UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Oceanic turbulence Nasmyth, Patrick Walden 1970

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

Item Metadata

Download

Media
831-UBC_1970_A1 N38.pdf [ 10.27MB ]
Metadata
JSON: 831-1.0302459.json
JSON-LD: 831-1.0302459-ld.json
RDF/XML (Pretty): 831-1.0302459-rdf.xml
RDF/JSON: 831-1.0302459-rdf.json
Turtle: 831-1.0302459-turtle.txt
N-Triples: 831-1.0302459-rdf-ntriples.txt
Original Record: 831-1.0302459-source.json
Full Text
831-1.0302459-fulltext.txt
Citation
831-1.0302459.ris

Full Text

OCEANIC TURBULENCE  by P a t r i c k Walden Nasmyth B . A . S c , U n i v e r s i t y o f B r i t i s h . Columbia, 1941 M.A. , U n i v e r s i t y o f B r i t i s h Columbia, 1952  A T h e s i s Submitted i n P a r t i a l F u l f i l m e n t o f the Requirements f o r t h e Begree o f Doctor of P h i l o s o p h y i n t h e Department of Physics  We accept t h i s t h e s i s as conforming t o t h e required standard  The U n i v e r s i t y o f B r i t i s h September 1970  Columbia  In  presenting  this  thesis  an a d v a n c e d d e g r e e a t the I  Library  further  for  agree  scholarly  by h i s of  shall  this  the  make  it  partial  University freely  that permission  for  It  financial  is  of  of  Columbia,  British for  for extensive by  the  gain  Department Columbia  shall  not  the  requirements  reference copying of  I  agree  and  copying or  be a l l o w e d  for  that  study.  this  thesis  Head o f my D e p a r t m e n t  understood that  written permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  fulfilment  available  p u r p o s e s may be g r a n t e d  representatives. thesis  in  or  publication  without  my  i ABSTRACT  I n two e x p e r i m e n t a l o p e r a t i o n s i n deep w a t e r o f f t h e west coast o f B r i t i s h Columbia, temperature  and v e l o c i t y m i c r o s t r u c t u r e have  been r e c o r d e d w i t h a s p a t i a l r e s o l u t i o n o f 2 m i l l i m e t e r s o r b e t t e r , from the t h e r m o c l i n e down t o a depth o f 330 m e t e r s .  Some measurements  have been taken a l o n g h o r i z o n t a l paths a t d i s c r e t e d e p t h s , and, by superimposing  a c y c l i n g v e r t i c a l v e l o c i t y on t h e c o n s t a n t f o r w a r d  o t h e r s have been t a k e n along "saw—tooth"  motion,  p a t h s , r e v e a l i n g some new f e a t u r e s  of t h e f i n e s t r u c t u r e o f t h e ocean and t h e o c c u r r e n c e o f t u r b u l e n c e below t h e t h e r m o c l i n e . On one o c c a s i o n sea-^water c o n d u c t i v i t y was a l s o measured, e n a b l i n g t h e computation  o f d e n s i t y and e x a m i n a t i o n  of the occurrence  and c h a r a c t e r i s t i c s o f t h e m i c r o s t r u c t u r e i n r e l a t i o n t o t h e d e n s i t y structure. Power s p e c t r a o f v e l o c i t y f l u c t u a t i o n s have been computed and energy d i s s i p a t i o n r a t e s o b t a i n e d .  E s t i m a t e s a r e made o f mean energy  d i s s i p a t i o n as a f u n c t i o n o f depth and t o t a l d i s s i p a t i o n throughout t h e ocean volume.  The v e l o c i t y s p e c t r a a r e compared w i t h e x i s t i n g  of Kolmogoroff's  universal spectral function for isotropic  ideas  turbulence  and d i s c r e p a n c i e s a t h i g h wavenumbers a r e a t t r i b u t e d , a t l e a s t i n p a r t , t o t h e e f f e c t o f buoyancy f o r c e s r e s u l t i n g from s m a l l s c a l e d e n s i t y fluctuations.  A new e m p i r i c a l v e r s i o n o f t h e u n i v e r s a l f u n c t i o n i s d e r i v e d  from what i s c o n s i d e r e d t o be t h e b e s t ocean t u r b u l e n c e d a t a a v a i l a b l e .  ii V e r t i c a l t r a n s p o r t o f h e a t i s c a l c u l a t e d f o r a number o f samples, from m i c r o s c a l e measurements o f temperature g r a d i e n t and mean v e r t i c a l gradient.  A mean eddy c o e f f i c i e n t  estimated f o r the region.  of thermal d i f f u s i v i t y i s  iii TABLE OF CONTENTS Page ABSTRACT TABLE OF 'CONTENTS  i i i i  LIST OF FIGURES  iv  LIST OF TABLES  vi  ACKNOWLEDGMENT  v i i  INTRODUCTION  1  THEORETICAL BACKGROUND I s o t r o p i c Turbulence V e r t i c a l Heat F l u x  4 4 12  INSTRUMENTATION General Temperature and V e l o c i t y Probes C o n d u c t i v i t y Meter  14 14 17 24  RESULTS General F o s s i l Turbulence Density Structure V e l o c i t y Spectra Energy D i s s i p a t i o n The F i t o f the U n i v e r s a l Curve T u r b u l e n t Heat F l u x  26 26 35 37 42 45 51 62  DISCUSSION  66  BIBLIOGRAPHY  68  iv LIST OF FIGURES Facing Page F i g u r e 1:  Tewed body and s e n s o r s i n c o n f i g u r a t i o n used f o r Sea O p e r a t i o n F-l-69.  15  F i g u r e 2:  C l o s e r v i e w o f c e n t r a l group o f s e n s o r s .  16  F i g u r e 3:  Photomicrographs of t i p of v e l o c i t y probe (a) and temperature probe (b) (x 70 a p p r o x i m a t e l y ) .  17  Close—up view of v e l o c i t y and temperature probes i n s e a - g o i n g mounting w i t h washing device. (Approximately l i f e s i z e ) .  17  F i g u r e 5:  C r o s s - s e c t i o n of c o n d u c t i v i t y head.  24  F i g u r e 6:  B l o c k diagram o f c o n d u c t i v i t y meter felectronics.  24  T y p i c a l gross oceanographic s t r u c t u r e f o r Sea O p e r a t i o n F - l l - 6 7 , from d a t a t a k e n a t 1818 hours 21 November 1967.  26  T y p i c a l gross oceanographic s t r u c t u r e f o r Sea O p e r a t i o n F-l-69, from d a t a t a k e n a t 0850 hours 3 F e b r u a r y 1969.  26  V e l o c i t y , temperature and c o n d u c t i v i t y r e c o r d s from a c y c l i n g run a t 128 meters depth. H o r i z o n t a l g r a d i e n t s are n o t a b l e .  27  F i g u r e 4:  F i g u r e 7:  F i g u r e 8:  F i g u r e 9:  F i g u r e 10:  F i g u r e 11:  F i g u r e 12:  Temperature and c o n d u c t i v i t y r e c o r d s from a c y c l i n g run a t 152 meters depth. H o r i z o n t a l gradients are s m a l l .  29  V e l o c i t y , temperature and c o n d u c t i v i t y r e c o r d s from a c y c l i n g r u n a t 305 meters depth. Very l i t t l e m i c r o s t r u c t u r e i s visible.  31  V e l o c i t y and temperature r e c o r d s from a c y c l i n g r u n a t 213 meters d e p t h , i l l u s t r a t i n g what appears t o be a sharply defined "front".  32  V  Figure  Figure  Figure  Figure  13:  14:  15:  16:  F i g u r e 17:  Figure  18:  Figure 1 9 :  F i g u r e 20:  Figure  Figure  21:  22:  Two temperature s p e c t r a and c o r r e s p o n d i n g s e c t i o n s of r e c o r d , i l l u s t r a t i n g a p o s s i b l e case of " f o s s i l t u r b u l e n c e " .  36  S e r i e s of a p r o f i l e s from the same s e c t i o n of r e c o r d as i l l u s t r a t e d i n F i g u r e 10.  39  A r t i f i c i a l a p r o f i l e c o r r e s p o n d i n g to the f i f t h t r a c e of F i g u r e 1 4 but w i t h o u t the i n f l u e n c e of s a l i n i t y .  40  V e l o c i t y spectrum from c y c l i n g run at 2 1 0 meters depth w i t h " u n i v e r s a l curve" f i t t e d .  43  V e l o c i t y spectrum from c o n s t a n t depth run at 2 1 5 meters, c o r r e c t e d f o r n o i s e and f i t t e d t o the " u n i v e r s a l c u r v e " .  43  Percentage of ocean volume t h a t i s t u r b u l e n t , as a f u n c t i o n of depth. The c i r c l e s are f o r F - l l - 6 7 runs and the c r o s s e s f o r F—1-69 r u n s .  47  D i s t r i b u t i o n of t u r b u l e n t d i s s i p a t i o n densities f o r successive short i n t e r v a l s w i t h i n two 5 2 second samples.  53  V e l o c i t y and temperature s p e c t r a from c y c l i n g run a t 2 1 3 meters depth, i l l u s t r a t i n g p o s s i b l e e f f e c t s of buoyancy f o r c e s on s p e c t r a l shape.  54  V e l o c i t y and temperature s p e c t r a from c o n s t a n t depth run a t 6 4 meters, i l l u s t r a t i n g p o s s i b l e e f f e c t s of buoyancy f o r c e s on s p e c t r a l shape.  54  A new e m p i r i c a l approach t o Kolmogoroff's u n i v e r s a l spectrum f u n c t i o n f o r i s o t r o p i c turbulence. E a r l i e r v e r s i o n due t o Stewart and Grant (1962) i s shown a l s o ( d i s p l a c e d t o the r i g h t and upwards) f o r comparison of shape.  61  LIST OF TABLES  Table I :  Energy D i s s i p a t i o n Rates  Table I I :  Table I I I :  Percentage of volume t h a t i s t u r b u l e n t and e s t i m a t e d d i s s i p a t i o n r a t e s V e r t i c a l heat f l u x and eddy c o e f f i c i e n t of thermal d i f f u s i v i t y  vii ACKNOWLEDGMENT The work I have done has been a c o n t i n u a t i o n and e x p a n s i o n of  a programme w h i c h has been i n p r o g r e s s i n t h i s l a b o r a t o r y f o r a number  of y e a r s .  I cannot name a l l t h o s e who have c o n t r i b u t e d t o i t i n the p a s t ,  and w i l l n o t attempt t o go back i n t o h i s t o r y except t o p o i n t out t h a t the p r e l i m i n a r y work was i n i t i a t e d about 1953 by Dr. R.W. S t e w a r t , now of t h e I n s t i t u t e o f Oceanography o f t h e U n i v e r s i t y o f B r i t i s h  Columbia.  Without h i s p i o n e e r i n g e f f o r t s and c o n t i n u i n g i n t e r e s t , t h e p r e s e n t programme would p r o b a b l y n e v e r have e v o l v e d . What p r o g r e s s I have made over the p a s t two and a h a l f y e a r s has been w h o l l y dependent on t h e s u c c e s s f u l e x e c u t i o n o f two e x p e r i m e n t a l o p e r a t i o n s under d i f f i c u l t c o n d i t i o n s a t s e a .  F o r each o f t h e s e , t h e  s e a - g o i n g team c o n s i s t e d o f seven d e d i c a t e d s c i e n t i f i c and t e c h n i c a l p e r s o n n e l o f the Defence Research E s t a b l i s h m e n t P a c i f i c , w i t h o u t whose wholehearted  support the programme would n o t have been p o s s i b l e a t a l l .  Dr. H.L. Grant has p r o b a b l y had more e x p e r i e n c e i n the measurement o f t u r b u l e n c e and the conduct laboratory.  o f experiments  a t s e a than anyone e l s e i n t h e  H i s e x p e r i e n c e and c o o p e r a t i o n have been p a r t i c u l a r l y v a l u a b l e .  Dr. B.A. Hughes, w i t h i n g e n u i t y a t s e a and c l e a r t h e o r e t i c a l i n s i g h t the problem  a t hand, has made a unique c o n t r i b u t i o n .  into  Mr. J . Smith  has been r e s p o n s i b l e f o r much o f t h e m e c h a n i c a l d e s i g n o f t h e e x p e r i m e n t a l equipment ( i n c l u d i n g t h e towing w i n c h ) and f o r making i t work a t s e a . Mr. R.W. C h a p p e l l has done much o f t h e e l e c t r o n i c d e s i g n ( i n c l u d i n g t h e c o n d u c t i v i t y meter) and, a l t h o u g h he s u f f e r s from s e a - s i c k n e s s  almost  from the moment he s e t s f o o t aboard s h i p , p e r s i s t e n t l y r e f u s e s t o s t a y  viii ashore.  Mr. R.S. Anderson and Mr. A.E. P a s t r o , e x p e r i e n c e d and extremely  v a l u a b l e hands a t s e a , have a l s o c o n t r i b u t e d s u b s t a n t i a l l y ashore, i n t h e building  and c a l i b r a t i o n o f equipment and a n a l y s i s o f d a t a .  M o i l l i e t , although n o t one o f t h e sea-going  Mr. A.  team, has a l s o c o n t r i b u t e d  s u b s t a n t i a l l y , p a r t i c u l a r l y i n t h e t e s t i n g and c a l i b r a t i o n o f v e l o c i t y probes. I am g r a t e f u l a l s o f o r the c o o p e r a t i o n and s k i l l f u l tance o f C a p t a i n MacFarlane and t h e o f f i c e r s  and ccew o f t h e Canadian  Armed Forces r e s e a r c h s h i p "ENDEAVOUR" throughout and t o p e r s o n n e l o f t h e P a c i f i c Oceanographic Research  Board  both sea o p e r a t i o n s ,  Group o f t h e F i s h e r i e s  o f Canada, who p r o v i d e d oceanographic  I wish p a r t i c u l a r l y t o thank Dr.- R.W.  support.  Stewart  and Dr. R.W.  B u r l i n g o f t h e I n s t i t u t e o f Oceanography f o r t h e i r i n t e r e s t , a d v i c e and a s s i s t a n c e throughout  assis-  suggestions,  t h e course of t h i s work, and o t h e r  members o f the I n s t i t u t e f o r i n t e r e s t i n g  and p r o f i t a b l e d i s c u s s i o n s .  The work has been p a r t o f t h e r e s e a r c h programme o f t h e Defence Research  Board  of Canada and I would l i k e ,  finally,  t o express my  a p p r e c i a t i o n o f t h e o p p o r t u n i t y they have a f f o r d e d me t o use i t as a thesis  topic.  1 INTRODUCTION In h i s book "The Dynamics of the Upper Ocean" Owen M.  Phillips  of Johns Hopkins U n i v e r s i t y i n t r o d u c e s the c h a p t e r on "Oceanic T u r b u l e n c e " w i t h the statement t h a t "Turbulence i s one of the most u b i q u i t o u s phenomena i n a l l of f l u i d mechanics".  In the ocean, i n d e e d , t u r b u l e n c e  seems t o be v e r y w i d e s p r e a d , and some e v i d e n c e l e a d s us t o b e l i e v e i t may  occur almost everywhere  While i t s presence may  over a v e r y wide range of p h y s i c a l  be r e a d i l y  observed and c e r t a i n  that scales.  qualitative  c h a r a c t e r i s t i c s determined by i n d i r e c t measurement i n a number of ways, d i r e c t q u a n t i t a t i v e o b s e r v a t i o n s o f the t u r b u l e n t f l u c t u a t i o n s i n water v e l o c i t y tend t o be d i f f i c u l t , because ments r e q u i r e d and because  of the s e n s i t i v i t y  of the measure-  of the d i s t u r b i n g i n f l u e n c e of o t h e r motions  a s s o c i a t e d w i t h the s e a , p a r t i c u l a r l y when one would l i k e t o make such measurements o f f - s h o r e and a t some depth, w i t h no more s t a b l e p l a t f o r m a v a i l a b l e than a s u r f a c e s h i p . I t has been known, or a t l e a s t surmised, f o r many y e a r s t h a t the t u r b u l e n t s t r u c t u r e of the ocean p l a y s an important r o l e i n the v e r t i c a l t r a n s p o r t of h e a t , momentum, and d i s s o l v e d or suspended arid, i n the s m a l l e r s c a l e s , the d i s s i p a t i o n of k i n e t i c energy viscosity.  matter,  through  L a c k i n g q u a n t i t a t i v e measurements o f t u r b u l e n t m i x i n g  p r o c e s s e s throughout the ocean, however, these phenomena are s t i l l  not  w e l l understood. To my  knowledge, the f i r s t  s u c c e s s f u l measurements of s m a l l  s c a l e t u r b u l e n c e i n the open s e a were made by t h i s  * Defence Research E s t a b l i s h m e n t P a c i f i c Defence Research Board of Canada  laboratory* i n  2 1962  - b e f o r e I became I n v o l v e d i n the programme.  Those e a r l y  measurements were made w i t h sensors mounted on a submarine and were l i m i t e d t o about 100 meters i n depth. microstructure  Both temperature  ( o r t u r b u l e n c e ) were measured w i t h sensor  and v e l o c i t y response  p e r m i t t i n g o b s e r v a t i o n s t o be c a r r i e d down t o s c a l e s o f 2 o r 3 m i l l i m e t e r s - w e l l down i n t o the range o f energy  d i s s i p a t i o n by  v i s c o u s e f f e c t s , o r , i n the t e r m i n o l o g y I s h a l l use, up_ i n t o the d i s s i p a t i o n range o f wavenumbers.  I s h a l l r e f e r t o the r e s u l t s o f  t h a t o p e r a t i o n l a t e r on. T h i s d i s s e r t a t i o n p r e s e n t s some of the r e s u l t s o f two more r e c e n t experiments  c a r r i e d out i n 1967 and 1969 i n deep water o f f the  west coast o f Vancouver I s l a n d .  The equipment has been m o d i f i e d f o r  towing b e h i n d a s u r f a c e s h i p , p e r m i t t i n g o b s e r v a t i o n s t o depths exceeding  300 meters, and, on one o c c a s i o n o n l y (1969), measurements  of sea-water c o n d u c t i v i t y have been made and d e n s i t y computed so t h a t the e x i s t e n c e and c h a r a c t e r i s t i c s o f t u r b u l e n c e might be examined i n r e l a t i o n t o the g r a v i t a t i o n a l s t a b i l i t y  o f the water column.  The work I have done has been a c o n t i n u a t i o n and expansion of the e a r l i e r programme, which has been a c t i v e f o r more than t e n y e a r s i n the measurement o f t u r b u l e n c e a t s e a .  As I have i m p l i e d , much  of the i n s t r u m e n t a t i o n and many o f the e x p e r i m e n t a l techniques I have i n h e r i t e d from e a r l i e r s t a g e s o f the programme, and f o r t h i s I am g r a t e f u l t o my p r e d e c e s s o r s .  Specifically  I have been r e s p o n s i b l e f o r  (a) t h e i n t r o d u c t i o n o f what I s h a l l d e s c r i b e l a t e r as the " c y c l i n g mode" o f o p e r a t i o n , by which i t has been p o s s i b l e t o develop a new understanding  o f the s m a l l s c a l e v e r t i c a l s t r u c t u r e o f the ocean,  3 (b) the a d d i t i o n of a c o n d u c t i v i t y meter t o the e x i s t i n g a r r a y s e n s o r s , p e r m i t t i n g the computation of h o r i z o n t a l and  of  vertical  d e n s i t y s t r u c t u r e , and (c) a l l the d a t a a n a l y s i s and i n t e r p r e t a t i o n of r e s u l t s . The measurements t o be r e p o r t e d have been l i m i t e d by a v a i l a b l e hardware t o the upper 330 meters of the ocean and by f a c t o r s t o the w i n t e r months.  environmental  They have been more or l e s s randomly  s c a t t e r e d over an a r e a of some t e n thousand square k i l o m e t e r s , p a r t way  down the c o n t i n e n t a l s l o p e w i t h ocean depths v a r y i n g upwards from  1000 meters but m o s t l y over 2000 m e t e r s . by any means, be the b e s t we  considered  The  r e s u l t s t h e r e f o r e cannot,  r e p r e s e n t a t i v e of the w o r l d oceans,  can s a y , p e r h a p s , i s t h a t t h e r e i s n o t h i n g  and  particularly  p e c u l i a r i n an o c e a n o g r a p h i c sense about our a r e a , and i t s dynamic f e a t u r e s , at l e a s t i n the s m a l l e r s c a l e s , may many o t h e r p a r t s of the ocean.  n o t be u n l i k e those i n  4 THEORETICAL BACKGROUND  Isotropic Turbulence As a bad d e f i n i t i o n but perhaps useful s t a r t i n g point, i t might be said that turbulence i s a f l u i d i n random motion.  This simply  stated s i t u a t i o n proves to be extremely d i f f i c u l t of mathematical analysis i n the general case, and i t i s necessary to s t a r t o f f with simplifying assumptions. assumption  The following discussion i s based on the  that the density and v i s c o s i t y of the f l u i d are constant  with respect to both space and time.  I s h a l l have reason l a t e r on to  question the v a l i d i t y of this assumption with respect to density i n some of the situations we encounter i n the ocean but, accepting i t for the moment, we can describe the f l u i d i n the usual way by the equation of continuity, V.u = 0,  (1)  and the Navier-Stokes equation, f| o  + u.Vu = -  Vp + vV u,  1  t  (2)  2  p  where u i s the vector velocity of the turbulent motion i n a frame of reference i n which there i s no mean v e l o c i t y , p i s the density of the f l u i d , p i s the pressure, and v the kinematic v i s c o s i t y .  V i s the  gradient operator as usual. Stated i n this way the problem s t i l l defies rigorous mathemat i c a l treatment because of the random nature of the motion and the non-linearity of the Navier-Stokes equation.  Many attempts have been  made, but most modern theories of turbulence are based on early work of  5 G.I. Taylor (1921 and 1935) which c l e a r l y stated for the f i r s t time the fundamental character of the turbulent motion as a continuous random function of both space and time, and recognized the need for a s t a t i s t i c a l solution on this basis.  Taylor was also one of the f i r s t to  introduce the simplifying assumptions of s t a t i s t i c a l homogeneity  and  isotropy. It i s not my intention to follow the evolution of turbulence theory i n any d e t a i l , or even to undertake a complete h i s t o r i c a l review, since this has already been done by several more competent authors; f o r example Batchelor (1953), Hinze (1959) and most recently Monin and Yaglom (1967).  I s h a l l mention only the most s i g n i f i c a n t  innovations i n the development of the theory and quote such results as w i l l be pertinent to l a t e r discussion. von Karman (1937(a) and (b) and 1938) made important c o n t r i butions during the late 1930's, amongst which was a further s i m p l i f i c a t i o n of the problem by introducing the idea of "self-preservation" whereby i t was assumed that a turbulent f i e l d maintained " s i m i l a r i t y " during decay.  The term " s i m i l a r i t y " i s used here i n the sense, suggested  by Stewart and Townsend (1951), that a length scale and a v e l o c i t y scale alone are s u f f i c i e n t to determine the structure of the f i e l d . A few years l a t e r Kolmogoroff (1941) set the stage f o r much of the work that has followed by expressing s i m i l a r ideas more e x p l i c i t l y i n what has become widely known as Kolmogoroff's Hypothesis that the small scale components of a turbulent f i e l d are i n s t a t i s t i c a l equilibrium (or almost so) and are independent of the mean flow and the large scale motions by which energy i s fed into the f i e l d .  The concept o f an "energy c a s c a d e " through wavenumber space from lower t o h i g h e r wavenumbers had been adopted by a number o f e a r l i e r workers.  A l t h o u g h i t cannot be proven r i g o r o u s l y , i t has been shown by  B a t c h e l o r ( 1 9 5 3 ) , f o r example, t h a t i t i s r e a s o n a b l e t o e x p e c t , as a r e s u l t o f i n e r t i a f o r c e s , a "cascade" o f energy i n t h i s manner.  It is  n o t d i f f i c u l t t o b e l i e v e t h e n , t h a t i n a range o f wavenumbers, s u f f i c i e n t l y f a r removed from t h e d r i v i n g m o t i o n s , the t u r b u l e n t motions might be s t a t i s t i c a l l y scales.  independent o f t h e l a r g e " e n e r g y - c o n t a i n i n g "  Kolmogoroff p o s t u l a t e d t h a t i n t h i s " e q u i l i b r i u m range",  i n t h e absence of o t h e r e x t e r n a l i n f l u e n c e s , t h e t u r b u l e n c e would be u n i q u e l y d e f i n e d by t h e two parameters v , the  the k i n e m a t i c v i s c o s i t y of  f l u i d , and e , t h e r a t e a t w h i c h energy i s b e i n g s u p p l i e d o r  a l t e r n a t i v e l y t h e r a t e a t w h i c h energy i s b e i n g removed by v i s c o s i t y , w h i c h i n a s t e a d y s t a t e s i t u a t i o n must o f course be t h e same. I t becomes c l e a r then by d i m e n s i o n a l r e a s o n i n g t h a t t h e s t a t e of e q u i l i b r i u m a t h i g h wavenumbers can be r e f e r r e d t o as " u n i v e r s a l " i n t h e sense t h a t v a r i a t i o n o f t h e parameters e and v can o n l y have the  e f f e c t o f changing the l e n g t h and time ( o r v e l o c i t y ) s c a l e s o f t h e  m o t i o n ; and i t i s p o s s i b l e t o d e f i n e t h e c h a r a c t e r i s t i c l e n g t h and v e l o c i t y s c a l e s r e f e r r e d t o e a r l i e r by 3 h  n = (^-) and  ,  , u = ( v e ) \  r e s p e c t i v e l y , and t h e a s s o c i a t e d Reynolds number by  C3)  (4)  7 As I have s a i d , t h e t h e o r i e s w h i c h have been d e v e l o p e d around t h e s e i d e a s have been c l e a r l y p r e s e n t e d by a number o f a u t h o r s and have been summarized v a r i o u s l y by G r a n t , S t e w a r t and M o i l l i e t f o r example and by Pond (1965). no u s e f u l purpose.  (1962)  Any f u r t h e r attempt h e r e w o u l d s e r v e  The f o l l o w i n g d e f i n i t i o n s and r e s u l t s , however, a r e  n e c e s s a r y as a b a s i s f o r l a t e r d i s c u s s i o n . I f E ( k ) i s t h e energy d e n s i t y f u n c t i o n r e p r e s e n t i n g t h e energy p e r u n i t mass a s s o c i a t e d w i t h a l l s c a l e s o f m o t i o n d e f i n e d by the wavenumber k, t h e n t h e t o t a l energy d e n s i t y i s :  /  E ( k ) d k = Js(u + v 2  2  + w ) ,  (6)  2  o where u,v, and w a r e t h e t h r e e o r t h o g o n a l components o f t h e t u r b u l e n t velocity. Using the e x p e r i m e n t a l techniques which I s h a l l d e s c r i b e l a t e r i t i s p o s s i b l e t o measure o n l y one component o f v e l o c i t y and we cannot work d i r e c t l y i n terms o f t o t a l energy.  We t h e r e f o r e d e f i n e a  o n e - d i m e n s i o n a l energy d e n s i t y f u n c t i o n , < f > ( k ) ( r e f e r r e d t o by H i n z e as E ( k ) ) by 1  CO  —  / <j>(k)dk = u , o 2  i n which u  (7)  i s t h e t u r b u l e n t v e l o c i t y component i n t h e d i r e c t i o n o f t h e  mean f l o w o r t h e d i r e c t i o n o f m o t i o n o f our towed body.  According  t o K o l m o g o r o f f ' s H y p o t h e s i s , f o r t h e s i m p l i f i e d case o f i s o t r o p i c t u r b u l e n c e (J>(k) must be o f t h e form  Kk) = e  1 / 4  v  5 / 4  F(k/k ) ,  (8)  where F(k/k  s  ) i s a u n i v e r s a l f u n c t i o n o f i t s argument, and k  s  = 1/n  i s a measure of the wavenumber a t which v i s c o u s e f f e c t s b e g i n t o dominate  the p r o c e s s o f energy  transfer.  cj)(k) i s r e l a t e d t o E(k) by  E(k) =  h  k  2  3 cj>(k) 2  _  k  3k  3 <Kk)  (9)  3k  and e, the energy d i s s i p a t i o n d e n s i t y can be e x p r e s s e d as oo  00  e = 2vf  k E ( k ) d k = 15v/ k <j)(k)dk, o o 2  2  2  i n which I s h a l l r e f e r t o k E ( k ) and k cj>(k) defining  (10)  2  a  s  the d i s s i p a t i o n  spectra,  the d i s t r i b u t i o n i n wavenumber space o f the r a t e o f decay o f  t u r b u l e n t energy through the a c t i o n o f v i s c o s i t y . The a c c u r a c y w i t h which  one s h o u l d expect Kolmogoroff's  H y p o t h e s i s t o d e s c r i b e t h e h i g h e r wavenumber r e g i o n o f a t u r b u l e n t w i l l depend  field  upon the s e p a r a t i o n i n terms of wavenumber between the  r e g i o n s which make the major  c o n t r i b u t i o n t o the energy spectrum and  d i s s i p a t i o n spectrum r e s p e c t i v e l y .  T h i s s e p a r a t i o n depends upon the  Reynolds number, and i f the Reynolds number i s s u f f i c i e n t l y h i g h may be a mid-range to e i t h e r spectrum.  o f wavenumbers which makes a n e g l i g i b l e I f this  there  contribution  c o n d i t i o n e x i s t s - and t h i s i s sometimes  r e f e r r e d t o as Kolmogoroff's second h y p o t h e s i s - then w i t h i n  this  mid-range  "energy-  the t u r b u l e n t motions  c o n t a i n i n g " eddies, but s t i l l  a r e independent o f the l a r g e  u n a f f e c t e d by v i s c o s i t y .  The t r a n s f e r  of energy by i n e r t i a l f o r c e s i s the dominating f a c t o r and the energy spectrum depends s o l e l y upon e.  9  T h i s , being p a r t o f the u n i v e r s a l e q u i l i b r i u m range, i s commonly r e f e r r e d t o as t h e " i n e r t i a l subrange", and h e r e t h e t h e o r y l e a d s t o a s p e c t r a l energy f u n c t i o n o f t h e form  E(k) = £  2 / 3  k"  5 / 3  F(£-) ,  (11)  s i n w h i c h t h e f u n c t i o n F must be a c o n s t a n t under t h e c o n d i t i o n s we have s p e c i f i e d f o r t h i s  subrange.  Here t h e n , F(|-) s  = K  (12)  and E(k) = K e  2 / 3  k  5  /  (13)  3  I t i s obvious from ( 9 ) t h a t , i n t h i s subrange, <j>(k) must have t h e same power law dependence on k as E ( k ) h a s , and we can t h e r e f o r e put cKk)  = K'e  2 / 3  k"  5 / 3  ,  (14)  18 i n which  K'  =  K  -  ( ) 1 5  A number o f r e s e a r c h e r s i n r e c e n t y e a r s have a c h i e v e d experimental r e s u l t s which tend t o confirm the p r e d i c t i o n s of t h i s t h e o r y i n many r e s p e c t s .  I n p a r t i c u l a r G r a n t , S t e w a r t and M o i l l i e t  ( 1 9 6 2 ) , w o r k i n g i n a t i d a l c h a n n e l i n w h i c h t h e Reynolds number, based on t h e depth o f t h e c h a n n e l and t h e mean t i d a l v e l o c i t y , was a p p r o x i g m a t e l y 3 x 1 0 , and w i t h an e a r l i e r g e n e r a t i o n o f equipment  similar to  what we a r e now u s i n g , have produced a number o f o n e - d i m e n s i o n a l energy  10 s p e c t r a w h i c h conform remarkably c l o s e l y t o the k subrange  f o r a f u l l two decades i n k.  -5/3  law o f t h e i n e r t i a l  From the same d a t a they have  d e r i v e d an e m p i r i c a l s p e c t r a l form f o r a n o t h e r decade and a h a l f , upwards through the d i s s i p a t i o n subrange t o the p o i n t where i n s t r u m e n t a l n o i s e a t the h i g h e r f r e q u e n c i e s becomes t r o u b l e s o m e .  The r e s u l t has come t o be  known w i t h i n the group as the " u n i v e r s a l c u r v e " and, c h e c k i n g w i t h o t h e r e x p e r i m e n t a l r e s u l t s , i t does i n d e e d e x h i b i t a h i g h degree of u n i v e r s a l i t y ( i f i t i s p e r m i s s i b l e t o q u a l i f y the concept o f u n i v e r s a l n e s s i n t h i s manner) i n those s i t u a t i o n s where the Reynolds number i s known t o be h i g h , and where a c c o r d i n g t o the t h e o r y one would e x p e c t t o f i n d an e q u i l i b r i u m range. I n examining t u r b u l e n c e s p e c t r a l a t e r on I s h a l l make use of a method, e v o l v e d by Stewart and Grant ( 1 9 6 2 ) , f o r d e t e r m i n a t i o n o f energy d i s s i p a t i o n r a t e s by f i t t i n g the s p e c t r a t o the u n i v e r s a l c u r v e . For an e x p l a n a t i o n of t h i s method I can do no b e t t e r t h a n quote d i r e c t l y from Stewart and G r a n t , as f o l l o w s (changing o n l y f i g u r e  and  e q u a t i o n r e f e r e n c e s t o match our numbering s e q u e n c e ) : " I t i s e v i d e n t t h a t i f l o g <j> i s p l o t t e d a g a i n s t l o g k, a l l  curves  of the form (8) can be d e r i v e d from one such curve by s i m p l e translations.  Moreover,  f o r g i v e n v, a change i n e by a f a c t o r a  r e s u l t s i n a d i s p l a c e m e n t of the curve by h l o g a, b o t h h o r i z o n t a l l y and v e r t i c a l l y .  I n p r a c t i c e the f o l l o w i n g p r o c e d u r e i s used:  A p l o t of l o g F ( k / k ) v e r s u s l o g k/k i s p r e p a r e d , and the p o i n t s s (0,0) i s l o c a t e d and marked.  F o r the measured spectrum, a p l o t  o f l o g cj>(k) v e r s u s l o g k i s p r e p a r e d on the same s c a l e .  Now i f  11 the measured spectrum i s f r e e o f n o i s e and n o n t u r b u l e n t s i g n a l s , and i f K o l m o g o r o f f ' s h y p o t h e s i s i s v a l i d f o r t h e measured t u r b u l e n t f i e l d , t h e two p l o t s can be made t o c o i n c i d e .  When  i n c o i n c i d e n c e , t h e p o i n t (0,0) on t h e F ( k / k ) curve w i l l g  pond t o t h e p o i n t ( l o g e  corres-  1/4 -3/4 1/4 5/4 v , log e v ) on t h e cj>(k) c u r v e .  F o r a g i v e n v a l u e o f v , b u t v a r y i n g v a l u e s o f e, t h e l o c u s o f t h e p o i n t (0,0) on t h e F ( k / k ) curve w i l l be a s t r a i g h t l i n e o f g  s l o p e +1 through ( l o g v  l o g v"*^) .  I f t h e measured <j)(k) spectrum c o n t a i n s n o i s e o r o t h e r s p u r i o u s s i g n a l s , t h e f i t may n e v e r t h e l e s s be attempted. -3/4 +1 i s drawn through t h e p o i n t ( l o g v  A l i n e of slope 5/4  , log v  )(marked 0  i n F i g u r e 16, f o r example) and t h e F ( k / k ) curve i s superimposed g  so t h a t t h e p o i n t (0,0) always l i e s  on t h i s l i n e .  With  this  c o n s t r a i n t t h e p o s i t i o n i s sought f o r which no p o i n t on t h e <j)(k) curve f a l l s w i t h i n ( t o t h e l o w e r l e f t o f ) t h e F ( k / k ) c u r v e . The s extreme p o s i t i o n o f t h e F ( k / k ) curve under these c o n d i t i o n s t h e n d e f i n e s t h e l a r g e s t v a l u e o f e, e , c o n s i s t e n t w i t h t h e measuremax' ments, p r o v i d e d t h a t K o l m o g o r o f f ' s h y p o t h e s i s i s v a l i d f o r t h e g  measured f i e l d . . (log e t  1/4  v  The p o i n t c o i n c i d e n t w i t h (0,0) i s  -3/4  . , log e  1/4  5/4 . , _ . _. ,x v )(marked X i n F i g u r e 16) w  n  and hence e may be c a l c u l a t e d . " max k k The p l o t o f l o g F ( ~ ) a g a i n s t l o g ^— i s o f course t h e s s " u n i v e r s a l curve" r e f e r r e d t o e a r l i e r . J  12 V e r t i c a l Heat F l u x From a knowledge o f temperature  gradients i n a turbulent  f i e l d upon which some mean g r a d i e n t i s superimposed,  i t i s possible  t o e s t i m a t e the h e a t f l u x and r e s u l t a n t c r e a t i o n o f entropy due t o turbulent mixing. In the absence  o f heat sources o r s i n k s , the temperature o f  a homogeneous, i n c o m p r e s s i b l e f l u i d may be d e s c r i b e d by  |^+U.VT = — V T, dt pC  (16)  2  ->•  where T i s the temperature  and U the v e c t o r v e l o c i t y o f the f l u i d and  K, p and c a r e thermal d i f f u s i v i t y , d e n s i t y and s p e c i f i c heat r e s p e c tively.  W i t h i n the p r e c i s i o n o f t h e f o l l o w i n g c a l c u l a t i o n s we  shall  f o r s i m p l i c i t y s e t b o t h p and c t o u n i t y f o r s e a water and put  T =T+  6  (17)  U = U + u,  and  i n which t h e b a r s denote  ->•  and u a r e the f l u c t u a t i n g  (18) averages  over a volume o f t h e f l u i d and 6  components.  I f we then assume a h o r i z o n t a l l y s t r a t i f i e d s t r u c t u r e , which i s u s u a l l y approximately 9 T t r u e f3o r0the ocean, and a steady s t a t e c o n d i t i o n such t h a t — = 0 and — ,2 — = 0, i t can be r e a d i l y shown t h a t at o t a l l terms c o n t a i n i n g time d e r i v a t i v e s or h o r i z o n t a l components o f v e l o c i t y v a n i s h and, w i t h t h e f u r t h e r assumption  that the v e r t i c a l 2  temperature  g r a d i e n t i s r o u g h l y u n i f o r m so t h a t V T i s a p p r o x i m a t e l y  z e r o , (16) reduces t o  13  - K6V 9  %w.V6 + w6 2  (19)  2  0  Z  i n which z i s the v e r t i c a l dimension and w i s the v e r t i c a l of  component  velocity. Now i f we i n t e g r a t e over a range o f depth l a r g e compared t o  the to  s c a l e of temperature  '2  f l u c t u a t i o n s which make t h e major  term i n ( 1 6 ) w i l l  (VG): , the f i r s t  2  may be approximated by (V6) .  w9(T  Z  w6 = - 3 K C — )  or  3 s  2  with  -  (V9) dz  (20)  ,  (21)  2  l  z„-z„ — — T~-T~ 2  to  2  - T ) * - KS  2  2  a p p r o x i m a t e l y v a n i s h and 6V 6  We a r e l e f t Z  contribution  1  the p r e c i s i o n w i t h which we can approximate  2 JB 0 2 (V6) by 3tp^*) (  a s  would be t h e case i n a p e r f e c t l y i s o t r o p i c medium), s b e i n g some p a t h through t h e volume. Z  and 1^ are t h e mean temperatures a t depths  2" 1 Z  z.. and z_ and 3 7 - ^ T -T 2  i s t h e r e c i p r o c a l o f the mean temperature  gradient.  1  w0 i s the t u r b u l e n t h e a t f l u x through t h e r e g i o n n e g l e c t i n g , by our s t i p u l a t i o n o f no heat s o u r c e s or s i n k s , any c o n t r i b u t i o n  resulting  from the d e g r a d a t i o n o f t u r b u l e n t energy t o heat through the a c t i o n of  viscosity. The  c o r r e s p o n d i n g r a t e o f entropy g e n e r a t i o n i s g i v e n by  *£|2i , T which  as b e f o r e may be approximated by 3  (22)  14 INSTRUMENTATION  General Sensors and i n s t r u m e n t a t i o n f o r measuring t u r b u l e n c e i n t h e sea  have been under development  some f i f t e e n y e a r s .  i n t h i s l a b o r a t o r y f o r a p e r i o d of  E a r l y measurements were made s u c c e s s f u l l y i n  p r o t e c t e d i n - s h o r e w a t e r s where r e l a t i v e l y h i g h l e v e l s o f t u r b u l e n c e were g e n e r a t e d by s t r o n g t i d a l c u r r e n t s , and s u r f a c e m o t i o n was n o t a s e r i o u s problem.  The f i r s t s u c c e s s f u l attempts t o work i n open  ocean areas were made i n 1962 w i t h s e n s o r s mounted on a submarine, b u t , w h i l e a submarine i s an i d e a l p l a t f o r m f o r t h i s s o r t o f measurement, the  o n l y one a v a i l a b l e a t t h e time was r e s t r i c t e d t o about 100 meters  i n depth and i t s a v a i l a b i l i t y was s e v e r e l y l i m i t e d by o t h e r t a s k s o f higher p r i o r i t y .  I have re-examined some o f t h e 1962 d a t a f o r comparison  w i t h t h e r e s u l t s o f more r e c e n t e x p e r i m e n t s , b u t o n l y b r i e f m e n t i o n be made i n t h i s  will  thesis.  Subsequent measurements have been made w i t h s e n s o r s mounted on a submerged body, towed from a s u r f a c e s h i p by a s e r v o - c o n t r o l l e d w i n c h , c a p a b l e o f compensating f o r s h i p m o t i o n t o an a c c u r a c y o f about 30 c e n t i m e t e r s i n body depth i n r e a s o n a b l e s e a s t a t e s .  The w i n c h  will  m a i n t a i n body depth a t any d e s i r e d v a l u e down t o a l i m i t o f about 330 meters imposed by t h e l e n g t h o f m u l t i - c o n d u c t o r towing w i r e w h i c h i s a v a i l a b l e t o u s ; o r , i n what I s h a l l r e f e r t o as t h e " c y c l i n g mode", may be programmed t o r e p e a t e d l y v a r y depth a t a c o n s t a n t r a t e over any p r e d e t e r m i n e d depth i n t e r v a l ( t y p i c a l l y 6-30 meters) s o t h a t , a t c o n s t a n t towing speed, t h e body f o l l o w s a " s a w - t o o t h " p a t h through t h e w a t e r . C y c l i n g time i s v a r i a b l e and i n r e c e n t experiments has ranged from about  15 60 t o 120 seconds.  At our u s u a l towing speed of 125 t o 150  centimeters  per second we would thus e x p e r i e n c e a forward advance of 75 to 180 meters p e r c y c l e . The a r r a y of sensors mounted on the towed body has e v o l v e d through a s e r i e s o f c o n f i g u r a t i o n s t o the most r e c e n t  arrangement  as shown i n F i g u r e 1, w i t h t h e body s e c u r e d i n i t s s a d d l e , p a r t through the l a u n c h i n g p r o c e d u r e .  way  P r o t r u d i n g from the f r o n t of the body  i s a c e n t r a l nose s p a r , below which a p a i r of p l a t i n u m f i l m probes one s e n s i t i v e t o temperature and the o t h e r t o v e l o c i t y - i s suspended on a v i b r a t i o n i s o l a t i o n mounting. i n more d e t a i l  These probes w i l l be  described  later.  To the l e f t  o f the main nose spar i s an a u x i l i a r y  spar  (of which only the t i p i s v i s i b l e i n t h i s view) on which i s mounted a v e r t i c a l s t r u t 61 c e n t i m e t e r s l o n g , c a r r y i n g  three t h e r m i s t o r s -  one a t the t o p , one a t the bottom, and one s l i g h t l y below c e n t e r , a t the l e v e l o f the temperature and v e l o c i t y p r o b e s . have a u s e f u l response up t o about 40  These t h e r m i s t o r s  Hz.  On an outer c o n c e n t r i c p i p e around the base o f the main nose spar are mounted ( i ) on t o p , a depth meter, ( i i ) t o the r i g h t , a p r o p e l l e r type c u r r e n t meter t o g i v e the mean v e l o c i t y of the body through the water, and ( i i i ) below the c u r r e n t meter a t the same l e v e l as the two p r o b e s , an i n d u c t a n c e type c o n d u c t i v i t y meter f o r which the frequency response i s l i m i t e d by the f l u s h i n g time of the head.  This  has n o t been measured p r e c i s e l y but the response s h o u l d extend beyond 5 Hz a t normal towing speeds. F i g u r e 2 i s a c l o s e r view showing the c e n t e r t h e r m i s t o r i n i t s p r o t e c t i v e h o u s i n g , the two probes and, to the r i g h t , the head  16 o f t h e c o n d u c t i v i t y meter. Those components of c i r c u i t r y w h i c h f o r e l e c t r o n i c reasons must be l o c a t e d c l o s e t o the s e n s o r s , a r e e n c l o s e d i n p r e s s u r e cases i n the towed body.  From t h e r e , i n f o r m a t i o n from a l l s e n s o r s i s f e d  up an armoured m u l t i - c o n d u c t o r t o w i n g c a b l e f o r f u r t h e r p r o c e s s i n g and r e c o r d i n g on the s h i p .  The lower 100 meters o f c a b l e a r e f a i r e d t o  reduce v i b r a t i o n i n the s e c t i o n a d j a c e n t t o the body.  F a i r i n g of t h e  e n t i r e l e n g t h o f c a b l e would no doubt f u r t h e r reduce c a b l e v i b r a t i o n " n o i s e " i n the v e l o c i t y system, but the m e c h a n i c a l problems o f h a n d l i n g long l e n g t h s of f a i r e d c a b l e have p r e c l u d e d t h i s measure. On b o a r d s h i p the s i g n a l from each t h e r m i s t o r i s d i v i d e d i n t o two c h a n n e l s .  One i s a m p l i f i e d and r e c o r d e d d i r e c t l y and t h e o t h e r i s  e l e c t r o n i c a l l y d i f f e r e n t i a t e d w i t h r e s p e c t t o time b e f o r e r e c o r d i n g , i n o r d e r t o a c h i e v e an a c c e p t a b l e s i g n a l - t o - n o i s e r a t i o a t the h i g h e r f r e q u e n c i e s where b o t h the response of the t h e r m i s t o r and the spectrum of temperature f l u c t u a t i o n s drop o f f t o the e x t e n t t h a t the dynamic range a v a i l a b l e on a s i n g l e c h a n n e l i s i n a d e q u a t e .  The  signal  from the v e l o c i t y probe f o r s i m i l a r reasons i s d i v i d e d i n t o t h r e e c h a n n e l s . The f i r s t of t h e s e w h i c h we r e f e r t o as "A" c h a n n e l i s r e c o r d e d b r o a d band w i t h no f i l t e r i n g .  The second o r "B" c h a n n e l i s a g a i n e f f e c t i v e l y  d i f f e r e n t i a t e d up t o about 10 Hz and c u t s o f f a t about 20 Hz. c h a n n e l d i f f e r e n t i a t e s up t o 1000 Hz and then c u t s o f f . The  "C" signal  from the temperature probe i s t r e a t e d s i m i l a r l y e x c e p t t h a t t h e r e i s a l o w - f r e q u e n c y c u t - o f f on A a t about 0.01 Hz, and B extends up t o about 100 Hz.  Figure  3.  Photomicrographs o f t i p o f v e l o c i t y probe (a) and temperature probe ( b ) . (x70 a p p r o x i m a t e l y ) .  F i g u r e A.  Close-up view of v e l o c i t y and temperature probes i n sea-going mounting w i t h washing device. (Approximately l i f e s i z e ) .  17  S i g n a l channels from a l l s e n s o r s t o g e t h e r w i t h coded s i g n a l s and a v o i c e commentary are r e c o r d e d on two magnetic  tapes w i t h m u l t i p l e x i n g  as r e q u i r e d .  timing  seven-channel  At the same time  s e l e c t e d channels are m o n i t o r e d on o s c i l l o s c o p e s as an a i d i n selecting  a p p r o p r i a t e g a i n s e t t i n g s , and twelve channels are r e c o r d e d  on two paper c h a r t s g i v i n g a permanent v i s u a l r e c o r d , i n v a l u a b l e as a p l a n n i n g a i d d u r i n g the experiment, and f o r l a t e r use d u r i n g a n a l y s i s .  Temperature  and V e l o c i t y  Probes  The temperature  and v e l o c i t y p r o b e s , b e i n g one of the unique  f e a t u r e s of the equipment, may element  be worth  f u r t h e r mention.  The  active  of each c o n s i s t s of an e v a p o r a t e d p l a t i n u m f i l m on a c o n i c a l  g l a s s t i p . E l e c t r i c a l c o n n e c t i o n t o the f i l m i s made through leads embedded i n the g l a s s stem.  T y p i c a l c o n f i g u r a t i o n s o f the two  shown i n F i g u r e 3 at a m a g n i f i c a t i o n o f about 70.  F o r the  types are  temperature  probe the f i l m covers the e n t i r e t i p of the cone and i s operated i n a bridge c i r c u i t  as a r e s i s t a n c e thermometer.  In the v e l o c i t y  case the  film  c o n s i s t s o f a narrow a n n u l a r r i n g around the g l a s s t i p and f u n c t i o n s i n the manner o f a hot w i r e anemometer.  In each case the maximum dimension of  the f i l m i s approximately 0.5 m i l l i m e t e r s , so t h a t r e s o l u t i o n of f e a t u r e s down t o perhaps  2 millimeters i n size i s possible.  e l e c t r o n i c compensation response up t o 1000 Hz.  With a p p r o p r i a t e  i t i s p o s s i b l e t o a c h i e v e a u s e f u l frequency The two probes are shown i n c l o s e - u p view i n  F i g u r e 4 , mounted and ready f o r use, w i t h the washing below.  device described  18 The v e l o c i t y probe i s , o f c o u r s e , e x t r e m e l y s e n s i t i v e t o v i b r a t i o n , and e x t e n s i v e p r e c a u t i o n s have been taken t o e l i m i n a t e e x c e s s i v e i n t e r f e r e n c e from t h i s s o u r c e . the  N e v e r t h e l e s s v i b r a t i o n remains  l i m i t i n g f a c t o r i n t h e s e n s i t i v i t y o f t h e v e l o c i t y system through  a mid-range  of t h e spectrum from about 1 Hz t o 20 Hz. The o t h e r major d i f f i c u l t y i n t h e use o f t h i s t y p e o f probe  i n t h e r e a l ocean a r i s e s from t h e p r e s e n c e o f p l a n k t o n , and i t i s f o r t h i s r e a s o n t h a t a l l s u c c e s s f u l measurements i n o f f - s h o r e w a t e r s have been made d u r i n g the w i n t e r months when t h e p l a n k t o n c o n c e n t r a t i o n i s minimal.  When a p l a n k t o n p a r t i c l e c o n t a c t s t h e v e l o c i t y p r o b e , o r even  passes c l o s e t o i t p e r h a p s , i t s e f f e c t i s t o m o m e n t a r i l y i n c r e a s e t h e e f f e c t i v e t h i c k n e s s o f the boundary  l a y e r over t h e f i l m .  The r e c o r d  shows a sharp t r a n s i e n t i n d i c a t i n g an apparent momentary d e c r e a s e i n velocity.  Sometimes one w i l l s t i c k t e m p o r a r i l y b u t c l e a r i t s e l f  a second o r two.  after  O c c a s i o n a l l y one w i l l be c a p t u r e d p e r m a n e n t l y on t h e  probe t i p , i n d i c a t i n g i t s p r e s e n c e by a sudden and p e r s i s t e n t d e c r e a s e i n i n d i c a t e d mean v e l o c i t y . the  When t h i s happens i t i s n e c e s s a r y t o c l e a n  probe b e f o r e m e a n i n g f u l measurements can be c o n t i n u e d . A pump and system of p i p i n g have been developed f o r t h i s  p u r p o s e , c a p a b l e o f g e n e r a t i n g a h i g h v e l o c i t y r e v e r s e f l o w over t h e t i p of  t h e p r o b e , w i t h o u t r e d u c i n g towing speed o r o t h e r w i s e i n t e r r u p t i n g t h e  experiment. are  The o u t p u t s o f t h e v e l o c i t y probe and t h e c u r r e n t meter  d i s p l a y e d s i d e by s i d e and a v i s u a l watch i s k e p t on t h e two r e c o r d s .  A p e r s i s t e n t d i s c r e p a n c y i s t a k e n as an i n d i c a t i o n t h a t t h e probe has become f o u l e d and a "wash" may then be a c c o m p l i s h e d w i t h i n a few seconds by manual c o n t r o l from t h e s h i p .  19 It i s reasonable to assume that the temperature  probe,  being of similar s i z e and shape, becomes fouled as frequently, on the average, as the v e l o c i t y probe.  Again the e f f e c t i v e thickness of the  boundary layer i s increased and one would expect a drop i n s e n s i t i v i t y i n the upper part of the frequency spectrum, but there i s no recognizable change i n the v i s u a l output.  The practice we have adopted, therefore,  i s to wash both probes whenever the v e l o c i t y probe becomes fouled. Following this procedure, and i f i t i s assumed that for each probe the length of the time i n t e r v a l between contact with p a r t i c l e s which s t i c k i s governed by a Poisson d i s t r i b u t i o n and that such events at the two probes are s t a t i s t i c a l l y independent, then as pointed out by Grant, Hughes, Vogel and M o i l l i e t  (1968), the temperature probe can  be expected to be clean 70 percent of the time.  In e a r l i e r configura-  tions with a separation of several centimeters between the probes, these assumptions were probably e s s e n t i a l l y true.  In the most recent  arrangement the two probes have been placed as close together as possible, with a l a t e r a l spacing of approximately 4 millimeters between t i p s . In this case, since many plankton organisms are 4 millimeters or more i n t h e i r maximum dimension, the events are probably no longer completely independent and the temperature probe should be clean something more than 70 percent of the time. Even under the most favorable conditions during the winter, one may expect to contact a plankton p a r t i c l e every few seconds but i t may be necessary to wash the probes only two or three times an hour. It i s thus possible to obtain records sometimes up to 30 minutes i n length with only minor contamination which w i l l have n e g l i g i b l e e f f e c t on the spectral content of the v e l o c i t y and temperature signals.  20 The s e n s i t i v i t y and frequency response of the v e l o c i t y probe are  determined from measurements i n a water tunnel i n the laboratory.  The mean flow can be varied over the range of towing speeds, and at each of several flow rates the dynamic response i s determined by vibrating the  probe along the d i r e c t i o n of flow with an electromagnetic driver.  The shape of the response curve varies somewhat from probe to probe but  generally i s e s s e n t i a l l y f l a t up to 50 or 75 Hz, then r i s e s  steadily up to 1000 Hz, which i s the maximum frequency we attempt to measure.  The s e n s i t i v i t y across the frequency band varies with the rate  of mean flow, according to King's law, but the shape of the curve for a given probe remains e s s e n t i a l l y unchanged. The dynamic response of the temperature probe i s determined by passing i t through the r i s i n g plume of warm water above a heated wire i n a small tank, using the method described by Fabula (1968). Since the operation of the velocity probe depends upon the rate of dissipation of heat from the platinum f i l m , i t w i l l exhibit some s e n s i t i v i t y to fluctuations i n the temperature of the water, and f o r this I have made no compensation.  At zero frequency the s e n s i t i v i t y to  temperature i s readily measured and, for probes i n current use, amounts to some 10-15 cm sec ^ per °C. When the velocity bridge i s balanced at the beginning of a run, the ambient temperature at the probe i s automatically taken into account and,'working below the thermocline, the mean temperature rarely changes enough that r e balancing i s required. The dynamic response of the v e l o c i t y probe to fluctuations i n temperature turns out to be much more d i f f i c u l t to determine. Lacking direct measurements I have nevertheless attempted to estimate,  21  by a number o f i n d i r e c t methods, t h e magnitude  of p o s s i b l e errors  from  t h i s source. F i r s t o f a l l i t seems u n l i k e l y t h a t the temperature response a t h i g h e r f r e q u e n c i e s s h o u l d be any g r e a t e r than i t i s a t z e r o f r e q u e n c y , and one would e x p e c t i t t o be l e s s , due t o t h e e f f e c t o f t h e boundary layer.  I t would n o t be s u r p r i s i n g i f t h e form o f t h e response were  s i m i l a r t o t h a t d e r i v e d f o r t h e temperature probes by F a b u l a  (1968)  i n which the amplitude response, r e l a t e d t o the zero frequency response, i s g i v e n by Y  (24)  = exp(-const / frequency), o  f o r a g i v e n mean temperature and mean v e l o c i t y . L o o k i n g a t t h e problem i n a d i f f e r e n t way we may e s t a b l i s h as a c r i t e r i o n t h e r a t i o R o f rms o r peak-to-peak f l u c t u a t i o n s i n v e l o c i t y i n u n i t s o f cm s e c ^ t o c o r r e s p o n d i n g f l u c t u a t i o n s i n temp e r a t u r e i n °C f o r s i g n a l s r e c o r d e d a t s e a .  I n a mid-range  of frequencies  from 15 t o 75 Hz, c o v e r i n g t h e p o r t i o n o f t h e v e l o c i t y spectrum i n w h i c h most o f t h e energy d i s s i p a t i o n t a k e s p l a c e , I have i n t e n s e l e c t e d samples measured v a l u e s o f R r a n g i n g from 2 . 2 5 t o 2 0 .  One can c o n c l u d e  t h a t , over t h i s range o f f r e q u e n c i e s a t l e a s t , t h e t e m p e r a t u r e s e n s i t i v i t y o f t h e v e l o c i t y probe must be s u b s t a n t i a l l y lower t h a n t h e z e r o f r e q u e n c y s e n s i t i v i t y , and cannot exceed something l i k e 2 cm s e c p e r °C. (24))  To produce t h i s r e s u l t t h e c o n s t a n t i n t h e e x p r e s s i o n ( E q u a t i o n  f o r A / A must be g r e a t e r than 0 . 2 5 ( i f t h i s e x p r e s s i o n i s v a l i d a t q  a l l f o r the v e l o c i t y p r o b e ) , n o t i c e a b l y l a r g e r than t y p i c a l values f o r temperature p r o b e s , w h i c h range around 0 . 1 .  This i s not a s u r p r i s i n g  c o n c l u s i o n because t h e v e l o c i t y f i l m (see F i g u r e 3 ) i s f a r t h e r from  22 the t i p o f t h e cone and t h e boundary l a y e r over t h e f i l m w i l l be t h i c k e r than i n t h e case o f t h e temperature r e s u l t of course.  probe.  Neither i s i t a fortuitous  I t was a p r i m a r y c o n s i d e r a t i o n i n t h e o r i g i n a l  d e s i g n o f t h e two probe t y p e s , - t o m i n i m i z e  t h e response  o f each t o the  unwanted s i g n a l o f t h e o t h e r k i n d . I have a l s o examined v a l u e s o f t h e d i m e n s i o n l e s s  ratio,  3/2  o r skewness o f t h e d i f f e r e n t i a t e d v e l o c i t y s i g n a l f o r f i f t e e n samples recorded a t sea. mean o f -0.237.  Computed v a l u e s range from -0.089 t o -0.487 w i t h a Wind t u n n e l measurements by Stewart  (1951) suggest a  l i m i t i n g v a l u e o f a p p r o x i m a t e l y -0.3 f o r h i g h Reynolds number t u r b u l e n c e w i t h l a r g e r n e g a t i v e v a l u e s f o r lower Reynolds numbers. In  o b t a i n i n g t h e above v a l u e s I have removed as much as  p o s s i b l e o f t h e n o i s e i n our r e c o r d s by f i l t e r i n g , b u t p a r t o f t h e d i f f e r e n c e from S t e w a r t ' s v a l u e s may s t i l l be accounted  f o r by some r e m a i n i n g  c o n t a m i n a t i o n by e l e c t r o n i c n o i s e a t h i g h e r f r e q u e n c i e s and s p u r i o u s s i g n a l s due t o v i b r a t i o n a t t h e lower f r e q u e n c i e s .  I t may be a l s o t h a t  some o f the' samples I have used (12-30 seconds i n d u r a t i o n ) a r e t o o s h o r t to g i v e a r e l i a b l e measure o f skewness.  I t i s these s h o r t e r samples t h a t  e x h i b i t most o f t h e f l u c t u a t i o n i n skewness v a l u e s as quoted above. Samples o f 60 seconds o r more i n l e n g t h (of w h i c h I have examined o n l y t h r e e ) a l l g i v e v a l u e s c l o s e t o -0.3 w i t h a mean o f -0.319. Corresponding  temperature  signals should, according to theory,  e x h i b i t z e r o skewness and, i n f a c t , t h e v a l u e s I have o b t a i n e d range between p l u s and minus 0.1 w i t h a mean v e r y c l o s e t o z e r o . There a r e some r e c e n t e x p e r i m e n t a l d a t a , r e p o r t e d by Stewart  23 (1969), w h i c h i n d i c a t e t h a t the skewness c o e f f i c i e n t of t h e temperature d e r i v a t i v e may n o t always be z e r o .  The measurements i n q u e s t i o n were  made i n a t u r b u l e n t a t m o s p h e r i c boundary  l a y e r and gave skewness  v a l u e s as h i g h as 1, u s i n g a s t a t i o n a r y s e n s o r i n the mean f l o w . Even i f a s i m i l a r c o n d i t i o n e x i s t e d i n our o c e a n i c s i t u a t i o n , the skewness o f the observed temperature s i g n a l s h o u l d depend on t h e r e l a t i o n s h i p between the d i r e c t i o n of towing and t h e d i r e c t i o n of mean s h e a r , and the average from a number of randomly o r i e n t e d runs s h o u l d n o t d i f f e r v e r y much from z e r o . I n any c a s e , t h e r e f o r e , i f our v e l o c i t y s i g n a l s were h e a v i l y contaminated w i t h temperature we would e x p e c t them t o d i f f e r more w i d e l y from S t e w a r t ' s v a l u e of -0.3 t h a n they appear t o .  We  are l e d to  the c o n c l u s i o n t h a t our v e l o c i t y s i g n a l s a r e a t l e a s t p r e d o m i n a n t l y r e a l v e l o c i t y w i t h o u t any major temperature component. I can advance o n l y one o t h e r argument i n t h i s r e s p e c t - a l s o qualitative.  Power s p e c t r a g e n e r a t e d from our v e l o c i t y s i g n a l s do n o t  ;  e x h i b i t any of the unique c h a r a c t e r i s t i c s of the s p e c t r a o f temperature f l u c t u a t i o n s i n t u r b u l e n t f l o w ( G r a n t , Hughes, V o g e l and M o i l l i e t (1968)) and the c o n c l u s i o n a g a i n i s t h a t our s i g n a l must be p r e d o m i n a n t l y due t o v e l o c i t y  fluctuations.  A l l of t h e s e arguments, a l t h o u g h n o t c o n c l u s i v e , appear t o be seif-consistent.  Even i f we assume the maximum temperature  sensitivity  of 2 cm s e c ^ p e r °C as s u g g e s t e d e a r l i e r (and i t may be much l e s s ) , then i n any r e a l s i t u a t i o n t h a t I have examined,  the i n f l u e n c e of  temperature f l u c t u a t i o n s would a l t e r t h e s p e c t r a l l e v e l s of v e l o c i t y by l e s s than 10 p e r c e n t i n the r e g i o n o f the peak of the d i s s i p a t i o n  Figure 6.  Block diagram of conductivity meter e l e c t r o n i c s .  24 spectrum.  Plotted on a logarithmic scale as we are i n the habit of  doing, (see Figure 1§, f o r example), this difference would be hardly noticeable.  I s h a l l proceed then on the assumption that the s e n s i t i v i t y  of the v e l o c i t y probe to fluctuations i n temperature i s usually not a factor of major s i g n i f i c a n c e , while bearing i n mind at the same time that there may be situations i n which i t cannot be neglected.  Conductivity Meter I s h a l l also describe the conductivity meter more f u l l y , since i t i s a new addition to the system and has not been covered i n any previous p u b l i c a t i o n . The design i s due primarily to R.W.  Chappell  of this laboratory. A cross section of the sensing head i s shown i n Figure 5 and a block diagram of the electronics i n Figure 6.  When i n use the  instrument i s towed i n a d i r e c t i o n from l e f t to right i n Figure 5. Water enters through the central hole or throat at the right and flows out through an annular o r i f i c e as shown.  Three tubular struts cross  the output o r i f i c e l o n g i t u d i n a l l y , supporting the head and also providing access for e l e c t r i c a l connections to the sensing c o i l s . instrument  A long tubular  case, not shown i n Figure 5 but v i s i b l e i n Figure 1, contains  the electronics.  A l l body parts are of brass except the l u c i t e sleeve  (as indicated i n Figure 5) at the center of the throat. The water path, through the throat and back around outside the head, forms an inductive l i n k between two t o r o i d a l c o i l s .  One c o i l i s  fed with a 2 kHz s i g n a l from an o s c i l l a t o r of constant frequency and  25 constant amplitude.  The output t h e n , t a k e n from the second  coil,  v a r i e s i n a m p l i t u d e a c c o r d i n g t o the r e s i s t a n c e of the w a t e r p a t h .  A  second l i n k between the two c o i l s , c o n s i s t i n g of a s i n g l e t u r n of w i r e and p a s s i n g through the second c o i l i n r e v e r s e d i r e c t i o n , can be j u s t e d t o g i v e z e r o output f o r any d e s i r e d v a l u e of w a t e r  ad-  conductivity.  The phase s e n s i t i v e d e t e c t o r s e r v e s t o determine whether any change from t h i s a r b i t r a r y z e r o i s p o s i t i v e or n e g a t i v e .  The m e t a l o f the  head c o n s t i t u t e s a p a r t i a l " s h o r t " on the w a t e r p a t h (broken by the l u c i t e s l e e v e a t the c e n t e r of t h e t h r o a t ) and i t s r e s i s t a n c e i s t h e r e fore important.  I t was  found t h a t the s t a b i l i t y o f t h e i n s t r u m e n t was  improved c o n s i d e r a b l y by a p p l y i n g a heavy s i l v e r p l a t i n g on a l l e x t e r n a l surfaces to minimize corrosion e f f e c t s . C a l i b r a t i o n i s a c c o m p l i s h e d by immersing  the head i n a s e r i e s  of samples of w a t e r a t known temperature and f o r w h i c h s a l i n i t y has been a c c u r a t e l y determined by o t h e r methods.  Short term  s e n s i t i v i t y i s b e t t e r t h a n t h e e q u i v a l e n t o f 0.005 i n a s a l i n i t y and temperature range of our measurements. good f i g u r e f o r l o n g term s t a b i l i t y .  relative w i t h i n the  I do n o t have a  The i n s t r u m e n t has been used  f o r o n l y one o p e r a t i o n at sea d u r i n g w h i c h i t s u f f e r e d some m e c h a n i c a l damage d u r i n g r e t r i e v a l of t h e towed body i n h i g h s e a s .  I t continued to  f u n c t i o n s a t i s f a c t o r i l y but t h e r e i s e v i d e n c e t h a t i t s s e n s i t i v i t y a l t e r e d s l i g h t l y at that time.  was  C a l i b r a t i o n s b e f o r e and a f t e r the  o p e r a t i o n (about t h r e e weeks a p a r t ) show a s h i f t i n a b s o l u t e a c c u r a c y e q u i v a l e n t t o about 0.07  i n a , b u t the r e s u l t s o f a n a l y s i s  indicate  t h a t most of t h i s change t o o k p l a c e a t the time of t h e a c c i d e n t . i s every r e a s o n t o b e l i e v e t h a t s t a b i l i t y s h o u l d be c o n s i d e r a b l y b e t t e r than i n d i c a t e d by t h i s  figure.  There  T E M P E R A T U R E  |  6  1  7  8  1  30  1  31  1  I—n—s 24  Figure 7.  25  —  32  :  26  1  9  1  SALINITY  I  (°C) 10  1  II  1  1  (%o) 3 3  1 1  27  1  3 4  1  1 — n 2 8  Typical gross oceanographic structure for Sea Operation F - l l - 6 7 , from data taken at 1818 hours 21 November 1967.  3 5  29  1  TEMPERATURE (°C) 7 8  6 1  1  1  SALINITY 31  30 1  1  (%o) 32  1  1  24  25 —O  i  1  °*  —— A —  26 1  9  10  1  1  33 1  34  27  28  x —  oi  o 50  100 to rr  UJ i-  o  I o I o I  o  150  Q_ UJ O  200  250 O  TEMPERATURE  X  SALINITY  300  Figure 8. Typical gross oceanographic structure for Sea Operation F-l-69, from data taken at 0850 hours 3 February 1969.  1  26 RESULTS  General Most of the r e s u l t s which w i l l be d i s c u s s e d here are d e r i v e d from d a t a o b t a i n e d d u r i n g two sea o p e r a t i o n s , - one i n November which I s h a l l r e f e r t o as F - l l - 6 7 , and the second 1969,  in  January-February  d e s i g n a t e d F-l-69 - b o t h c a r r i e d out i n water exceeding  meters depth  o f f the west coast of Vancouver I s l a n d , B r i t i s h F i g u r e s 7 and  1969  In February  the t h e r m o c l i n e has observe  Columbia.  s t r u c t u r e i n the a r e a d u r i n g November  respectively.  c l i n e i s decaying but s t i l l 75 meters.  1000  8 taken from s t a n d a r d b o t t l e c a s t s i n d i c a t e  t y p i c a l g r o s s oceanographic and e a r l y February  1967  In November the summer thermo-  amounts t o some 3°C between about 25  1969,  1967  and  towards the end of an u n u s u a l l y c o l d w i n t e r ,  d i s a p p e a r e d almost  completely w h i l e we  a s i g n i f i c a n t h a l o c l i n e between 100  still  and 200 meters or s o .  Most  bathythermograph t r a c e s (which were taken more f r e q u e n t l y than b o t t l e c a s t s ) show a s m a l l i r r e g u l a r i t y then n e g a t i v e , between 75 and  of 0.5  t o 1.5°C, u s u a l l y p o s i t i v e  150 m e t e r s , but n o t h i n g which can  and  be  c o n s i s t e n t l y i d e n t i f i e d as a t h e r m o c l i n e . A s h o r t sample of the paper r e c o r d s i s reproduced The from  first  three traces s t a r t i n g  i n F i g u r e 9.  from the top are d i f f e r e n t i a t e d  the lower, c e n t e r and upper t h e r m i s t o r s r e s p e c t i v e l y .  i d e n t i f i c a t i o n on the f i g u r e s , the t h e r m i s t o r s , from as p o s i t i o n e d on the towed body, are numbered 1,2  and  signals  ( F o r ease of  top t o bottom 3).  n o t e d here t h a t i n a n a l y s i s of the e x p e r i m e n t a l d a t a and  I t should throughout  the f o l l o w i n g d i s c u s s i o n I s h a l l assume T a y l o r ' s h y p o t h e s i s t o be On t h i s b a s i s time d e r i v a t i v e s of temperature d e s i g n a t e d as space  and v e l o c i t y  be  valid.  are  d e r i v a t i v e s i n F i g u r e 9, t a k i n g x as the  direction  27 of mean r e l a t i v e motion between the towed body and the water. The l a s t trace on the four-channel chart i s depth, designated d, i l l u s t r a t i n g the cycling mode of operation.  The f i r s t three traces on  the eight-channel chart (counting again from top to bottom) are the direct signals from the lower, center and upper thermistors.  The next  two channels are Temperature A and then Temperature B (temperature from the temperature probe being designated T, without a subscript), followed by Velocity B and Velocity A, and f i n a l l y Conductivity, G. Time progresses from right to l e f t at just under 200 seconds per depth cycle.  Each d i v i s i o n along the time axis i s five seconds.  Minutes are  indicated along the upper margin of each chart, with a coded time mark every ten minutes.  The same timing marks are recorded on the magnetic  tapes so that i t i s possible to locate any event to within one second on either paper or tape records.  Conductivity and a l l channels of temperature  increase upwards i n the figure, while depth increases downwards. The sample shown i s for purposes of i l l u s t r a t i o n only.  It  was recorded from about 0532 to 0546 hours on 2 February, 1969, during Sea Operation F-l-69.  The body was cycling through 30 meters i n depth  about a mean depth of 128 meters.  As w i l l be noted, the sea state at  the time s l i g h t l y exceeded the a b i l i t y of the winch servo system to compensate, with resulting i r r e g u l a r i t i e s i n the depth trace.  In spite  of wave heights ranging around 5 to 8 meters (trough to crest) however, the body rarely deviates from i t s prescribed track by more than 30 centimeters and almost never reaches one meter. The d i f f e r e n t i a t e d v e l o c i t y channel (as usual) i s quite noisy with a considerable l e v e l of interference from cable v i b r a t i o n and other  28 v i b r a t i o n s w i t h i n the towed body.  On t h i s account the s i g n a l i s n o t  clearly v i s i b l e i n this reproduction.  I t w i l l be n o t e d , however,  t h a t where v e l o c i t y s i g n a l can be seen through the n o i s e , i t c o i n c i d e s i n time w i t h the o c c u r r e n c e of temperature m i c r o s t r u c t u r e - and t h i s i s g e n e r a l l y the case.  The r e v e r s e i s n o t t r u e ; we o f t e n observe  ture microstructure without  any d e t e c t a b l e t u r b u l e n c e .  t h e r e may be t u r b u l e n c e p r e s e n t  tempera-  I n such cases  a t some l e v e l below our t h r e s h o l d o f  d e t e c t i o n , - o r we assume t h a t t h e r e must r e c e n t l y have been t u r b u l e n t mixing  t o g e n e r a t e the temperature s t r u c t u r e .  I s h a l l have more t o  say on t h i s s u b j e c t l a t e r . A l t h o u g h i t i s more common t o f i n d a f a i r l y r e g u l a r h o r i z o n t a l l y l a y e r e d s t r u c t u r e , as i n F i g u r e 10, we observe marked h o r i z o n t a l g r a d i e n t s o f temperature and c o n d u c t i v i t y i n the sample shown i n F i g u r e 9, as e v i d e n c e d by changes i n the p a t t e r n o f the r e c o r d s  from  c y c l e t o c y c l e ( o f depth) and asymmetry w i t h i n i n d i v i d u a l c y c l e s . There a r e v e r t i c a l temperature i n v e r s i o n s throughout the l e n g t h of the sample, n o t a b l y i n the l a s t depth c y c l e a t the l e f t where an i n v e r s i o n extends o v e r most of the 30 meters of the depth e x c u r s i o n .  (The  two  lower t h e r m i s t o r s and c o n d u c t i v i t y s i g n a l show an e l e c t r o n i c o v e r l o a d at the bottom of t h i s c y c l e ) .  I n most c a s e s , as we s h a l l see l a t e r ,  temperature i n v e r s i o n s o f t h i s s o r t a r e u s u a l l y compensated by s a l i n i t y s t r u c t u r e so t h a t the d e n s i t y g r a d i e n t remains s t a b l e . F i g u r e 10 shows a n o t h e r s h o r t s e c t i o n of s i g n a l from s e l e c t e d c h a n n e l s , t h i s t i m e r e c o n s t i t u t e d from the magnetic tape r e c o r d , to i l l u s t r a t e the h o r i z o n t a l l y l a y e r e d s t r u c t u r e commonly o b s e r v e d . sample was  recorded  from about 0222 t o 0230 hours on 5 F e b r u a r y  1969.  This  &  -  r  m 1  2  X  ?  11 5:!  \  C  I  7  s if  5  II Figure  10. Temperature and c o n d u c t i v i t y r e c o r d s a c y c l i n g run at 152 meters depth. H o r i z o n t a l g r a d i e n t s are s m a l l .  from  29 Time, i n t h i s c a s e , p r o g r e s s e s  from l e f t t o r i g h t .  Mean o p e r a t i n g  depth was 152 meters and a g a i n t h e depth range was 30 meters i n t h e c y c l i n g mode.  S t a r t i n g from the t o p o f t h e f i g u r e , the f i r s t  channel  i s t h e d i f f e r e n t i a t e d s i g n a l from the upper t h e r m i s t o r f o l l o w e d by the d i r e c t s i g n a l from the upper, c e n t e r and lower t h e r m i s t o r s i n sequence.  The maximum temperature v a r i a t i o n i s a p p r o x i m a t e l y  The n e x t t r a c e i s c o n d u c t i v i t y ( a t t h e l e v e l o f t h e c e n t e r and t h e l a s t , a t t h e b o t t o m , i s depth.  0.35°C.  thermistor)  A l l s i g n a l s i n c r e a s e upwards  e x c e p t d e p t h , w h i c h as b e f o r e i n c r e a s e s downwards as depth s h o u l d . The  c y c l i n g p e r i o d i s approximately  115 seconds; t h e v e r t i c a l c h a r t  d i v i s i o n s marking 5 second i n t e r v a l s as b e f o r e . I n t h i s case h o r i z o n t a l g r a d i e n t s a r e much s m a l l e r than b e f o r e and even v e r y t h i n l a y e r s may e x t e n d f o r s u r p r i s i n g d i s t a n c e s h o r i z o n t a l l y , a l t h o u g h sometimes d i s p l a c e d v e r t i c a l l y by i n t e r n a l waves. Take f o r example t h e s m a l l l a y e r i d e n t i f i e d as (a) i n F i g u r e 10 and c h a r a c t e r i z e d by a temperature a p p r o x i m a t e l y water immediately  above o r below.  0.03°C warmer than t h e  By v i s u a l e x a m i n a t i o n  o f t h e paper  r e c o r d t h i s l a y e r can be i d e n t i f i e d c o n t i n u o u s l y f o r a t l e a s t 1500 m e t e r s , over w h i c h range i t v a r i e s i n t h i c k n e s s from l e s s than 20 centimeters  t o between one and two m e t e r s .  10 c e n t i m e t e r s  I n a few c a s e s , l a y e r s o f .  and perhaps l e s s i n t h i c k n e s s a r e i d e n t i f i a b l e f o r a t  l e a s t 200 m e t e r s , and, a t t h e o t h e r end o f t h e s c a l e , l a r g e r l a y e r s 10 t o 15 meters t h i c k - have been f o l l o w e d c o n t i n u o u s l y f o r 13 k i l o meters ; t h i s l a t t e r f i g u r e r e p r e s e n t i n g t h e d u r a t i o n o f o u r r e c o r d and probably n o t the f u l l extent of the l a y e r . S p e c u l a t i o n by Stommel and Fedorov (1967) on t h e mechanism o f formation of t h i n l a y e r s , o r "laminae"  as they c a l l them, i s o f i n t e r e s t  30 i n this context.  They come to the tentative conclusion that "layers  as thin as 10 centimeters could never occur by a process of spreading from larger layers; by the time they reached such fine dimensions  they  would be conducted away" - and their reasoning seems to be v a l i d . Nevertheless we do observe c l e a r l y defined layers of this sort of thickness and, as I have s a i d , up to at least 200 meters i n h o r i z o n t a l extent.  I cannot at this stage offer any explanation of the apparent  contradiction; nor do I have any clear evidence of an alternative mechanism for the formation of such thin layers - f a r below the seasonal thermocline.  One might suggest the p o s s i b i l i t y of the net transport of  f l u i d which can take place when an i n t e r n a l wave propagates sharp density gradient.  along a  By v i s u a l examination of my data i t does  appear that the very thin layers usually occur i n the v i c i n i t y of strong and steep temperature  gradients but, as I s h a l l point out s h o r t l y ,  I cannot resolve density structure on a fine enough scale to add any further support to the idea. Neither can I give an unqualified answer to Stommel and Federov's question:  "Is there a smallest observed lamina thickness?"  Ten centimeters or a l i t t l e less i s about the l i m i t of resolution by the simple v i s u a l technique I have used for this purpose.  There i s f i n e r  d e t a i l i n the data, but the i d e n t i f i c a t i o n of thinner layers, i f they e x i s t , w i l l require a more sophisticated  approach.  I have already pointed out that small scale turbulence (or velocity microstructure) i s always accompanied by thermal microstructure and i s presumably the cause of the thermal structure.  It w i l l  Figure  11. V e l o c i t y , temperature and c o n d u c t i v i t y r e c o r d s a c y c l i n g run at 305 meters depth. structure i s v i s i b l e .  from  Very l i t t l e m i c r o -  31 be p e r t i n e n t t o l a t e r d i s c u s s i o n t o note here a l s o , i n both  Figure 9  and F i g u r e 10 - and i t i s g e n e r a l l y the case - that thermal  micro-  s t r u c t u r e almost always occurs  i n r e g i o n s o f h i g h mean temperature  g r a d i e n t - e i t h e r p o s i t i v e or n e g a t i v e . During  our p e r i o d o f o b s e r v a t i o n i n January - February 1969,  r e g i o n s such as d e p i c t e d i n F i g u r e s 9 and 10 o c c u p i e d perhaps 30 percent  of the ocean volume from the t h e r m o c l i n e  depth of j u s t over  300 meters.  I n November 1967 the p r o p o r t i o n was  n o t i c e a b l y h i g h e r - some 60 o r 65 p e r c e n t . f i l l e d with  down t o our l i m i t i n g  The r e s t of t h e volume i s  f a i r l y r e g u l a r g r a d i e n t s o f temperature and s a l i n i t y  corresponding  roughly  t o the gross s t r u c t u r e as d e r i v e d from  standard  oceanographic  c a s t s , and c o n t a i n i n g o n l y s m a l l s c a t t e r e d patches o f  m i c r o s t r u c t u r e a t low i n t e n s i t y . To  f u r t h e r i l l u s t r a t e t h e p o i n t , F i g u r e 11 shows a t y p i c a l  s e c t i o n of r e c o r d from a r e g i o n o f uniform  gradients.  from about 1951 t o 2006 hours on 5 February,  I t was  recorded  1969, d u r i n g O p e r a t i o n  F-l-69.  The body was c y c l i n g through 30 meters about a mean depth o f 305 meters. A l l t r a c e s a r e the same as i n F i g u r e 9.  Here the temperature (and  c o n d u c t i v i t y ) g r a d i e n t s a r e q u i t e u n i f o r m , b u t always i n s m a l l i r r e g u l a r s t e p s o f perhaps 0.002 t o 0.02°C. gradient. with  I have never seen a t r u l y smooth  The mean g r a d i e n t i s approximately  temperature d e c r e a s i n g  7 x 10  as depth i n c r e a s e s .  °C p e r c e n t i m e t e r  H o r i z o n t a l gradients are  very s m a l l . There i s always some temperature m i c r o s t r u c t u r e v i s i b l e on the d i f f e r e n t i a t e d t h e r m i s t o r t r a c e s ( a t the top) and t h i s almost always occurs w i t h i n the s t e e p e r g r a d i e n t s o f the s m a l l s t e p s  that we have  32 a l r e a d y examined.  (Note t h a t t h e r e was  some s l i p p a g e i n one of the  c h a r t d r i v e s , and, w h i l e the two r e c o r d s of F i g u r e 11 are i n phase a t the l e f t , they a r e d i s p l a c e d by almost a m i n u t e at the r i g h t ) .  There i s  n o t h i n g b u t n o i s e on the v e l o c i t y channels and i t seems u n l i k e l y t h e r e would be a c t i v e t u r b u l e n c e i n such an u n d i s t u r b e d  that  r e g i o n as  this.  On the o t h e r hand, the temperature m i c r o s t r u c t u r e c o u l d not e x i s t f o r long without being continuously One  i s l e d to suspect  ( o r at l e a s t p e r i o d i c a l l y )  t h a t , w i t h i n each of the s m a l l s t e p s of temperature  v i s i b l e on these r e c o r d s , t h e r e may i n a continuous  regenerated.  process  be an even s m a l l e r l a y e r e d s t r u c t u r e  of f o r m a t i o n and r e - f o r m a t i o n as s u g g e s t e d by  Stommel and Federov (1967), o r , w i t h i n each s t e p p e r h a p s , a dynamic p r o c e s s more a k i n t o the d o u b l e - d i f f u s i v i t y c o n n e c t i o n d i s c u s s e d by and Stommel (1964) f o r example. process  (or processes)  I have not attempted t o i d e n t i f y  Turner  the  i n v o l v e d , b u t I b e l i e v e t h a t , from the d a t a on hand,  one might be a b l e t o d e r i v e some c l u e s as t o i t s n a t u r e . F i g u r e 12 i l l u s t r a t e s an i n t e r e s t i n g o c c u r r e n c e w h i c h appears t o be a v e r y s h a r p l y d e f i n e d " f r o n t " , or boundary between two w a t e r masses, s l o p i n g at about 1.5° towed body.  T h i s sample was  t o the h o r i z o n t a l along the p a t h of the recorded  from about 0327 t o 0340 hours  on  22 November, 1967, w h i l e c y c l i n g through 6.5 meters i n d e p t h , about a s mean depth of 213 m e t e r s . f i e d i n the same way  The v a r i o u s channels of the r e c o r d are  as b e f o r e .  Temperature i n c r e a s e s upwards and  maximum e x c u r s i o n s i n t h i s s e c t i o n of r e c o r d are a p p r o x i m a t e l y  identithe  0.25°C.  Time, a g a i n , advances from l e f t t o r i g h t , but each v e r t i c a l d i v i s i o n time r e p r e s e n t s 10 seconds i n s t e a d of 5. seconds.  The  this  C y c l i n g time i s about 50  depth s i g n a l has been i n a d v e r t e n t l y i n v e r t e d i n t h i s  w i t h the peaks o f the t r a c e r e p r e s e n t i n g maximum depth.  figure,  33 For more than 15 m i n u t e s ( o r more than one k i l o m e t e r ) b e f o r e the b e g i n n i n g o f t h e s e c t i o n of r e c o r d shown, the w a t e r i s almost p e r f e c t l y i s o t h e r m a l and, a l t h o u g h the towing w i n c h i s i n the c y c l i n g mode, the temperature  t r a c e s are very n e a r l y s t r a i g h t .  About one m i n u t e  from the l e f t m a r g i n of the f i g u r e , the lowest t h e r m i s t o r touches c o l d e r w a t e r a t the bottom o f a c y c l e .  Each c y c l e t h e r e a f t e r p e n e t r a t e s  the c o l d e r w a t e r more deeply u n t i l , t h r e e c y c l e s l a t e r , t h e upper t h e r m i s t o r e n t e r s i t f o r the f i r s t  t i m e , and, by about the c e n t e r of the  figure,  a l l t h e r m i s t o r s remain i n the u n d e r l y i n g body o f c o l d e r w a t e r a l l the time.  The boundary between the two b o d i e s of w a t e r i s v e r y s h a r p ,  and,  w h i l e the warm upper w a t e r i s q u i e t , the w a t e r below the boundary i s s t r o n g l y t u r b u l e n t and c o n t a i n s i n t e n s e t h e r m a l m i c r o s t r u c t u r e .  One  s u s p e c t s t h a t t h e r e must be v e l o c i t y shear a c r o s s the boundary, b u t , u n f o r t u n a t e l y we have n o t y e t been a b l e t o measure s h e a r .  Turbulent  i n t e n s i t i e s below t h i s boundary are t h e h i g h e s t so f a r observed below the t h e r m o c l i n e .  (Note f i r s t e n t r y i n T a b l e I ) .  A p i c t u r e of the ocean b e g i n s t o take form t h e n , c o n s i s t i n g of f a i r l y e x t e n s i v e r e g i o n s of u n i f o r m g r a d i e n t s c o r r e s p o n d i n g more or l e s s t o e a r l i e r i d e a s of the s t r u c t u r e of t h e ocean below the t h e r m o c l i n e . I n t e r s p e r s e d between or w i t h i n these u n i f o r m o r " i n a c t i v e " r e g i o n s , and occupying o n e - t h i r d t o over o n e - h a l f of t h e t o t a l volume, are h o r i z o n t a l l y s t r a t i f i e d r e g i o n s w h i c h I d e s c r i b e as " a c t i v e " f o r l a c k of a b e t t e r term.  These a c t i v e r e g i o n s e x h i b i t an i r r e g u l a r temperature  q u i t e u n r e l a t e d t o the mean g r a d i e n t s i n the a r e a .  They may  structure, vary i n  t h i c k n e s s from a few meters t o a few tens of meters and i n h o r i z o n t a l e x t e n t up t o tens o f k i l o m e t e r s and perhaps more.  34 The  a c t i v e r e g i o n s u s u a l l y c o n s i s t of a number of i r r e g u l a r  l a y e r s , t y p i c a l l y a few  c e n t i m e t e r s t o a few meters i n  thickness,  s e p a r a t e d by t h i n boundary r e g i o n s of r e l a t i v e l y s t e e p e r temperature gradients  o f t e n e x c e e d i n g 0.01  b o u n d a r i e s may and  be  °C cm \  These l a y e r s and i n t e r - l a y e r  compared w i t h Woods (1966-67) d e s c r i p t i o n of " l a y e r s "  " s h e e t s " as o b s e r v e d a t s h a l l o w e r depths i n the M e d i t e r r a n e a n .  Temperature i n v e r s i o n s  ( i . e . temperature i n c r e a s i n g w i t h depth so  w i t h o u t compensation by  o t h e r f a c t o r s , the s t r u c t u r e w o u l d be  gravi-  t a t i o n a l l y u n s t a b l e ) , w i t h i n or between l a y e r s are common and may quite intense  - sometimes 0.2  Scattered t u r b u l e n c e and  or 0.3°C w i t h i n a few  f a c t o r of 10 t o 100)  be  centimeters.  throughout the a c t i v e r e g i o n s we  thermal microstructure,  that,  f i n d p a t c h e s of  u s u a l l y much s m a l l e r  (by  a  i n the v e r t i c a l dimension than the h o r i z o n t a l ,  o f t e n i n t e r m i t t e n t w i t h i n i n d i v i d u a l p a t c h e s , and a d j a c e n t t o the s t e e p e r temperature g r a d i e n t s  u s u a l l y l o c a t e d i n or  of the boundary r e g i o n s  between l a y e r s .  Comments by Stommel and Federov (1967) w i t h r e s p e c t t o  the " p a t c h i n e s s "  of t u r b u l e n c e i n the ocean r e p o r t e d  and V o g e l (1968) are c e r t a i n l y v a l i d . the l a y e r s  et a l could obviously  a h o r i z o n t a l s a m p l i n g t e c h n i q u e as used by l e a d to i n c o r r e c t c o n c l u s i o n s  d i s t r i b u t i o n . The  and i n t e r m i t t e n t , and and  More o f t e n than n o t , i t seems,  (and b o u n d a r i e s ) are d i s t o r t e d v e r t i c a l l y by what appear t o  be i n t e r n a l waves, and  s i z e and  by G r a n t , M o i l l i e t  t u r b u l e n c e we  Grant,  as r e g a r d s p a t c h  ^  observe i s n e v e r t h e l e s s p a t c h y  a s t a t i s t i c a l e x a m i n a t i o n of p a t c h c h a r a c t e r i s t i c s  d i s t r i b u t i o n w o u l d be a r e w a r d i n g s t u d y i n i t s e l f .  t a k e n such an a n a l y s i s i n any  quantitative  detail.  I have not  under-  35 Fossil  Turbulence I have made the statement t h a t t u r b u l e n c e i s always accompanied  by temperature m i c r o s t r u c t u r e b u t t h a t t h e r e v e r s e i s f r e q u e n t l y n o t t r u e . I have suggested  f u r t h e r t h a t the e x i s t e n c e of temperature m i c r o s t r u c t u r e  may be taken as an i n d i c a t i o n t h a t , although  t h e r e may be no measurable  t u r b u l e n c e p r e s e n t , the r e g i o n must have been t u r b u l e n t i n the r e c e n t p a s t , - otherwise  the thermal s t r u c t u r e would have decayed by  Batchelor  conduction.  (1959) has c o n s t r u c t e d a theory d e s c r i b i n g the  d i s t r i b u t i o n of a s c a l a r contaminant  ( l i k e temperature) i n a t u r b u l e n t  f l u i d , and the a p p l i c a t i o n o f t h i s theory t o the ocean environment has r e c e i v e d s u b s t a n t i a l support (1968) .  Consider  from G r a n t , Hughes, V o g e l and M o i l l i e t  a t u r b u l e n t s i t u a t i o n i n which the spectrum o f tempera-  t u r e f l u c t u a t i o n conforms t o B a t c h e l o r ' s t h e o r y , and suppose t h a t , a t some s t a g e , the t u r b u l e n t mixing  ceases.  The s m a l l e s t s c a l e s o f m i c r o -  s t r u c t u r e w i l l q u i c k l y d i e away by c o n d u c t i o n , w h i l e the l a r g e r s c a l e s w i l l persist  f o r longer p e r i o d s .  w i l l be a p r o g r e s s i v e drooping  The e f f e c t on the temperature spectrum  a t the upper end, s t a r t i n g f i r s t  a t the  h i g h e s t wavenumbers, and r e a c h i n g f a r t h e r back w i t h time t o lower and lower wavenumbers. has  The temperature s t r u c t u r e l e f t b e h i n d  disappeared  a f t e r the t u r b u l e n c e  has been r e f e r r e d t o as " f o s s i l t u r b u l e n c e " o r t h e  " f o o t p r i n t s o f t u r b u l e n c e " , - the l a t t e r term a t t r i b u t e d by Stewart (1969) t o Markovin o f Johns Hopkins U n i v e r s i t y . The  two power s p e c t r a o f temperature f l u c t u a t i o n s p l o t t e d  i n F i g u r e 13 may i l l u s t r a t e t h i s s i t u a t i o n . Operation  Both s p e c t r a a r e taken  from  F-l-69 w h i l e i n the c y c l i n g mode i n a r e g i o n c o n t a i n i n g many  t h i n l a y e r s w i t h s p o r a d i c patches  of turbulence.  The l e n g t h of the  36 samples was only about 11 seconds (limited by the thickness of the layers) and the spectra are therefore quite ragged at the low end. spectra are i d e n t i f i e d as coming from Tape at  2141:20 hours, respectively.  The two  16 at 0300:10 hours and Tape 13  The sample from Tape  16 contained strong  turbulence, as may be seen from the short section of the o r i g i n a l record reproduced also i n Figure 13, with d i f f e r e n t i a t e d channels of temperature and v e l o c i t y indicated.  The sample from Tape 13 contained  no detectable turbulence. So far as I am able to t e l l , the v e l o c i t y s i g n a l seen on the record i s e n t i r e l y due to v i b r a t i o n . The s p e c t r a l form predicted by Batchelor's theory i s l a i d over the  spectrum from Tape 16, and the f i t i s as good as we have any reason  to expect.  The f l a t portion at the high wavenumber end of the spectrum  i s due to electronic noise, and the sharp peak at log k = 1.3 i s an a r t i f a c t of the electronic equipment.  The minor deviation from the theore-  t i c a l curve before the spectrum flattens o f f into pure noise, i s probably also due to the presence of some noise mixed with the s i g n a l . The spectrum from Tape 13 has been s h i f t e d upwards by 0.24 i n log  to a r t i f i c i a l l y match the two spectra at the low end, - and i t  shows just the sort of drooping c h a r a c t e r i s t i c at the high end that we would expect i n a case of " f o s s i l turbulence", i f the ideas I have expressed above are v a l i d . the  From the separation of the two curves and  thermal d i f f u s i v i t y of water, we can calculate a time - about h a l f -  an-hour i n this case - since the region ceased to be turbulent. Having made the point I must admit that I am not r e a l l y convinced that Figure 13 i l l u s t r a t e s a genuine case of f o s s i l i z e d turbulence.  The theory predicts a horizontal s h i f t of the whole pattern  37 a l o n g the l o g k a x i s , a c c o r d i n g t o t h e r a t e , e , o f d i s s i p a t i o n o f energy i n t h e t u r b u l e n t f i e l d , - and my s p e c t r a , because o f t h e s h o r t n e s s of t h e samples, a r e n o t good enough t o d i s t i n g u i s h c l e a r l y between a droop a t t h e h i g h end and h o r i z o n t a l s h i f t o f t h e whole c u r v e .  Perhaps  F i g u r e 13 s i m p l y i l l u s t r a t e s one sample c o n t a i n i n g r e l a t i v e l y s t r o n g t u r b u l e n c e , and another i n w h i c h t h e t u r b u l e n c e , though s t i l l i s a t a l e v e l below our t h r e s h o l d o f d e t e c t i o n .  active,  I b e l i e v e , however,  t h a t w i t h l o n g e r samples from w h i c h smoother s p e c t r a c o u l d be g e n e r a t e d , i t s h o u l d be p o s s i b l e t o i d e n t i f y f o s s i l t u r b u l e n c e by t h e method I have d e s c r i b e d .  Density Structure I t becomes a m a t t e r o f some i n t e r e s t a t t h i s p o i n t t o examine the e f f e c t s o f s a l i n i t y . I t i s s t a t e d i n the s e c t i o n on " I n s t r u m e n t a t i o n " t h a t t h e c o n d u c t i v i t y s e n s o r s h o u l d have a response  e s s e n t i a l l y f l a t and u n d i s -  t o r t e d up t o about 5 Hz ( a t n o r m a l towing speeds) and i t i s c l e a r from the r e c o r d s t h a t t h e response  does i n d e e d extend w e l l beyond 10 Hz,  a l t h o u g h perhaps n o t p r e c i s l y f l a t .  From the geometry o f t h e s e n s i n g  head and f l o w p a t h , one would expect i t t o b e g i n dropping o f f s e r i o u s l y a t something l i k e 30 Hz.  No d e t a i l e d a n a l y s i s o f t h e response  of t h i s  i n s t r u m e n t has been undertaken because u n f o r t u n a t e l y i t s u s e f u l response i s l i m i t e d by o t h e r f a c t o r s i n t h e p r e s e n t  application.  As mounted on the towed body, t h e e f f e c t i v e c e n t e r o f t h e c o n d u c t i v i t y c e l l was d i s p l a c e d some 22 c e n t i m e t e r s l o n g i t u d i n a l l y and 33 c e n t i m e t e r s l a t e r a l l y from t h e c e n t e r t h e r m i s t o r w h i c h i s used t o  38 p r o v i d e temperature i n f o r m a t i o n f o r computing d e n s i t y .  Knowing t h e  mean v e l o c i t y o f advance, a c o r r e c t i o n f o r t h e l o n g i t u d i n a l d i s p l a c e m e n t , t o an a c c u r a c y o f 10 p e r c e n t o r b e t t e r , can be i n c l u d e d i n t h e computation.  I n t h e p r e s e n c e o f unknown h o r i z o n t a l s t r u c t u r e however, and  r e c o g n i z i n g t h e p o s s i b i l i t y o f some s m a l l "bank" a n g l e o f t h e body, t h e r e i s no way o f c o r r e c t i n g f o r t h e l a t e r a l d i s p l a c e m e n t .  I n computati  of s a l i n i t y o r d e n s i t y t h e r e f o r e , no r e l i a n c e s h o u l d be p l a c e d on s p a t i a l r e s o l u t i o n s m a l l e r t h a n perhaps f i v e times t h e s p a c i n g o f s e n s o r s , o r some 150 c e n t i m e t e r s i n t h e l o n g i t u d i n a l d i r e c t i o n , c o r r e s p o n d i n g t o about 50 c e n t i m e t e r s v e r t i c a l l y  ( i n the c y c l i n g mode) o r a frequency o f  about 1 Hz a t o u r normal towing speed. F o r computation o f d e n s i t y from c o n d u c t i v i t y and temperature I have combined i n t o a s i n g l e o p e r a t i o n a two-stage p r o c e s s w h i c h d e r i v e s f i r s t a v a l u e f o r s a l i n i t y by l i n e a r i n t e r p o l a t i o n i n t h e t a b l e s p u b l i s h e d by t h e U.S. Navy H y d r o g r a p h i c O f f i c e i n H.O. t i o n No. 619 (1956).  J U  i n which  For t h i s  Publica-  step,  = G-28.3-0.8(T-4) 0.839+0.02233(T-4)  '  K  J  T i s temperature i n °C S i s s a l i n i t y i n °/oo G i s conductivity i n millimhos,  g i v e s a v a l u e f o r S a c c u r a t e t o ±.1% f o r a temperature range o f 4—9°C and s a l i n i t y from 31-34 °/oo, w h i c h i s s u f f i c i e n t f o r a l l o f our measurements.  F o r t h e second s t a g e a q u a d r a t i c f i t t o t h e t a b u l a t e d v a l u e s i n  H.O. P u b l i c a t i o n No. 615 (1952) l e a d s t o the f o l l o w i n g e x p r e s s i o n f o r a^:  39 a  = 23.8395-0.0921(T-4)-0.00584(T-4) + (S-30)  [ o . 7395-0.00256 (T-4)^|  2 ,  (26)  i n w h i c h a , i n t h e u s u a l o c e a n o g r a p h i c s e n s e , i s d e f i n e d as 1000(p  ^ - 1 ) , where p ^ i s the s p e c i f i c g r a v i t y of sea water a t specis,t,o s,t,o  f i e d t e m p e r a t u r e , t , s a l i n i t y , s , and a t m o s p h e r i c p r e s s u r e . values f o r a and  Resulting  a r e a c c u r a t e t o ±0.1% over t h e same range o f t e m p e r a t u r e  salinity. Combining (25) and (26) and rounding  to the extent p o s s i b l e without  o f f the c o e f f i c i e n t s  l o s s i n o v e r a l l accuracy we g e t f i n a l l y  0.7935G-0.00256GL-0.10729L-.00491L -.00013L -2.4547, 0.839+0.02233L 2  a  t  i n w h i c h L = T-4.  3  (27)  I t i s t h i s f o r m u l a t h a t I have used f o r a l l c a l -  culations ofa . t F i g u r e 14 shows a s e r i e s o f p l o t s o f a same s e c t i o n o f r e c o r d as shown i n F i g u r e 10. from the l e f t , c o r r e s p o n d  Successive p l o t s , s t a r t i n g  t o s e q u e n t i a l h a l f c y c l e s i n d e p t h , w i t h each  p l o t a r t i f i c i a l l y s h i f t e d t o t h e r i g h t b y 0.1 i n a one.  c a l c u l a t e d from t h e  The v a l u e s shown f o r a  from t h e p r e v i o u s  are appropriate only t o the f i r s t  (incomplete) h a l f c y c l e a t the l e f t . Since the u s e f u l r e s o l u t i o n o f density f l u c t u a t i o n s i s l i m i t e d by t h e s e p a r a t i o n o f t h e t e m p e r a t u r e and c o n d u c t i v i t y s e n s o r s , most o f the m e a n i n g l e s s h i g h f r e q u e n c i e s have been removed by f i l t e r i n g . Still,  t h e s m a l l e s t s c a l e o f f l u c t u a t i o n s i n F i g u r e 14 and t h e o c c a s i o n a l  sharp " t r a n s i e n t " o c c u r r i n g where t h e body passes through s t e e p of temperature and/or s a l i n i t y , a r e p r o b a b l y  gradients  u n r e a l and s h o u l d be i g n o r e d .  o  to  CM  cn CD  I  cr z:  i —< LO i cn u_ O J o i 2 O O CM  aa  <otn  *-> CM o  I—  cr  CC  U J Ln o  UJ CE Q_ UJ cr  CO t —  oi * fie i  02'Ofil  (Sb313W) oe *9fti ofi'2si  00 'OfrTi  00'09h  00*08*1  Hld30 os'esi  00*005 00*029 (133J) Hld3Q  0 9 *Ti9I  OL'Ol  OO'OfiS  00*09^  Figure 15. A r t i f i c i a l a p r o f i l e corresponding to the f i f t h trace of Figure 14 but without the influence of s a l i n i t y .  (13  40 I b e l i e v e any f e a t u r e s e x t e n d i n g over 50 c e n t i m e t e r s or more i n depth to be  real. The e f f e c t s of t h e s t e e p g r a d i e n t s of temperature  of  F i g u r e 10 are n o t i c e a b l y subdued i n the d e n s i t y p r o f i l e , b e i n g compensated l a r g e l y but n o t always  c o m p l e t e l y , by c o r r e s p o n d i n g g r a d i e n t s o f s a l i n i t y .  A few r e g i o n s o f minor i n s t a b i l i t y , amounting t o some 0.02 i n a , remain uncompensated.  or  0.03  I am c o n f i d e n t t h a t these a r e r e a l  and  i n d e e d , such i n s t a b i l i t i e s e x i s t i n most of the samples f o r w h i c h have computed p r o f i l e s of t h i s t y p e . exceeded 0.05  None i n my  I  e x p e r i e n c e so f a r has  in a .  To emphasize the s t a b i l i z i n g e f f e c t of s a l i n i t y on the d e n s i t y p r o f i l e , I have reproduced  i n F i g u r e 15 an a r t i f i c i a l a  curve  c o r r e s p o n d i n g to the f i f t h t r a c e o f F i g u r e 14 as i t w o u l d appear w i t h s a l i n i t y h e l d constant at i t s i n i t i a l value f o r t h i s t r a c e .  (Note t h a t  t h i s i s an upwards h a l f - c y c l e i n depth and s t a r t s a t the b o t t o m ) . I t w i l l be observed t h a t o c c a s i o n a l l y i n F i g u r e 14 the a t r a c e doubles back on i t s e l f f o r a meter or two i n depth. r e v e r s a l s r e p r e s e n t o c c a s i o n s on w h i c h , because i t was adjustment,  These  not i n proper  o r because o f e x c e s s i v e s e a s t a t e , the s e r v o c o n t r o l on the  towing winch a l l o w e d the body depth t o f l u c t u a t e m o m e n t a r i l y . times the t r a c e s o v e r l a p q u i t e n e a t l y .  Some-  A t o t h e r t i m e s , because of  h o r i z o n t a l g r a d i e n t s o r more l i k e l y because of i r r e g u l a r body m o t i o n when the s e r v o l o s e s c o n t r o l , the r e c o r d shows a marked d i f f e r e n c e i n shape each time t h e depth increment i s r e t r a c e d . e x i s t e n c e I do n o t f e e l t h a t any importance irregularities.  Beyond n o t i n g t h e i r  s h o u l d be a t t a c h e d t o these  41 I t i s i n t e r e s t i n g t o n o t e t h a t w h i l e t h e temperature p r o f i l e may be v e r y i r r e g u l a r i n d i s t u r b e d r e g i o n s , b e a r i n g no apparent r e l a t i o n t o the mean temperature g r a d i e n t i n t h e a r e a , t h e mean s l o p e o f t h e d e n s i t y p r o f i l e i n a l l cases t h a t I have examined corresponds q u i t e closely  ( b e t t e r than a f a c t o r o f 2) t o t h e mean d e n s i t y g r a d i e n t as  d e r i v e d from o c e a n o g r a p h i c s t a t i o n s .  I cannot make any more e x a c t  comparison i n t h i s r e s p e c t , because o c e a n o g r a p h i c s t a t i o n s were  taken  o n l y once o r t w i c e a day d u r i n g t h e e x p e r i m e n t , and t h e r e may be a l a p s e o f s e v e r a l hours (and tens o f k i l o m e t e r s ) between t h e t i m e o f any p a r t i c u l a r sample and t h e t i m e o f the c l o s e s t s t a t i o n . I t has so f a r n o t been p o s s i b l e t o r e l a t e t h e p r o b a b i l i t y o f occurrence  o r t h e i n t e n s i t y o f t u r b u l e n c e t o any o u t s t a n d i n g  the density s t r u c t u r e .  feature of  V e l o c i t y m i c r o s t r u c t u r e seems e q u a l l y l i k e l y t o  occur i n s t r o n g l y s t a b l e , n e u t r a l o r u n s t a b l e r e g i o n s .  As a l r e a d y n o t e d ,  however, temperature m i c r o s t r u c t u r e shows a s t r o n g p r e f e r e n c e where t h e mean temperature g r a d i e n t i s s t e e p  f o r regions  ( e i t h e r p o s i t i v e or negative)  and t u r b u l e n c e , when d e t e c t a b l e , tends t o occur where t h e t e m p e r a t u r e m i c r o s t r u c t u r e i s most i n t e n s e .  Q u i t e c o n t r a r y t o Woods' (1966-67)  observation that turbulence i s of vanishing i n t e n s i t y w i t h i n the "sheets", the p r o b a b i l i t y o f o c c u r r e n c e  o f t u r b u l e n c e i n our s i t u a t i o n i s much  g r e a t e r and maximum t u r b u l e n t i n t e n s i t i e s almost i n v a r i a b l y o c c u r w i t h i n the steep temperature g r a d i e n t s between l a y e r s .  I t i s frequently  i m p o s s i b l e , however, t o i d e n t i f y these steep g r a d i e n t s o f temperature on the d e n s i t y p r o f i l e s .  42 Velocity  Spectra I have computed power s p e c t r a from a number of samples o f  v e l o c i t y f l u c t u a t i o n s r e c o r d e d d u r i n g Sea O p e r a t i o n s  F - l l - 6 7 and  F-l-69.  For s a t i s f a c t o r y s p e c t r a l a n a l y s i s i t i s of course d e s i r a b l e t o work w i t h r e a s o n a b l y u n i f o r m samples of as l o n g a d u r a t i o n as p o s s i b l e .  There  a r e , however, many hazards t o be e n c o u n t e r e d i n the c o l l e c t i o n of d a t a . T u r b u l e n c e occurs i n p a t c h e s w i t h i n l a y e r s - and t h e r e i s no way  of  p r e d i c t i n g i n advance what the s i g n a l l e v e l s i n the n e x t p a t c h w i l l  be.  Many good samples a r e l o s t because of i n a p p r o p r i a t e g a i n s e t t i n g s , o r g a i n changes made t o o e a r l y o r t o o l a t e . from time t o time and may Any  Probe washes are  necessary  s p o i l an o t h e r w i s e u s e f u l s e c t i o n of r e c o r d .  a p p r e c i a b l e change i n s h i p ' s speed d u r i n g r e c o r d i n g w i l l d i s t o r t  r e s u l t i n g spectrum.  the  When one compounds these i n h e r e n t problems w i t h  the g e n e r a l l y u n c o o p e r a t i v e  n a t u r e of w i n t e r weather i n the n o r t h  P a c i f i c , the p o s s i b i l i t y of e l e c t r o n i c or m e c h a n i c a l  failure,  operator  e r r o r o r o t h e r m i s f o r t u n e , one i s l e f t w i t h v e r y few s u i t a b l e samples of any l e n g t h t o choose from. D u r i n g O p e r a t i o n F - l l - 6 7 we  accomplished  some 32 hours of  r e c o r d i n g i n two weeks a t sea and i n O p e r a t i o n F-l-69 about 35 hours out of t h r e e weeks.  From these raw d a t a t h e r e are perhaps 20 o r  25  samples, v a r y i n g i n l e n g t h from t e n seconds t o two m i n u t e s , from w h i c h meaningful  s p e c t r a might be d e r i v e d .  I n the c y c l i n g mode, w i t h the  t u r b u l e n t p a t c h e s u s u a l l y c o n f i n e d t o r e l a t i v e l y t h i n l a y e r s , samples are n e c e s s a r i l y q u i t e s h o r t , - except  i n two or t h r e e u n u s u a l  In the c o n s t a n t depth mode the chance o f e n c o u n t e r i n g  cases.  a turbulent layer  at a l l i s lower than when cycling, but when one i s found the useful sample lengths tend to be longer and i t has been possible to obtain several spectra from samples of about 52 seconds duration.  I have  processed only one longer sample. Figures 16 and 17 are t y p i c a l examples from Tape 11 of F-ll-67 and Tape 12 of F-l-69 respectively.  Both are from 52 second  samples, the former commencing at 0338:15 hours on 22 November 1967 and the l a t t e r at 2027:40 on 4 February 1969.  The sample of Figure 16  was recorded i n the cycling mode at a mean depth of 210 meters. Figure 17 comes from a constant depth run at 215 meters. The s o l i d l i n e i n each case i s the spectrum as computed from the raw s i g n a l .  As noted e a r l i e r i n the section on instrumentation,  a considerable amount of low frequency noise i s generated by ship motion and v i b r a t i o n i n the towing system. large peaks of energy at low wavenumbers.  This i s the source of the At high frequencies, also  where the s p e c t r a l levels of turbulent energy drop very low, electronic noise becomes troublesome and l i f t s the spectrum noticeably at the highest values of k.  In order to minimize the effects of these  extraneous signals on the turbulence spectra I have, when possible, computed a second spectrum of background noise from an adjacent section of tape on which there i s no detectable s i g n a l .  This noise spectrum  i s then subtracted from the o r i g i n a l and the resultant "noise-free" spectrum i s plotted i n small c i r c l e s on the same axes, as i n Figure 17. The technique works reasonably w e l l i n the high frequency range, but not so w e l l at the low frequencies where the vibration tends to be  44 s p o r a d i c and n o i s e l e v e l s v a r y g r e a t l y from moment t o moment and wave t o wave.  The m i s s i n g p o i n t s a t the low frequency  end o f the c o r r e c t e d  spectrum are o f f - s c a l e a t the bottom o f the page, r e p r e s e n t i n g  occasions  on w h i c h the n o i s e l e v e l approached v e r y c l o s e t o , or perhaps exceeded the t o t a l s i g n a l .  We  can f o r t h i s reason p l a c e no r e l i a n c e on  s p e c t r a l shape below about l o g k = -1 or k = 0.1, eddy s i z e of some 60 The  corresponding  the t o an  centimeters.  dashed curve drawn i n by hand i n each case ( h e a v i e r dashed  curve i n F i g u r e 16) i s the " u n i v e r s a l c u r v e " f i t t e d t o the  original  spectrum i n F i g u r e 16 and t o the n o i s e - c o r r e c t e d spectrum of F i g u r e by the method o f Stewart  and Grant (1962)(see Page 10). 2  v i s c o s i t y of the w a t e r i s t a k e n as 0.0142 cm s l o p e +1 i s drawn through  the p o i n t (v  The  17,  kinematic  -1 sec  and the l i n e of  = 1.386, v ~ ^  =  4  -2.31).  A few p o i n t s have been a l l o w e d t o f a l l s l i g h t l y below the u n i v e r s a l curve where i t seems p r o b a b l e  t h a t the s c a t t e r , towards the low  frequency  end o f the s p e c t r u m , i s due t o the r e l a t i v e s h o r t n e s s o f the sample and/or inadequate spectral level.  n o i s e c o r r e c t i o n , and does not r e p r e s e n t the t r u e N e i t h e r spectrum shows a c l e a r l y d e f i n e d i n e r t i a l  subrange w i t h -5/3  s l o p e as p r e d i c t e d by t h e o r y , but i t i s easy t o b e l i e v e  t h a t such a r e g i o n e x i s t s i n b o t h .  For O p e r a t i o n F - l - 6 9 more e f f e c t i v e  v i b r a t i o n i s o l a t i o n d e v i c e s were developed,  and the spectrum from t h a t  o p e r a t i o n i n p a r t i c u l a r , b e i n g somewhat c l e a n e r i n the  mid—frequencies,  shows something v e r y c l o s e t o the p r e d i c t e d s l o p e of -5/3 of perhaps h a l f a decade i n k;  f o r a range  45 Energy  Dissipation F o r each spectrum the energy d i s s i p a t i o n " d e n s i t y " , e,  i s c a l c u l a t e d .from the f i t of the u n i v e r s a l curve and from E q u a t i o n w i t h the f o l l o w i n g  (10)  results: e ( e r g s s e c '''cm  3  )  U n i v e r s a l Curve  E q u a t i o n (10)  F i g u r e 16  2.75 x 1 0 ~  3  2.94 x  10~  3  F i g u r e 17  1.74 x 1 0 ~  4  2.52 x  10"  4  ' I t i s obvious why i s l a r g e r i n each case.  the v a l u e of £ d e r i v e d from E q u a t i o n (10)  W h i l e t h e s p e c t r a f i t t h e u n i v e r s a l curve  r e a s o n a b l y w e l l through the h i g h e r wave number r e g i o n of what  appears  t o be an i n e r t i a l subrange and i n t o the lower end of the d i s s i p a t i o n subrange, they b e g i n t o d e v i a t e b e f o r e the peak of t h e d i s s i p a t i o n curve i s reached (where the s l o p e o f the energy spectrum on t h i s  log-log  p l o t i s -2) and a t h i g h e r wavenumbers l i e w e l l above the u n i v e r s a l c u r v e . T h i s has been the p a t t e r n i n most of the t u r b u l e n c e s p e c t r a from the open s e a , i n c o n t r a s t w i t h e a r l i e r s p e c t r a from i n s h o r e w a t e r s r e p o r t e d by G r a n t , Stewart and M o i l l i e t and M o i l l i e t  as  (1962) and G r a n t , Hughes, V o g e l  ( 1 9 6 8 ) , many o f w h i c h match the u n i v e r s a l c u r v e w i t h  remarkable p r e c i s i o n . I have spent a good d e a l of time s e a r c h i n g f o r a b e l i e v a b l e e x p l a n a t i o n o f the d i f f e r e n c e , w i t h o u t f i n d i n g any c l e a r answer.  There  a r e , however, a number of p o s s i b l e c o n t r i b u t i n g f a c t o r s , w h i c h t o p r e s e r v e c o n t i n u i t y o f argument h e r e , I s h a l l l e a v e f o r d i s c u s s i o n i n a separate s e c t i o n .  I n the meantime i t i s not unreasonable t o  r e g a r d t h e d i s s i p a t i o n v a l u e s d e r i v e d from the f i t of the u n i v e r s a l  o rH  c O •H  U cd  CO  CO  1  !•  o> VO •  W  rH  CO  <-  • CN  1  1  CM m • CM  r~co •  CO il a» m  ro I*  vo  •  CO  •  -3-  T3  cu  4-> U CU  u u  o a  CO  cu  0)  >  CD •H  I  CO  CO  O  CO  CM  i-l  I  CTi CM  oo  o  a  I  I  o  53  I  I CM  r-  cd  co u  >  CU  4-1  •rl  o  B  cu  Cu  cl  CO  CM 1  in  O •  • CM  i—1  ( 1 <N rH •  i  1 rH  CO • VO  <-  •  1 CO • CO  11 rH  1 CT\  • CM  CM • CM  rH  CM m  m  CO 1 1 m  CO 1i  •  1 rH  •  rH  rH  m  • CM  • CM  m  a\ • rH  PS  ca ^ !  4J  <U  4-)  A, a) cu e  CO  CO  CO  CM  CM  CM  CM  o o  <f  CM m  CM m  CM m  oo CM  oo CM rH  CM  CM  CM  m  CM m  CM  CM  m o  in rH  o m  O CO  m o  O  o <r  m CM  CO CO CO o  m CO CO o  oo CO CO o  oo CO o CM  O CO  CO CM o CM  CM o CM  CM o CM  vO  vo  VO  vo  vo VO  Ov vO  av VD  VO  vo  vo  vo  vo  vo  vo  CM  CM  CM  CM  CM  CM  CM  CM  CM  CM  m  m  m  m  m  m  m  rH  rH  tH  rH  rH  CM  CM  rH  rH  rH  rH  VO  vO  tH  <r VO  oo 00  oo 00  CM  CM  CM  CM  CM  m  m  m  rH  CO  id rH  4J  O  a CO u gem ca  cu co  cu  O  m  CM  in  rH  CM  CU cd  n  CM CM  CM CM  CM CM  <N  CM  CM CM  m  TABLE I:  m  m  o rH  m  m  rH  o o  00 CM  O O  CO  m co  o  O  o o CO o  •H  r^.  m CM o  ;o CO o  m o o  oo o o  r~~ CM o  a\ CO  <r  CM  CM  CTv  cy>  o  rH  CO O  Energy D i s s i p a t i o n  rH  rH  <7>  Rates  rH  rH  rH rH  vo  rH rH  vO  rH  rH  00  00  46 curve and from E q u a t i o n (10) as lower and upper l i m i t s , d i f f e r i n g  by  a f a c t o r r a n g i n g from s l i g h t l y g r e a t e r than 1 t o ij.ust over 2, which a f t e r a l l i s n o t a l a r g e f a c t o r , compared t o the many o t h e r u n c e r t a i n t i e s of  t h i s game. For  most of the s u i t a b l e samples  d i s s i p a t i o n r a t e s by f i t t i n g  a v a i l a b l e I have o b t a i n e d  the u n i v e r s a l c u r v e .  In a few cases I  have gone through the procedure of c o r r e c t i n g f o r background  noise,  but n o i s e l e v e l s through the range of maximum d i s s i p a t i o n are u s u a l l y such t h a t the c o r r e c t i o n makes only a s m a l l d i f f e r e n c e t o the v a l u e o b t a i n e d f o r e.  For those samples  f o r which  t h e r e i s n o t too much  s c a t t e r of p o i n t s i n the c r i t i c a l p a r t of the spectrum I have, as above, o b t a i n e d a second v a l u e f o r E from E q u a t i o n (10).  The r e s u l t s are  summarized i n T a b l e I , where f o r convenience I have w r i t t e n 1.90  x 10  , f o r example, as 1.90-2. The v a l u e s shown are arranged i n c h r o n o l o g i c a l o r d e r , except  the  l a s t two which  come from one of the deepest submarine  runs of  O p e r a t i o n F - l l - 6 2 and are i n c l u d e d h e r e f o r comparison o n l y .  To make  some s o r t of e s t i m a t e of mean and t o t a l t u r b u l e n t d i s s i p a t i o n of energy, I have, u s i n g the computed v a l u e s o f T a b l e If as a g u i d e , v i s u a l l y scanned a l l the paper r e c o r d s from O p e r a t i o n s F - l l - 6 7 and F - l - 6 9 , e s t i m a t i n g the t o t a l percentage of time (which I i n t e r p r e t as a p e r centage o f the volume) t h a t t u r b u l e n c e was the  p r e s e n t , arid have d i v i d e d  t o t a l percentage i n t o t h r e e c a t e g o r i e s on the b a s i s of i n t e n s i t y  h i g h , medium and low.  T o t a l percentages are p l o t t e d i n F i g u r e 18  as a f u n c t i o n of depth, w i t h each p o i n t r e p r e s e n t i n g one run - the  -  o  «8  o ox  ro  o  o  Xv  -  O CM  XX XX  OO  XX  oo  CO  cr  X  UJ  o i00 Ld  2  Xo  xo  X  o x  I  X  rQ.  o  X  x  o o X  o  x  O  ^Xo  o  CM  X  o  o  X  i  X  o  CD  o  _L_  o  o  (0  X  L  CM  Figure 18. Percentage of ocean volume that i s turbulent, as a function of depth. The c i r c l e s are for F-ll-67 runs and the crosses for F—1-69 runs.  Estimated  Dissipation  Turbulence L e v e l  Percentage T u r b u l e n t F-l-69 F-ll-67  High  2.3  1.6  3 x 10"  3  Medium  9.1  5.1  4 x 10~  4  Lew  18.4  7.1  5 x 10~  5  TABLE I I : Percentage o f volume t h a t i s t u r b u l e n t and e s t i m a t e d dissipation rates.  (ergs cm  sec  ^ )  47 duration of a magnetic tape or approximately one hour. are for F-ll-67 and the crosses for F-l-69.  The c i r c l e s  Then, for each operation  separately, I have taken percentages, averaged over a l l runs for each of the three levels of i n t e n s i t y .  The results are set down i n Table IT  with estimated d i s s i p a t i o n levels assigned by comparison with samples for which spectra and dissipation rates have been computed. In this analysis I have made no attempt to take account of the much higher levels of turbulence found above the thermocline and p a r t i c u l a r l y i n the top few meters which w i l l be strongly influenced by breaking surface waves.  Values for a range of depths from 15 to  90 meters have been published by Grant, M o i l l i e t and Vogel (1968) but I have not included these data because, as I have suggested, the mechanism of generation i s probably quite different i n this region. The method i s admittedly rough and subjective i n certain aspects, but I believe the results to be v a l i d within about 20 percent. The crosses of F-l-69 i n Figure 18 seem to indicate a decrease i n the t o t a l percentage of turbulence with increasing depth.  The c i r c l e s of  F-ll-67 show a wider scatter, with higher percentages on the average, and i t i s d i f f i c u l t to discern any s i g n i f i c a n t trend with depth.  Looking  at the two sets of data together i t i s probably safe to say that there i s some decreasing trend with increasing depth.  In any case I cannot with  these data, confirm the apparent increase i n the occurrence of turbulence between 250 and 350 meters reported by Grant, M o i l l i e t and Vogel  (1968).  Obviously any conclusions based on a major extrapolation from the two limited sets of data available (November 1967 and February 1969)  are subject to question and c r i t i c i s m .  Nevertheless I thought i t  48 m i g h t be amusing t o t r y . Munk and MacDonald (1960) examine e a r l i e r views t h a t d i s s i p a t i o n o f t i d a l energy  took p l a c e p r i m a r i l y  through  bottom " f r i c t i o n " i n s h a l l o w a r e a s , and come t o t h e c o n c l u s i o n t h a t t h i s 19 -1 p r o c e s s a l o n e cannot account f o r more t h a n 10 ergs s e c . A s t r o 19 n o m i c a l o b s e r v a t i o n s c a l l f o r a t i d a l d i s s i p a t i o n o f 3 x 10 and they p o s t u l a t e t h a t perhaps  -1  ergs s e c  " t h e energy o f t h e s u r f a c e t i d e s i s  e f f e c t i v e l y c o n v e r t e d i n t o i n t e r n a l wave m o t i o n and then d i s s i p a t e d w i t h i n t h e ocean volume." U s i n g the v a l u e s from T a b l e I I as r e p r e s e n t a t i v e o f t h e deep oceans o f t h e w o r l d , and making t h e assumption  t h a t t h e average  d i s s i p a t i o n decreases by a f a c t o r o f two f o r each 300 meter i n t e r v a l of d e p t h , we g e t f o r t h e p e r i o d o f O p e r a t i o n F - l l - 6 7 a t o t a l 19 -1 d i s s i p a t i o n r a t e o f j u s t 2 x 10  ergs s e c  worldwide  w h i c h , s u r p r i s i n g l y enough,  i s e x a c t l y t h e d i f f e r e n c e we a r e l o o k i n g f o r between Munk and MacDonald's e s t i m a t e o f t h e maximum d i s s i p a t i o n i n s h a l l o w seas and t h e t o t a l required.  The o b s e r v a t i o n s o f F - l l - 6 7 were t a k e n d u r i n g a p e r i o d o f  moderate s p r i n g t i d e s .  S i m i l a r l y t h e f i g u r e s from O p e r a t i o n F - l - 6 9 ,  d u r i n g a p e r i o d o f t i d a l d e c l i n e from s p r i n g t o neap, l e a d t o a t o t a l 19 -1 d i s s i p a t i o n o f 1.3 x 10  ergs s e c  . The answers seem t o be e n t i r e l y  c o n s i s t e n t and o f t h e r i g h t o r d e r o f magnitude a l t h o u g h , as I have p o i n t e d o u t , they a r e based on a r a t h e r w i l d e x t r a p o l a t i o n . There i s one a d d i t i o n a l o b s e r v a t i o n w h i c h may h e l p us t o b e l i e v e t h a t a t l e a s t some o f t h e energy o f t h e t u r b u l e n c e may be o f tidal origin.  D u r i n g t h e p e r i o d o f d a t a r e c o r d i n g i n F - l l - 6 7 t h e r e was  no apparent t r e n d i n t u r b u l e n t i n t e n s i t i e s - and t i d a l a m p l i t u d e s were approximately constant.  D u r i n g F - l - 6 9 on t h e o t h e r hand, t h e r e was  49 a n o t i c e a b l e decay i n t u r b u l e n c e l e v e l s a t a l l depths as t i d a l  ampli-  tudes d e c l i n e d from s p r i n g t o neap. Having made t h e p o i n t I must q u i c k l y go on t o s a y t h a t I do n o t t h i n k much i m p o r t a n c e s h o u l d be a t t a c h e d t o i t - n o t , a t l e a s t , f u r t h e r experimental evidence  i s available.  until  I t i s , a f t e r a l l , based  on o n l y two o b s e r v a t i o n s and may be q u i t e c o i n c i d e n t a l .  Furthermore t h e r e  were o t h e r f a c t o r s w h i c h t e n d t o c o m p l i c a t e t h e p i c t u r e .  Firstly,  the l o c a l e o f t h e experiment changed by some 200 k i l o m e t e r s d u r i n g t h e p e r i o d t h a t t u r b u l e n t i n t e n s i t i e s were observed  t o decrease i n the  l a t t e r p a r t o f F-l-69, and t h e r e may be a g e o g r a p h i c a l v a r i a t i o n i n v o l v e d . Secondly,  t h e r e was a moderate storm on 3-4 February  40 k n o t s and over. possible.  1969 w i t h winds o f  Heavy seas b u i l t up and no measurements were  The storm was f o l l o w e d by t h r e e days o f l i g h t winds  (less  than 10 k n o t s ) and t h e experiment was resumed l a t e on 4 F e b r u a r y . t h a t s t a g e r e l a t i v e l y h i g h l e v e l s o f t u r b u l e n c e were observed  At  at a l l  d e p t h s , and i t was d u r i n g t h e f o l l o w i n g t h r e e days o f r e l a t i v e calm t h a t the l e v e l decreased  s t e a d i l y and q u i t e c o n s p i c u o u s l y throughout t h e  volume as t h e s e a s t a t e d i e d down - w h i l e a t t h e same time  tidal  a m p l i t u d e s were d e c r e a s i n g . I t seems u n l i k e l y t h a t even q u i t e v i o l e n t s u r f a c e d i s t u r b a n c e s c o u l d produce t u r b u l e n c e by d i r e c t m i x i n g a c t i o n a t depths as g r e a t as 300 m e t e r s . generate  I t may be p o s s i b l e , however, t h a t s u r f a c e a c t i o n c o u l d  i n t e r n a l waves a t such d e p t h s , and i f we suggest then t h a t ,  under a p p r o p r i a t e c i r c u m s t a n c e s , t h e s e i n t e r n a l waves might b r e a k (as has been observed  and photographed by Woods (1966-67) a t s h a l l o w e r  depths i n t h e M e d i t e r r a n e a n )  we might expect t o produce t h e s o r t o f  50 s p o r a d i c a l l y o c c u r r i n g patches o f t u r b u l e n c e t h a t we observe a l o n g a boundary between l a y e r s . Our o b s e r v a t i o n s seem t o be c o n s i s t e n t w i t h i d e a s o f t u r b u l e n c e g e n e r a t i o n by i n d i r e c t a c t i o n o f s u r f a c e winds and a l s o by c o n v e r s i o n o f t i d a l energy.  Perhaps b o t h mechanisms c o n t r i b u t e .  Each supposes  an i n t e r m e d i a t e s t a g e d u r i n g w h i c h t h e energy i s c o n t a i n e d i n i n t e r n a l waves - and we have many i n d i c a t i o n s 'of t h e p r e s e n c e o f i n t e r n a l waves i n and below t h e t h e r m o c l i n e .  F o r example t h e s h o r t h o r i z o n t a l b a r s  on F i g u r e 14 mark t h e upper l i m i t o f an almost v e r t i c a l s e c t i o n near t h e c e n t e r o f each d e n s i t y p l o t . wave w i t h an a m p l i t u d e 700 o r 800 m e t e r s .  The p a t t e r n s t r o n g l y suggests  an i n t e r n a l  o f about 5 meters and apparent w a v e l e n g t h o f  No r e l i a b l e e s t i m a t e o f r e a l w a v e l e n g t h can be made,  s i n c e t h e d i r e c t i o n and v e l o c i t y o f p r o p a g a t i o n w i t h r e s p e c t t o t h e s h i p ' s course and speed a r e n o t known.  The w a v e - l i k e p a t t e r n , however,  c o n t i n u e s f o r some d i s t a n c e i n b o t h d i r e c t i o n s beyond t h e l i m i t s o f F i g u r e 14. I t i s p r o b a b l e a l s o t h a t s h e a r v e l o c i t i e s e x i s t between l a y e r s ( a g a i n t h i s has been observed by Woods (1966-67) i n t h e M e d i terranean)  and we may s p e c u l a t e t h a t i n s t a b i l i t y occurs from time t o  time and from p l a c e t o p l a c e as t h i s i n t e r - l a y e r shear i s r e i n f o r c e d by t h e a c t i o n o f i n t e r n a l waves, and t h e l o c a l R i c h a r d s o n ' s becomes u n s t a b l e .  number  U n f o r t u n a t e l y , as I have s a i d , a l t h o u g h our v e l o c i t y  probe has t h e r e q u i r e d s e n s i t i v i t y , i t has so f a r n o t been p o s s i b l e t o measure shear between l a y e r s because o f e x c e s s i v e n o i s e l e v e l s a t low frequencies.  The F i t o f the U n i v e r s a l Curve I have examined s e v e r a l areas f o r a p o s s i b l e e x p l a n a t i o n of the f a c t t h a t none of our deep s e a s p e c t r a f i t the " u n i v e r s a l c u r v e " a t h i g h wavenumbers.  I w i l l f i r s t l i s t the p o s s i b i l i t i e s c o n s i d e r e d  and  then q u i c k l y r e j e c t s e v e r a l of them: (a) Low  Reynolds number.  (b) N o n - i s o t r o p i c regime. (c) I n t e r m i t t e n c y of the t u r b u l e n c e s i g n a l . (d) V a r i a t i o n s i n speed d u r i n g r e c o r d i n g . (e) C o n t a m i n a t i o n  of the v e l o c i t y s i g n a l by  temperature.  ( f ) The e f f e c t of buoyancy f o r c e s . (g) E r r o r ( s ) i n my method of computing s p e c t r a . (a) and  (b) are r e l a t e d and may  be c o n s i d e r e d t o g e t h e r .  The  t h e o r y b e h i n d the u n i v e r s a l curve assumes a h i g h Reynolds number and i s o t r o p i c turbulence.  Below the t h e r m o c l i n e we have found t h a t t u r b u l e n c e  occurs i n p a t c h e s , u s u a l l y i n r e l a t i v e l y t h i n l a y e r s and accommpanied by  (and d r i v e n by) v e l o c i t y s h e a r .  probably  One w o u l d n o t  expect  the Reynolds number t o be h i g h and, i n t h e l a r g e r s c a l e s a t l e a s t , one would n o t e x p e c t i s o t r o p y .  A c c o r d i n g to c u r r e n t i d e a s of t h e  mechanism of t u r b u l e n c e however, p r e s s u r e f o r c e s i n t h e f l u i d  (see  B a t c h e l o r (1953), page 8 8 ) , t e n d t o e q u a l i z e the d i r e c t i o n a l components and thus e r a s e any i n i t i a l a n i s o t r o p y , w h i l e i n e r t i a l f o r c e s a c t t o d r i v e the "cascade" o f energy from low wavenumbers to h i g h e r wavenumbers. We  s h o u l d t h e r e f o r e approach more and more c l o s e l y t o i s o t r o p y as  move upwards i n wavenumber and, i f our spectrum was  we  t o f i t the u n i v e r s a l  curve a t a l l , the r e g i o n of b e s t f i t s h o u l d be a t the h i g h e s t wavenumbers. A c t u a l l y we  o f t e n observe a w i d e n i n g  d e v i a t i o n as wavenumber i n c r e a s e s .  52 It might be argued that I have not f i t t e d the universal curve properly arid that i t should be s h i f t e d up to the position of the l i g h t e r dashed curve of Figure 16, so that i t would match the spectrum at high wavenumbers where i t should.  I have examined this  alternative  rather carefully and compared the results with those of other experimenters - i n p a r t i c u l a r Stewart and Townsend (1951). way,  Looked at i n this  our spectra show none of the established characteristics  Reynolds number turbulence  and my  the analysis i n d e t a i l , i s that we  of low  conclusion, without going through cannot explain away our d i f f i c u l t y  i n this manner. "Intermittency" of turbulence.  (c) i s one of the w e l l known characteristics  Even i n a f u l l y developed turbulent f i e l d there tend  to be regions of a c t i v i t y interspersed with regions of quiescence, and the energy associated with the larger wavenumbers i s unevenly d i s tributed i n space.  Grant, Stewart and M o i l l i e t (1962) have discussed  the e f f e c t of intermittency on the shape of the energy spectrum and point out that the result should be some reduction i n curvature at the "knee" - the t r a n s i t i o n region between the i n e r t i a l subrange and region of viscous dissipation - and this i n fact i s what we  the  observe.  They conclude, however, that the degree of intermittency i n their samples, recorded  i n in-shore t i d a l waters has a n e g l i g i b l e e f f e c t on the shape of  t h e i r spectra. We might speculate that, for some reason which i s not immediately clear, the degree of intermittency i n our off-shore, deepwater samples i s much greater and the e f f e c t correspondingly  magnified.  To check this p o s s i b i l i t y , I have taken two 52 second samples, one from  20  UJ o z  r-  16  UJ CC cc  O  o o u. o  81  cc  UJ GO 3 100 (a) Sample F - 6 - 6 7 30  200 300 ' PERCENTAGE OF MEAN  400  500  Tape 2 1513:30 10 June 1967  r—  c/> 25  UJ  o z  Ul  cc 20  CC  o o o 15 u. o  5  m  10  100 (b) Sample F - l - 6 9  200  300  400  500  PERCENTAGE OF MEAN Tape 19 1005:00 5 February 1969  Figure 19. D i s t r i b u t i o n of turbulent d i s s i p a t i o n densities f o r successive short intervals within two 52 second samples.  53 an e a r l i e r i n - s h o r e o p e r a t i o n (F-6-67) which  fits  the u n i v e r s a l curve  very c l o s e l y , and t h e o t h e r from F-l-69, w i t h an extreme m i s f i t .  I  have d i v i d e d each i n t o 64 s e c t i o n s and computed a v a l u e o f e f o r each s e c t i o n .  The d i s t r i b u t i o n o f e as a percentage o f the mean i s  shown f o r the two samples  i n F i g u r e 19 (a) and ( b ) .  The two d i s t r i -  b u t i o n s a r e s i m i l a r and t h e grouping i s even a l i t t l e b i t c l o s e r f o r our F-l-69 sample  than f o r the o t h e r .  I am n o t q u i t e s u r e how one d e f i n e s i n t e r m i t t e n c y  quantita-  t i v e l y , b u t i f what I have done i s a r e l i a b l e method o f e s t i m a t i n g the degree o f i n t e r m i t t e n c y i n a q u a l i t a t i v e or comparative way, then i t seems c l e a r t h a t i n t e r m i t t e n c y i s n o t the cause o f our problem. V a r i a t i o n s i n towing speed (d) d u r i n g the l e n g t h o f a sample w i l l have a s i m i l a r e f f e c t on the shape o f the spectrum p l o t t e d on l o g - l o g axes.  Towing speed determines the p o s i t i o n o f the spectrum  on the l o g k a x i s , and changes  i n speed w i l l cause i t t o s h i f t back and  f o r t h w i t h o u t changing shape.  The shape of t h e average spectrum  will,  however, be a l t e r e d , and the e f f e c t a g a i n w i l l be a r e d u c t i o n o f c u r v a t u r e i n the t r a n s i t i o n r e g i o n .  Even i f the s h i p ' s speed i s h e l d c o n s t a n t  t h e r e may be an a p p r e c i a b l e v a r i a t i o n i n speed o f t h e towed body, depending on s e a s t a t e .  The winch i s designed t o m a i n t a i n c o n s t a n t  depth and i n doing so can i n t r o d u c e f l u c t u a t i o n s i n forward v e l o c i t y an e f f e c t which would not be p r e s e n t , or would  -  a t l e a s t be much s m a l l e r ,  f o r e a r l i e r measurements taken i n p r o t e c t e d c o a s t a l w a t e r s . I have examined speed v a r i a t i o n s over the l e n g t h o f t h r e e samples which show major d e v i a t i o n s from the u n i v e r s a l curve a t h i g h wavenumbers.  I n these t h r e e samples  the v a r i a t i o n never  exceeded  10 p e r c e n t o f the mean speed and might produce an e f f e c t j u s t b a r e l y v i s i b l e on our s p e c t r a .  I t c o u l d not by a l a r g e f a c t o r produce the  Ii  Figure 20. Velocity and temperature spectra from cycling run at 213 meters depth, i l l u s t r a t i n g possible effects of buoyancy forces on spectral shape.  F i g u r e 21. V e l o c i t y and temperature s p e c t r a from c o n s t a n t depth run a t 64 m e t e r s , i l l u s t r a t i n g p o s s i b l e e f f e c t s o f buoyancy forces~'bn s p e c t r a l shape-.-''  54 effect  observed. There i s always the p o s s i b i l i t y  o f e r r o r (g) i n my  (using a v e r s i o n of the Fast F o u r i e r Transform) f o r computing spectra.  I have, however, checked a l l steps very  procedure  power  c a r e f u l l y and I am  a b l e t o reproduce p r e c i s e l y s p e c t r a which have been computed i n d e p e n d e n t l y arid by q u i t e d i f f e r e n t methods.  I do not b e l i e v e the  discrepancy  i s due t o e r r o r or improper t e c h n i q u e . I have a l r e a d y  discussed  the q u e s t i o n  (e) o f the s e n s i t i v i t y  of the v e l o c i t y probe t o f l u c t u a t i o n s i n temperature, and concluded t h a t the e f f e c t would be n e g l i g i b l y s m a l l through the wavenumber range of maximum d i s s i p a t i o n .  At h i g h e r wavenumbers the magnitude  o f the e f f e c t  i s i n some doubt. Two p a i r of s p e c t r a - v e l o c i t y and temperature - are p l o t t e d on common l o g k axes i n F i g u r e s  20 and 21 f o r samples  from O p e r a t i o n s F - l l - 6 7 and F-l-69 r e s p e c t i v e l y . i s f i t t e d t o the n o i s e - c o r r e c t e d described  as i n d i c a t e d  The u n i v e r s a l curve  v e l o c i t y s p e c t r a by the method  e a r l i e r and the t h e o r e t i c a l spectrum of temperature f l u c t u a t i o n s  ( h e a v i e r dashed l i n e ) d e r i v e d by B a t c h e l o r  (1959) i s f i t t e d t o the  e x p e r i m e n t a l temperature s p e c t r a as d e s c r i b e d by G r a n t , Hughes, V o g e l and Moilliet  (1968).  The sharp r i s e at the h i g h end of the temperature  s p e c t r a i s due t o e l e c t r o n i c n o i s e i n the system, but b e f o r e t h e r e i s a n o t i c e a b l e d e v i a t i o n from the B a t c h e l o r n o t i c e a s i m i l a r d e v i a t i o n i n most of the o c e a n i c p u b l i s h e d by G r a n t , e t a l (1968). really  the r i s e  c u r v e , - and temperature  we  spectra  I f we b e l i e v e t h a t the spectrum  f o l l o w s the t h e o r e t i c a l curve and t h a t the d e v i a t i o n i s the  r e s u l t o f n o i s e , then i t i s c l e a r t h a t the temperature f l u c t u a t i o n s  55 are d i s s i p a t i n g much t o o f a s t t o cause t h e observed d i f f e r e n c e between the u n i v e r s a l c u r v e and the v e l o c i t y spectrum a t t h e h i g h e s t wavenumbers. I f , on t h e o t h e r hand, t h e d e v i a t i o n i s r e a l and t h e temperature spectrum i n f a c t does n o t drop o f f as f a s t as p r e d i c t e d by theory '(and a g a i n we might blame i n t e r m i t t e n c y i n t h e temperature f i e l d f o r such an e f f e c t ) , then i t i s j u s t p o s s i b l e t h a t temperature c o n t a m i n a t i o n cause o f t h e d i s c r e p a n c y  c o u l d be t h e  i n the v e l o c i t y s p e c t r a at the highest  wavenumbers ( o r c o u l d a t l e a s t be a c o n t r i b u t i n g f a c t o r ) b u t n o t , as I have s a i d , i n t h e v i c i n i t y o f t h e peak o f t h e energy d i s s i p a t i o n spectrum. I cannot c l e a r l y r e s o l v e t h i s p o i n t a t my p r e s e n t We a r e l e f t t o c o n s i d e r forces.  stage of a n a l y s i s .  ( f ) , t h e p o s s i b l e e f f e c t s o f buoyancy  I f by some means w h i c h need n o t be s p e c i f i e d , t u r b u l e n c e i s  g e n e r a t e d i n a s t a b l e d e n s i t y g r a d i e n t , some work must i n i t i a l l y be done a g a i n s t g r a v i t y , and energy w i l l be e x t r a c t e d from t h e t u r b u l e n c e at s m a l l wavenumbers.  A t some l a t e r s t a g e i n t h e m i x i n g p r o c e s s ,  small  s c a l e g r a v i t a t i o n a l i n s t a b i l i t i e s w i l l e x i s t throughout t h e r e g i o n and buoyancy f o r c e s w i l l tend t o d r i v e a secondary mechanism t o r e s t o r e stability.  One may s p e c u l a t e t h a t a t h i g h wavenumbers t h e v e l o c i t i e s  a s s o c i a t e d w i t h t h i s mechanism may become predominant and mask t h e true turbulent  velocities.  Or, t a k i n g another v i e w , we develop a somewhat more c o m p l i c a t e d model.  I t i s n o t uncommon t o f i n d a v e r t i c a l s t r u c t u r e i n w h i c h  compensating temperature and s a l i n i t y g r a d i e n t s r e s u l t i n n e u t r a l o r near-neutral s t a b i l i t y .  I f such a s t r u c t u r e i s mixed by  turbulence  t h e r e may i n i t i a l l y be no i n s t a b i l i t i e s and no r e s t o r i n g f o r c e s .  The  d i f f u s i v i t i e s o f h e a t and s a l t , however, d i f f e r by some two o r d e r s o f  56 magnitude, and i n due course the temperature f l u c t u a t i o n s w i l l by  c o n d u c t i o n a t the h i g h e r wavenumbers, l e a v i n g  salinity  d i e away  the more p e r s i s t a n t  f l u c t u a t i o n s with corresponding i n s t a b i l i t i e s  and r e s t o r i n g  forces. For velocity and  a f i e l d i n which s m a l l  of p a r t i c l e s subject  density  f l u c t u a t i o n s e x i s t , the  t o buoyancy f o r c e s w i l l be v e r y  small  f o r t h e s o r t o f order-of-magnitude c a l c u l a t i o n which I propose t o  undertake I b e l i e v e  i t i s safe  to ignore accelerations  i n the upper  wavenumber range w i t h which we a r e concerned, where the t u r b u l e n c e Reynolds number i s known t o be low. be  i n equilibrium  accelerating  under the i n f l u e n c e  Any p a r t i c l e of f l u i d  o f two e q u a l and o p p o s i t e  f o r c e s , one due t o g r a v i t y  and the o t h e r t o v i s c o s i t y .  I f we r e p r e s e n t by <j>(k), ^ ( k ) , and i(>(k) s p e c t r a l d e n s i t y v e l o c i t y , density sense t h a t  then w i l l  functions of  and temperature r e s p e c t i v e l y , i n t e r r e l a t e d i n the  density  fluctuations described  by f2(k) , c o r r e s p o n d i n g t o a  temperature f i e l d d e f i n e d by i K k ) , w i l l , through buoyancy  forces,  generate a v e r t i c a l v e l o c i t y f i e l d d e f i n e d by <j>(k), i t can be r e a d i l y shown t h a t  V(k)  -£&|4  ,  (28)  k vp i n which g i s t h e a c c e l e r a t i o n o f g r a v i t y the medium  (which I s h a l l take as u n i t y  and p i s the mean d e n s i t y o f  f o r s e a w a t e r , as a r e a s o n a b l e  a p p r o x i m a t i o n f o r the purpose o f t h i s a n a l y s i s ) .  3 functions gm^cm  w i l l i n a l l cases be i n u n i t s  f o r density  and ° C  2  cm  The t h r e e spectrum  -2  o f cm s e c  for velocity,  f o r temperature, b u t t o a v o i d  frequent  r e p e t i t i o n i n the n e x t few paragraphs I w i l l quote o n l y n u m e r i c a l values. C o n s i d e r f i r s t the p o s s i b i l i t y are  that the density  due s o l e l y t o v a r i a t i o n s i n t e m p e r a t u r e .  fluctuations  The temperature  dent v a r i a t i o n i n d e n s i t y i s a p p r o x i m a t e l y 0.1 i n a  depen-  p e r °C, o r  «(k) = 1 0 " K k ) ,  (29)  8  Now  i n F i g u r e 21, f o r example, i f we t a k e <j>(k) as d e s c r i b i n g the excess  of t h e measured v e l o c i t y spectrum o v e r the u n i v e r s a l c u r v e ( t h e d e v i a t i o n w h i c h we a r e a t t e m p t i n g t o e x p l a i n ) then a t l o g k = 0 (or k = 1, c o r r e s p o n d i n g t o a s c a l e of about 6 c e n t i m e t e r s ) <f>(l) _3 i s a p p r o x i m a t e l y 2 x 10  .  From the temperature s p e c t r u m , ijj(l) i s  -4 r o u g h l y 2.2 x 10  and from (28) and (29) t h i s would g i v e us a  _2 cf)(l) o f 1 x 10 - w h i c h i s more t h a n we r e q u i r e t o e x p l a i n the v e l o c i t y e x c e s s , by a f a c t o r of 5. S i m i l a r l y a t l o g k = 0.5  (k - 3 and a s c a l e of about 2  -4 c e n t i m e t e r s ) $(3) = 2.7 x 10 2.8 x 10  .  The c o r r e s p o n d i n g tj>(3) i s about  w h i c h by the same argument would produce a <j>(3) of 1.7 x 10  - which i s too s m a l l . differential  We may however, a t t h i s s t a g e , i n v o k e t h e i d e a o f  d i f f u s i v i t i e s o f h e a t and s a l t .  By B a t c h e l o r ' s t h e o r y the  v a l u e of k a t w h i c h d i f f u s i v i t y becomes the predominant f a c t o r d e t e r m i n i n g the s p e c t r a l form, and the curve drops o f f s h a r p l y , i s p r o p o r t i o n a l t o the square r o o t of the d i f f u s i v i t y . approximate t h i s e f f e c t by s l i d i n g  I have attempted t o  B a t c h e l o r ' s curve outwards a l o n g  i t s i n i t i a l s l o p e of -1 t o p o s i t i o n the "knee" one decade f a r t h e r out i n k - t h e l i g h t e r dashed curve i n F i g u r e s 20 and 21. w a t e r s t r u c t u r e i n i t i a l l y n e u t r a l l y s t a b l e , the d e n s i t y  Now,  from a  fluctuations  58 l e f t b e h i n d a f t e r t h e temperature m i c r o s t r u c t u r e has been removed by d i f f u s i o n w i l l be o f t h e same magnitude as would have e x i s t e d i n i t i a l l y as a r e s u l t o f temperature a l o n e , i f t h e r e h a d been no s a l i n i t y  structure.  I t seems s a f e t h e n , f o r t h e p r e s e n t p u r p o s e , t o c o n s i d e r t h i s extended B a t c h e l o r c u r v e as s t i l l r e p r e s e n t i n g temperature f l u c t u a t i o n s , b u t o f a more p e r s i s t a n t k i n d . we g e t i^(3) = 8 x 10  I n t h i s c a s e , s t i l l a t l o g k = 0.5  and t h i s s h o u l d g i v e us a <J>(3) o f 5 x 10 ^,  w h i c h a g a i n i s a l i t t l e b i t l a r g e r than r e q u i r e d . A g a i n a t l o g k = 1 (k = 10 and a s c a l e o f 0.5 c e n t i m e t e r s ) cj)(10) = 2.8 x 10  and (from t h e extended c u r v e ) ip(10) = 2.2 x 10  l e a d i n g t o a <J)(10) o f 1 x 10 For  w h i c h i s much t o o s m a l l .  two reasons I do n o t f i n d i t d i s t u r b i n g t h a t t h i s  rather  crude approach i n d i c a t e s an o v e r - c o i ? r e c t i o n a t l o w e r v a l u e s o f k. F i r s t l y , t h e c a l c u l a t e d v e l o c i t i e s due t o buoyancy f o r c e s w i l l be i n the  v e r t i c a l d i r e c t i o n , whereas i n o u r e x p e r i m e n t s we measure h o r i z o n t a l ,  or n e a r l y h o r i z o n t a l v e l o c i t i e s .  Some s o r t o f c o n v e c t i v e c e l l s w i l l o f  course be s e t up by t h e v e r t i c a l buoyancy f o r c e s , w i t h h o r i z o n t a l v e l o c i t i e s w h i c h one would expect t o be s m a l l e r i n g e n e r a l (and p r o b a b l y w i t h a d i f f e r e n t s p e c t r a l shape) t h a n t h e v e r t i c a l v e l o c i t i e s w h i c h drive the convection. estimate.  How much s m a l l e r , I have n o t attempted t o  S e c o n d l y , I have assumed (a) t h a t temperature was t h e o n l y  c o n t r i b u t i n g f a c t o r a t l o g k = 0 and (b) t h a t a l l t h e temperature s t r u c t u r e had decayed a t l o g k = 0.5.  I n f a c t we almost c e r t a i n l y  s t a r t o f f w i t h some c o m b i n a t i o n o f temperature and s a l i n i t y , and t h e r e i s o b v i o u s l y some temperature component l e f t a t l o g k = 0.5.  I t i s not  d i f f i c u l t , t h e n , t o b e l i e v e t h a t t h e e f f e c t c o u l d be r e a l and t h a t i t  59 c o u l d produce the observed d i f f e r e n c e between the v e l o c i t y spectrum and  the u n i v e r s a l curve through t h i s range of wavenumbers.  The s i t u a t i o n  at l a r g e wavenumbers, where the a v a i l a b l e c o r r e c t i o n seems to be small, i s less satisfactory. <K10)  = 2.8  x 10~  To produce the observed v a l u e  would r e q u i r e , from (28) ft(10) = 5.6  6  x  too  of 10~  12  —6 x 10  or f l u c t u a t i o n s of 7.5 density  I am w i l l i n g  f l u c t u a t i o n s of t h i s magnitude and  i s d i f f i c u l t t o e x p l a i n how we  i n density.  to b e l i e v e  that  s c a l e might e x i s t , but i t  they c o u l d a r i s e , on the b a s i s of the  data  have on hand. Without i n c l u d i n g the numbers h e r e , a p a r a l l e l a n a l y s i s of  the example of F i g u r e 20 larger under-correction  y i e l d s s i m i l a r r e s u l t s but w i t h a somewhat at h i g h wavenumbers.  F u r t h e r examination of t h i s phenomenon ( i f i t i s r e a l ) s h o u l d be it  the s u b j e c t  does not  of a s e p a r a t e s t u d y .  appear to be  For the p r e s e n t ,  a complete answer, t h e r e seems to b.e a good  b a s i s on which t o suggest t h a t a secondary c o n v e c t i v e buoyancy f o r c e s , may  wavenumbers.  My  process,  be the primary cause of the d i s c r e p a n c y  our v e l o c i t y s p e c t r a and best  although  driven  between  the u n i v e r s a l curve through some mid-range of  guess at t h i s time i s t h a t the temperature  sensiti-  v i t y of the v e l o c i t y probe i s an a d d i t i o n a l c o n t r i b u t i n g f a c t o r at wavenumber, l i f t i n g  the v e l o c i t y spectrum even h i g h e r  e x p l a i n e d by buoyancy f o r c e s The  than can  higher  be  alone.  f a c t t h a t s p e c t r a from i n - s h o r e waters have u s u a l l y  shown t h i s e f f e c t - at l e a s t not sistent.  by  t o the same degree - i s not  not  incon-  Those experiments were c a r r i e d out g e n e r a l l y i n w e l l mixed  waters w i t h a h i g h e r  l e v e l of t u r b u l e n c e  and  r e l a t i v e l y lower temperature  60 and d e n s i t y g r a d i e n t s .  Both temperature c o n t a m i n a t i o n of t h e  v e l o c i t y s i g n a l and masking by the e f f e c t s of buoyancy f o r c e s s h o u l d t h e r e f o r e be l e s s apparent.  I n f a c t i t has n o t been uncommon f o r  v e l o c i t y s p e c t r a t o show some excess over the u n i v e r s a l curve a t h i g h wavenumbers. F i n a l l y , a r e - e x a m i n a t i o n o f some 1967 d a t a ( O p e r a t i o n F-6-67) from i n - s h o r e w a t e r s , w i t h h i g h t u r b u l e n t i n t e n s i t i e s and low " n o i s e " l e v e l s , r e v e a l s t h a t s e v e r a l v e r y " c l e a n " s p e c t r a f a l l below the u n i v e r s a l curve a t h i g h wavenumbers.  W h i l e I have n o t y e t had  an  o p p o r t u n i t y t o i n v e s t i g a t e t h i s e f f e c t e x h a u s t i v e l y , I am tempted  to  b e l i e v e t h a t some of t h e phenomena w h i c h I have d i s c u s s e d i n the l a s t few pages may  have been e f f e c t i v e t o some minor degree i n many of the  ocean t u r b u l e n c e s p e c t r a w h i c h have been p r o c e s s e d i n the p a s t , i n c l u d i n g those from i n - s h o r e w a t e r s (see G r a n t , S t e w a r t and M o i l l i e t ( 1 9 6 2 ) , Stewart and Grant (1962), G r a n t , Hughes, V o g e l and M o i l l i e t ( 1 9 6 8 ) , G r a n t , M o i l l i e t and V o g e l (1968)) and, i n p a r t i c u l a r , i n the d a t a from w h i c h the p r e s e n t u n i v e r s a l c u r v e was  derived.  I f we  can  assume the t h e o r y of " u n i v e r s a l e q u i l i b r i u m " t o be v a l i d t h e r e seems t o be no a l t e r n a t i v e c o n c l u s i o n . reasons (and t h e r e may  I have s u g g e s t e d s e v e r a l p o s s i b l e  be o t h e r s ) why  an e x p e r i m e n t a l spectrum  might  appear f l a t t e r a t h i g h wavenumbers t h a n the t h e o r e t i c a l c u r v e , b u t I see no way  to explain a steeper slope. W i t h t h i s argument i n mind I have ( f o l l o w i n g the p r o c e d u r e  o f Stewart and Grant (1962)) produced a new universal.function.  approximation to Kolmogoroff's  F i g u r e 22 shows t h i s "new"  u n i v e r s a l curve i n  comparison t o the o l d one w h i c h has been a c c e p t e d by t h i s  laboratory  Figure 22. A new empirical approach to Kolmogoroff's universal spectrum function f o r i s o t r o p i c turbulence. E a r l i e r version due to Stewart and Grant C1962) i s shown also (displaced to the right and upwards) for comparison of shape.  61 s i n c e 1962.  The  two  l i e so c l o s e t o g e t h e r i n the low and mid-range  of wavenumbers t h a t I have found i t c o n v e n i e n t t o d i s p l a c e the o l d (dashed l i n e ) by about 2.5 m i l l i m e t e r s h o r i z o n t a l l y and so t h a t the shapes may  be compared more r e a d i l y .  ( p l o t t e d w i t h a s l o p e of e x a c t l y - 5/3  The  vertically  new  curve  i n the i n e r t i a l subrange)  i n f a c t l i e s something l e s s t h a n a l i n e w i d t h  above the o l d one i n the  i n e r t i a l subrange; i s s l i g h t l y s h a r p e r i n the "knee"; then c r o s s e s f a l l s below the o l d c u r v e , r e a c h i n g a s l o p e v e r y c l o s e t o -7 a t extreme o u t e r  Operation  and  the  end. The new  samples, one  one  curve i s a composite d e r i v e d from t h r e e  of 95 seconds and two  F-6-67.  (as i n E q u a t i o n  separate  of 175 seconds d u r a t i o n , from  For e a c h , a d i s s i p a t i o n r a t e o b t a i n e d by i n t e g r a t i o n  10) has been used f o r n o r m a l i z a t i o n , and  the r e s u l t i n g  p o i n t s are a l l p l o t t e d t o g e t h e r t o produce the curve of F i g u r e  22.  I have shown o n l y a few of the computed p o i n t s i n t h i s f i g u r e , s e l e c t e d by a s a m p l i n g p r o c e d u r e d e s i g n e d s i m p l y t o g i v e a r e a s o n a b l y d i s t r i b u t i o n of p o i n t s along the c u r v e .  uniform  I n q u i t e a number of cases  p o i n t s have f a l l e n so c l o s e t o g e t h e r t h a t they c o u l d n o t be shown s e p a r a t e l y and  I have p l o t t e d o n l y a s i n g l e p o i n t .  For one sample I  have i d e n t i f i e d the p o i n t s t o i l l u s t r a t e the s c a t t e r , b u t , t o a v o i d undue c l u t t e r on the diagram, I have l e f t the o t h e r s The  new  curve l e a d s t o a v a l u e of the  K o l m o g o r o f f c o n s t a n t , K' = 0.56, reported  unmarked.  one-dimensional  - somewhat l a r g e r t h a n most p r e v i o u s l y  results. I n the l i g h t of e a r l i e r d i s c u s s i o n i t may  be s i g n i f i c a n t  the temperature s p e c t r a a s s o c i a t e d w i t h the samples from w h i c h the  new  that  62 curve has been d e r i v e d show n o t i c e a b l y lower l e v e l s of t h e r m a l  micro-  s t r u c t u r e (by f a c t o r s of 3 t o 10 i n s p e c t r a l l e v e l ) t h a n those f o r o t h e r samples from the same a r e a d u r i n g the same o p e r a t i o n , b u t f o r w h i c h the v e l o c i t y s p e c t r a do n o t show such a steep s l o p e at h i g h wavenumbers. Lower temperature m i c r o s t r u c t u r e p r o b a b l y  indicates a w e l l  mixed body of w a t e r w i t h c o r r e s p o n d i n g l y s m a l l d e n s i t y f l u c t u a t i o n s . I f my  e a r l i e r s p e c u l a t i o n s come anywhere c l o s e t o the t r u t h t h e n ,  we  would expect a r e l a t i v e l y u n d i s t o r t e d v e l o c i t y spectrum and, s i n c e the Reynolds number (see Page 9) i s known t o be h i g h - t h i s spectrum m i g h t come c l o s e t o the u n i v e r s a l form p r e d i c t e d by t h e o r y .  My new  "universal  c u r v e " , i n f a c t , shows a v e r y c l o s e match a t h i g h wavenumbers t o some of the e a r l y s p e c t r a by Stewart and Townsend (1951) i n a w i n d t u n n e l , and comes c l o s e r t h a n the o l d one t o more r e c e n t r e s u l t s by Pond (1965) i n the atmosphere.  T u r b u l e n t Heat F l u x A method of e s t i m a t i n g the v e r t i c a l t r a n s p o r t of h e a t by t u r b u l e n t m i x i n g i s o u t l i n e d b r i e f l y under " T h e o r e t i c a l Background". I have a n a l y s e d s i x samples i n t h i s way from F - l - 6 9 .  - t h r e e from F - l l - 6 7 and  S u i t a b l e samples r a n g i n g i n l e n g t h from p a r t o f a depth  c y c l e t o s e v e r a l c y c l e s are s e l e c t e d from r e c o r d s taken i n the mode.  Primary  three  c r i t e r i a f o r s e l e c t i o n are ( i ) r e a s o n a b l e  cycling  uniformity  i n the l e v e l of temperature f l u c t u a t i o n s , ( i i ) no m a j o r temperature i n v e r s i o n s w i t h i n the depth range, ( i i i ) h o r i z o n t a l g r a d i e n t s  of  temperature as s m a l l as p o s s i b l e , ( i v ) no g a i n changes o r o t h e r  disturbances.  63 The d i f f e r e n t i a t e d s i g n a l from the temperature  probe,  suitably f i l t e r e d to remove as much as possible of the noise, i s f i r s t processed through an analogue c i r c u i t designed to compensate for the frequency response of the probe.  From the corrected s i g n a l , a mean  square value i s computed, and, with application of c a l i b r a t i o n factors and adjustment f o r recording gain settings, the result may be designated 2 Q 2  vj~^")  (see Page 13) .  2  From t h i s we would l i k e t o e s t i m a t e (V6) , ,3 6 2  The ocean tends to be h o r i z o n t a l l y s t r a t i f i e d and v^") w i l l 3 0 2 ,3 0 2 normally be larger than £ — ) or t — ) . I f we assume a uniform ox 3 y  structure i n the horizontal plane however, there w i l l be an optimum 2 angle .(to the horizontal) at which to.make a angle one-dimensional measurement to give a best approximation to (V9) This would weight the >3 0 2 horizontal component of G—) by a factor of 2 with respect to the piS  v e r t i c a l component, and turns out to be just over 35°. In our cycling mode the angles of ascent and descent are usually s l i g h t l y less than 30°, which i s a l i t t l e b i t low, but nevertheless close to the optimum, ,3 9* 2 as 3 ( ~ ) .  2 I s h a l l therefore take (V9)  0  The depth range i s then determined from the depth record and the mean temperature range from one of the thermistors. For samples having a low signal-to-noise r a t i o I have computed a mean square value of the background  from an adjacent section  of record, or sometimes from a short quiescent period within the s i g n a l sample being processed, and have made appropriate correction to the value 5 0 2 of C^~) • Resulting values of v e r t i c a l turbulent heat flux, with and without noise correction, are summarized i n Table I I I . The l a s t column  vO  o  co  CM  rH  o\  co VD  in  00 St cn  CM  m co  m m  rH  stst  o>  00 st  oo o  VD  o rH  vO CM  o  m  St  m  rH  vO cn CM  O VO  cn  oo oo r-  oo  rH  cn  cn  O  •n  co rH  cn sl-  ST CM  CO  m m rH  vo  00  00  rH  rH  m rH  rH  CM rH  CO rH CM  CM  o  oo  m sr  m m  CM  rH  o oo o  o  m oo o  vo  vo  vo  CM CM  rH  co CM  CM  TABLE I I I :  co CM  CO  00  00  O  CM  CM VO CM  CM H  o in  rH  CO CM  oo  00  CO  rH  o  00  o  sr a\  o m o CO  CO  CO  o  CTv CM  CO VO  st st  00  cn  co m o  o rH  rco o oo CO  m o  vO  CO  m  rH  o  CO rH CM  vo  vO  vO  CM  CM  CM  CM  m  V e r t i c a l heat f l u x and eddy c o e f f i c i e n t of t h e r m a l d i f f u s i v i t y .  64 shows t h e e f f e c t i v e eddy c o e f f i c i e n t o f d i f f u s i v i t y where a p p l i c a b l e ) f o r each  (noise-corrected  sample.  Samples 4 and 5 were t a k e n from r e g i o n s o f q u i t e i n t e n s e temperature s t r u c t u r e , r e p r e s e n t a t i v e o f o n l y 1 o r 2 p e r c e n t perhaps of t h e volume o f ocean covered by our e x p e r i m e n t s .  The o t h e r samples  are more r e p r e s e n t a t i v e o f commonly o c c u r r i n g i n t e n s i t i e s w h i c h might be found throughout 25 t o 30 p e r c e n t o f t h e volume. Compensation  f o r n o i s e by t h e method used p r o b a b l y o v e r -  c o r r e c t s , because t h e r e i s almost c e r t a i n l y some r e s i d u a l s i g n a l i n t h e s e c t i o n o f n o i s e used f o r c o r r e c t i o n .  temperature  The c o r r e c t e d  figure,  f o r samples 2 and 3 i n p a r t i c u l a r , where t h e c o r r e c t i o n s a r e l a r g e , s h o u l d be r e g a r d e d w i t h some s u s p i c i o n .  The r e s u l t s may p r o b a b l y be r e l i a b l y  r e g a r d e d as l o w e r l i m i t s . My r e s u l t s a r e t o o few and t h e s c a t t e r t o o g r e a t t o e s t i m a t e a r e l i a b l e mean v a l u e f o r h e a t f l u x o r eddy c o e f f i c i e n t f o r t h e r e g i o n . 2 -1 The average o f t h e l a s t column i n T a b l e I I I i s 1.12 cm s e c w h i c h i s 2 -1 c l o s e t o the v a l u e o f 1 cm s e c  s u g g e s t e d by Munk (1966) and o t h e r s .  However, my r e s u l t s a r e from s e l e c t e d samples and each c o v e r s o n l y a l i m i t e d range i n depth.  My e s t i m a t e (which I cannot s u p p o r t q u a n t i -  t a t i v e l y ) from v i s u a l e x a m i n a t i o n o f t h e r e c o r d s , i s t h a t a mean v a l u e f o r t h e volume o f ocean covered by our experiments would be s m a l l e r 2 -1 by a f a c t o r o f about 5 - something l i k e 0.2 cm s e c T h i s c o n c l u s i o n may be compared w i t h a s i n g l e r e s u l t r e p o r t e d by Osborn (1969) from measurements o f t h e v e r t i c a l component o f temperature g r a d i e n t i n t h e San Diego Trough i n August 1968. H i s v a l u e f o r v e r t i c a l h e a t f l o w i m p l i e s an e f f e c t i v e eddy c o e f f i c i e n t  65 2 i n t h e range 0.02 t o 0.06 cm s e c between  a  n c !  (V9) .  -1 , depending  on the r e l a t i o n s h i p  S i n c e h i s measurements were t a k e n v e r t i c a l l y ,  i n t h e d i r e c t i o n o f maximum g r a d i e n t s , t h e f a c t o r s h o u l d p r o b a b l y be 2 l e s s than 3 - perhaps  2, w i t h an i m p l i e d eddy c o e f f i c i e n t o f 0.04  cm  s e c "*". H i s measurements were made over a much g r e a t e r range o f depth t h a n ours and t h e r e s u l t i s t h e r e f o r e more l i k e a mean v a l u e f o r t h e area.  On t h i s b a s i s h i s r e s u l t seems t o be l o w e r a g a i n than m i n e , by  another f a c t o r o f 5.  66 DISCUSSION  There are not many s p e c i f i c c o n c l u s i o n s t o be have p r e s e n t e d  data which I hope w i l l  drawn.  I  c o n t r i b u t e i n some u s e f u l way  to  our meager s t o r e of knowledge on the t u r b u l e n t s t r u c t u r e of the ocean, and  I have d i s c u s s e d c e r t a i n of the c h a r a c t e r i s t i c s of the  we  observe.  by  c u r r e n t t h e o r i e s of i s o t r o p i c t u r b u l e n c e , and  does n o t .  In some r e s p e c t s i t seems t o f a l l i n t o the p a t t e r n p r e d i c t e d  We  i n other respects i t  have d i s c o v e r e d t h a t , throughout the volume of ocean  by our experiments, t u r b u l e n c e e x i s t s i n a patchy t i v e l y t h i n l a y e r s and t h e r e i s p r o b a b l y throughout the l a y e r s .  dimensional  observations  over such a s m a l l volume,  We would l i k e t o know much more about  f o r t h i s we  From such a  m a t e r i a l s which are of i n t e r e s t  and  of  continued  c o u l d a l s o l e a r n more about the  t r a n s p o r t of h e a t , momentum, s a l t  throughout  simply r e q u i r e more of the s o r t  t h a t have a l r e a d y been made.  It  f o r which  dissipation  of t u r b u l e n t patches and t h e i r d i s t r i b u t i o n  programme of o b s e r v a t i o n we  important  observe resembles more c l o s e l y  observations  the r e s u l t i s of d o u b t f u l v a l u e .  oceans, and  perhaps  the t u r b u l e n c e t o be  the t o t a l , world-wide, t u r b u l e n t  on energy, b u t , based on so few  the w o r l d  rela-  developed.  I have e s t i m a t e d  the c h a r a c t e r i s t i c s  structure within  s i t u a t i o n d e s c r i b e d by Kraichman (1967), but  the theory i s not y e t w e l l  covered  v e l o c i t y shear between and  We would not r e a l l y expect  i s o t r o p i c , and perhaps the p a t t e r n we the two  turbulence  vertical  o t h e r d i s s o l v e d or suspended  to the marine e c o l o g i s t s .  appears t h a t s a l i n i t y  and d e n s i t y s t r u c t u r e may  e f f e c t s on the mechanism of ocean t u r b u l e n c e .  To  have  develop  67 a b e t t e r understanding  of t h e s e e f f e c t s w i l l r e q u i r e improved r e s o l u t i o n  of the s m a l l s c a l e f e a t u r e s of s a l i n i t y and d e n s i t y . difficult  I t should not  be  t o improve our r e s o l u t i o n by an o r d e r of magnitude, and perhaps  more, w i t h o u t  s a c r i f i c e of a c c u r a c y .  I n o r d e r t o c a s t some l i g h t on  the  q u e s t i o n of i s o t r o p y ( o r l a c k of i t ) i t would be v e r y v a l u a b l e , a l s o , t o be a b l e t o measure a c r o s s - s t r e a m  component of v e l o c i t y .  In p r i n c i p l e  this  i s not d i f f i c u l t , but i n p r a c t i c e the geometry of the v e l o c i t y probe i s l i m i t e d by the problem of f o u l i n g by p l a n k t o n . c u l t but perhaps n o t  A s o l u t i o n w i l l be  diffi-  impossible.  We w o u l d l i k e t o be a b l e t o measure s h e a r , and  thereby  o b t a i n l o c a l R i c h a r d s o n number, as a f u r t h e r c o n t r i b u t i o n t o our unders t a n d i n g of the n a t u r e  of the t u r b u l e n c e  This, also, i s a d i f f i c u l t  and the mechanism of  t a s k , but probably  Throughout the p r o g r e s s s t r e s s e d the p o i n t , I have had  not  generation.  impossible.  of the work, a l t h o u g h  I have not  a nagging s u s p i c i o n t h a t t h e r e might be  some s o r t of s m a l l s c a l e wave a c t i o n mixed w i t h the t u r b u l e n c e . not y e t made any attempt t o d i s t i n g u i s h between the two  I have  types of m o t i o n ,  but t h e r e are a number of ways t h a t one might go about i t .  Perhaps  the  f i r s t t o t r y would be t o determine the c o r r e l a t i o n between v e l o c i t y  and  temperature f l u c t u a t i o n s and the phase a n g l e between them. My p r e d e c e s s o r s have e s t a b l i s h e d a b a s i s on w h i c h t o b e g i n , and have p o i n t e d the way. remains t o be  done.  I have t a k e n a s m a l l s t e p f o r w a r d .  Much  68 BIBLIOGRAPHY B a t c h e l o r , G.K.  1953:  Homogeneous T u r b u l e n c e .  Cambridge U n i v e r s i t y P r e s s  B a t c h e l o r , G.K. 1959: Small S c a l e V a r i a t i o n of Convected Q u a n t i t i e s l i k e Temperature i n T u r b u l e n t F l u i d (Part 1). J . F l u i d Mech. _5, 113. F a b u l a , A.G. 1968: The Dynamic Response of Towed Thermometers. J . F l u i d Mech. 34, 449. G r a n t , H.L., Stewart, R.W. and M o i l l i e t , A. 1962: Turbulence S p e c t r a from a T i d a l Channel. J . F l u i d Mech. 12, 241. G r a n t , H.L., Hughes, B.A., V o g e l , W.M. and M o i l l i e t , A. 1968: The Spectrum o f Temperature F l u c t u a t i o n s i n T u r b u l e n t Flow. J . F l u i d Mech. 34, 423. G r a n t , H.L. , M o i l l i e t , A. and V o g e l , W.M. 1968: Some O b s e r v a t i o n s of the Occurrence of Turbulence i n and above the Thermocline. J . F l u i d Mech. 34, 443. H i n z e , J.O.  1959:  Turbulence.  McGraw-Hill Book Company, New  von Karman, T. 1937(a): On the S t a t i s t i c a l Theory P r o c . Nat. Acad. S c i . Wash. 23, 98.  York.  of T u r b u l e n c e .  von Karman, T. 1937(b): The Fundamentals of the S t a t i s t i c a l Theory of T u r b u l e n c e . J . Aero. S c i . 4_, 131. von Karman, T. 1938: Some Remarks on the S t a t i s t i c a l Theory P r o c . 5th I n t . Congr. App. Math. 347.  of Turbulence  Kolmogoroff, A.N. 1941: The L o c a l S t r u c t u r e of Turbulence i n Incompressib V i s c o u s F l u i d f o r v e r y l a r g e Reynolds Numbers. C.R. Acad. S c i . U.R.S.S. 30, 301. Monin, A.S.  and Yaglom, A.M. Nauka.  Munk, W.H.  1966:  Munk, W.H.  and MacDonald, G.J.F. 1960: Cambridge U n i v e r s i t y P r e s s .  Osborn,  1967:  Abyssal Recipes.  S t a t i s t i c a l Hydrodynamics ( V o l 2).  Deep-Sea Res.  13,  707.  The R o t a t i o n o f the E a r t h .  T.R. 1969: Oceanic F i n e S t r u c t u r e . D o c t o r a l D i s s e r t a t i o n . U n i v e r s i t y of C a l i f o r n i a , San Diego.  P h i l l i p s , O.M. 1966: The Dynamics of the Upper Ocean. University Press.  Cambridge  69 Pond, S. 1965: Turbulence S p e c t r a i n the Atmospheric Boundary L a y e r over t h e Sea. D o c t o r a l D i s s e r t a t i o n , U n i v e r s i t y o f B r i t i s h Columbia. Stewart, R.W. 1951: T r i p l e V e l o c i t y C o r r e l a t i o n s i n I s o t r o p i c T u r b u l e n c e . P r o c . Camb. P h i l . Soc. .47, 146. Stewart, R.W. 1969: Turbulence and Waves i n a S t r a t i f i e d Atmosphere. Radio S c i e n c e 4^, 1269. Stewart, R.W.  arid Townsend, A.A. 1951:  P h i l . T r a n s . A. 243, 359.  Stewart, R.W. and G r a n t , H.L. 1962: D e t e r m i n a t i o n o f the Rate o f D i s s i p a t i o n o f T u r b u l e n t Energy near the Sea S u r f a c e i n t h e Presence of Waves. J . Geophys. Res. 6^7, 3177. Stommel, H. and Federov, K.N. 1967: S m a l l s c a l e S t r u c t u r e i n Temperature and S a l i n i t y near Timor and Mindanao. T e l l u s 19_, 306. T a y l o r , G.I. 1921: D i f f u s i o n by Continuous Movements. Math. Soc. 20_, 196. T a y l o r , G.I. 1935: S t a t i s t i c a l Theory A, 151, 421.  of Turbulence.  P r o c . Lond.  P r o c . Roy. Soc.  T u r n e r , J.S. and Stommel, H.: A new Case o f C o n v e c t i o n i n t h e Presence of V e r t i c a l S a l i n i t y and Temperature G r a d i e n t s . P r o c . N a t . Acad. S c i . j>2, 49. Woods, J.D. and F o s b e r r y , G.G. 1966-67: The S t r u c t u r e of the T h e r m o c l i n e . Underwater A s s o c i a t i o n ( o f M a l t a ) Report 1966-67. - - -  1952: T a b l e s f o r Sea Water D e n s i t y . O f f i c e , H.O. P u b l i c a t i o n No. 615.  U.S. Navy H y d r o g r a p h i c  - - -  1956: T a b l e s f o r Rapid Computation o f D e n s i t y and E l e c t r i c a l C o n d u c t i v i t y o f Sea Water. U.S. Navy H y d r o g r a p h i c O f f i c e . H.O. P u b l i c a t i o n No. 619.  Positions Held:  1947-present  Defence Scientific Service Officer D e f e n c e R e s e a r c h B o a r d of C a n a d a 1947- 48  1948- 50  D i r e c t o r a t e of E l e c t r o n i c s  Research.  S e c r e t a r y of E l e c t r o n i c s A d v i s o r y Committee; E l e c t r o n i c s R e s e a r c h Panel; Canadian Radio Wave Propagation Committees. Pacific Naval Laboratory. Research in underwater a c o u s t i c s and oceanography.  1950-53  G r a d u a t e S t u d i e s ( P h y s i c s ) at U B C o n F i n a n c i a l A s s i s t a n c e . M . A. T h e s i s : "The F e r r o e l e c t r i c P r o p e r t i e s of B a r i u m T i t a n a t e " .  1953-58  H e a d S e a w a r d Defence Section, PNL. R e s e a r c h i n u n d e r w a t e r a c o u s t i c s and low f r e q u e n c y m a g n e t i c s r e l a t e d to d e t e c t i o n of s u b m a r i n e s.  1959- 63  D i r e c t o r o f S c i e n t i f i c S e r v i c e s and  Deputy  S c i e n t i f i c A d v i s o r to C h i e f of N a v a l Staff. 1960- 63  D i r e c t o r of M a r i t i m e R e s e a r c h (in addition  1963-66  to D i r e c t o r of S c i e n t i f i c S e r v i c e s ) . Deputy Chief, Canadian Defence R e s e a r c h S t a f f , W a s h i n g t o n , D. C. a n d D e p u t y D e f e n c e R e s e a r c h Attache, Canadian Embassy, W a s h i n g t o n , D. C.  1966- 67  D i r e c t o r of P h y s i c a l R e s e a r c h ,  1967- 70  Defence  Research Establishment Pacific  I n s t i t u t e of O c e a n o g r a p h y , on o c e a n i c t u r b u l e n c e .  Note:  DRB/HQ.  UBC.  W a r t i m e s e r v i c e w i t h the C a n a d i a n A r m y a n d p r i o r  service  w i t h the N a t i o n a l R e s e a r c h C o u n c i l of C a n a d a h a v e not b e e n included.  and  Research  Publications: Progress  Report on R e s e a r c h on Titanates.  D R B 52/11858.  Unclassified.  U B C 1952.  Piezoelectric Effects in P o l a r i z e d Titanates. D R B 53/9517.  U B C 1953.  The F e r r o e l e c t r i c Properties M . A .  Thesis,  Unclassified.  of B a r i u m  Titanate.  U B C 1952.  The Fluctuation P r o b l e m s inUnderwater Sound. Naval Paper IV: D R B Fifth S y m p o s i u m 1953. Confidential. D R B 54/6638. Water Temperature Structure  a n d i t s E f f e c t o n the  Performance  o f H a r b o u r D e f e n c e A s d i c s i n t h e A p p r o a c h e s to E s q u i m a l t a n d Victoria Harbours. Confidential.  P N L Interim Report PIR-6,  1954.  D R B 54/8211.  S u r v e y o f the State of D e v e l o p m e n t of L F a n d V L F S o u n d Surveillance Systems.  P N L 1955.  The D e s i g n of Indicator L o o p S y s t e m s for D e t e c t i n g S m a l l and Slowly Moving Targets. P N L R e p o r t 10. 1955. Secret. D R B 55/15668. Some  C o n s i d e r a t i o n s i n the D e s i g n of M a g n e t i c I n d i c a t o r  Systems  f o r the  D e t e c t i o n of Slow T a r g e t s .  Navy Harbour Defence and Countermeasures  Loop  Secret.  U.S.  Bulletin,  1956.  A N o t e o n L o w F r e q u e n c y E l e c t r o m a g n e t i c S t u d i e s at P N L . PNL A  1957.  P r e l i m i n a r y Study of Indicator L o o p s in Deep Water.  Technical Memorandum 57-1,  1957.  Secret.  DSIS  P N L  57/2736.  Geographical Variations in Geomagnetic Micropulsations. PNL  Tech M e m o 58-6,  1958.  Unclassified.  S u b - A u d i o Spectra of M a g n e t i c S t o r m s  Unclassified.  DSIS  59/14330.  and Solar W h i s t l e r s .  J o u r n a l o f the A m e r i c a n P h y s i c a l S o c i e t y , Sub-Audible Geomagnetic Fluctuations.  DSIS  1958.  Nature,  1958.  58/13663.  M a r i t i m e R e s e a r c h for Defence Staff P a p e r , 1961.  in Canada.  The New R C N R e s e a r c h Ship A G H 171. Review, F i r s t Q u a r t e r 1962.  Secret.  R C N Naval  D M R  Technical  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0302459/manifest

Comment

Related Items