d i s s i p a t i o n measurements u s i n g Camel p r o f i l e r s . D e p a r t m e n t of O c e a n o g r a p h y , U n i v e r s i t y of B r i t i s h C o l u m b i a , m a n u s c r i p t r e p o r t n o . 4 0 , 49pp. Munk ,W.H. (1 9 6 6 ) : A b y s s a l  recipes.  Deep Sea R e s . ,  j_3 , 7 0 7 - 7 3 0 .  M u n k , W . H . ( 1 9 8 1 ) : I n t e r n a l waves and s m a l l s c a l e p r o c e s s e s . in E v o l u t i o n of P h y s i c a l O c e a n o g r a p h y , Warren and Wunsch, e d s . , 264-291. Nasmyth,P.W.(1970): Oceanic turbulence. Ph.D. thesis, I n s t i t u t e of O c e a n o g r a p h y , U n i v e r s i t y of B r i t i s h C o l u m b i a , 69pp. Ninnis,R.N.(1984): probe. Ph.D. U n i v e r s i t y of  S p a t i a l t r a n s f e r f u n c t i o n of t h e a i r f o i l t h e s i s , Department o f O c e a n o g r a p h y , B r i t i s h Columbia.  Oakey , N . S . ( 1 9 8 2 ) : D e t e r m i n a t i o n , of t h e r a t e o f d i s s i p a t i o n of t u r b u l e n t e n e r g y f r o m s i m u l t a n e o u s t e m p e r a t u r e and v e l o c i t y shear m i c r o s t r u c t u r e measurements. J . P h y s . O c e a n o g r . , J_2 , 256-271. Oakey,N.S. and J . A . E l l i o t t ( 1 9 8 2 ) : D i s s i p a t i o n w i t h i n t h e s u r f a c e mixed l a y e r . J . Phys . O c e a n o g r . , _1_4 , 171-185. 0 1 b e r s , D . J . ( 1 9 8 3 ) : Models of the o c e a n i c i n t e r n a l R e v . G e o p h y s . S p a c e P h y s . , 2_1. > 1567-1606. Osborn,T.R.(1974):  Vertical  microstructure.  p r o f i l i n g of  J.Phys.Oceanogr.,  wave  field.  velocity  4 ,  109-115.  O s b o r n , T . R . ( 1 9 8 0 ) : E s t i m a t e s of t h e l o c a l r a t e of v e r t i c a l d i f f u s i o n from d i s s i p a t i o n m e a s u r e m e n t s . J.Phys.Oceanogr., 10 , 8 3 - 8 9 . Osborn,T.R. and C . S . C o x ( 1 9 7 2 ) : O c e a n i c G e o p h y s . F l u i d . D y n . , 3 , 321-345.  finestructure.  Osborn,T.R. and L . E . B i l o d e a u ( 1 9 8 0 ) : Temperature m i c r o s t r u c t u r e measurements i n t h e e q u a t o r i a l A t l a n t i c . J.Phys.Oceanogr., 7 , 66-82. Osborn,T.R. and W . R . C r a w f o r d ( 1 9 8 0 ) : An a i r f o i l p r o b e f o r measuring turbulent v e l o c i t y f l u c t u a t i o n s in water. in A i r - S e a I n t e r a c t i o n , D o b s o n , H a s s e and D a v i e s , e d s . , 369386.  156  Pacanowski,R.C. and S . G . H . P h i l a n d e r ( 1 9 8 1 ) : v e r t i c a l m i x i n g i n n u m e r i c a l m o d e l s of J.Phys.Oceanogr., , 1443-1451.  P a r a m t e r i z a t i o n of t r o p i c a l oceans.  P h i l l i p s , 0 . M . ( 1 9 7 7 ) : The d y n a m i c s o f t h e upper o c e a n , 2nd e d i t i o n , Cambridge U n i v e r s i t y P r e s s , Cambridge, 336pp. Pond,S.  and G . L . P i c k a r d ( 1 9 8 3 ) :  Oceanography  ,  2nd e d i t i o n ,  Introductory  Dynamic  Pergamon P r e s s ,  Oxford,  329pp.  Schmitt,R.W.,Jr. and D . L . E v a n s ( 1 9 7 9 ) : An e s t i m a t e of t h e o f v e r t i c a l m i x i n g due t o s a l t f i n g e r s b a s e d on o b s e r v a t i o n s i n the N o r t h A t l a n t i c C e n t r a l Water. J . G e o p h y s . R e s . , 83 , 2 9 1 3 - 2 9 1 9 . S c h m i t z , W . J . , J r . , P . P . N i i l e r , R . L . B e r n s t e i n and W . R . H o l l a n d ( 1 9 8 2 ) : R e c e n t l o n g - t e r m moored o b s e r v a t i o n s i n the western N o r t h P a c i f i c . 87 , 9 4 2 5 - 9 4 4 0 . Stewart,R.W. and A . A . T o w n s e n d ( 1 9 5 2 ) : S i m i l a r i t y preservation in isotropic turbulence. P h i l . T r a n s . R o y . S o c . L o n d o n , 243A , 3 5 9 - 3 8 6 .  rate  instrument J.Geophys.Res., and  self-  S t e w a r t , R . W . , J . R . W i l s o n and R . W . B u r l i n g ( 1 9 7 0 ) : Some s t a t i s t i c a l p r o p e r t i e s of s m a l l s c a l e t u r b u l e n c e i n an a t m o s p h e r i c boundary l a y e r . J . F l u i d . M e c h . , 4j_ , 141-152. Turner,J.S.(1973): Buoyancy E f f e c t s i n F l u i d s U n i v e r s i t y P r e s s , Cambridge, 368pp. Van D y k e , M . ( 1 9 8 2 ) : An Album of S t a n f o r d , 176pp.  F l u i d Motion  , Cambridge  , Parabolic  Wyrtki,K.(1983): An a t t e m p t t o m o n i t o r t h e E q u a t o r i a l Undercurrent. J . G e o p h y s . R e s . , 88 , 7 7 5 - 7 7 7 .  Press,  157  APPENDIX A The i n s t r u m e n t , buoyant to  the  in water.  HYDRODYNAMICS  Camel I I I ,  Ballast  is  is  shear  wire c y l i n d e r  The b u o y a n t which measures thick.  force  is  is  release  chiefly  is  of  material  is  simply c a l c u l a t e d  (using  2.77.  a nominal  The end c a p s t o (A536-T6). surface  The shape  making i t  buoyancy  the  of  the  is  preamplifier  The i n s t r u m e n t Acania, It  was  act  the  It  weights  plus  added.  Another  that  the  very  large  acts  further  3.1  kg of 2.0  instrument  the c e n t r e  density  of  changing the  to  solely  as  1028  the  however, other  in Monterey  after  would c o n t i n u e  kg/m ). 3  aluminum' a l l o y irregular  effect  than  harbour  on  the The  the  the  to  the  nosepiece  instrument  and i n c r e a s e  the  to  fall  ensure where  The a d d e d a d d i n g mass rate,  An u n d e s i r a b l e  lead  were  in a region  (by  R/V  School.  expendable  nosepiece  sink  from the  Postgraduate  change w i t h d e p t h o c c u r s .  sensitivity.  tube  be m e a s u r e d .  12.2 kg of to  kg were added t o  gravity)  the  and  ballast.  lead attached  the  net  cm  geometry  a cast  States Naval  kg heavy  stabilize  shear  of  tube are  instrument,  was w e i g h e d  1.2  density  can,  o p e r a t e d by t h e U n i t e d f o u n d t o be  by t h i s  tube,  with a  be 4 2 . 0 kg o v e r  to c a l c u l a t e  instrument.  case,  (6061-T6)  h e m i s p h e r i c a l but w i t h an  difficult  r e m a i n i n g components of  t h e main p r e s s u r e  given to  pressure  pressure  152 cm l o n g and 1.9  The l i f t  seawater  with a  fastened  system.  an aluminum a l l o y  gravity then  series  due t o  specific  length  in  3 0 . 5 cm i n d i a m e t e r ,  The m a t e r i a l  positively  p r o v i d e d by l e a d w e i g h t s  body by AWG20 w i r e w h i c h  sensitive  d e s i g n e d t o be  weight below  thereby  side effect  is  158  the  i n c r e a s e d energy a v a i l a b l e  limiting (see  factor  Appendix  in  the  safety  all,  the  instrument  fall  off  the  case  of  instrument,  link  connection to  to  buoyant  one w e i g h t  fall  the  which  is  dissipation  met by t h e buoyant for  the  calculation  system  is  system.  release thought  the ambient p r e s s u r e , case.  First  should only  some m a r g i n o f  the p r e s s u r e  in the  safety  t o be t h e is  a  in  As .  pressure  threaded  The i n s t r u m e n t case  of  one w e i g h t  mechanism.  which  s h o u l d the p r e a m p l i f i e r  will  flood,  be  and o n l y  off.  s p e e d of  b u o y a n c y of  instrument  in  allowing  the p r e a m p l i f i e r  positively  The f a l l  of  are  positively  a malfunction  transducer  of  criteria  is  t h e weak l i n k  negative  resolution  vibration,  G).  Two o t h e r  well,  for  the  the  in motion.  instrument  instrument  is  and t h e d r a g  The d r a g f o r c e  a s q u a r e d d r a g law D = kW  g o v e r n e d by  is  force  on.the  empiricized in  where k = pAC /2g  2  the  (A  is  the  form  the  d frontal  c r o s s - s e c t i o n and C  is  the  drag c o e f f i c i e n t )  is  a  d quantity  w h i c h can be d i r e c t l y  the  rate  fall  of  the  k,  was d e t e r m i n e d f r o m d r o p s made  1981 a b o a r d t h e  measurements were c o n f i r m e d on o t h e r added l e a d weight 1.1  m/s, It  for  the  resulting is  (7.7  kg i n w a t e r )  in a value  interesting  instrument  knowing t h e mass and  instrument.  The d r a g p a r a m e t e r , Howe Sound i n A p r i l ,  calculated  for  these  cruises.  and  these  W i t h 8.5  kg of  t h e measured f a l l  k of  to c a l c u l a t e  under  CNAV E n d e a v o u r  the  in  rate  was  2 7 . 5 kg/m. drag c o e f f i c i e n t ,  circumstances.  The  area  C , d  159  projected  to  the  n o m i n a l v a l u e of  flow  is  A = TT(.305/2)  1028 kg/m  3  for  2  = .07m . 2  seawater,  C  Using a  = 0.8.  To c o m p a r e ,  d Hoerner(1965)  cites  C  = 0.35 as a measured d r a g c o e f f i c i e n t  for  d a t o r p e d o and C  = 0.8  for  the  flow.  a blunt-nosed cylinder  aligned  d longitudinally not  blunt  aft  of  drag.  the  to  The shape of  b u t added p r o j e c t i o n s main body l i k e l y  on t h e  contribute  Camel III  surface  and  is  certainly  especially  substantially  to  the  160  APPENDIX B - PRESSURE The p r e s s u r e type  pressure  by t h e is  R  1 6  C  is  2  shown  shown.  different  s e n s e d by a V i a t r a n  transducer.  circuit  also  is  The p r e s s u r e  in Figure  B.1.  S w i t c h e s on t h e  full  scale  a low p a s s  Calibration  gains  the  second stage  pressure  signal  curve  the  calibration  over  data  The a c c u r a c y is  0.2  percent  a transducer worst  the  is  the  full  scale.  The r e s o l u t i o n  of  the  r e c o r d e d on t h e  t o e a c h VCO.  or  6.8  the  at  1.4  range.  the  A  B.1. manufacturer  PEQUOD and WESPAC resulting  density  of  in a  is  by t h e  g o v e r n e d by  FM/tape the  Camel III  w i t h DC  the  tape  cassettes  lab.  noise  e x p e c t e d due t o  spectrum are On t h e  the  n o i s e on a p a r t i c u l a r  frequency the  attributed  400 Hz FM c h a n n e l  r a n g e of  incomplete  (which i s  inputs  tape  that  KDA11 system.  FM c h a n n e l  Integration  interest  signal processing.  to  A  p l a y e d back on a JVC  d e t e r m i n e d w i t h an HP3582A s p e c t r u m a n a l y s e r . spectrum over  cruises  dbar.  signal  is  lab  typical  n o i s e c a n be m e a s u r e d i n  The r e c o r d e d s i g n a l  Hz.  calibration  q u o t e d by t h e the  pole  deck and d e m o d u l a t e d u s i n g a Sonex FM d i s c r i m i n a t o r  The s p e c t r a l  the  The  p r e s s u r e measurement  n o i s e added t o This  For  allow  conducted in  r a n g e was u s e d ,  10 p s i  is  transducer  transducer  of  system.  amplifier  tester.  shown i n T a b l e  case accuracy  recording  tape  of  full  w i t h 0-5000 p s i  electronic  tape  of  table  amplifier  The s i n g l e  is  gauge  preamplified  w i t h a measured -3db p o i n t  452 dead w e i g h t  linear  is  The s e c o n d s t a g e  u s i n g an Amthor t y p e is  104 s t r a i n  signal  t o be s e l e c t e d .  filter  of  model  yields  Peaks  in  is  of  the  this  speed compensation.  used to c a r r y  the  161  pressure  signal)  Hz w h i c h  is  peak v a l u e the  there  is  an rms n o i s e  equivalent  to  1.0  of  the  r e s o l u t i o n of  noise  is  psi  taken  or  level  of  0.7 d b a r .  to  be f i v e  t h e p r e s s u r e measurement  fizA  is  in  1  SMt  —WW  If  about  0-0.5  t h e peak  times the  in *W4 -AWVW— Alt -VWVvV  1 mv o v e r  rms  3.5  to  level  dbar.  ->vwv—  w  Mr  -^IvVvV*  —<vvw-  —'WW-"-—•  1  gain s e l e c t  V,  V  are V i a t r a n Model 104 outputs  F i g u r e B.I  -  Camel III amplifier.  preamplifier  and  lowpass  filter-  162 date  - O c t 27,  transducer  1981  -Viatran  Pressure  model  V _P  104, s e r i a l  fit  -2.440  24  50  -2.414  49  100  -2.363  99  200  -2.260  200  300  -2.157  300  400  -2.054  401  500  -1.952  501  600  -1.850  600  800  -1 .645  801  1000  -1.440  1001  1200  -1.236  1201  1 400  -1.031  1401  1600  -0.827  1600  1800  -0.622  1801  2000  -0.418  2000  2200  -0.214  2199  2400  -0.009  2400  2600  0. 195  2599  2800  0.400  2800.  3000  0.605  3000  3200  0.809  3199  3400  1.014  3400  3600  1 .219  3600  3800  1 .423  3799  4000  1 .628  4000  4200  1 .833  4200  4400  2.038  4401  regression  routine  gives  P fit  Table  B.1  -  Camel III  0-5000psi  P  25  HP33E l i n e a r  #116419,  =977.4V +2408.6. P  pressure c a l i b r a t i o n  data.  163  APPENDIX C - FALL RATE The f a l l  r a t e of  differentiation The c i r c u i t similar the  to  output  of  the  the  signal  diagram i s that  instrument  is  calculated  from the p r e s s u r e  shown i n F i g u r e  C.I.  A  , V  , of  the  electronic  preamplifier. calibration  d e s c r i b e d in Appendix B y i e l d s  voltage  by  a linear  pressure preamplifier  fit of  to the  P1 form V ,  where P i s  t h e measured c a l i b r a t i o n av  The d i f f e r e n t i a t o r  is  easily  f  fall  Figure  The g a i n  measured at  0.8  P  rate.  Hz.  A p p e n d i x B shows t h e  is  voltage.  Then,  /at = bap/at.  is  = K av  converted  instrument's C.2.  p1  output v  3P/at  P1  = a+bP  pi  to  /at = K  p  bap/at.  3z/3t = W which  The d i f f e r e n t i a t o r  represents gain  412±5 s e c o n d s w i t h t h e  A similar resolution  measurement t o be a b o u t  to  is  plotted  in  -3db p o i n t  that  1.5  the  described  cm/s.  in  164  "ft  Figure  C.1  -  Camel III fall differentiator).  rate  4  m  circuit  (pressure  —i  1  1  1  1  -i  1—r  • •• •  ••  52  1  1  i  •  xt TJ  i / p HP3582A random n o i s e s o u r c e t o PP-1 1 o/p PP-12  tt  u n i f o r m window used f o r t r a n s f e r  function  o  50 EH  >< t-H  EH  z w tt u Pu  48  LOG FREQUENCY 01  '  F i g u r e C.2 -  Camel III  (Hz) 1.0  0.1  • •  Pressure  derivative  transfer  function.  166  APPENDIX D Temperature  TEMPERATURE  i s measured u s i n g a T h e r m o m e t r i e s  Fastip  Thermoprobe model F P 0 7 . The t h e r m i s t o r in Figure  D.1.  R  preamplifier represents  and low p a s s  the  thermistor  filter in  the  are  shown  bridge.  The  t low p a s s  filter  has a measured -3db p o i n t  Calibration temperature  bath  room t e m p e r a t u r e using a jet  of  individual  in  the  very  lab.  slowly  at  thermistors  7 Hz.  is  Ice  water  is  while  the  bath  carried  allowed is  out  in a  t o warm t o  t h o r o u g h l y mixed  stirrer.  The f l o w  past  temperature  is  thermometer  which  the  thermistor  is  of  the  order  of  1 m/s.  measured u s i n g a Dymec model 2801A q u a r t z is  p o s i t i o n e d a s c l o s e as p o s s i b l e t o  the  thermistor. The i c e p o i n t i s V and V . V i s the tst4 tst5 tst5  r e c o r d e d , as a r e t h e v o l t a g e s i n p u t t o t h e t e m p e r a t u r e VCO,  while V  in order  tst4  is  differentiated  temperature  gradient.  temperature  data,  typical Table  The  A cubic  which g i v e s  calibration  sheet  to c a l c u l a t e  polynomial agreement  and t h e  fit  is  made t o  to about  resulting  fit  the  .01°C. are  shown  the A in  D.1. The a c c u r a c y  is  l i m i t e d by t h e  t h e FM/tape  recording system.  temperature  r e s o l u t i o n of  the  electronic  n o i s e added by  N o i s e measurements system  is  about  show t h a t  0.1°C.  the  Figure  D.1  -  Thermistor  preamplifier  and t e m p e r a t u r e  circuit.  168  d a t e O c t 29, Thermistor  1981  #B2  ice  V  T  T  TST5  e  V fit  TST4  TST4  -1 .061  6.497  -0.844  0. 162  7.510  -0.856  7.510  -0.681  0.161  8.500  -0.656  8.500  -0.523  0.161  9.550  -0.443  9.558  -0.353  0.160  10.500  -0.254  10.500  -0.202  0. 159  11.540  -0.047  11.537  -0.036  0. 158  12.600  0. 164  12.601  0. 130  0. 157  13.500  0.341  13.499  0.272  0.156  14.500  0.537  14.500  0.427  0.155  15.500  0.731  15.499  0.582  0. 154  16.510  0.926  16.511  0.736  0. 153  17.500  1.114  17.497  0.887  0.151  18.510  1 .305  18.508  1.039  0. 150  19.500  1 .490  19.498  1.185  0. 148  20.500  1 .675  20.499  .1.333  0. 146  21.520  1 .862  21.522  1 .482  22.500  2.041  22.513  1 .623  0.143  23.500 •  2.217  23.499  1 .764  0.141  24.510  2.394  24.503  1 .905  0. 139  = 11.77 +6.32V fit  T  • 0.12V TST4  = 11.77 fit  -  -0.020 C  6.500  T  T a b l e D.1  point  Camel III of c u b i c  +5.03V  + 0.07V TST5  2  + 0.04V  TST4 2  TST5  '  0.145  1  TST4 + 0.02V  3  TST5  temperature c a l i b r a t i o n polynomial f i t .  data  and  result  169  APPENDIX E - VELOCITY The c a l i b r a t i o n used at  and t h e  the Department  Columbia  of  behaviour  SHEAR of  Oceanography,  the  airfoil  University  probes  of  British  have been d e s c r i b e d by O s b o r n and C r a w f o r d ( 1 9 8 0 ) .  same t e c h n i q u e  for  probe c a l i b r a t i o n  The e l e c t r o n i c  p r o c e s s i n g of  the  was u s e d f o r  signal,  this  however,  is  The  study.  somewhat  different. The c r o s s  stream  force f  where p i s the  angle  the of  perpendicular  This  illustrated  The n e t probe t i p  to  force the  of  the  to  the  since  flow  are,  the  point  flow  identity  at  to  it.  varying a  linear  Since A is  probe  is  change of  integrating  a  is  cross-  a l o n g the  over  body.  x from  the  is  s t r e a m components of  U c o s a and u = U s i n a , = 2sinacosa, F  is  the  and u s i n g given  (E.1) the  proportional while  tip to  p and W a r e  measured, cross  the  by  = pAWu  is  constant  d e p e n d e n c e on t h e  of  speed,  2  sin(2a)  and i n d e p e n d e n t l y  rate  flow  = lpU Asin(2a) 2  W=  which  the  E.1.  The p i e z o c e r a m i c beam mounted i n a voltage  U is  w h i c h dA/dx = 0 and  F  generates  the  with distance  downstream and c r o s s  respectively,  trigonometric  the  o b t a i n e d by  F but,  fluid,  in Figure is  l e n g t h of  2  and dA/dx i s  section is  unit  = J_pU (dA/dx) s i n (2a) 2  density  attack  per  the probe  of the  the  probe  force  both  applied  slowly  force/voltage  stream v e l o c i t y  has  component o f  170 i  > i i  *6.4 mm i*  '•"Wh  W u U -V? + u  [T "Jl.Smm 0.5 m m j  Figure  E.1  -  . Piezocercmic moment  The a i r f o i l  bending  sensor  p r o b e showing f l o w c o m p o n e n t s .  171  the  flow, For  water  u,  which  is  calibration  (the  expressed in p u r p o s e s , the  calibrator  The a n g l e  of  attack  is  of  the  axis.  The s i n u s o i d a l v o l t a g e  in  jet  rms m e t e r .  +22°,  flow  from - 2 2 ° t o  is  It  is  the is  by  the  rotating  is  its motion  bandpass f i l t e r  and  voltage,  pU sin2asina;t, 2  rotational  frequency  p r o p o r t i o n a l to the c r o s s  convenient  probe, a,  r o t a t e d about  g e n e r a t e d by t h e  of  Crawford(1976)).  shear  t r a n s m i t t e d to a p r e a m p l i f i e r ,  E  directly  against  and t h e p r o b e  The i n s t a n t a n e o u s  (where u> i s  p r o b e i s mounted i n a j e t  described in d e t a i l  varied  the  (E.1).  to consider  the  in  radians/second),  stream f o r c e  o u t p u t of  the  is  on t h e p r o b e . rms m e t e r ,  E  , rms  *E The c o n s t a n t S,  is  of  pU sin(2a) . 2  rms  proportionality,  d e t e r m i n e d by p l o t t i n g E  sensitivity  is  the  s l o p e of S = d(E  A typical  calibration  S has u n i t s constant  over  stability. probe to  sensitivity  rms  a large  sin(2a).  The  curve, 2  rms  is  shown i n F i g u r e and i s  2  attack  the  of  less  a n g l e s of  than  E.2.  approximately 10°  attack  (see  the  of  a n g l e of  the  instrument  attack  thereby  O s b o r n and  sensitivity  i m p o r t a n c e of m a i n t a i n i n g  tilting  the p r o b e .  vs  sensitivity,  /(pu ))/d(sin(2a))  At g r e a t e r  Any l a r g e  of  2  volts/(dyne/cm ),  illustrating  'see'  /(pU )  this  curve  a n g l e s of  Crawford(1980)). increases,  of  termed the probe  will  vehicle cause  changing  A c c e l e r o m e t e r s mounted i n  the  the  the  172  Figure  E.2  -  Typical  airfoil  probe c a l i b r a t i o n  curve.  173  instrument  body a r e  occasional  tilting  a maximum v a l u e  monitored. of  2°  in  and r a r e .  Experience  regions Thus,  of  indicates  large  a constant  that  mean s h e a r value  of  is  both  S may be  used. E x p r e s s i n g the probe v o l t a g e E  =  rms  i n terms  of  the  sensitivity,  SpU sin(2a) 2  = 2SpWu and t h e  peak v o l t a g e ,  E,  for E  This pass  signal  is  a sinusoid is  »/2E  transmitted  (E.2)  to a p r e a m p l i f i e r ,  and t o a s e c o n d s t a g e  amplifier  to a v o l t a g e  controlled-oscillator  (VCO)  This processed signal  amplification  stage  The p u r p o s e of signal  this  to noise  a voltage t h e VCO a t  at  high values of  (Figure  E.4).  are  the  circuit  a l s o added to  is  of  velocity FM b a n d s .  is  Its  to  being the  sent  FM  t h e FM s i g n a l .  is  to  velocity  shear  100 Hz low  further  improve  shear.  required to prevent  the  However,  saturation  of  and p o s s i b l e  A b l o c k d i a g r a m of  the  included.  differentiates  V /V = 1 + o i where  of  E.3)  The p r e a m p l i f i e r probe  is  prior  routed to a  low v a l u e s  adjacent  (Figure  is  a  and added t o  second a m p l i f i e d s i g n a l  limiting circuit  contamination processing  and t h i s  ratio  that  = 2v/2SpWu  filter,  signal.  rms  , so  transfer  the  input  function  is  signal given  from  the  by  (jwR^zJ/Cd+j^RiCjd+jcoRzCz)}  parameters  are  given  in Figure  E.4.  The  poles  probe  Si  at  1—r-  1—1  Mtoht iff  as  TV!  SI  ma  VtolS  SI YCO  at 1  1  S4(  CfT  Ul  vteti  SZ VCo  I I  probe  S  I  1  2  sx  Ctl  f>re**j>  3  C  SZ hi  6  A  lower e l e c t r o n i c s  B  underwater  c o n n e c t o r t o preamp h o u s i n g  C  underwater  connector to  D  upper  F i g u r e E.3  electronics  -  71111  too  package  SZ  D-connector  Cfl4  S41  4*f  endcap  package  Camel III  7SOT  CfK Vtotl  25-way D - c o n n e c t o r  velocity  VCO  shear  signal  processing.  SAl Vco  175  Szout  Figure  E.4  -  Velocity  shear  preamplifiers.  1 76  (2JTRTC2 )" ( 27rR! C , ) -  The m e a s u r e d p r e a m p l i f i e r p l o t t e d as a c o n s t a n t gain  is  d i v i d e d by  = 253 Hz  1  2  gain  Hz  = 200 Hz  1  ( 2 T T R C )" 2  = 0.2  1  is  shown  differentiator  27rf and c o n v e r t e d  in  gain  Figure in  dbv  E.5.  It  (the  actual  t o dbv = 201og(V /V o  gain  is  point  approximately  is  at  The  Devices  p r o v i d e d by t h e was  used p r i o r  circuit  at  elliptic  filter  (#7438).  to  and has  the  as  filter.  -3db  of  by  amplification  in Figure  E.6.  7438 f i l t e r  into  an a m p l i f i e r  function  is  This the  a l t h o u g h no  6  5  of  longer this  5  6  are 1  = .11  1  (27TR6C, )" (27TR C„ ) " 7  5  = 706 Hz  1  5  The t o t a l  the  is  = 1 .6 Hz function  probe  p l o t t e d as a d i f f e r e n t i a t o r gain  1  measured t r a n s f e r  which p r o c e s s e s  = 234 Hz  1  2  (27rR C 1 ) -  approximately  Hz  = 0.5 Hz  1  ( 2 T T R C )"  the  the  7  7  that  i  and t h e  manufactured  The t r a n s f e r  (2?TR C ) "  is  The  + jcoR C (, ) ( 1 + J C J R C ^ + j ( j R C , + jo>R C ^ ( 1 + jcoR C 1 ) ) }  7  circuit  is  shown  i n c l u s i o n of  been r e t a i n e d  amplifier is V /V = ( - jcuR C o i poles  seconds,  The s e c o n d s t a g e  bandpass a m p l i f i e r  r e q u i r e d as a low p a s s  the  0.85  )  150 H z .  100 Hz C a u e r  Frequency  constant  is  signal  gain 2.7  of  the  complete  and s e n d s  in F i g u r e  E.7.  it It  to is  t h e VCO seen  s e c o n d s w i t h -3db p o i n t s  at  f  1  I  I  I  I I I I  1  ~ r  1 — i — i  — i  l i l t  1  1 — i — i — i  i i  -~CM \  o  * *  II ad  -1.0  I 4 Tl  • •• 4  <  o  tt  • S,  o  EH  +  <  S  K,=.85±.02 sees K = . 8 5 ± . 0 2 sees  3  2  EH  -2.0  W  tt W |X4  En n Q  LOG FREQUENCY i  Figure  E.5  i  -  i  1.0  i i i  Velocity  i  i  shear  i  (Hz) I  I  l  10.  I I i  preamplifier  1  transfer  1  1—l—i—I—I—L  function.  178  1 •  IHHot  VWVUci  Figure  E. 6 -  Velocity  shear  amplifiers.  T  •12  1  1—I  I I I I  T  I  I  i  l  i  ~l  1—I—I I I  j  I  •« CM \  o II  X  •  +  h8  <  « o  E-  < I-i  k4  • S,  K,«8.75 db (2.74 s e e s )  t  K,=8.62 db ( 2 . 7 0 s e e s )  S  2  E-i 2 W « W Cu Cn  i—i Q  LOG  FREQUENCY  (Hz)  1.0 i  Figure  i  E.7  i  i  -  i i  10, I  i  i — i — I  I  I l i  Complete s h e a r c i r c u i t  transfer  function.  i  I i i  180  < 1 Hz and f Further  > 100 H z . amplification  p r o v i d e d by t h e a m p l i f i e r Figure  E.8.  The g a i n  is  for  low v a l u e s  and v o l t a g e given  circuit  theoretically parameters.  P r o c e s s i n g of  e q u a l t o about  Actual values  the measured t r a n s f e r  function  the  by a d i f f e r e n t i a t o r  is  velocity  E  is  shown  in  2  30.5 g i v e n  are  slightly  plotted  shear  w i t h a g a i n of  E  shear  by 2  is  velocity  limiting circuit  V /V = (R,+R )/R o i which  of  s i g n a l c a n be  »~E  = GKE  k  nominal  different  in Figure  GK, a s  9t>  the  and  E.9. represented  below,  vco  =  G/27rf  VCO where E  is  the probe v o l t a g e  and E  vco  is  t h e VCO i n p u t  voltage,  Then, E  vco  = GKE = Kk9E/9t  where k i s  the d i f f e r e n t i a t o r  functional  form  If  E is  r e p r e s e n t e d by a  exp(icot), E  Using equation  gain.  vco  = wKkE = 27rf K k E .  (E.2), E  vco  = Kk9E/9t  = Kk2|/2SpW9u/9t  181  Figure  E.8  -  Velocity  shear  high gain  amplifier.  1  T  1  1—I—I I I I  1  1  1  1—I 1 I I I  1  1  1  1—I I I I  30 ~  «  4  •  4  4  4  4  *  *  *  f 4 4 4  4 4 4 4  4  * *  4  *  *  4*  +  i  -3 db-> S 33 Hz ^ A. ^ •O T3  . S Al *  10 S  S 30 Hz A2  G=29 d b  S A2  .  *  t  . *  G=29 d b  - -10 LOG FREQUENCY  Figure  I  i  E.9  -  1.0  l I i il i  Velocity funct i o n .  | shear  i  i  high  (Hz)  10.  i i i l li gain  I  amplifier  I  I  1 I—I—L_L  transfer  183  provided that  u is  invoking T a y l o r ' s  the  only  time dependent p a r a m e t e r .  f r o z e n flow  hypothesis,  Then,  w h i c h c a n be s t a t e d  as  9u/9t = W9u/9z, one  obtains 9u/9z = E  It  is  necessary  inherent  gain  of  to  /(2»/2KkSpW ) . 2  vco  include another  t h e VCO-FM s y s t e m  factor  to account  (which i s  for  termed a ) .  the Then,  9u/9z = aE /(2v/2KkSpW ) , d 2  where E  is  d  factor,  K,  and e q u a l  the is  to  voltage  equal the  to  gain  of  the d e m u l t i p l e x e d s i g n a l .  1 for of  the  the  standard v e l o c i t y  final  stage  amplifier  PEQUOD and 30 f o r WESPAC) when t h e a m p l i f i e d s h e a r used f o r  low  signal  values.  The  shear (10  gain signal  for  signal  is  184  APPENDIX F - CALCULATION OF The method o f spectral  values  converted  calculating  are  calculated  , u s i n g the  A p p e n d i x E)  to  spectra  units  in  suitable of  SPECTRA  is  units  described here.  of  calibration  velocity  shear  bits /Hz  and  2  constants  spectral  The  (see  density  (sec" /Hz). 2  Due t o  the  t h e method o f routine  for  Phideck  calculating  doing t h i s  The d a t a the  importance of  tape  identical  sets  of  an L S I - 1 1  The mode o f  t w o ' s complement numbers w i t h f u l l volts.  The c o n v e r s i o n  from b i t s  -2048 b i t s 0 bits 2047 b i t s 1 bit The s p e c t r a l Leszko  for  tailored for  the  follows:  to  the the  routine  of  t o UBC by  routine  needs of  scale  = -5 = 0  used b l o c k s  III.  two different  of  400 Hz u s i n g 12-bit  is  volts  = (5/2048)  volts  of  using  volts  volts  this  tape  Camel  was as  then,  = 4.997  of  the  c o r r e s p o n d i n g t o ±5  to v o l t s ,  was o r i g i n a l l y  Dolphin data  a rate  digitization  of  here.  mounted i n s i d e  were d i g i t i z e d a t  thesis,  calibration  outlined  were t r a n s p o r t e d  data  computer.  the  were made on b o a r d s h i p and t h e  tapes  At UBC t h e  is  and t h e  to  r e c o r d e d onto analogue  recording units  each tape  calculation  spectra  calculation  were o r i g i n a l l y  C o p i e s of  means.  the  this  w r i t t e n at  T . R . O s b o r n , and project.  UBC by  subsequently  The c a l i b r a t i o n  4096 d a t a p o i n t s  P.  scheme  and o p e r a t e d  as  185  a)  first  b)  removal  c)  a cosine  points  differencing  of  of  the  is  block,  t h e end p o i n t s .  data,  mean  taper  the  to d e t r e n d the  a p p l i e d to to  force  The f o r m of  the  the the  first  time  and l a s t  series  taper  is  to  200  zero  at  J_(l-cos(k2  1)/200), d)  an F F T  is  e)  the c a l i b r a t i o n  domain d a t a f)  the  g)  averaged  done on t h e  to  not  i n c l u d e d i n the  over is  listing  the  variance.  4096 p o i n t s  Final  made t o t h e  taper the  velocity  frequency  3/8's  points are  together  units,  value.  in Table F.1.  calculations  output  band,  The a v e r a g e  and  0.98 H z ,  fall  the v e l o c i t y  is  rate  shear  and  1024 p o i n t s  for  listing.  were made u s i n g  r e s o l u t i o n and t h e  frequency  A sample p r o g r a m and  used to c a l c u l a t e the  with the  frequency  appropriate  taper  reduces  the v a r i a n c e  of  the  total  tapered.  variance.  The v a r i a n c e ,  1-400/4096(1-3/8) total  shear  frequency  bands.  of  having a white s p e c t r u m , the v a r i a n c e is  the  changes  were  routine.  The c o s i n e signal  series,  used to c o n v e r t  The l o w e s t  b o t t o m of  spectral  improved s p a t i a l  is  time  squared and,  printed  cumulative  aire shown  p r i n t e d on t h e  are  8 adjacent  data are  cumulative  output  values  over  the  are  the a p p r o p r i a t e  spectral  The o u t p u t  data  tailored  of  the  variance.  is  d i v i d e d by t h e  factor  To r e c o v e r .939.  the  In  the  with a f u l l  this  then,  signal.  case  only  For  a  cosine 400 o f  is  = .939 total  variance  the  output  1  a  3 4 9 6 7  a 9  10 11 12 13 14 15 16 17 .8  19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 39 40 41 42 43 44 45 46 47 48 49 50 51 52 83 54 55 66 57 58 59 60  C  c c c c c c c  c  c c c c c c c c c c  CALCULATE SPECTRA FROM TAPED DATA USING 4088 PT8 THIS PROGRAM REQUIRES THE FOLLOWING INPUTS :TAPE ON. UNIT B CALIBRATION OATA FILE(777) ON UNIT4 :PREVIOUSLY CALCULATED FALL RATES ON DATA FILE(1234) ON UNIT 7 UNIT 6 IS THE OUTPUT IF1LE-FILE NO. TO BE READ FROM 1RECSTARTING RECORD NO. ICHAN-CHANNEL NO. K-NO. OF SPECTRA L-NO. OF SPECTRA TO BE AVERAGED OVER A-2.5/4 RO-DENSITY OF WATER IN GMS/CM«3 (1.028) S-PROBE SENSITIVITY IN V0LTS/(0YNE/CM»«2) GF-DIFFERENTIATOR GAIN IN SEC/RAD NTO-NO. OF RECORDS ON THE FILE  c  COMMON/TAPEM/CNTR.LENGHT.MESG(100) COMMON/PARAM/A.RO.USUB.S.GF.NLO COMMQN/MAT/US(2500) LOCICAL'1 MESQ INTEGER CNTR,LENGTH INTEGERS LIST(t) DATA LIST/1H*/ CALL PLCTRLCSCAL'. .6666) CALL PALPHA('ROMAN.2 '.0.0) 777 REAOU. LIST. EN0-899)IFIL£. IREC. KHAN.K.L. A, R0.S.6F.NT0 WRITE(6.LIST)IFILE.IREC,ICHAN.K.L,A.RO,S.GF.NTO REA0(7,1234)(US(IB),IS»1,NT0) 1234 FORMAT!10E12.4) NLO.IREC CALL TP0SN(IFILE,5) CALL SK!P{0.IREC-1.5,8700.8800,8900) CALL PLOHS. ,0. .-3) 00 1 11-1.K 1 CALL SPEC(ICHAN.L) GO TO 777 999 CALL PLOTND STOP too WRITE(6,6100) 6100 FORMAT)' UNIT 5 NOT ATTACHED TO A LEGAL TAPE7 ') STOP 200 WRtTE(e,6200)CNTR 8300 FORMAT(' ERROR FROM TAPE DSR: RETURN CODE > ',15) STOP 300 WRITE(6.6300)CNTR. (MESGd ), I • 1. LENGTH) 6300 FORMAT(' ERROR FROM TAPE DSR: RETURN CODE -'.IS. 8 -MESSAOE RETURNED FOLLOWS BELOW 7'/1X.100*1 > STOP 400 STOP 400 500 STOP SCO 600 STOP 600 700 STOP 700 800 STOP 800 800 STOP 900  Table  F.1  -  The spectral v e r t i c a l shear  *  • •  • • *  • •  • • • * • • • • • * •  61 62 63 64 65 68 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 . 84 89 86 87 88 89 80 91 92 93 94 99 96 97 98 89 100  C C  c  c •••••••••  2 1 100 10 101 102 103 3  c  108  1 10 1I1 113 113 114 115 116 117 118 118 120  SUBROUTINE TPOSN POSITIONS READ HEAD TO CORRECT FILE.  C •  101  102 103 104 103 106 . 107 108  END  •  •  SUBROUTINE TPOSNt IPSN, IUNIT ) COMMON /TAPEM/ CNTR,LENGTH.MESG(100) INTEGER CNTR.LENGTH INTEGERS PSN(5)/'P0','SN'.'«»',2«' '/.LEN/10/ LOGICAL* 1 CHARM), STAR/'**/, BLANK/' '/.MESG EQUIVALENCE (CHAR(1),PSN(4)) CALL BT0(IPSN.CHAR(1),3,N0,' ') NI-3-N0 NJ-4-NI IFCNI .LE.OjGOTO I NK'NI+1 CALL M0VEC(ND,CHAR(NK),CHAR(1)> LJ-NU*! DO 2 L-LJ.4 CHAR(L j-BLANK CONTINUE CHAR(NJ)-STAR CALL CNTRL(PSN,LEN, IUNIT.CNTR,8100,»IOI,4102) GOTO 3 WRITE(G.tO) FORMATP ILLEGAL UNIT SPECIFICATION?') CALL QUIT WRITE(6.103) CNTR CALL QUIT WRITEC6.103) CNTR,(MESO(I).1-1.LENGTH) FORMAT(' ','RC-".13./' DSR ERR-',100A1) CALL OUIT RETURN END SUBROUTINE SPEC(177,IFLA1) COMMON/PARAM/A,R0,USUB,S.GF,NLO COMMON/MAT/US(2500) INTEGERS C( 10,4097) REAL«4 P(8192).AVP(B12),FREQ(812),AINT(B12) COMPLEX'S 0ATA(8192) DATA PI/3.1415927/ DATA FREQ.AVP/1024*,0/  CO oY  N-4098 DT',002 WRITE(6,6000)177,1FLA1,N,DT 6000 FORMAT(//26X.80( 1H»)/36X,1H*,78X,1H»/26X.1H«.5X, 8 30X,'C(',I 1,')',SX,'AVERRAGEO BY ',12.28X, IH«/ 826X, 1H*,78X,1H*/26X, IH*,5X,15. 14H DATA POINTS,54X,1H*/26X,1H* 578X. 1H«/26X, 1H«.5X.F5.4.3 IH TIME INTERVAL ( SEC). 47X. 1HV26X . 1H» 878X,1H*/26X.80(1H*)///IX.3(33HP0SN. FREQU. VAR. CUMULATIVE, 86X)/) t  c  NDIM-N/2 RN-FLOAT(NDIM) N8-N/B IN-N/16 N3-IN/3*1 DF-4./RN/0T  routine used to s p e c t r u m and sample  estimate output.  the  121 122 123 124 129 128 127  158  129 130 131 132 133 134 135 13S 137 138 139 140 141 142 143 144 145 146 147 148 149 160  C  C  C C  C  C C  C  169  170 171 172 173 174 175 176 177 178 179 180  DO  C C  26  128-1,312  AVP(I28)-0. 26 CONTINUE -  DO «B 188-1,IFLA1 NUP-NL0.15 USUB-O. 00 124 H24-NL0.NUP 124 USUB«USUB+US(I124)«100. USUB-USUB/16. NLO-NLO+16 USUB - VELOCITY OF SUBMARINE (M/SEC) IFfI77.E0.1.0R.I77.E0.2)FACT-(B.»PI«A/<2O4B.»S0RT(2.)-R0 »»S»USUB««2«0F))««2/.a390 IF(I77.EQ.3)FACT-4.3E-6/USUB»«3 IFU77.EQ.4.0R. I77.E0.B)FACT-< 1 .7/FL0AT(3048)>«-2 IF(I77.EQ.6)FACT-(I./FLOAT(3048))««3 CALL PAWEL2(C) 1  161  152 153 154 155 156 157 158 159 160 161 162 163 164 169 166 167 ' 168  FREO<O-I./DT/N IN1-IN-1 DO 2T 127*1.INI FRE0(2-I27)-0F*FL0AT(I2T) 2T FRE0(2-I27*1)«FRE0<2M27) FREQ(BI3)-DF«2S6.  13  1 H-I.N 0ATA{I1)-C(I77.I1*1)-C(IT7,I1) CALL AVER(DATA.N)  00  00  13 1 1 3 - 1 , N  0ATA(I13)-SCB(I13)«REAL(0ATA(113))  CALL F0UR2I0ATA.N,1.1,1) 0 0 2 I2-2.NDIM A1-REAL(0ATA(I2>) A2-AIMAG(DATA(12) ) P(12)-FACT»(A1*A1*A2«A2)«DT/RN/(4.-SIN(PI»(I2-1)/4086.)««2) 2 CONTINUE H-0. 00 3 13-2.8 H-H»P(I3) 3 CONTINUE AVP(3)-»VP(2)*H/7./FL0AT(IFLA1) AVP(1)-AVP(2) 00 4 14-2,IN H-0. 00 6 IB-1.8 H-H*P(16*(I4-1)»B> 9 CONTINUE AVP(2'I4)-AVP(2M4)*H/8./FL0AT(IFlA1) AVP(2-I4-1)-AVP(2M4) 4 CONTINUE 88 CONTINUE 00 84 194-1,N8 84 AINT(I94)-0.  Table  F.I  181 182 183 184 tas 186 187 188 189 190 191 182 193 194 195 196 197 198 199 200 201 202 203 ' 204 205 206 207 208 209 210 211 212 213 214 219 216 217 21B 2 19 220 221 222 233 224 229 226 227 2 28 229 230 231 232 233 234 335 336 237 338 239 24Q  0 0 85 193-2.IN AINT(2*I9S)-AtNT(2*!93-2)+0F*AVP(2*I9S) AINr(2-I95-1)-.S»(AINT(3*I85)-AINT(2<I8B-3)) 00 86 I86-1.N3 96 WRITE(6.G010)(K,rRE0(2*K),AVP(2*K).AINT(2«K).K-I86.IN,N3) 6010 FORMAT(IX, 3(0PI3, 3X, F6.2, JX,1PE9.3,2X,E8.3,6X)) WRITE(6.6123)USUB 6123 FORMAT{// 5IHAVG VALUE OF FALL RATE USED TO CALCULATE SHEAR 4.F10.4.9H CM/SEC) C CALL PLOUREO.AVP.S^BO.WT) 93  c c  C  c  RETURN END FUNCTION SCB(K) DATA PI/3.1415927/ 1F(K.OT.200)GO TO 1 SCB-.S«(1.-COS(P1«K/2CO.)) RETURN 1 IF(K.GT.3B96)G0 TO 2 SCB-1. RETURN 2 5CB-.5-(l.-C0S(PI«(4O96-K)/2OO.)) RETURN END SUBROUTINE AVER(A.N) COMPLEX'S A(ai82) SUM-O. 00 1 I-1.N 1 SUM-SUM*REAL(A(I)) SUM-SUMZFLOAT(N) DO 2 K-1.N 2 A(K)-REAL(A(K))-SUH RETURN END SUBROUTINE PAWEL2CC) INTEGER'S C(10.4097),A(3B60).LEN INTEGER LMJM  c  c  7 2 1 20  00 1 11-1. 17 CALL READ(A,LEN.0.LNUM,B,630) DO 3 13-1.256 K-2S6-(I1-1)+12 IFfK.QT.4087)00 TO 30 DO 7 17-1. 10 C(I7.K)-A(IO-(I2-l)*I7) CONTINUE CONTINUE CONTINUE RETURN  30 STOP 30 END SUBROUTINE AXL0G(XO.YO.IFLAG.NMIN.DN. I) DIMENSION TNUM(IS) DATA TNUM/2H-1.2H-2.3H-3.2H-4,2H-5.2H-6.2H-7.2H-8.2H-8, » 3H-10.3H-11,3H-12,3H-13,3H-14.3H-18/  cont'd  301 303 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 330 33 1 333 333 334 333 326 337 32B 329 330 331 333 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 330 331 352 353 354 355 356 357 356 339 360 .  CALL AXCTRLC'YORI'.Y0RI+YS12E) CALL A X P L 0 T ( ' ; ' . 0 . . X S I Z E . 0 . . X S l Z E D X ) CALL AXCTRLC'SIDE',-1) CALL AXCTRLC *X0RI',X0RI*XSIZE) CALL PLOTCXORI»XSIZE,YORI,3) IF(USUB.GE.1.)G0 TO 3 AL0"AL0G1O(1./USUB«»2) MM'NMIN-I-INT(ALO) Y0RIR*Y0RI*(1.-AM0D(AL0.1.))/DY GO TO 4 3 AL-AL0G10(USUB"2) MM'NNIN-MNT(AL) YORIR*YORI»AMO0(AL,1.)/0Y 4 CALL P L 0 T ( X 0 R I » X S I Z E , Y 0 R I R , 2 ) CALL AXCTRL('YORI'.YORIR) CALL AXPLOTC'i'.8O..YSIZE-1./0Y.O..CYSIZE-1./DY)*0Y) CALL PL0TCX0RI*XSIZE.Y0R1R»YSIZE-1./DY,3) CALL PL0T(X0RI*XSIZE,YSIZE*Y0RI,2) KR*(YSIZE-(Y0RIR-Y0RI)>«DY*1 CALL AXLOGtXORH-XSlZE,YORIR.-I,MH,DY.KR) CALL P S Y M ( X D R I * X S I Z E * 2 . , Y 0 R I » 2 . / 3 . * Y S l Z E . H T X . U N I T S ( 2 > . - 8 0 . , 4 , CALL PSYM(-0.,-0.,HTX.UNITS!3).-DO..4,0) CALL P5YMC-0.,-0.,HTX.UNITS(4),-00.,4,0) C DRAW INQ NUMBERS 1,10,100,1000 UNOER OX(LOO) AX 2 YX*Y0RI-3.«HTX CALL SYMB0L(X0Rl-4./7.*HTX.YX,HTX,1H1.0.,1) CALL SYMB0L(X0RI*1./DX-6./7.«HTX,YX,HTX.3H10.0.,3) CALL SYMB0L(X0RI*2./0X-10./7.»HTX.YX.HTX.3H100.0..3) CALL SYMB0L(XORI*3./OX-12./7.»HTX,YX,HTX,4H1OO0.0..4) CALL P5YM(XORI+XSIZE°2./3.,-HTX,HTX,UNITS(1) , 0 . .4,0) KL-(YSIZE-(YORIL-YORI))»OY*l C CALL AXL0G(XORI.YORIL.1,NMIN.DY,KL) ,  C  C  I ,  CALL LINE(X.Y.K.1) CALL PLOT( 13. , 0 . .-3)  C  ft C C C  DO 1 I1-N1.N3 X(I1*1-N1)«AL0010(X(I1))/0X»XORl Y(I1*1-N1)-(ALOG10(Y(I1))«FLOAT(NMIN))/DY+YORI  RETURN END SUBROUTINE AXLOG(XO.YO,IFLAG.NMIN.DN.I) DIMENSION TNUMC15) DATA TNUM/2H-1. 2H-2.2H-3. 2H-4. 2H-5.3H-6. 3H-T. 2H-8.2H-8, 3H-10,3H-11.3H-I2.3H-I3,3H-14,3H-15/ DATA HTYL/.S/ HTYS*.4»HTYL IFLAO- I COUNTERCLOCK SIDE IFLAG'-1 CLOCK SIDE IF(I FLAG.EQ.DXI"XO"10./7.*HTYL-18./7.'HTYS-.2 IF(IFLAG.EO.-1)X1*XO*.2 00 1 11*1,1 Y 1*Y0-.4*HTYL*1./ON*FLOAT(11-1) CALL SYMB0L(X1,Y1,HTYL,2H10..0.2) N-NMIN»1-I1 J-3 IF(N.GT.9)J-3  Table  F.1  -  341 342 343 344 245 246 247 248 249 250 231 232 253 234 255 236 267 238 259 260 261 262 363 264 363 366 367 268 369 270 371 272 373 374 275 376 277 278 379 280 381 383 383 384 383 286 287 288 388 290 291 393 293 294 393 296 397 398 299 300  OATA HTYL/.S/ HTYS*.4*HTYL IFLAG* 1 COUNTERCLOCK SIOE IFLAG--I CLOCK SIOE IF(I FLAG.EQ.1)X1*X0-10./7.*HTYL-18./7.•HTVS-.2 IF(IFLAG.E0.-1)X1*XO*.2  C  c c  c  DO 1 11*1.1 • Y1 *Y0- . 4*HTYL+'l ./DN*FL0AT( 11-1) CALL SYM80L(X1,VI.HTYL.2H10,.0.2) N*NM1N»1-I1 . d-2 IFCN.GT.8)0*3 IF(N.LT.1) RETURN CALL SVMS0L(X1*1O,/7.•MTYL*2./7.*HTYS.V1+HTYL-MTYS.HTYS. ft TNUM(N),0.,0) 1 CONTINUE RETURN END SUBROUTINE PLO(X.Y,N1,N2,J) REAL*4 X(312),Y(312) OATA XDRI,YORI,VORIL,YORIR,XSIZt.VS1Z6,OX,DY INTEOER C(6)/ZE6O87D4O,ZtBO87040.Z7BE3404O.ZC138A84O.ZC138A7.4O t,ZC13BA940/ INTEGER UNITS(9)/ZAD88A9BO.ZA0A28583.ZO86OF238.Z6188A88b, •ZAD409461,ZA2BS8309,ZO9F23B50.Z08F23861.Z88A9B040/ INTEGER UNIT3(41/ZA04DC3A1.Z61848008,Z09F23888,ZASBD4040/ INTEGER L E N ( 6 ) / 4 , 4 , 3 , 4 , 4 . 4 / COMMON/SUB/USUB HTX*.33 IFCU.LE.3)NMIN*8 If(J.CE.3)NMIN*10 K*N3-N1*1 CALL AXCTRLC'SYMISIZE'..137) CALL AXCTRL('SIDE'.0) CALL AXCTRLC YORI', YORI) CALL AXCTRL('XORI'.XORI) CALL AXCTRLC'LABELS',0) CALL AXCTRLC'LOGS', 1) CALL A X P L O T I ' ; ' . 0 . . X S I Z E . O . . X S I Z E ' O X ) CALL AXPLOT(' ; ' . 90. . VSIZE , 0 . . VSI ZE*OY ) CALL P S Y M ( H T X . V 0 R I « Y S l Z E / 3 . . H T X . C ( O ) . 8 0 . . L E N ( J ) . O ) IF(J-3)10.11,12 10 CALL PSYMC-O.,-0.,HTX,UNITSC3).90..4.0) CALL PSYM(-0..-0..HTX,UNITS(3),90..4.0) CALL PSYM(-0. , - 0 . ,HTX,UNITS(4 ),90. .4.0) GO TO 2 11 CALL PSYM(-0..-O..HTX,UNIT3<1),80..4.0) CALL PSYM(-0.,-0.,HTX,UNIT3(2),90.,4,0) CALL PSYM(-0.,-0..HTX.UNIT3C3).90.,4.0) CALL PSYM(-0.,-0..HTX.UN1T3C4).80..2.0) GO TO 2 12 CALL PSYM(-0.,-0.,HTX:UNITS(5),80..4.0) CALL PSYM(-0.,-0..HTX,UNITS(6),90..4.0) CALL PSYM(-0..-0.,HTX,UN1TS(7).B0..4,0) CALL PSVM(-0.,-0.,HTX.UNITS(8),80.,4,0) CALL PSYM(-0.,-0..HTX,UNITS(8).80.,3,0) CALL AXCTRLC SIDE ' . D  cont'd  f  fn0  361 363 363 364 365 366 367 368 368 370 371 373 373 374 375 376 of  PM*  IF(N.LT.1) RETURN CALL SVMaOL(X1»10./T.-HTVL*J./7.-MTYS.V1*HTVL-HTyS,HTy5. 8 TNUM(N),0.,U) 1 CONTINUE RETURN END BLOCK DATA COMMON/NUM/TNUM COMMON/TAPE/MOUN COMMON/FILE/POSN COMMON/RECORO/FSR LOGICAL* 1 POSN(8)/'P'.'0'.'S'.'N', '.'•'/ LOGICAL*1 TNUM(10)/'1'.'a'.'3'.'4'.'B'.*«'.'7'.'8'.'9','0'/ INTEGER FSR(S)/'FSR '.* '/ INTEGER'S MOUN(30)/30*' '/ END  CO  Table F.1  -  c  o  n  t  ,  d  1,317, I.I.I..023,1.028..4330000E-04.17.,512,  7 B a 10 11 12 13 14 13 IC 17 10 13 30 21 23 23 24 25 28 27 38 30 30 31 33 33 34 35 30 37 38 30 40 41 42 43 44 45 48 47 48 49 50 31 83 33 54 55 56 57 58 59 60  CO) 4096 .0030  POSN. FREOU. 1 3 3 4 8  6 7 8  8 10 11 13 13 14 15 (6 17 18 19 30 31 33 33 34 35 20 27 2A 30 30 31 32 33 34 33 36 37 38 39 40 41 43 43 44  VAR.  O.08 6.00IE-04 1 .83 4.333E-03 3.93 1.004E-04 3.91 4.834E-09 4.88 3.37GE-05 3.00 3.327E-03 6.84 4.654E-05 7.01 9.77IE-OS 8.79 9.780E-03 9.77 5.705E-O3 10.74 3.281E-09 11.72 3.S04E-09 12.70 I.644E-03 13.07 3.3SOE-03 14.65 7. 03(31-oa 15.63 1.373E-03 16.60 2.200E-0S 17.58 1.070E-03 10.53 7. 130E-0G 10.53 1.I03E-03 30.91 1.279E-00 31.40 S.3D0E-07 22.40 7.039E-07 33.44 1.05 IE-OG 24.41 1.80 IE-06 25.39 2.34GE-0fi 26.37 I.2D0E-0G 27.34 3. 103E-00 30.33 1.743E-00 30.30 1.53GE-00 30.37 2.393E-06 31.33 4.1S6E-06 32.33 0.547E-07 33.30 3.3O1E-O0 34. 18 2.5I8E-06 39. 10 4.333E-0G 36. 13 1.515E-06 37. 1 1 5.087E-0G 30.09 5.f)62E-06 39.06 4.421E-OG 40.04 2. I32E-OG 41.03 1.fil9E-0G 41.09 I.G7SE-0S 42.87 3.850E-08  CUMULATIVE  1  TINE INTERVAL (SEC)  POSN. FREOU  0.0 4.334E-0S 1.403E-04 1 .075E-O4 2.22SE-04 3.550E-04 3.004E-04 3.5GOE-04 4.324E-04 3.08 IE-04 5.40IE-04 3.743E-04 5.904E-04 8.I35E-04 6.2I3E-04 6.347E-04 6.SG3E-04 6.745E-04 G.ni5E-01 G.033E-OI 0.033E-04 6.04 IE-04 6.047E-O4 6.0G0E-O4 6.003E-O4 7.00GE-04 7.0IDE-04 7.040E-04 7.0B7E-04 7.072E-04 7.000E-04 7.I3GE-04 7.I4GE-04 7.1G8E-04 7.192E-04 7.234E-04 7.249E-04 7.299E-04 7.357E-04 7.401E-04 7.421E-04 7.437E-04 7.G0IE-04 7.G29E-0-I  AVERRAOED BV  DATA POINTS  VAR.  07 84.86 6.414E-06 80 03.94 3.730E-00 89 80.91 2.130E-06 90 87 .83 3.SOOE-06 9 1 BB.87 1.3G5E-OG 82 on.84 2.477E-OG 93 90.82 3.263E-06 94 81.00 6.879E-06 95 92.77 1.804E-05 00 93.78 3.084E-03 87 94.73 7.IS3E-0S 98 95.70 2.068E-04 99 98 .GO 2.040E-04 100 07.66 S.04SE-09 101 08.63 6.724E-0S 00.61 0.3GOE-OS 102 103 100.59 2.704E-05 104 101.GG 2.BGOF-05 103 102.54 3.7741:-05 106 103.53 2.334C-03 107 104.49 3.63IE-03 100 103.47 1.053C-OS 109 106.45 4.741E-0G 110 107.43 7.17DE-0G 1 1 1 100.40 1.047E-05 112 103. 38 8.222E-OG 113 110.33 0.I5SE-0G 1 14 111.33 3.780E-O0 118 1 12.30 2.374E-08 1 10 113.28 3.SAVE-06 117 114.2G 3.37IE-O0 118 115.33 3.837E-06 119 1 1G.2 1 3.3I7E-06 130 117. 19 1.20-IE-OG 131 118.16 1 .03IE-0G 122 119.14 3.073E-06 123 120.13 9.233E-06 124 131.00 3.3G4E-0G 12S 132.07 7.87SE-07 138 123.03 3.501E-06 127 124.02 3.540E-06 138 123.00 I.636E-0G 12S 128.90 I.7I3E-OG 130 136.95 1.37 IE-06  T a b l e F.1  -  CUMULATIVE t. I09E-03 I.107E-03 1 IOE-03 1I3E-03 1ISE-03 II7E-03 I20E-03 137E-03 I45E-03 183E-03 1.353E-03 1.454E-03 I.634E-03 1.713E-03 1.7686-03 1.849E-03 1.87GE-03 I.90IE-03 1.9JDE-03 I.030E-03 1.07GE-03 I.093C-03 1.998E-03 3.005E-03 2.015E-03 2.023E-03 3.033E-03 2.O3GE-03 3.03nE-03 3.047E-03 2.044E-03 3.048E-03 2.05IE-03 2.0S3E-03 2.053E-03 3.05GE-03 3.0G5E-03 3.0G8E-03 3.060E-03 2.O73E-03 2.07SE-03 2.077E-03 3.O70E-O3 2.080E-03  cont'd  POSN. FREOU. 173 •174 175 176 177 170 179 180 181 183 183 184 183 180 187 ISO 188 100 191 193 103 104 103 106 107 100 100 200 201 203 203 204 205 20G 207 200 209 210 211 212 213 214 215 218  168.05 109.92 170.80 171.88 172.85 173.83 174.80 175.78 176.76 177.73 178.7 I 178.69 180.66 1(11.64 103.62 183.50 184.37 185.55 106.52 107.GO 188.48 1HD.45 100.43 19 1.41 192.38 103.36 104.34 193.31 100.29 197.37 198.24 199.22 300.30 301. 17 202.15 203.13 204. 10 205.00 206.03 207.03 208.01 308.98 203.96 210.94  VAR.  CUMULATIVE  4.7846-07 3. I38E-03 2.426E-07 3.130E-03 3. BODE-07 3.130E-03 7.042E-07 2. I39E-03 I39E-03 1.618E-07 HOE-03 5.237E-07 14 1E-03 8.5S8E-07 I42E-03 8.976E-07 I43E-03 B.751E-07 143E-03 4. BI7E-07 144E-03 1.0B7E-06 144E-03 3.B67E-07 145E-03 5.2S0E-07 3.347E-07 2. MSE-03 3.GG0E-O7 2.I45E-03 2.571E-07 2.143E-03 2.777E-07 3.I46E-03 6.373E-07 3.14GE-03 5.711E-07 3. 147E-03 3.733E-07 2. I4 7E-03 4.01GE-O7 3. 148E-03 5.447E-07 3. 148E-03 6.5G2E-07 2.149E-03 0. 122E-07 3. 149E-03 4 .313E-07 2.IS0E-03 I.072E-O7 2. 150E-O3 3.0AGC-0? 2. ISOE-03 S.00GE-07 2.IS1E-03 7.707E-O7 3.IS 11-03 4.230E-07 2.1321-03 8.070E-07 3.1521-03 I.981E-07 3.IS3E-03 . 4. I01E-07 2.I53E-03 3.304E-O7 3.153E-03 2.921E-07 154E-03 4.2I6E-07 154E-03 5.137E-07 I54E-03 3.571E-07 155E-03 7.088E-07 I55E-03 3.0I1E-O7 15GE-03 5.962E-07 2. 1S6E-03 B.579E-07 7.-674E-07 3. 1S7E-03 3.O0OE-O7 3.150E-O3 2. I58E-03  O  191  S33-SS33SSS83?S3?S8SS83  liiiliiiiUHH ????S?SSSS8SfSSS8SS333S3SS8S88^  SS5S3Sr:£S?SS33gS5S55?5SSSS8SS5»22^ = 8S838  SS38333SS388333388S383338333883S3383353S8  S88888888S888888S8SSSSSS^  2SB2S8R8SS;5555H|58sSSS^  s  I  ???????????????????????????????????????? I .88888888888838888888888888888888^  S 3 § S S S g S S S ^ S S S S S K S S g 5 ! S ? ^ S 8 S o S J ; 5 S S c s = 23S35S  -  8  SSS33SS8S2^SS2SSt:?SS = 3 S S S S 5 S S g S S S S S 8 £ S S 8 o S 3 5 S o  192  As a means of routine,  a time  c h e c k i n g the c a l c u l a t i o n  series  p e r f o r m e d by  was g e n e r a t e d and i n p u t  to  the  this  routine.  4 The form of represent  this  the  time  series  was g ( t )  a m p l i t u d e s of  the  =  Z a sinw  i=1  specific  i  i  sinusoid,  t,  where  co  a  is  the  frequency,  N is  is  the  inverse  the  For so t h a t  the  of  test  the  total  sampling  The p a r a m e t e r s  = 100  a  =50  n  = 150  a n  = 75  •—  give i  f  the  n  for  the parameters  i  reduces  the .  2  f,  = 12.2 Hz  f  = 18.3 Hz  2  given  = 200 = 300 of  = 2 4 . 4 Hz  3  = 3 6 . 6 Hz  T = _]_/ g ( t ) d t . T 0 2  form t o  used,  i  f,  a  3  = n /NAt v a l u e s i  is  2  n„  f  - The v a r i a n c e  n  = 100  4  and At  u s e d were  n,  3  points,  500 Hz was  = 25 b i t s  2  i  rate.  a,  a  of  data  f u n c t i o n , a s a m p l i n g r a t e of  At = .002 s e c o n d s .  These v a l u e s  number of  /NAt  = 2itn  i  i  a  2  Using  = Ea / 2 , w h i c h i i  above.  2  integer is  values  = 9375  bits  for 2  1 93  f (Hz)  numerical cumulative  f ( H z ) a n a l y t i c a l cumulative v a r i a n c e , o'  v a r i a n c e , o'  11 .72  '  12.70  312.0  13.67  314.8  17.58  322.9  18.55  1547.  19.53  1 563.  23.44  1575.  24.41  1619.  25.39  4367.  26.37  4377.  36. 13  4424.  37. 1 1  9310.  38.09  9358.  39.06  9362.  f (Hz)  T a b l e F.2 -  3.4 12.2  312.5  18.3  1562.5  24.4  4375.0  36.6  9375.0  ((a -o )/<r )xl00 N A A 2  J  z  12.2  0.7%  18.3  0.03%  24.4  0.05%  36.6  0.14%  Comparison of cumulative variances calculated using the spectral r o u t i n e with the expected values (units are b i t s ) . 2  194  The d i r e c t l y  calculated  output  numerically  w i t h the  variance  calculated  routine,  which  9363 b i t s .  fact  that  the  to  zero at  of  cycles  signal the  is  the occur  is  not  routine  i n the  is  i n T a b l e F.2  by t h e  the  tapered  is  block,  not  of  the  spectral is  In  actual  due t o  random but  and o n l y  region.  along  this  the is  equal  a small  number  respect  the  shear  signal  to  test which  applied.  to appropriate  appropriate  function  representative  The r e l i a b i l i t y bits  test  b e g i n n i n g of  listed  The d i s c r e p a n c y  2  generated  is  of  the program i n c o n v e r t i n g  shear  calibration  units  the data  was c o n f i r m e d by a p p l y i n g  factors  in the  to  9u/9z = ( 2 . 5 / 4 ) ( 5 / 2 0 4 8 ) X / ( 2 / 2 K k S p W ) 2  where K,  k,  S,  the magnitude from b i t s  p and W have been d e f i n e d in b i t s  to v o l t s  following values  of  and  of  the  spectral  (2.5/4)  is  the  the c a l i b r a t i o n k = 2.7 S = 4x10'  5  in Appendix E  value,  (5/2048)  FM g a i n .  For  .  X  converts the  constants:  seconds volts/(dyne/cm ) 2  K = 1 p = 1 .028 gm/cm  3  W = 48 cm/sec it  follows  that 9u/9z = 2. 1 1 x 1 0 " X 3  The a n a l y t i c a l  and n u m e r i c a l c a l c u l a t i o n s  are  is  shown i n  Table  195  f (HZ)  numerical  cumulative  variance,  11.72  1 .493x10"  12.70  1.382x10"  13.67  1.394x10"  17.58  1.430x10"  18.55  6.853x10"  19.53  6.923x10"  23.44  6.976x10"  24.41  7.173x10"  25.39  1.935x10"  26.37  1.939x10'  36. 13  1.959x10"  37. 1 l  4.125x10"  38.09  4.146x10"  39.06  4.147x10"  f (Hz)  o'  -  analytical  cumulative  variance,  o'  12.2  1.379x10"  1  18.3  6.897x10"  1  24.4  1.931x10"  36.6  4.138x10"  2  ((o -o )/o )xl00 2  N  Table F.3  f(Hz)  2  2  A  A  12.2  0.80%  18.3  0.38%  24.4  0.40%  36.6  0.20%  Comparison of cumulative variances calculated using the spectral routine with the expected values ( u n i t s are s e c ) . - 2  196  APPENDIX G - RESOLUTION OF THE DISSIPATION MEASUREMENT The r e s o l u t i o n the c o n t r i b u t i o n system.  to  of  a measuring technique  the  n o i s e of  scale  on an  instrument  shear  electronically. measurement  u s i n g the a i r f o i l h o u s i n g and t h e Sources  of  2)  electronic  noise  3)  instrument  vibration  A number of  noise  source  noise  or  level  noise  Initial itself  probe.  signal  i n the a i r f o i l  is  case  The p r o b e  is  the of  is  mounted  processed  probe  the  itself  p i c k e d up by t h e  of  noise  resolution  to  probe.  of  sources w i l l  the  be d i s c u s s e d i n  were c o n d u c t e d i n t h e  E n g i n e e r i n g Department  Columbia.  The measurement  c o u p l e the a n e c h o i c  the  at  the  noise  level  however,  of  by  c o n d u i t which  building,  of  chamber of  the U n i v e r s i t y  was a f f e c t e d ,  to  actual The  turn.  anechoic  an e l e c t r i c a l  chamber  the  dissipation calculation.  t e s t s made t o d e t e r m i n e  m i s l a y i n g of  both  t h e measurement and t h e  Mechanical  the  made i n t h i s  t e s t s were made t o d e t e r m i n e  predominant  that  components of  are:  inherent  unfortunate  d e t e r m i n e d by  noise associated with  1)  probe  various  The f u n d a m e n t a l measurement  small  various  the  is  and i t  s i g n a l p i c k e d up by t h e p r o b e was c h i e f l y  the the British  an served  to  appeared building  noise. An a l t e r n a t e  test  was c o n d u c t e d i n  A p r o b e was p o t t e d up i n epoxy r e s i n s u s p e n d e d by a r u b b e r  to  the Oceanography restrain  band ( w h i c h p e r f o r m e d t h e  its role  huts.  m o t i o n and of  a  rather  i 97  crude  vibration  isolation  system)  60 Hz u s i n g aluminum f o i l . differentiated  and t h e  The s i g n a l  output  HP3582A s p e c t r u m a n a l y s e r ) the  calculation  G.1.  and w i l l  calculations integrated  this  sensitivity  of is  t r a n s m i s s i o n of the  lab.  connections the  as  input  for  to  the  the  m i x e d FM s i g n a l Phideck  recorder  the  was  shear  shear  effect  r e c o r d e d on a s e c o n d c h a n n e l  back,  the  signal  calculated.  Table  the  other  units  of  probe rate  of  75  tape  due t o FM  r e c o r d i n g were m e a s u r e d  the  the  signals  signals  noise  (3.9  (1.3  spectral  airfoil  probe  fed d i r e c t l y  The o u t p u t s  of  and 5.4  and  into  the  1.7  density  of  the  tape  recording  r e c o r d e d on one c h a n n e l  of  in  kHz)  kHz)  as  were  function  40 H z .  while a tape  wow and f l u t t e r  and  density  the  and t h e VCO o u t p u t s  the  to  noise  FM c o n t r i b u t i o n ,  HP3582A and t h e  To d e t e r m i n e  of  and a f a l l  the  and t h e  the  amplified  m e a s u r e d and i n t e g r a t e d  for  to  Sonex FM d e m o d u l a t i o n s y s t e m .  well  The d a t a  3  signal  used f o r  and  the  shown  spectral  from  W/m .  were s h o r t e d ,  discriminators  are  values,  2  To measure  with  G.1.  Converted to  volts/(dyne/cm ) 1 0  shielded  be r e p r e s e n t a t i v e The n o i s e  contribution  the  noise  nominal c i r c u i t  5  2x10"  (measured  in Figure  the  62 M v o l t s .  the  3X10~  The r e l a t i v e  in  section.  40 Hz i s  using  this  shown  be c o n s i d e r e d t o  dissipation  cm/sec,  is  pail  was p r e a m p l i f i i e d  spectrum  made t o d e t e r m i n e  in  to  in a metal  of  speed r e f e r e n c e to provide  tape  drive.  d e m o d u l a t e d and t h e  system  the  instrument's  signal  a means of This  noise  tape  the  was  accounting was  spectral  played  density  861  199  date  M a r c h 26,  198l  time  2000  PST  b a n d w i d t h ( B W ) = 0.6 Hz  f(Hz)  V(nvolts)  V/VBW  0-5  3.  4.  5-10  7.  9.  10-15  6.  8.  15-20  8.  10.  20-25  7.  9.  25-30  9.  12.  30-35  8.  10.  35-40  11.  14.  = / U ( V / , / B W ) A f ) = 62<iV  V  I  l  NOISE preamplifier  S = 3x10"  5  g a i n = .85  volts/(dyne/cm )  Ou/3z)  /(W2SW*/v)  = 1.6xl0"* s e c '  1  NOISE  = 7.5KUU/3Z) NOISE  W = 75 cm/sec  J  =V NOISE  t  seconds  = 2xlO"  j  1 0  W/m  J  NOISE  Integration of the noise spectral density function and calculation of equivalent d i s s i p a t i o n due t o the inherent noise of the shear probe.  200  The r e s u l t s terms  of  shear  signals  these  equivalent  addition the  of  of  noise.  are  tape  The v e r y  the  noise  level  inherent Since  than  5X10"  quiet  noise  the  stretches  electronic made f o r  noise  the  to d i s s i p a t e the  energy  we c a n d o ,  p r o m p t e d an  for  of  its  data  not  given  u s i n g the 2.2x10"  tape W/m ,  1 0  which  3  are  the  more l i k e the  1-3X10~  probe n o i s e  factors.  (Lambeck(1977))  reported  profiles  turbulent  of  wave f i e l d  q u i e s c e n c e and f o r  vehicle  hydrodynamically limit  significant  that  replacement  to this  of of  the  n o i s e of  noise  level  4 by r e m o v a l  of  over  in  the  3X10~  7  required  range  noise  From a  Columbia i n l e t  W/m . 3  it  broadband v i b r a t i o n a l  It  body  result  is  recovery  chatter  was  be  instrument  rear  noted  accelerometer  c a n be r e d u c e d f u r t h e r the  of  This  induced  w h i c h must the  been  maintain  probe measurements,  accelerations  i n d u c e d by f l o w  i n an u p p e r  a factor  shear  which  in  3  level  i n Mourn and L u e c k ( l 9 8 4 ) . British  W/m  (Olbers(1983)).  hydrodynamically  made i n a l o c a l  smaller  and  and t o  by Lambeck and O l b e r s a r e  investigation is  the  rivals  A r g u m e n t s have  a background turbulence  internal  7  d i s s i p a t i o n measurements made t o d a t e .  determined that  the  10 and  probe.  limiting  measurements were c o m p a r e d t o  least  is  record,  energy  tidal in  of  measurements made have been no  the  sources which series  the  of  balance  smallest  of  existence  The e s t i m a t e s the  the  are  by a f a c t o r  recording  level  of  amplified  best  and g e n e r a l l y  3  the  increases  smallest  W/m  8  Use of  in  r e c o r d i n g system s u b s t a n t i a l l y  s y s t e m and b o t h a m p l i f i e d s h e a r s the  summarized i n T a b l e G . 2 ,  dissipation units.  reduces  the  tests  ring,  (1-10HZ)  by  at  due  to  which  201  contaminates instrument  the d e s i r e d s i g n a l  w h i c h can be f i l t e r e d  background t u r b u l e n c e of  the  Camel.  r e d e s i g n of  It  levels  out.  frequency This  must be l e s s  also provides  Camels.  by low  guidelines  tilting  implies  that  of  the  any  than  the  noise  level  for  the  ongoing  202  date  10, 1 9 8 1  August  noise  spectral density  S = 3x10"  5  function  integrated  t o 40 Hz  volts/(dyne/cm ) J  W = 75 cm/sec  e  -S±  FM  FM/TR  *  _S_2_  e  e  SA 1  SA2  1.3x10"'  1.2x10-'  1.1x10""  1.4x10""  2.3x10"'  2.7x10''  2.2xlO"  7.4x10""  1 0  Comparison of noise levels due t o FM and t a p e r e c o r d i n g s y s t e m s on a l l o f t h e s h e a r c h a n n e l s .  203  APPENDIX H ~ ERRORS IN THE DISSIPATION CALCULATION A d i s c u s s i o n of necessary  so t h a t  the  faults  that  our  estimates.  exist In  recognized errors 1)  the  at in  the c a l c u l a t i o n  some f u t u r e the  are  due in  of  e  is  individual  time,  be a b l e  to  correct  s y s t e m and i m p r o v e t h e a c c u r a c y  no p a r t i c u l a r  inaccuracy  electronics  in  we may be w e l l aware of  c o n t r i b u t i o n s and may, the  errors  order  of  importance  of  the  to: t h e measurement  used to p r o c e s s the  2)  the  estimate  of  the  fall  3)  the  estimate  of  the  shear  4)  the  lack  of c o r r e c t i o n  of  the  gain  of  the  signal  rate probe  for  the  sensitivity frequency  r e s p o n s e of  the  electronics 5)  t h e a s s u m p t i o n of  6)  the  limited  7)  the  spectral  isotropic  spatial  r e s p o n s e of  variance  scheme d o e s not  track  turbulence the  missed since  the  probe the  viscous cutoff  integration wavenumber  exactly. The f i r s t  four  o b v i o u s and a r e electronics likely  C,  the  instrument smallest  than  2.6)  fall  more e a s i l y  g a i n u s i n g the  worse  (Equation  s o u r c e s of  1%.  this  rate  is  error  on t h e  discussed.  HP3582A s p e c t r u m a n a l y s e r  As a s q u a r e d t e r m  results  i n a 2% e r r o r  known w i t h i n  r a t e s of  are  Measurement  in the in  about  e.  ±1.5 cm/sec.  slows c o n s i d e r a b l y as the d e n s i t y  fall  list  the of is  estimate  no for  e  From A p p e n d i x Since  the  increases,  50 cm/sec o c c u r a t  most  the  depth, giving a  204  3% e r r o r  in  the  W*.  Lueck,  the  frequency  error,  or  accurate results  fall  and .hence a  C r a w f o r d and O s b o r n ( l 9 8 3 ) response of  10% i n to  rate,  e.  the  i n an e r r o r  The p r o b l e m of the a p p r o p r i a t e  of  of  h i g h or  computation. routine  how f a r  to  for  low g a i n  were b a s e d a r e  integrate  shows  four  labelled  cm/sec,  f  the  to  the  A closely  shear  channel  The c r i t e r i a  four  shear  decades  frequency  of  dissipation wavenumber  a cyclic  in  is  spectrum to  related used i n  s p e c t r a which  e and a r e  s  figure  frequency  recover and  problem i s  the  the by my  decisions  the  is  , where k  i)  over  from a p r e l i m i n a r y Island  routine  in A p r i l ,  test 1981.  d i s c u s s e d in Appendix  in descending magnitude. rj = (v /e)^, fall  Also  which  3  u s i n g the  k/k  s  shear  seen. s  rate  s p e c t r a as t h e  The c o n s t a n c y  = 1/TJ) of  been g e n e r a l l y  found t h a t :  range  of  is  50  The e x p e c t e d downward and l e f t w a r d s h i f t  t h e peak of  k/k  5%  This  upon w h i c h t h e  Kolmogoroff m i c r o s c a l e ,  decreases  s p e c t r u m has have  in the  = W/2TTT>.  s  probes  c o m p u t i n g e i s more s u b t l e  T h e s e have been computed u s i n g t h e  converted  shear  e a  neglecting  causes a d i r e c t  the  d r o p made i n Q u a t s i n o Sound on V a n c o u v e r  computed i s  since  discussed here.  H.1  approximately  F and a r e  that  T h e s e d e c i s i o n s were made a u t o m a t i c a l l y  'DISSIPATION'.  Figure  e,  e.  hence w a r r a n t s more a t t e n t i o n . choice  of  in  personal communication).  20% i n  variance  estimate  electronics  The c a l i b r a t i o n  10% ( R . N i n n i s ,  12% e r r o r  the  peak  a c c e p t e d due t o  = 0.1  in a t i d a l  (in  energy dimensionless  in the  dissipation  investigations  channel  in  (Grant  et  which  205  1  10 LOG  100  1000  F (Hz)  Four shear spectra from Quatsino Sound on Vancouver Island taken in April, 1981. The d i s s i p a t i o n s c a l c u l a t e d from e a c h spectrum are: 1)6.2x10-*; 2)1.0x10-'; 3 ) 1 . 3x 1 0'" ; and 4)1.3X10' W/m . The f a l l r a t e was 48 cm/sec. The arrows refer to k/k = 0.15 for each spectrum. 5  6  3  s  206  al.(l962))  and i i )  k/k  » 0.15  in a g r i d produced  turbulence  s ( S t e w a r t and T o w n s e n d ( 1 9 5 1 ) ) . over  the  spectrum at  k/k  For  c o m p a r i s o n , an a r r o w  =0.15 and t h e  agreement  is  w i t h the  drawn peak  s is  quite  good - e x c e p t i n g s p e c t r u m 4,  overestimated calculation,  u s i n g the thereby  low  shifting  Spectrum 4 in F i g u r e gain a m p l i f i c a t i o n peaks at of  the  6 and  system  and f l u t t e r incomplete  unwanted  f o r m of  incomplete  spectrum of  the  high frequency  in F i g u r e  smaller  dissipations. before  spectrum 3 past  H.1  easily  The e f f e c t i v e n e s s  problem w i l l  noise  is  of  noise  is  d o m i n a t e d by  The s p e c t r a l H.2,  for  tape  the  percent  recording t a p e s p e e d wow The e f f e c t  of  signal  the h i g h g a i n  channel  further.  increasing  among t h e  importance  1 may be i n t e g r a t e d  to  30  d e m o n s t r a t e d by  to  However,  i n c l u s i o n of  a n d s p e c t r u m 4 must be r e p l a c e d by t h e is  The  constant  encountered.  15 Hz l e a d s  recording.  a tape recorded  be d i s c u s s e d  and becomes of Spectrum  high  system u s e d .  of  right. of  compensation for  output  the  this  directly  s i g n a l a d d e d by t h e  speed compensation i s  spectra  in Figure  to  20 Hz and a r e  The a m b i e n t  it  signal prior  to  necessity  to  in overcoming t h i s  since  shear  the  integrated  with grounded i n p u t .  estimate,  illustrates  by t h e FM d i s c r i m i n a t o r  examining the  of  e s t i m a t e d peak  spectrum 4 account  tape  (120 cyc/m)  the  the  likely  w h i c h was u s e d f o r  of  to  in the  H.1  shear  is quite  12 Hz a l o n e  variance  attributable  of  gain  which  four for  60 Hz  integration noise  in  high gain  the shear  noise.  integration  cutoff  p l o t t e d with the  frequencies  integrated  used are  universal  shown  dissipation  207  o  v< L U C J  CC  e •  CC  (W/m ) 3  IO'  4> 1 0 "  Q'o  X  IO'  +  10-  A 10©  C O  IO"  2  3  4  5  6  7  L U  Chi  •t  o o  _±_  0 . 0  _2_ 0 . 4  • X 0 . 8  K/KS F i g u r e H.2  -  P e r c e n t a g e o f t h e v a r i a n c e r e s o l v e d by t h e shear probe vs n o r m a l i z e d wave number. The c u r v e i s the i n t e g r a t e d u n i v e r s a l dissipation wavenumber spectrum. Symbols at the very bottom r e p r e s e n t t h e p r o b e c u t o f f (70 cyc/m) w h i l e s m a l l e r s y m b o l s above r e p r e s e n t i n t e g r a t i o n c u t o f f s .  208 curve.  The o r i g i n a l  converted to Oakey(1982) Lueck,  the  energy  spectrum i s  transverse  s p e c t r u m and d i s s i p a t i o n  and i n t e g r a t e d  to  show t h e  C r a w f o r d and O s b o r n ( 1 9 8 3 ) .  r e s o l v e d by  integrating  from N a s m y t h ( 1 9 7 0 ) ,  It  cumulative shows t h e  s p e c t r u m by  variance  by  variance  t o d i m e n s i o n l e s s wavenumber  k/k  .  The  s upper  limit  rolloff  of  to  the  integration  must a c c o u n t  for  the  t h e p r o b e , e s t i m a t e d t o be a p p r o x i m a t e l y  Ninnis(1984).  The e q u i v a l e n t  spatial 70 cyc/m by  d i m e n s i o n l e s s wavenumber  k/k  for s  70 cyc/m i s  shown a d j a c e n t  to  the  k/k  axis  for  values  of  e  s d e n o t e d by t h e .01  cm /sec. 50% of  the  probe c u t o f f , values  than  thousand) 3X10  cm/sec), a  the  variance  w h i l e at  - 3  10"  is  10"  to  hence  the  W/m ,  3  integrated  the  wavenumber  10"  a dozen  )  spatial Below  10"  W/m  3  resolved.  (of  3  to  the  Since  more t h a n  the  largest  no  were ten of  56 Hz (70 cyc/m a t  noise  Below a b o u t  5x10"  5  than  the  greater  integration  3  is  in  the  terminated at W/m , 3  30 Hz  however  these  80  the measurement.  For  values  the  was  15 Hz  the  probe  and  80  cutoff  wavenumber, of  be  cutoff  computation,  and  e < lO" W/m ,  (19 cyc/m a t  c h o i c e t o be made, b e s i d e s t h e  probe  (38 cyc/m a t  the  viscous cutoff  terminated at  to  variance  does not a f f e c t  The o t h e r  W/m ,  2  integrating  (and  3  to  W/m ,  3  integration  integration  10"  v =  r e s o l u t i o n p r o b l e m was n o t c o n s i d e r e d t o  i n c l u s i o n of  is  of  viscosity,  f r o m PEQUOD o r WESPAC w h i c h  and o n l y  3  w h i c h were  80% i s  3  than  the  cm/sec).  W/m ,  r e s o l v e d by  were g r e a t e r  serious one.  leads  2  key and a k i n e m a t i c  high d i s s i p a t i o n rates  were m e a s u r e d e i t h e r  greater  was  in  At q u i t e  2  barely  symbols  5  3  80 c m / s e c ) .  frequency at  which  209  to  terminate  high gain series  integration  shear.  of  the  F i g u r e s H.3  with respective  spectrum i s  and H.4  spectra  shear for  the  time  two  series  each s e c t i o n  from e a c h low series  from four a d j a c e n t  qualitative  and a l l  in  incomplete  the  low g a i n  10"  this  W/m  5  the  high  four  shown i n H . 3 .  gain  signals  The  time  only  included  is  attributed  channel  factor the  in  (as  3  of  20 a t  reduction  shear  units.  (turbulent  On t h e  n o i s e above  other the  for  the  Spectra 1.5x10"  velocity  5  channels W/m ).  is  r e c o r d e d on  turbulence  indicate  for  block  W/m  spectra  exhibit the  signal  i n the  is  shear  due  low g a i n  to  noise)  predominance  noise  2  the  recorder  between t h e  At h i g h e r  spectra  n o i s e by a b o u t  attenuated  agreement  probes.  considerably  5 7 , where  60 shows t h e  less  shear  a g r e e much b e t t e r  3  the  dissipation  High gain  3  signal)/(tape  hand, block  amplified  and t h e  the h i g h frequency  o r t h o g o n a l l y mounted s h e a r shown h e r e ,  7  to  At d i s s i p a t i o n s  signal  shear  w h i l e the h i g h g a i n c h a n n e l s These s p e c t r a a l s o  signal  Camel I I I .  4x10"  of  is  the  computed from t h e h i g h g a i n  low g a i n  computed d i s s i p a t i o n the h i g h e r  of  n o i s e dominates the  higher  the  1981.  The d i s s i p a t i o n computed  and a r e  shear  recorder  from the  level.  blocks  i n November,  from t h e  or  time  data  w i t h one of  spectra  is  been c a l i b r a t e d  estimated  decades  the  t a p e s p e e d c o m p e n s a t i o n of  than about  indicate  Bay  series  (numbered 5 7 - 6 0 ) .  cassette  (a  of  low  comparison.  Noise  channel)  time  or h i g h g a i n p a i r  have n o t  internal  low g a i n  use of  show a c o n t i n u o u s  computed from a d r o p made i n M o n t e r e y Shown a r e  the  of  channels, peaks. two  dissipations,  c l i p p e d by t h e VCO t o  not  which  210  S2  S i A  57 E-2-2x10- W/m  3  5  E «..5*l(r A  5  58 E = l-O*10~  5  E -2.5xK)  H  A  59 E-87K10-  6  E «96xl0A  7  60 E»82*Kr E -4.1xi(r 6  A  Figure  H.3  -  7  E x a m p l e o f s h e a r p r o b e o u t p u t s f r o m d r o p made in Monterey Bay in November, 1 9 8 1 . The s i g n a l on the r i g h t i s the h i g h gain amplified signal of that on the l e f t w h i l e the m i d d l e s i g n a l i s the h i g h g a i n a m p l i f i e d shear signal from a probe which is mounted perpendicular to the f i r s t . T h e s e were d i v i d e d i n t o b l o c k s of 1024 p o i n t s f o r w h i c h t h e d i s s i p a t i o n was calculated from both r e g u l a r and h i g h g a i n s i g n a l s ( s u b s c r i p t A ) .  s  i  s  s  2  A1  s  A2  I I I !  1  F i g u r e H.4  100  -  Spectra f r o m t h e f o u r a d j a c e n t b l o c k s (57-60) o f the time series shown in Figure H.3. The horizontal axis is log f r e q u e n c y (Hz) a n d t h e vertical axis is shear spectral density (sec" /Hz). T h e s e a r e s c a l e d i n l o w e r l e f t hand corner. The r e f e r e n c e d o t on each spectrum is . l o c a t e d at (1Hz, 1 0 " s e c ~ / H z ) . 2  5  2  212  it  is  input  and hence u n d e r e s t i m a t e s  t h e d i s s i p a t i o n and t h e  g a i n c h a n n e l must be u s e d .  A plot  d i s s i p a t i o n computed by t h e  low and h i g h g a i n  against  that  computed by t h e  threshold level gain  is  used. W/m  3  10 (as  of for  When t h e  It  to a poor c h o i c e  which broad,  is  is  3  of  low  the plotted  indicates  that  gain  shear  a threshold level to estimate shear.  level  but  the  of  the to  the  computed e s t i m a t e  is 10"  error  Obviously, since  a  amplifier  low g a i n  well assured that  the  of  shears  c a n be c h o s e n a p p e a r s  we can be r e a s o n a b l y  has been made and a c c e p t  shear  which the  difficult  threshold  threshold level  ratio  s h o u l d ~be""used when t h e above  h i g h or  the  gain  30 (WESPAC),  very  away from t h e  the  W/m  9  PEQUOD),  gain  was u s e d .  critical  10"  low  of  low  due  it  is  range  be  5  over  relatively  best  choice  from t h e  chosen  signal. The r e m a i n i n g c o n t r i b u t i o n a s s u m p t i o n of  isotropic  to  turbulence  use of  Equation  (2.6)  for  on t h e  vertical  shear  component,  Gargett  et  dissipation Errors  summed, 10"  9  scales  1)~4)  3  are  initial  made t o e n a b l e  the  information  2,  The v a l u e o f  by up t o a f a c t o r of  however,  that  about  of  2,  40% i s  a recent  the assumption of  the  44% when t h e a b s o l u t e  worst  case.  Dissipations  r e s o l v e d t o 80% or b e t t e r ,  the  the  more  paper  by  isotropy  may be a good a s s u m p t i o n .  contribute  representing  W/m  indicates  the  We have no  and a v a r i a t i o n  As d i s c u s s e d i n C h a p t e r  at  is  9u/9z and 9 v / 9 z .  usual.  al.(l984)  which  is  9w/9z, and c a n o n l y compare  two h o r i z o n t a l components c a n v a r y frequently,  error  c o m p u t i n g e.  two h o r i z o n t a l c o m p o n e n t s ,  a l t h o u g h not  the  values less  although larger  are  than but  213  infrequent  values  rolloff  the  of  integration  noise  These e r r o r s these  estimate  of  but  e is  cannot  worst  then,  be c o n t i n u e d t o  shear  large  resulting  a s s u m p t i o n of  the  spatial  s p e c t r u m becomes l i m i t e d by n o i s e  occasional  clipped,  r e s o l v e d due t o represents  3  The h i g h g a i n  represent,  and t h e  the  and i n t e g r a t i o n  here  electronically  10."* W/m  since  wavenumber. ratio  more p o o r l y  probe.  error  high frequency cutoff  are  improves  turbulent  case  i s o t r o p y made, a factor  of  of I  64%. believe  2.  probe  signal  to  b u r s t s may be  i n p o s s i b l y worse  a worst  good t o w i t h i n  the  the  at  errors. Considering that  the  214  APPENDIX I There are  a number o f  The u n i t s  used in t h i s  change of  energy  density will is  of  seawater  cause a worst  rates,  Units  of  case  error  is  factor  the  2  Since a l l  of  the  4% i n of  3  is  into  1 W/m  of  10"  1 W/kg «  is  2  equal  1  1 e r g . s e c " /gm  1  to  is  e,  which  the  cm /sec 2  cm /sec 2  included If  one  is  easily  and a r e  3  3  3  lcm /sec 2  1 cm /sec . 2  it  more in  W/kg.  following  2  3  assumption  however,  3  reader.  4  constant  transfer  not  calculation  1 m /sec  1 e r g . s e c " /cm 1  mass a r e ,  and m / s e c .  the  of  3  the  = IO"  3  rate  for  believe  have been u s e d ,  convenience 3  I  density  3  the  researchers,  2  estimate  e.  J/m .  unit  2  1 m /sec  the  of  cm /sec  units  This  3  in comparing energy  approximately  these  represent  kg/m ).  2 which  the c o r r e c t  density  be u s e d by v a r i o u s  presented for  (1028  r a t e per  These a r e  used for  and t h e a s s u m p t i o n of  commonly i n u n i t s  calculation.  shown t h a t m / s e c  of  useful  if  which  3  has been made  correct  chooses to put  a r e W/m ,  volume,  dissipation  fundamentally  to  unit  This unit  which are  commonly q u o t e d u n i t s  thesis  s m a l l compared t o t h e  accuracy.  the  per  - UNITS OF e  3  3  table  continuing is  215  APPENDIX J  - TREATMENT OF WHITE HORSE VELOCITY  White Horse v e l o c i t y  data  were r e c e i v e d  G.Needell  o f WHOI.  1000 m of  each White Horse p r o f i l e  III  profile.  A magnetic  The v e l o c i t i e s  White Horse p r o f i l e s order  to c a l c u l a t e  using a 3 point differences and u,  smoothed d a t a ,  E-W and and N-S  Some of  the  plots  estimate  significance  of  in t h i s of  the  trends.  Thompson(1982).  They  cm/sec u s i n g a 25 d b a r u s i n g the  t h e p u r p o s e of to  infer  calculating  the a b s o l u t e  the estimate  of  m a g n i t u d e of  the  values  of  the  to  from  first  = (u +v ),  2  2  2  is  The amount of  of  and  resolved to 4  smoothing,  substantial  in v e l o c i t y I  understand  limitations  Needell  the v e l o c i t y  (as  and,  for  opposed  have u s e d an e r r o r  5u = 1 c m / s e c .  U , then  In  a d i s c u s s i o n of  in order  in Luyten,  velocity),  data.  were smoothed  ,where U  require  differences  of  these  components.  r u n n i n g mean i s  the v e l o c i t y  of  calculated  S = AU/Az  parameters  that  the  velocity  shear  thesis  is  upper  25 m i n t e r v a l s .  the p r o f i l e s  velocity  spacing.  3 point  are  A d i s c u s s i o n of  t h e W h i t e H o r s e measurements  however,  thesis  r u n n i n g mean and t h e the  the  and  w h i c h c o r r e s p o n d e d t o a Camel  however,  the  i n the  was p r e p a r e d of  this  v are  errors the  of  from J . L u y t e n  were c a l c u l a t e d a t  shown i n  shears,  tape  AND CTD DATA  The e r r o r  in  in the  is  S U = |9U/9u|6u + |9U/9v|5v S U = |u/U|8u + But  |v/U|5v.  6u = 5v so 8U = ( I u | + | v | ) 5 u w h i c h  is  largest  for  the  U  smallest for  values  of  u,  v.  w h i c h U = y/2 c m / s e c ,  S i n c e the I  will  l i m i t i n g values  take a worst  case  are  1cm/sec,  estimate.of  5U  216  = / 2 8 u = \J2 c m / s e c . The a c c u r a c y percent the  of  full  resolution  differences of  of  t h e p r e s s u r e measurement  scale is  (0.1/100x6500 dbar  the c r i t i c a l  the White Horse  results  = 6.5 d b a r ) .  parameter  and must be c o n s i d e r a b l y  i s quoted as  in  However,  determining  smaller.  i n an e r r o r  0.1  The  12-bit  system  of  6z = 6 5 0 0 / 2  1.6  in d i f f e r e n c i n g  two a d j a c e n t  points  6(AU)  6(Az)  1 2  meters. The w o r s t twice the 28z,  case  error  of  error each  where 8 r e f e r s  adjacent  values.  individual  to the  error  The e r r o r 8S =  9S 3(AU)  in  value,  and A t o  the  6(AU)  shear +  the  = 25U,  difference  estimate,  is =  in  S = AU/Az,  is  6(Az)  as  3(Az)  giving 5S/S Az i s  f i x e d at  25 d b a r  depends c r i t i c a l l y adjacent  points.  undercurrent  worse,  say  5S/S  In  the  the  data  Scripps  the  shear  difference surface  resulting  signal  estimate  between  current  is  ratio  5S/S  is  two  -  differences  to noise  the  differences  error  where v e l o c i t y  from t h e  and g i v e n a t  PEQUOD t r i p  a l o n g with the  Institute  f r o m t h e WESPAC t r i p .  calibrated  the  over  25  = 2/2/50 + are  considerably  = 3.  by J . L u y t e n and G . N e e d e l l of  in  r e g i o n where v e l o c i t y  W h i t e H o r s e CTD d a t a  P.Niiler  error  equatorial  However,  1 cm/sec,  + 2|6z/Az|.  velocity  50 c m / s e c ,  2(1.6)/25 = 0.2. smaller,  so t h e  on t h e  interface  d b a r may r e a c h  = 2|6U/AU|  was a l s o  velocity  provided  data.  of O c e a n o g r a p h y p r o v i d e d t h e CTD  In  2 meter  both cases intervals.  the  data  was  fully  217  The i n  situ  international  Grosso(1974),  N,  N  sound i n  seawater  long,  of  the  his  the  due t o  error  instrumental  interpretation  of  the  from the  I  2  it  is  not a t  quantization noise, lower  bound on t h e  I  gravity, is  the  do not  of  WESPAC. the  the  N ranges  from 1 0 " for  greater  3  that  this is  a  the  example, than  rarely.  For  Az = 20m w h i c h  than  t h e Az = 25m u s e d i n t h i s  3x10"  results  following  to in 2  Del  s p e e d of  density.  f r o m CTD d a t a of  study,  8N/N  10"  3  1.0  10"  2  .03  is  the  it  has I  already  rely  on  work. 12-bit  s y s t e m and  limitation  is as a  of N from PEQUOD and 16-bit  10" the  2  system used  rad/sec  i n most  equatorial  rad/sec  in a s l i g h t l y  errors.  N(rad/sec)  by  11 of G r e g g ( l 9 7 9 )  rad/sec  core at  a s s o c i a t e d w i t h the  situ  i n N from the  undercurrent  for  the  and s i n c e  the c a l c u l a t i o n  error  ocean w i t h s p i k e s ,  in  is  have a l l  in N for  use F i g u r e  in  c  manner by G r e g g ( l 9 7 9 ) ,  certain  shall  noise  as an upper bound t o for  all  form g i v e n  Brunt-  2  behaviour  error  the  g /c ,  The CTD mounted on t h e W h i t e H o r s e although  by Pond and  in N c a l c u l a t e d  since  general  1980 UNESCO  from  and p = p ( S , T , p )  been done i n a q u i t e  given  = -gAp/pAz -  2  u s i n g the  sound u s e d t o c a l c u l a t e  calculated  tedious process,  specifics  (as  calculated  acceleration  Since estimating a  state  is  and N i s  the  calculated  The s p e e d of  frequency,  where g i s  is  e q u a t i o n of  Pickard(1983)). Vaisala  density  occurring greater  these values  of  only error N are  218  3x10A bulk Richardson parameters  as R i  number  = N /S , 2  can be e s t i m a t e d  or,  and t h e  2  = |9Ri/aS|6S 5Ri/Ri  Ri  estimated give  Ri  a  is  calculated error  feel  the  these  estimate  of  Ri  + |3Ri/aN|6N,  = 2|6S/S|  + 2|5N/N|.  depends on i n d e p e n d e n t v a l u e s the  in  from  from 6S and 6N, 8Ri  Since  .01  2  ranges  for  of  each  the e r r o r  N(rad/s)  for  in  of  N and S,  a number of  I  values  have of  Ri  to  Ri.  S(s- ) 1  8N/N  8S/S  5Ri/Ri  . 1 5  (.002-.02)  (.005-.03)  .05  .15  .40  .50  (.0005-.01)  (.0005-.01)  .25  .30  1.1  2.0  (.0004-.01)  ( .0002-.005)  .30  1 .0  2.6  10.  (.0003-.003)  (.0001-.001)  .50  2.0  5.0  It  is  have  fortunate a better  that  signal  smaller to  noise  and more ratio.  interesting  values  of  Ri  219  APPENDIX K - PEQUOD DROPS T h i s appendix c o n t a i n s b a s e t e n of  turbulent  d r o p s of  the  w i t h the  right  units  individual  kinetic  energy  PEQUOD c r u i s e .  of W/m  end of  The l o g  e axis  vertical  axis  over  has a t i c  a d r o p l o g which  lists  The W h i t e H o r s e net  from 1 0 "  is  data  listed  logarithm  for  dissipation  Preceding  the  plotted.  and B r u n t - V a i s a l a  Temperature  The r a n g e s ppt,  salinity  is  on t h e h o r i z o n t a l  and 0.  velocities  plots  as  is  solid lines  For  gave  the  shorter  is  flow flow  are  dashed.  3 4 . 5 - 35.7  profiles > 0) >0).  t o d r o p 13 were s t a r t e d  the  opportunity  Camel.  However,  simultaneously  show z o n a l  and Full  scale  approximately  of  the  we were a b l e  one W h i t e H o r s e  to  recover  drops  the  This  on  13 and f o l l o w i n g  cycle.  Camel to  procedures. (the  as  the  Due t o t h e  the  before  were made crew  gained  much  W h i t e H o r s e goes a l l  l a u n c h and r e c o v e r  four  procedure  instrument  w i t h White Horse d r o p s ,  i n our o p e r a t i o n a l  drop time  to bottom),  (with eastward  those  profiles  0 - 30°C,  The v e l o c i t y  drop.  velocity,  salinity  t h e W h i t e H o r s e had been d r o p p e d .  crew  confidence  are  is  ± 100 c m / s e c .  l a u n c h i n g the nearly  frequency  while  dashed (northward  D r o p s made p r i o r hours a f t e r  scales  - 0.024 r a d / s e c .  meridional velocities the  a solid line  plots  to each  under WH N E T .  in  The  3  pertaining  the  intervals.  W/m .  2  to  histograms  d r o p s w h i c h were a c c o m p a n i e d by W h i t e H o r s e d r o p s , temperature,  e a c h of  2 meter  - 10"  7  200 d b a r .  relevant  code  the  approximately  every  the  p l o t t e d as  representing  spans 5 d e c a d e s  of  dissipation  These are  e a c h bar  calculated  3  plots  Camel  the  way  within  220  DROP  DATE  TIME  POSITION  2  02/07/82  1900  2N,138W  20-1540  B  3  02/08/82  1502  .50N,138W  20-1245  D  4  02/09/82  1210  ON,138W  20-900  E  5  02/09/82  2014  .50S,138W  20-365  F  6  02/10/82  1 247  1 .25S,138W  20-920  G  7  02/13/82  1236  ON,144.7W  8  02/13/82  1449  ON,144.7W  10  02/15/82  0835  ON,145W  12  02/17/82  1 108  .25N,144.7W  20-900  1 3 02/20/82  0417  . 50S,145W  20-920  L  14  02/20/82  1054  0N,145W  20-920  K  15  02/20/82  1947  . 50N,145W  20-900  16  02/21/82  0604  1.25N,145W  20-930  0  1 7 02/21/82  1618  0N,145W  20-930  K  18  02/22/82  1 355  ON,148W  200-280,390-815  19  02/24/82  0845  ON,153W  20-220,550-925  TOTAL DATA  Table  GOOD DATA(m)  20-835 20-130,270-820 200-565,590-810  12335m  20-300m  3780  300-I000m  8015  >!000m  540  K.I  -  PEQUOD d r o p  log.  WH NET  none none K none  none  none Q  221  222  TEMPERATURE (^C) 10 20  -1 34.5  •  1  1  34.9  35.3  SALINITY  (ppt)  30  ^  35.7  0  BUOYANCY FREQUENCY ( r » d / s e c ) 0.00S 0.016 0.024  223  224  TEMPERATURE (*C) 10 20  0  _l  34.5  1  ,  34.9  ,  35.3  SALINITY ( p p t )  SO  f. 35.7  B F  0  BUOYANCY FREQUENCY (r»cV»«c) 0.006 O.OU 0.02«  225  226  227  LOG  € (W/m')  HORIZONTAL V E L O C I T Y  PEQUOD NET  F  (cm/Bee)  09/02/82  228  0  34.5  TEMPERATURE ( * C ) 10 20  34.9 SALINITY  35.3 (ppt)  30  35.7  0  BUOYANCY FREQUENCY ( r a d / t e c ) 0.008 0.016 0.024  229  LOG  io-'  t  io-*  (W/mM  io-»  HORIZONTAL V E L O C I T Y  -too  0  (cm/sec)  100  230  TEMPERATURE C O 10 20  0  -r-  34.5  1  1  34.9 SALINITY  1  35.3 (ppt)  30  0  BUOYANCY FREQUENCY ( r « « / » t c ) 0.00B 0.016 0.024  1-  35.7  231  LOG  e (W/m»)  PEQUOD DROP 7 I  11 M i l l — i 11  mil—i  111 m  l—i  i m m — i  i mill  232  233  234  235  LOG t (w/m»)  PEQUOD DROP n — i 11nm  12  i i M i n i — i i n u n — i i Mini  236  237  024  1  34.5  ,  34.9 SALINITY  ,  35.3 (ppt)  1  35.7  238  LOG  i  i ium—i  i min—I  t  (W/m»)  11mil—i  Imin—I  HORIZONTAL V E L O C I T Y  111HIT/  "1  I  (cm/sec>  T'  239  240  LOG  t  ( W / m » )  PEQUOD DROP  15  i 11 n m — i i nun—i i mm—i mini—i i nmr  241  LOG iO"'  * (W/m»)  IO"'  10"»  HORIZONTAL V E L O C I T Y -100  0  (cm/sec) 100  242  TEMPERATURE C O  -i  34.5  •  —i  34.9 SALINITY  1  35.3 (ppt)  BUOYANCY  r  35.7  FREQUENCY  (r«<S/*ec)  243  LOG 10"'  t  IO"'  (W/m') 10-*  HORIZONTAL V E L O C I T Y -''00  0  (cm/sec) 100  244  245  246  LOG 10-'  *  (W/m')  10"»  i i ium—i 11 nm—i 11nm  IO''  i 11 inn—i 11iiiif  HORIZONTAL V E L O C I T Y -100  0  I  r  (cm/sec) 100  247  TEMPERATURE (*C) 10 20  SALINITY  (ppt)  30  0  BUOYANCY FREQUENCY ( r * d / » e c ) O.OOB 0.016 0.024  248  APPENDIX L - WESPAC DROPS Vertical  profiles  and B r u n t - V a i s a l a  of  frequency  along with a drop log are same a s  for  A p p e n d i x K,  from 3 3 . 8 - 3 5 . 0 p p t . been p h o t o g r a p h i c a l l y s t a n d a r d page surface  size.  shortly  e and a s s o c i a t e d t e m p e r a t u r e ,  after  profiles  from t h e WESPAC  included here.  except Note  for  that  the  the deepest  reduced in order  are  which  drops  the  ranges  11-13 have  t o a c c o m o d a t e them on  D r o p s were t i m e d so t h a t the  cruise  The s c a l e s  salinity  salini  the  Camel  CTD had been b r o u g h t back  broke  on d e c k .  249  DROP  DATE  TIME  POSITION  1  05/24/82  1010  22.7N.149E  20-840  2  05/26/82  01 54  27.7N,152E  20-1470  3  4  05/27/82  0833  28.5N,152E  20-1400  5  5  05/28/82  0847  30N,152E  20-670  7  6  05/28/82  1830  30.7N,152E  20-975  8  8  05/30/82  1447  32.5N,152E  9  05/31/82  1240  34N,152E  20-1655  10  06/01/82  1239  35N,152E  420-1510  16  1 1 06/03/82  0121  37.5S,152E  930-2240  none  12  06/03/82  0837  38.25N,152E  1380-2270  21  13  06/05/82  0213  41N,152E  20-340,990-2240  24  TOTAL DATA  GOOD DATA(m)  20-135,195-1400  13070m  20-300m  2180  300-l000m  5085  >l000m  5805  T a b l e L.1  -  WESPAC d r o p l o g .  CTD none  11 1 3,1 4  250  LOG * (W/V)  WESPAC DROP 1 i i m m — i n i n n — i t n u n — i 11nm—i i  IIIIII  251  LOG t '0-'  (W/m»)  10"»  10"'  WESPAC DROP 2 i m m — i  iiinn—i  m i n i  i m n n — i  m m «  252  253  LOG f (VJ/oiM  WESPAC DROP 4 1600  11mil—i i m i n — i i i u m — i i m m — i i n m r  254  TEMPERATURE (*C)  33.8  ,  ,  _^ ,  3«.2 34.6 SALINITY ( p p t )  BUOYANCY FREQUENCY (r«cV«ec)  r  35.0  255  LOG  t  (W/m»)  WESPAC DROP 5  800  TTTinn—i 111fm—i' i n m * — r r r r n n — i  iiniir  256  TEMPERATURE (*C)  -i 33.8  1  34.2  1  34.6  SALINITY ( p p t )  BUOYANCY FREQUENCY  1-  35.0  (r«d/«ec)  257  LOG * (w/m»)  258  TEMPERATURE  33.8  (»C)  34.2 34.6 SALINITY (ppt)  BUOYANCY  35.0  FREQUENCY  (rad/sec)  259  LOG  e (W/»»)  WESPAC DROP 8 1600  l M i lli<—l I l l l l l l — I  111 nil—i 11 mil—l I 11 III  260  TEMPERATURE CO  _L_J  33.8  ,  J  ,  34.2 34.6 SALINITY (ppt)  BUOYANCY FREQUENCY  [. 35.0  R  (r«a/«ec)  261  LOG  c  (W/m*)  WESPAC DROP 9 i  11 m n  i i MIIII  i i niiii  i 11mn—i  i  I  262  TEMPERATURE 10 20  0  i—  33.8  1  1  '  1  34.2 34.6 SALINITY ( p p t )  30  1  35.0  0  BUOYANCY FREQUENCY ( r » d / » e c ) 0.008 0.016 0.024  263  TEMPERATURE ( * C )  H  33.8  1  1  :  1  34.2 34.6 SALINITY ( p p t )  BUOYANCY FREQUENCY  r  35.0  H  :  1  r  (md/sec)  264  265  TEMPERATURE <*C) 10 20  34.2  SALINITY  34.6  (ppt)  30  35.0  0  BUOYANCY FREQUENCY ( r a d / s e c ) 0.008 0.016 0.024 J L  266  267  LOG t  10  -»  04  10" J  (W/»») io-» LUU1  I I I I III*  200 J  400 A  ~  600  m •o W B S  1/1 IA U «  800-^  a  1000 H  1200H  WESPAC DROP 12 2400  — I I l i l i " — ' 11HUB—i  MMIH—i  i Hum  i i iimf  268  TEMPERATURE 0  10  (°C) 20  BUOYANCY FREQUENCY 30  0  0.008  >  0 33.B  34.2 34.6 SALINITY ( p p t )  35.0  (rad/sec)  0.016  0.024  269  WESPAC DROP 13 2400  I I n u n — i 111inn—i i Minn—i 1 1 nun—i m m  270  

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