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.Sc, U n i v e r s i t y of B r i t i s h . Columbia, 1941 M.A. , U n i v e r s i t y of B r i t i s h Columbia, 1952 A Thesis Submitted i n P a r t i a l F u l f i l m e n t of the Requirements f o r the Begree of Doctor of Philosophy i n the Department of Physics We accept t h i s t h e s i s as conforming to the re q u i r e d standard The U n i v e r s i t y of B r i t i s h Columbia September 1970 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I ag ree tha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d tha t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada i ABSTRACT In two experimental operations i n deep water o f f the west coast of 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 recorded w i t h a s p a t i a l r e s o l u t i o n of 2 m i l l i m e t e r s or b e t t e r , from the thermocline down t o a depth of 330 meters. Some measurements have been taken along h o r i z o n t a l paths at d i s c r e t e depths, 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 the constant forward motion, others have been taken along "saw—tooth" paths, r e v e a l i n g some new features of the f i n e s t r u c t u r e of the ocean and the occurrence of turbulence below the thermocline. On one occasion sea-^water c o n d u c t i v i t y was a l s o measured, enabling the computation of de n s i t y and examination of the occurrence and c h a r a c t e r i s t i c s of the m i c r o s t r u c t u r e i n r e l a t i o n to the density s t r u c t u r e . Power s p e c t r a of 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 rates obtained. Estimates are made of mean energy d i s s i p a t i o n as a f u n c t i o n of depth and t o t a l d i s s i p a t i o n throughout the ocean volume. The v e l o c i t y s p e c t r a are compared w i t h e x i s t i n g ideas of Kolmogoroff's u n i v e r s a l s p e c t r a l f u n c t i o n f o r i s o t r o p i c turbulence and d i s c r e p a n c i e s at high wavenumbers are a t t r i b u t e d , at l e a s t i n p a r t , to the e f f e c t of buoyancy forces r e s u l t i n g from s m a l l s c a l e density f l u c t u a t i o n s . A new e m p i r i c a l v e r s i o n of the u n i v e r s a l f u n c t i o n i s derived from what i s considered t o be the best ocean turbulence data a v a i l a b l e . i i V e r t i c a l t r a n s p o r t of heat i s c a l c u l a t e d f o r a number of samples, from microscale measurements of temperature gradient and mean v e r t i c a l g r a d i e n t . A mean 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 i s estimated f o r the re g i o n . i i i TABLE OF CONTENTS Page ABSTRACT i TABLE OF 'CONTENTS i i i LIST OF FIGURES i v LIST OF TABLES v i ACKNOWLEDGMENT v i i INTRODUCTION 1 THEORETICAL BACKGROUND 4 Isot r o p i c Turbulence 4 V e r t i c a l Heat Flux 12 INSTRUMENTATION 14 General 14 Temperature and V e l o c i t y Probes 17 Conductivity Meter 24 RESULTS 26 General 26 F o s s i l Turbulence 35 Density Structure 37 Ve l o c i t y Spectra 42 Energy D i s s i p a t i o n 45 The F i t of the Universal Curve 51 Turbulent Heat Flux 62 DISCUSSION 66 BIBLIOGRAPHY 68 i v LIST OF FIGURES Facing Page Figure 1: Tewed body and sensors i n c o n f i g u r a t i o n used f o r Sea Operation F-l-69. 15 Figure 2: C l o s e r view of c e n t r a l group of sensors. 16 Figure 3: Photomicrographs of t i p of v e l o c i t y probe (a) and temperature probe (b) (x 70 approximately). 17 Figure 4: 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 Figure 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 Figure 6: Block diagram of c o n d u c t i v i t y meter felectronics. 24 Figure 7: T y p i c a l gross oceanographic s t r u c t u r e f o r Sea Operation F - l l - 6 7 , from data taken at 1818 hours 21 November 1967. 26 Figure 8: T y p i c a l gross oceanographic s t r u c t u r e f o r Sea Operation F-l-69, from data taken at 0850 hours 3 February 1969. 26 Figure 9: V e l o c i t y , temperature and c o n d u c t i v i t y records from a c y c l i n g run at 128 meters depth. H o r i z o n t a l gradients are notable. 27 Figure 10: Temperature and c o n d u c t i v i t y records from a c y c l i n g run at 152 meters depth. H o r i z o n t a l gradients are s m a l l . 29 Figure 11: V e l o c i t y , temperature and c o n d u c t i v i t y records from a c y c l i n g run at 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 v i s i b l e . 31 Figure 12: V e l o c i t y and temperature records from a c y c l i n g run at 213 meters depth, i l l u s t r a t i n g what appears to be a sharply defined " f r o n t " . 32 V Figure 13: Two temperature spectra and corresponding sections of record, i l l u s t r a t i n g a possible case of " f o s s i l turbulence". 36 Figure 14: Series of a p r o f i l e s from the same section of record as i l l u s t r a t e d i n Figure 10. 39 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 1 4 but without the influence of s a l i n i t y . 40 Figure 1 6 : V e l o c i t y spectrum from c y c l i n g run at 2 1 0 meters depth with "universal curve" f i t t e d . 4 3 Figure 17: V e l o c i t y spectrum from constant depth run at 2 1 5 meters, corrected for noise and f i t t e d to the "un i v e r s a l curve". 4 3 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 - l l - 6 7 runs and the crosses for F—1-69 runs. 47 Figure 1 9 : 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 i n t e r v a l s within two 5 2 second samples. 5 3 Figure 20: V e l o c i t y and temperature spectra from cycl i n g run at 2 1 3 meters depth, i l l u s t r a t i n g possible e f f e c t s of buoyancy forces on s p e c t r a l shape. 5 4 Figure 21: V e l o c i t y and temperature spectra from constant depth run at 64 meters, i l l u s t r a t i n g possible e f f e c t s of buoyancy forces on s p e c t r a l shape. 5 4 Figure 22: A new empirical approach to Kolmogoroff's u n i v e r s a l spectrum function f or i s o t r o p i c turbulence. E a r l i e r version due to Stewart and Grant (1962) i s shown also (displaced to the righ t and upwards) for comparison of shape. 6 1 LIST OF TABLES Table I: Energy D i s s i p a t i o n Rates Table I I : Percentage of volume that i s turbulent and estimated d i s s i p a t i o n rates Table I I I : V e r t i c a l heat flux 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 v i i ACKNOWLEDGMENT The work I have done has been a c o n t i n u a t i o n and expansion of a programme which has been i n progress i n t h i s l a b o r a t o r y f o r a number of years. I cannot name a l l those who have c o n t r i b u t e d to i t i n the p a s t , and w i l l not attempt t o go back i n t o h i s t o r y except to p o i n t out that 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. Stewart, now of the I n s t i t u t e of Oceanography of the U n i v e r s i t y of 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 continu i n g i n t e r e s t , the present programme would probably never have evolved. What progress I have made over the past two and a h a l f years has been wh o l l y dependent on the s u c c e s s f u l execution of two experimental operations under d i f f i c u l t c o n d i t i o n s at sea. For each of these, the sea-going team c o n s i s t e d of seven dedicated s c i e n t i f i c and t e c h n i c a l personnel of the Defence Research Establishment P a c i f i c , without whose wholehearted support the programme would not have been p o s s i b l e at a l l . Dr. H.L. Grant has probably had more experience i n the measurement of turbulence and the conduct of experiments at sea than anyone e l s e i n the la b o r a t o r y . His experience and cooperation 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 at sea and c l e a r t h e o r e t i c a l i n s i g h t i n t o the problem at hand, has made a unique c o n t r i b u t i o n . Mr. J . Smith has been r e s p o n s i b l e f o r much of the mechanical design of the experimental equipment ( i n c l u d i n g the towing winch) and f o r making i t work at sea. Mr. R.W. Chappell has done much of the e l e c t r o n i c design ( i n c l u d i n g the c o n d u c t i v i t y meter) and, although he s u f f e r s from sea-sickness almost from the moment he sets foot aboard s h i p , p e r s i s t e n t l y refuses to stay v i i i ashore. Mr. R.S. Anderson and Mr. A.E. Pastro, experienced and extremely valuable hands at sea, have also contributed s u b s t a n t i a l l y ashore, i n the bui l d i n g and c a l i b r a t i o n of equipment and analysis of data. Mr. A. M o i l l i e t , although not one of the sea-going team, has also contributed 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 the tes t i n g and c a l i b r a t i o n of v e l o c i t y probes. I am g r a t e f u l also f or the cooperation and s k i l l f u l a s s i s -tance of Captain MacFarlane and the o f f i c e r s and ccew of the Canadian Armed Forces research ship "ENDEAVOUR" throughout both sea operations, and to personnel of the P a c i f i c Oceanographic Group of the Fi s h e r i e s Research Board of Canada, who provided oceanographic support. I wish p a r t i c u l a r l y to thank Dr.- R.W. Stewart and Dr. R.W. Burling of the I n s t i t u t e of Oceanography for t h e i r i n t e r e s t , suggestions, advice and assistance throughout the course of t h i s work, and other members of the I n s t i t u t e f or i n t e r e s t i n g and p r o f i t a b l e discussions. The work has been part of the research programme of the Defence Research Board of Canada and I would l i k e , f i n a l l y , to express my appreciation of the opportunity they have afforded me to use i t as a thesis t o p i c . 1 INTRODUCTION In h i s book "The Dynamics of the Upper Ocean" Owen M. P h i l l i p s of Johns Hopkins University introduces the chapter on "Oceanic Turbulence" with the statement that "Turbulence i s one of the most ubiquitous phenomena i n a l l of f l u i d mechanics". In the ocean, indeed, turbulence seems to be very widespread, and some evidence leads us to b e l i e v e that i t may occur almost everywhere over a very wide range of p h y s i c a l scales. While i t s presence may be r e a d i l y observed and c e r t a i n q u a l i t a t i v e 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 quantitative observations of the turbulent f l u c t u a t i o n s i n water v e l o c i t y tend to be d i f f i c u l t , because of the s e n s i t i v i t y of the measure-ments required and because of the disturbing influence of other motions associated with the sea, p a r t i c u l a r l y when one would l i k e to make such measurements off-shore and at some depth, with no more stable platform a v a i l a b l e than a surface ship. It has been known, or at least surmised, for many years that the turbulent structure of the ocean plays an important r o l e i n the v e r t i c a l transport of heat, momentum, and dissolved or suspended matter, arid, i n the smaller 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 through v i s c o s i t y . Lacking quantitative measurements of turbulent mixing processes 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 successful measurements of small scale turbulence i n the open sea were made by t h i s laboratory* i n * Defence Research Establishment P a c i f i c Defence Research Board of Canada 2 1962 - before I became Involved i n the programme. Those early measurements were made with sensors mounted on a submarine and were li m i t e d to about 100 meters i n depth. Both temperature and v e l o c i t y microstructure (or turbulence) were measured with sensor response permitting observations to be c a r r i e d down to scales of 2 or 3 millimeters - w e l l down i n t o the range of energy d i s s i p a t i o n by viscous e f f e c t s , or, i n the terminology 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 of wavenumbers. I s h a l l r e f e r to the r e s u l t s of that operation l a t e r on. This d i s s e r t a t i o n presents some of the r e s u l t s of two more recent experiments c a r r i e d out i n 1967 and 1969 i n deep water o f f the west coast of Vancouver Island. The equipment has been modified for towing behind a surface ship, permitting observations to depths exceeding 300 meters, and, on one occasion only (1969), measurements of sea-water conductivity have been made and density computed so that the existence and c h a r a c t e r i s t i c s of turbulence might be examined i n r e l a t i o n to the g r a v i t a t i o n a l s t a b i l i t y of the water column. The work I have done has been a continuation and expansion of the e a r l i e r programme, which has been active f or more than ten years i n the measurement of turbulence at sea. As I have implied, much of the instrumentation and many of the experimental techniques I have i n h e r i t e d from e a r l i e r stages of the programme, and for t h i s I am g r a t e f u l to my predecessors. S p e c i f i c a l l y I have been responsible f o r (a) the introduction of what I s h a l l describe l a t e r as the "c y c l i n g mode" of operation, by which i t has been possible to develop a new understanding of the small scale v e r t i c a l structure of 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 to the e x i s t i n g array of sensors, p e r m i t t i n g the computation of h o r i z o n t a l and v e r t i c a l d e n s i t y s t r u c t u r e , and (c) a l l the data 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 reported have been l i m i t e d by a v a i l a b l e hardware to the upper 330 meters of the ocean and by environmental f a c t o r s to the w i n t e r months. They have been more or l e s s randomly s c a t t e r e d over an area of some ten 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 slope w i t h ocean depths v a r y i n g upwards from 1000 meters but mostly over 2000 meters. The r e s u l t s t h e r e f o r e cannot, by any means, be considered r e p r e s e n t a t i v e of the world oceans, and the best we can say, perhaps, i s that there i s nothing p a r t i c u l a r l y p e c u l i a r i n an oceanographic sense about our area, 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 not be u n l i k e those i n many other p a r t s of the ocean. 4 THEORETICAL BACKGROUND Isotropic Turbulence As a bad definition but perhaps useful starting point, i t might be said that turbulence i s a fl u i d in random motion. This simply stated situation proves to be extremely d i f f i c u l t of mathematical analysis i n the general case, and i t is necessary to start off with simplifying assumptions. The following discussion is based on the assumption that the density and viscosity of the fl u i d are constant with respect to both space and time. I shall have reason later on to question the validity of this assumption with respect to density i n some of the situations we encounter in the ocean but, accepting i t for the moment, we can describe the fl u i d in the usual way by the equation of continuity, V.u = 0, (1) and the Navier-Stokes equation, f | + u.Vu = - 1 Vp + vV 2u, (2) o t p where u is the vector velocity of the turbulent motion in a frame of reference in which there i s no mean velocity, p is the density of the fl u i d , p is the pressure, and v the kinematic viscosity. V i s the gradient operator as usual. Stated in this way the problem s t i l l defies rigorous mathema-tic 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 clearly 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 is not my intention to follow the evolution of turbulence theory i n any detail, 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; for example Batchelor (1953), Hinze (1959) and most recently Monin and Yaglom (1967). I shall mention only the most significant innovations i n the development of the theory and quote such results as w i l l be pertinent to later discussion. von Karman (1937(a) and (b) and 1938) made important contri-butions during the late 1930's, amongst which was a further simpli-fication of the problem by introducing the idea of "self-preservation" whereby i t was assumed that a turbulent f i e l d maintained "similarity" during decay. The term "similarity" is used here in the sense, suggested by Stewart and Townsend (1951), that a length scale and a velocity scale alone are sufficient to determine the structure of the f i e l d . A few years later Kolmogoroff (1941) set the stage for much of the work that has followed by expressing similar ideas more expli-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 is fed into the f i e l d . The concept of an "energy cascade" through wavenumber space from lower to higher wavenumbers had been adopted by a number of e a r l i e r workers. Although i t cannot be proven r i g o r o u s l y , i t has been shown by Batch e l o r (1953), f o r example, that i t i s reasonable to expect, as a r e s u l t of i n e r t i a f o r c e s , a "cascade" of energy i n t h i s manner. I t i s not d i f f i c u l t to b e l i e v e then, that i n a range of wavenumbers, s u f f i -c i e n t l y f a r removed from the d r i v i n g motions, 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 independent of the large "energy-containing" s c a l e s . 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 the absence of other e x t e r n a l i n f l u e n c e s , the turbulence would be uniquely defined by the two parameters v , the kinematic v i s c o s i t y of the f l u i d , and e , the r a t e at which energy i s being s u p p l i e d or a l t e r n a t i v e l y the r a t e at which energy i s being removed by v i s c o s i t y , which i n a steady s t a t e s i t u a t i o n must of course be the same. I t becomes c l e a r then by dimensional reasoning that the s t a t e of e q u i l i b r i u m at high wavenumbers can be r e f e r r e d to as " u n i v e r s a l " i n the sense t h a t v a r i a t i o n of the parameters e and v can only have the e f f e c t of changing the length and time (or v e l o c i t y ) s c a l e s of the motion; and i t i s p o s s i b l e to define the c h a r a c t e r i s t i c length and v e l o c i t y s c a l e s r e f e r r e d to e a r l i e r by 3 h n = (^ -) , C3) and , u = ( v e ) \ (4) r e s p e c t i v e l y , and the as s o c i a t e d Reynolds number by 7 As I have s a i d , the th e o r i e s which have been developed around these ideas have been c l e a r l y presented by a number of authors and have been summarized v a r i o u s l y by Grant, Stewart and M o i l l i e t (1962) f o r example and by Pond (1965). Any f u r t h e r attempt here would serve no u s e f u l purpose. 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, are necessary 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 the energy density f u n c t i o n representing the energy per 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 of motion defined by the wavenumber k, then the t o t a l energy density i s : / E(k)dk = Js(u 2 + v 2 + w 2) , (6) o where u,v, and w are the three orthogonal components of the t u r b u l e n t v e l o c i t y . Using the experimental techniques which I s h a l l describe l a t e r i t i s p o s s i b l e to measure only one component of v e l o c i t y and we cannot work d i r e c t l y i n terms of t o t a l energy. We t h e r e f o r e define a one-dimensional energy density f u n c t i o n , < f > ( k ) ( r e f e r r e d to by Hinze as E 1 ( k ) ) by CO — / <j>(k)dk = u 2 , (7) o i n which u i s the t u r b u l e n t v e l o c i t y component i n the d i r e c t i o n of the mean flow or the d i r e c t i o n of motion of our towed body. According to Kolmogoroff's Hypothesis, f o r the s i m p l i f i e d case of i s o t r o p i c turbulence (J>(k) must be of the form Kk) = e 1 / 4 v 5 / 4 F ( k / k ) , (8) where F(k/k ) i s a un i v e r s a l function of i t s argument, and k = 1/n s s i s a measure of the wavenumber at which viscous e f f e c t s begin to dominate the process of energy t r a n s f e r . cj)(k) i s rela t e d to E(k) by E(k) = h k 2 3 2cj > ( k ) _ k 3 <Kk) (9) 3 k 3 k and e, the energy d i s s i p a t i o n density can be expressed as 00 oo e = 2vf k 2E(k)dk = 15v/ k2<j)(k)dk, (10) o o 2 2 i n which I s h a l l r e f e r to k E(k) and k cj>(k) a s the d i s s i p a t i o n spectra, defining the d i s t r i b u t i o n i n wavenumber space of the rate of decay of turbulent energy through the action of v i s c o s i t y . The accuracy with which one should expect Kolmogoroff's Hypothesis to describe the higher wavenumber region of a turbulent f i e l d w i l l depend upon the separation i n terms of wavenumber between the regions which make the major contribution to 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 . This separation 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 high there may be a mid-range of wavenumbers which makes a n e g l i g i b l e contribution to e i t h e r spectrum. I f th i s condition e x i s t s - and th i s i s sometimes referred to as Kolmogoroff's second hypothesis - then wi t h i n t h i s mid-range the turbulent motions are independent of the large "energy-containing" eddies, but s t i l l unaffected by v i s c o s i t y . The transf e r of energy by i n e r t i a l forces i s the dominating factor and the energy spectrum depends s o l e l y upon e. 9 T h i s , being p a r t of 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 to as the " i n e r t i a l subrange", and here the theory leads to a s p e c t r a l energy f u n c t i o n of the form E(k) = £ 2 / 3k" 5 / 3F(£-) , ( 1 1 ) s i n which the f u n c t i o n F must be a constant under the co 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 then, F(|-) = K ( 1 2 ) s and E(k) = K e 2 / 3 k 5 / 3 ( 1 3 ) I t i s obvious from ( 9 ) t h a t , i n t h i s subrange, <j>(k) must have the same power law dependence on k as E(k) has, and we can there f o r e put c K k ) = K ' e 2 / 3 k " 5 / 3 , ( 1 4 ) 1 8 i n which K' = K- ( 1 5) A number of researchers i n recent years have achieved experimental r e s u l t s which tend to confirm the p r e d i c t i o n s of t h i s theory i n many res p e c t s . In p a r t i c u l a r Grant, Stewart and M o i l l i e t ( 1 9 6 2 ) , working i n a t i d a l channel i n which the Reynolds number, based on the depth of the channel and the mean t i d a l v e l o c i t y , was a p p r o x i -g mately 3 x 10 , and w i t h an e a r l i e r generation of equipment s i m i l a r to what we are now u s i n g , have produced a number of one-dimensional energy 10 -5/3 s p e c t r a which conform remarkably c l o s e l y to the k law of the i n e r t i a l subrange f o r a f u l l two decades i n k. From the same data they have derived an e m p i r i c a l s p e c t r a l form f o r another decade and a h a l f , upwards through the d i s s i p a t i o n subrange to the p o i n t where i n s t r u m e n t a l noise at the higher frequencies becomes troublesome. The r e s u l t has come to be known w i t h i n the group as the " u n i v e r s a l curve" and, checking w i t h other experimental r e s u l t s , i t does indeed e x h i b i t a high 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 to q u a l i f y the concept of 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 to be h i g h , and where according to the theory one would expect to f i n d an e q u i l i b r i u m range. In examining turbulence s p e c t r a l a t e r on I s h a l l make use of a method, evolved by Stewart and Grant (1962), f o r determination of energy d i s s i p a t i o n rates by f i t t i n g the s p e c t r a to the u n i v e r s a l curve. 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 than quote d i r e c t l y from Stewart and Grant, as f o l l o w s (changing only f i g u r e and equation references to match our numbering sequence): " I t i s evident that i f log <j> i s p l o t t e d against log k, a l l curves of the form (8) can be derived from one such curve by simple t r a n s l a t i o n s . Moreover, f o r given 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 displacement of the curve by h log a, both h o r i z o n t a l l y and v e r t i c a l l y . In p r a c t i c e the f o l l o w i n g procedure i s used: A p l o t of l o g F(k/k ) versus l o g k/k i s prepared, and the p o i n t s s (0,0) i s l o c a t e d and marked. For the measured spectrum, a p l o t of log cj>(k) versus log k i s prepared on the same s c a l e . Now i f 11 the measured spectrum i s f r e e of noise and nonturbulent s i g n a l s , and i f Kolmogoroff's hypothesis i s v a l i d f o r the measured tu r b u l e n t f i e l d , the two p l o t s can be made to c o i n c i d e . When i n c oincidence, the p o i n t (0,0) on the F ( k / k g ) curve w i l l c o r r e s -1/4 -3/4 1/4 5/4 pond to the p o i n t (log e v , log e v ) on the cj>(k) curve. For a given value of v, but varying values of e, the locus of the po i n t (0,0) on the F( k / k g ) curve w i l l be a s t r a i g h t l i n e of slope +1 through (log v log v"*^) . I f the measured <j)(k) spectrum contains noise or other spurious s i g n a l s , the f i t may nevertheless be attempted. A l i n e of slope -3/4 5/4 +1 i s drawn through the p o i n t ( l o g v , l o g v )(marked 0 i n Figure 16, f o r example) and the F( k / k g ) curve i s superimposed so that the p o i n t (0,0) always l i e s on t h i s l i n e . With t h i s c o n s t r a i n t the p o s i t i o n i s sought f o r which no p o i n t on the <j)(k) curve f a l l s w i t h i n (to the lower l e f t of) the F(k/k ) curve. The s extreme p o s i t i o n of the F ( k / k g ) curve under these c o n d i t i o n s then defines the l a r g e s t value of e, e , c o n s i s t e n t w i t h the measure-max' ments, provided that Kolmogoroff's hypothesis i s v a l i d f o r the measured f i e l d . The p o i n t c o i n c i d e n t w i t h (0,0) i s t. 1/4 -3/4 . 1/4 5 / 4 w . , _ . _. n,x (l o g e v , log e v )(marked X i n Figure 16) and hence e may be c a l c u l a t e d . " max J k k The p l o t of log F ( ~ ) against log ^ — i s of course the s s " u n i v e r s a l curve" r e f e r r e d to e a r l i e r . 12 V e r t i c a l Heat Flux From a knowledge of temperature gradients i n a turbulent f i e l d upon which some mean gradient i s superimposed, i t i s possible to estimate the heat flux and resultant creation of entropy due to turbulent mixing. In the absence of heat sources or sinks, the temperature of a homogeneous, incompressible f l u i d may be described by |^+U.VT = — V2T, (16) d t p C ->• where T i s the temperature and U the vector v e l o c i t y of the f l u i d and K, p and c are thermal d i f f u s i v i t y , density and s p e c i f i c heat respec-t i v e l y . Within the p r e c i s i o n of the following c a l c u l a t i o n s we s h a l l f or s i m p l i c i t y set both p and c to unity f o r sea water and put T = T + 6 (17) and U = U + u, (18) i n which the bars denote averages over a volume of the f l u i d and 6 ->• and u are the f l u c t u a t i n g 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 usually approximately true f o r the ocean, and a steady state ,2 9 T 3 0 condition such that — = 0 and — — = 0, i t can be r e a d i l y shown that at o t a l l terms containing time derivatives or h o r i z o n t a l components of v e l o c i t y vanish and, with the further assumption that the v e r t i c a l 2 temperature gradient i s roughly uniform so that V T i s approximately zero, (16) reduces to 13 %w.V62 + w6 - K6V29 ( 1 9 ) 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 component of v e l o c i t y . Now i f we integrate over a range of depth large compared to the scale of temperature fluctuations which make the major contribution '2 2 to (VG): , the f i r s t term i n ( 1 6 ) w i l l approximately vanish and 6V 6 2 may be approximated by (V6) . We are l e f t with Z 2 -w9(T 2 - T ) * - KS (V9) 2dz ( 2 0 ) Z l z„-z„ or w6 = - 3KC — ) 2 — — , ( 2 1 ) 3 s T~-T~ 2 1 2 JB 0 2 to the p r e c i s i o n with which we can approximate (V6) by 3tp^*) ( a s would be the case i n a p e r f e c t l y i s o t r o p i c medium), s being some path through the volume. and 1^ are the mean temperatures at depths Z 2 " Z 1 z.. and z_ and 3 7 - ^ i s the r e c i p r o c a l of the mean temperature gradient. T -T 2 1 w0 i s the turbulent heat flux through the region neglecting, by our s t i p u l a t i o n of no heat sources or sinks, any contribution r e s u l t i n g from the degradation of turbulent energy to heat through the action of v i s c o s i t y . The corresponding rate of entropy generation i s given by *£|2i , ( 2 2 ) T which as before may be approximated by 3 14 INSTRUMENTATION General Sensors and instr u m e n t a t i o n f o r measuring turbulence i n the sea have been under development 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 some f i f t e e n years. E a r l y measurements were made s u c c e s s f u l l y i n prote c t e d in-shore waters where r e l a t i v e l y high l e v e l s of turbulence were generated by strong t i d a l c u r r e n t s , and surface motion was not a serious problem. The f i r s t s u c c e s s f u l attempts to work i n open ocean areas were made i n 1962 w i t h sensors mounted on a submarine, but, 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 of measurement, the only one a v a i l a b l e at the time was r e s t r i c t e d to about 100 meters i n depth and i t s a v a i l a b i l i t y was seve r e l y l i m i t e d by other tasks of higher p r i o r i t y . I have re-examined some of the 1962 data f o r comparison w i t h the r e s u l t s of more recent experiments, but only b r i e f mention w i l l be made i n t h i s t h e s i s . Subsequent measurements have been made w i t h sensors mounted on a submerged body, towed from a surface ship by a s e r v o - c o n t r o l l e d winch, capable of compensating f o r sh i p motion to an accuracy of about 30 centimeters i n body depth i n reasonable sea s t a t e s . The winch w i l l m aintain body depth at any de s i r e d value down to a l i m i t of about 330 meters imposed by the length of multi-conductor towing w i r e which i s a v a i l a b l e to us; o r , i n what I s h a l l r e f e r to as the " c y c l i n g mode", may be programmed to repeatedly vary depth at a constant r a t e over any predetermined depth i n t e r v a l ( t y p i c a l l y 6-30 meters) so t h a t , at constant towing speed, the body f o l l o w s a "saw-tooth" path through the water. C y c l i n g time i s v a r i a b l e and i n recent experiments has ranged from about 15 60 to 120 seconds. At our usual towing speed of 125 to 150 centimeters per second we would thus experience a forward advance of 75 to 180 meters per cycle. The array of sensors mounted on the towed body has evolved through a seri e s of configurations to the most recent arrangement as shown i n Figure 1, with the body secured i n i t s saddle, part way through the launching procedure. Protruding from the front of the body i s a c e n t r a l nose spar, below which a p a i r of platinum f i l m probes -one s e n s i t i v e to temperature and the other to 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. These probes w i l l be described i n more d e t a i l l a t e r . To the l e f t of 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 this view) on which i s mounted a v e r t i c a l s t r u t 61 centimeters long, carrying three thermistors -one at the top, one at the bottom, and one s l i g h t l y below center, at the l e v e l of the temperature and v e l o c i t y probes. These thermistors have a useful response up to about 40 Hz. On an outer concentric pipe around the base of the main nose spar are mounted ( i ) on top, a depth meter, ( i i ) to the r i g h t , a p r o p e l l e r type current meter to give the mean v e l o c i t y of the body through the water, and ( i i i ) below the current meter at the same l e v e l as the two probes, an inductance type conductivity meter for which the frequency response i s l i m i t e d by the flushing time of the head. This has not been measured p r e c i s e l y but the response should extend beyond 5 Hz at normal towing speeds. Figure 2 i s a closer view showing the center thermistor i n i t s protective housing, the two probes and, to the r i g h t , the head 16 of the 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 which 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 to the sensors, are enclosed i n pressure cases i n the towed body. From there, i n f o r m a t i o n from a l l sensors i s fed up an armoured multi-conductor towing cable f o r f u r t h e r processing and recording on the s h i p . The lower 100 meters of cable are f a i r e d to reduce v i b r a t i o n i n the s e c t i o n adjacent to the body. F a i r i n g of the e n t i r e length of cable would no doubt f u r t h e r reduce cable 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 mechanical problems of handling long lengths of f a i r e d cable have precluded t h i s measure. On board ship 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 channels. One i s a m p l i f i e d and recorded d i r e c t l y and the other 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 respect to time before r e c o r d i n g , i n order t o achieve an acceptable s i g n a l - t o - n o i s e r a t i o at the higher frequencies where both the response of the th 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 to the extent that the dynamic range a v a i l a b l e on a s i n g l e channel i s inadequate. The s i g n a l 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 three channels. The f i r s t of these which we r e f e r to as "A" channel i s recorded broad-band w i t h no f i l t e r i n g . The second or "B" channel i s again 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 to about 10 Hz and cuts o f f at about 20 Hz. "C" channel d i f f e r e n t i a t e s up to 1000 Hz and then cuts o f f . The s i g n a l from the temperature probe i s t r e a t e d s i m i l a r l y except that there i s a low-frequency c u t - o f f on A at about 0.01 Hz, and B extends up to about 100 Hz. Figure 3. Photomicrographs of t i p of v e l o c i t y probe (a) and temperature probe (b). (x70 approximately). Figure A. Close-up view of v e l o c i t y and temperature probes i n sea-going mounting with washing device. (Approximately l i f e s i z e ) . 17 Signal channels from a l l sensors together with coded timing signals and a voice commentary are recorded on two seven-channel magnetic tapes with multiplexing as required. At the same time selected channels are monitored on oscilloscopes as an a i d i n s e l e c t i n g appropriate gain s e t t i n g s , and twelve channels are recorded on two paper charts giving a permanent v i s u a l record, invaluable as a planning aid during the experiment, and for l a t e r use during 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 probes, being one of the unique features of the equipment, may be worth further mention. The active element of each consists of an evaporated platinum f i l m on a c o n i c a l glass t i p . E l e c t r i c a l connection to the f i l m i s made through leads embedded i n the glass stem. T y p i c a l configurations of the two types are shown i n Figure 3 at a magnification of about 70. For the 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 resistance thermometer. In the v e l o c i t y case the f i l m c o n sists of a narrow annular ring around the glass t i p and functions i n the manner of a hot wire 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 that r e s o l u t i o n of features down to perhaps 2 millimeters i n s i z e i s p o s s i b l e . With appropriate e l e c t r o n i c compensation i t i s possible to achieve a useful frequency response up to 1000 Hz. The two probes are shown i n close-up view i n Figure 4 , mounted and ready for use, with the washing device described below. 18 The v e l o c i t y probe i s , of course, extremely s e n s i t i v e to v i b r a t i o n , and extensive precautions have been taken to e l i m i n a t e excessive i n t e r f e r e n c e from t h i s source. Nevertheless v i b r a t i o n remains the l i m i t i n g f a c t o r i n the s e n s i t i v i t y of the v e l o c i t y system through a mid-range of the spectrum from about 1 Hz to 20 Hz. The other major d i f f i c u l t y i n the use of t h i s type of probe i n the r e a l ocean a r i s e s from the presence of pla n k t o n , and i t i s f o r t h i s reason that a l l s u c c e s s f u l measurements i n off-shore waters have been made during the w i n t e r months when the plankton co n c e n t r a t i o n i s minimal. When a plankton p a r t i c l e contacts the v e l o c i t y probe, or even passes cl o s e to i t perhaps, i t s e f f e c t i s to momentarily i n c r e a s e the e f f e c t i v e thickness of the boundary l a y e r over the f i l m . The record 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 decrease i n v e l o c i t y . Sometimes one w i l l s t i c k t e m p o r a r i l y but c l e a r i t s e l f a f t e r a second or two. O c c a s i o n a l l y one w i l l be captured permanently on the probe t i p , i n d i c a t i n g i t s presence by a sudden and p e r s i s t e n t decrease i n i n d i c a t e d mean v e l o c i t y . When t h i s happens i t i s necessary to clean the probe before meaningful measurements can be continued. A pump and system of p i p i n g have been developed f o r t h i s purpose, capable of generating a high v e l o c i t y reverse flow over the t i p of the probe, without reducing towing speed or otherwise i n t e r r u p t i n g the experiment. The outputs of the v e l o c i t y probe and the current meter are d i s p l a y e d s i d e by si d e and a v i s u a l watch i s kept on the two records. A p e r s i s t e n t discrepancy i s taken as an i n d i c a t i o n that the probe has become fo u l e d and a "wash" may then be accomplished w i t h i n a few seconds by manual c o n t r o l from the s h i p . 19 It is reasonable to assume that the temperature probe, being of similar size and shape, becomes fouled as frequently, on the average, as the velocity probe. Again the effective thickness of the boundary layer is increased and one would expect a drop in sensitivity in the upper part of the frequency spectrum, but there is no recognizable change in the visual output. The practice we have adopted, therefore, is to wash both probes whenever the velocity probe becomes fouled. Following this procedure, and i f i t i s assumed that for each probe the length of the time interval between contact with particles which stick is governed by a Poisson distribution 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 Moilliet (1968), the temperature probe can be expected to be clean 70 percent of the time. In earlier configura-tions with a separation of several centimeters between the probes, these assumptions were probably essentially true. In the most recent arrangement the two probes have been placed as close together as possible, with a lateral spacing of approximately 4 millimeters between tips. In this case, since many plankton organisms are 4 millimeters or more in their 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 particle every few seconds but i t may be necessary to wash the probes only two or three times an hour. It is thus possible to obtain records sometimes up to 30 minutes i n length with only minor contamination which w i l l have negligible effect on the spectral content of the velocity and temperature signals. 20 The sensitivity and frequency response of the velocity probe are determined from measurements in a water tunnel in the laboratory. The mean flow can be varied over the range of towing speeds, and at each of several flow rates the dynamic response is determined by vibrating the probe along the direction of flow with an electromagnetic driver. The shape of the response curve varies somewhat from probe to probe but generally i s essentially f l a t up to 50 or 75 Hz, then rises steadily up to 1000 Hz, which is the maximum frequency we attempt to measure. The sensitivity 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 essentially unchanged. The dynamic response of the temperature probe is determined by passing i t through the rising plume of warm water above a heated wire in 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 film, i t w i l l exhibit some sensitivity to fluctuations in the temperature of the water, and for this I have made no compensation. At zero frequency the sensitivity 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 is balanced at the beginning of a run, the ambient temperature at the probe is automatically taken into account and,'working below the thermocline, the mean temperature rarely changes enough that re-balancing is required. The dynamic response of the velocity probe to fluctuations in 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, 2 1 by a number of i n d i r e c t methods, the magnitude of p o s s i b l e e r r o r s from t h i s source. F i r s t of a l l i t seems u n l i k e l y that the temperature response at higher frequencies should be any grea t e r than i t i s at zero frequency, and one would expect i t to be l e s s , due to the e f f e c t of the boundary l a y e r . I t would not be s u r p r i s i n g i f the form of the response were s i m i l a r to that derived f o r the temperature probes by Fabula ( 1 9 6 8 ) i n which the amplitude response, r e l a t e d to the zero frequency response, i s given by Y = exp(-const / frequency), ( 2 4 ) o f o r a given mean temperature and mean v e l o c i t y . Looking at the 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 the r a t i o R of rms or 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 of cm sec ^  to corresponding f l u c t u a t i o n s i n tem-perature i n °C f o r s i g n a l s recorded at sea. In a mid-range of frequencies from 15 t o 75 Hz, covering the p o r t i o n of the v e l o c i t y spectrum i n which most of the energy d i s s i p a t i o n takes p l a c e , I have i n ten s e l e c t e d samples measured values of R ranging from 2 . 2 5 to 2 0 . One can conclude t h a t , over t h i s range of frequencies at l e a s t , the temperature s e n s i t i v i t y of the 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 than the zero frequency s e n s i t i v i t y , and cannot exceed something l i k e 2 cm sec per °C. To produce t h i s r e s u l t the constant i n the expression (Equation ( 2 4 ) ) f o r A / A q must be gr e a t e r than 0 . 2 5 ( i f t h i s e xpression i s v a l i d at a l l f o r the v e l o c i t y probe), 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 probes, which 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 the v e l o c i t y f i l m (see Figure 3 ) i s f a r t h e r from 22 the t i p of the cone and the boundary l a y e r over the f i l m w i l l be t h i c k e r than i n the case of the temperature probe. N e i t h e r i s i t a f o r t u i t o u s r e s u l t of course. I t was a primary c o n s i d e r a t i o n i n the o r i g i n a l design of the two probe types, - to minimize the response of each to the unwanted s i g n a l of the other k i n d . I have a l s o examined values of the dimensionless r a t i o , or skewness of the 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 at sea. Computed values range from -0.089 to -0.487 w i t h a mean of -0.237. Wind tunnel measurements by Stewart (1951) suggest a l i m i t i n g value of approximately -0.3 f o r high Reynolds number turbulence w i t h l a r g e r negative values f o r lower Reynolds numbers. In o b t a i n i n g the above values I have removed as much as p o s s i b l e of the noise i n our records by f i l t e r i n g , but p a r t of the d i f f e r e n c e from Stewart's values may s t i l l be accounted f o r by some remaining contamination by e l e c t r o n i c noise at higher frequencies and spurious s i g n a l s due to v i b r a t i o n at the lower frequencies. I t may be a l s o that some of the' samples I have used (12-30 seconds i n duration) are too s h o r t to g i ve a r e l i a b l e measure of skewness. I t i s these s h o r t e r samples that e x h i b i t most of the f l u c t u a t i o n i n skewness values as quoted above. Samples of 60 seconds or more i n length (of which I have examined only three) a l l give values c l o s e to -0.3 w i t h a mean of -0.319. Corresponding temperature s i g n a l s should, according to theory, e x h i b i t zero skewness and, i n f a c t , the values I have obtained range between plus and minus 0.1 w i t h a mean very c l o s e to zero. There are some recent experimental data, reported by Stewart 3/2 23 (1969), which i n d i c a t e that the skewness c o e f f i c i e n t of the temperature d e r i v a t i v e may not always be zero. The measurements i n question were made i n a tur b u l e n t atmospheric boundary l a y e r and gave skewness values as high as 1, using a s t a t i o n a r y sensor i n the mean flow. 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 oceanic s i t u a t i o n , the skewness of the observed temperature s i g n a l should depend on the 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 the d i r e c t i o n of mean shear, and the average from a number of randomly o r i e n t e d runs should not d i f f e r very much from zero. In any case, 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 expect them to d i f f e r more wide l y from Stewart's value of -0.3 than they appear t o . We are l e d to the conclusion that our v e l o c i t y s i g n a l s are at l e a s t predominantly r e a l v e l o c i t y without any major temperature component. I can advance only one other argument i n t h i s respect - a l s o q u a l i t a t i v e . Power s p e c t r a generated from our v e l o c i t y s i g n a l s do not ; 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 of 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 (Grant, Hughes, Vogel and M o i l l i e t (1968)) and the conclusion again i s that our s i g n a l must be predominantly due to v e l o c i t y f l u c t u a t i o n s . A l l of these arguments, although not c o n c l u s i v e , appear to be s e i f - c o n s i s t e n t . Even i f we assume the maximum temperature s e n s i t i v i t y of 2 cm sec ^ per °C as suggested 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 that 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 the 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 percent i n the region of the peak of the d i s s i p a t i o n Figure 6. Block diagram of conductivity meter electronics. 24 spectrum. Plotted on a logarithmic scale as we are in the habit of doing, (see Figure 1§, for example), this difference would be hardly noticeable. I shall proceed then on the assumption that the sensitivity of the velocity probe to fluctuations in temperature is usually not a factor of major significance, while bearing in mind at the same time that there may be situations in which i t cannot be neglected. Conductivity Meter I shall 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 in any previous publication. The design i s due primarily to R.W. Chappell of this laboratory. A cross section of the sensing head is shown in Figure 5 and a block diagram of the electronics in Figure 6. When in use the instrument i s towed in a direction from lef t to right in Figure 5. Water enters through the central hole or throat at the right and flows out through an annular orifice as shown. Three tubular struts cross the output orifice longitudinally, supporting the head and also providing access for e l e c t r i c a l connections to the sensing coils. A long tubular instrument case, not shown in Figure 5 but visible in Figure 1, contains the electronics. A l l body parts are of brass except the lucite sleeve (as indicated in Figure 5) at the center of the throat. The water path, through the throat and back around outside the head, forms an inductive link between two toroidal coils. One c o i l is fed with a 2 kHz signal from an oscillator of constant frequency and 25 constant amplitude. The output then, taken from the second c o i l , v a r i e s i n amplitude according to the r e s i s t a n c e of the water path. 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 passing through the second c o i l i n reverse d i r e c t i o n , can be ad-j u s t e d to give zero output f o r any d e s i r e d value of water c o n d u c t i v i t y . The phase s e n s i t i v e detector serves to determine whether any change from t h i s a r b i t r a r y zero i s p o s i t i v e or negative. The metal of 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 water path (broken by the l u c i t e sleeve at the center of the throat) and i t s r e s i s t a n c e i s there-fore important. I t was found t h a t the s t a b i l i t y of the instrument was improved considerably by applying 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 c o r r o s i o n e f f e c t s . C a l i b r a t i o n i s accomplished by immersing the head i n a s e r i e s of samples of water at known temperature and f o r which s a l i n i t y has been a c c u r a t e l y determined by other methods. Short term r e l a t i v e s e n s i t i v i t y i s b e t t e r than the e q u i v a l e n t of 0.005 i n a w i t h i n the s a l i n i t y and temperature range of our measurements. I do not have a good f i g u r e f o r long term s t a b i l i t y . The instrument has been used f o r only one operation at sea during which i t s u f f e r e d some mechanical damage during r e t r i e v a l of the towed body i n high seas. 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 there i s evidence t h a t i t s s e n s i t i v i t y was a l t e r e d s l i g h t l y at t h a t time. C a l i b r a t i o n s before and a f t e r the operation (about three weeks apart) show a s h i f t i n absolute accuracy equivalent to about 0.07 i n a , but the r e s u l t s of a n a l y s i s i n d i c a t e that most of t h i s change took place at the time of the accident. There i s every reason to b e l i e v e that s t a b i l i t y should be considerably b e t t e r than i n d i c a t e d by t h i s f i g u r e . T E M P E R A T U R E ( ° C ) 6 7 8 9 10 I I | 1 1 1 1 1 1 S A L I N I T Y ( % o ) 3 0 31 3 2 3 3 3 4 3 5 I 1 1 — : 1 1 1 1 2 4 2 5 2 6 2 7 2 8 2 9 I—n—s 1 1 1 — n Figure 7. Typical gross oceanographic structure for Sea Operation F-ll-67, from data taken at 1818 hours 21 November 1967. TEMPERATURE (°C) 6 7 8 9 10 1 1 1 1 1 1 SALINITY (%o) 30 31 32 33 34 1 1 1 1 1 1 24 25 —O i — °* — A — 26 1 x — 27 28 50 100 to rr UJ i -150 Q_ UJ O 200 250 300 o i o o I o I o I o O TEMPERATURE X SALINITY Figure 8. Typical gross oceanographic structure for Sea Operation F-l-69, from data taken at 0850 hours 3 February 1969. RESULTS 26 General Most of the results which w i l l be discussed here are derived from data obtained during two sea operations, - one i n November 1967 which I s h a l l r e f e r to as F - l l - 6 7 , and the second i n January-February 1969, designated F-l-69 - both c a r r i e d out i n water exceeding 1000 meters depth o f f the west coast of Vancouver Island, B r i t i s h Columbia. Figures 7 and 8 taken from standard b o t t l e casts i n d i c a t e t y p i c a l gross oceanographic structure i n the area during November 1967 and early February 1969 r e s p e c t i v e l y . In November the summer thermo-c l i n e i s decaying but s t i l l amounts to some 3°C between about 25 and 75 meters. In February 1969, towards the end of an unusually cold winter, the thermocline has disappeared almost completely while we s t i l l observe a s i g n i f i c a n t h a l o c l i n e between 100 and 200 meters or so. Most bathythermograph traces (which were taken more frequently than b o t t l e casts) show a small i r r e g u l a r i t y of 0.5 to 1.5°C, usually p o s i t i v e and then negative, between 75 and 150 meters, but nothing which can be consistently i d e n t i f i e d as a thermocline. A short sample of the paper records i s reproduced i n Figure 9. The f i r s t three traces s t a r t i n g from the top are d i f f e r e n t i a t e d s i g n a l s from the lower, center and upper thermistors r e s p e c t i v e l y . (For ease of i d e n t i f i c a t i o n on the f i g u r e s , the thermistors, from top to bottom as positioned on the towed body, are numbered 1,2 and 3). I t should be noted here that i n analysis of the experimental data and throughout the following discussion I s h a l l assume Taylor's hypothesis to be v a l i d . On t h i s basis time derivatives of temperature and v e l o c i t y are designated as space derivatives i n Figure 9, taking x as the d i r e c t i o n 27 of mean relative motion between the towed body and the water. The last trace on the four-channel chart is depth, designated d, illu 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 fi 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 division along the time axis is 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 is 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 in the figure, while depth increases downwards. The sample shown is 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 slightly exceeded the abi l i t y of the winch servo system to compensate, with resulting irregularities in 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 differentiated velocity channel (as usual) is quite noisy with a considerable level of interference from cable vibration 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 not c l e a r l y v i s i b l e i n t h i s r e production. I t w i l l be noted, however, that 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 occurrence 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 reverse i s not t r u e ; we o f t e n observe tempera-ture m i c r o s t r u c t u r e without any detectable turbulence. I n such cases there may be turbulence present at some l e v e l below our t h r e s h o l d of d e t e c t i o n , - or we assume that there must r e c e n t l y have been t u r b u l e n t mixing to generate the temperature s t r u c t u r e . I s h a l l have more to say on t h i s s u b j e c t l a t e r . Although i t i s more common to 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 ayered s t r u c t u r e , as i n Figure 10, we observe marked h o r i z o n t a l gradients of temperature and c o n d u c t i v i t y i n the sample shown i n Figure 9, as evidenced by changes i n the p a t t e r n of the records from c y c l e to c y c l e (of 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 are v e r t i c a l temperature i n v e r s i o n s throughout the length of the sample, notably i n the l a s t depth c y c l e at the l e f t where an i n v e r s i o n extends over most of the 30 meters of the depth e x c u r s i o n . (The two lower thermistors 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 overload at the bottom of t h i s c y c l e ) . In most cases, as we s h a l l see l a t e r , temperature i n v e r s i o n s of t h i s s o r t are 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 that the density gradient remains s t a b l e . Figure 10 shows another short s e c t i o n of s i g n a l from s e l e c t e d channels, t h i s time 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 observed. This sample was recorded from about 0222 to 0230 hours on 5 February 1969. & r -1 m X 2 ? 11 5:! C s i f \ 5 I II 7 Figure 10. Temperature and conductivity records from a cy c l i n g run at 152 meters depth. Horizontal gradients are small. 29 Time, i n t h i s case, progresses from l e f t to r i g h t . Mean operating depth was 152 meters and again the depth range was 30 meters i n the c y c l i n g mode. S t a r t i n g from the top of the f i g u r e , the f i r s t channel i s the d i f f e r e n t i a t e d s i g n a l from the upper thermistor followed by the d i r e c t s i g n a l from the upper, center and lower thermistors i n sequence. The maximum temperature v a r i a t i o n i s approximately 0.35°C. The next t r a c e i s c o n d u c t i v i t y (at the l e v e l of the center thermistor) and the l a s t , at the bottom, i s depth. A l l s i g n a l s i n c r e a s e upwards except depth, which as before increases downwards as depth should. The c y c l i n g p e r i o d i s approximately 115 seconds; the v e r t i c a l chart d i v i s i o n s marking 5 second i n t e r v a l s as before. In t h i s case h o r i z o n t a l gradients are much s m a l l e r than before and even very t h i n l a y e r s may extend f o r s u r p r i s i n g distances h o r i z o n t a l l y , although 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 the s m a l l l a y e r i d e n t i f i e d as (a) i n Figure 10 and ch a r a c t e r i z e d by a temperature approximately 0.03°C warmer than the water immediately above or below. By v i s u a l examination of the paper record t h i s l a y e r can be i d e n t i f i e d continuously f o r at l e a s t 1500 meters, over which range i t v a r i e s i n thickness from l e s s than 20 centimeters to between one and two meters. In a few cases, l a y e r s of . 10 centimeters and perhaps l e s s i n thickness are i d e n t i f i a b l e f o r at l e a s t 200 meters, and, at the other end of the 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 followed continuously 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 representing the dur a t i o n of our record and probably not 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 the mechanism of formation of t h i n l a y e r s , or "laminae" as they c a l l them, i s of i n t e r e s t 30 in 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 valid. Nevertheless we do observe clearly defined layers of this sort of thickness and, as I have said, up to at least 200 meters in horizontal 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 - far below the seasonal thermocline. One might suggest the possibility of the net transport of fl u i d which can take place when an internal wave propagates along a sharp density gradient. By visual examination of my data i t does appear that the very thin layers usually occur in the v i c i n i t y of strong and steep temperature gradients but, as I shall point out shortly, 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 is about the limit of resolution by the simple visual technique I have used for this purpose. There is finer detail in the data, but the identification of thinner layers, i f they exist, w i l l require a more sophisticated approach. I have already pointed out that small scale turbulence (or velocity microstructure) is always accompanied by thermal micro-structure and is presumably the cause of the thermal structure. It w i l l Figure 11. V e l o c i t y , temperature and conductivity records from a cy c l i n g run at 305 meters depth. Very l i t t l e micro-structure i s v i s i b l e . 31 be pertinent to l a t e r discussion to note here a l s o , i n both Figure 9 and Figure 10 - and i t i s generally the case - that thermal micro-structure almost always occurs i n regions of high mean temperature gradient - e i t h e r p o s i t i v e or negative. During our period of observation i n January - February 1969, regions such as depicted i n Figures 9 and 10 occupied perhaps 30 percent of the ocean volume from the thermocline down to our l i m i t i n g depth of j u s t over 300 meters. In November 1967 the proportion was noticeably higher - some 60 or 65 percent. The rest of the volume i s f i l l e d with f a i r l y regular gradients of temperature and s a l i n i t y corresponding roughly to the gross structure as derived from standard oceanographic casts, and containing only small scattered patches of microstructure at low i n t e n s i t y . To further i l l u s t r a t e the point, Figure 11 shows a t y p i c a l section of record from a region of uniform gradients. I t was recorded from about 1951 to 2006 hours on 5 February, 1969, during Operation F-l-69. The body was cycl i n g through 30 meters about a mean depth of 305 meters. A l l traces are the same as i n Figure 9. Here the temperature (and conductivity) gradients are quite uniform, but always i n small i r r e g u l a r steps of perhaps 0.002 to 0.02°C. I have never seen a t r u l y smooth gradient. The mean gradient i s approximately 7 x 10 °C per centimeter with temperature decreasing as depth increases. Horizontal gradients are very small. There i s always some temperature microstructure v i s i b l e on the d i f f e r e n t i a t e d thermistor traces (at the top) and t h i s almost always occurs within the steeper gradients of the small steps that we have 32 already examined. (Note t h a t there was some s l i p p a g e i n one of the chart d r i v e s , and, w h i l e the two records of Figure 11 are i n phase at the l e f t , they are d i s p l a c e d by almost a minute at the r i g h t ) . There i s nothing but noise on the v e l o c i t y channels and i t seems u n l i k e l y that there would be a c t i v e turbulence i n such an undisturbed region as t h i s . On the other hand, the temperature m i c r o s t r u c t u r e could not e x i s t f o r long without being continuously (or at l e a s t p e r i o d i c a l l y ) regenerated. One i s l e d to suspect t h a t , w i t h i n each of the s m a l l steps of temperature v i s i b l e on these r e c o r d s , there may 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 i n a continuous process of formation and re-formation as suggested by Stommel and Federov (1967), o r , w i t h i n each step perhaps, a dynamic process more akin to the d o u b l e - d i f f u s i v i t y connection discussed by Turner and Stommel (1964) f o r example. I have not attempted to i d e n t i f y the process (or processes) i n v o l v e d , but I b e l i e v e t h a t , from the data on hand, one might be able to derive some clues as to i t s nature. Figure 12 i l l u s t r a t e s an i n t e r e s t i n g occurrence which appears to be a very s h a r p l y defined " f r o n t " , or boundary between two water masses, s l o p i n g at about 1.5° to the h o r i z o n t a l along the path of the towed body. This sample was recorded from about 0327 to 0340 hours on 22 November, 1967, w h i l e c y c l i n g through 6.5 meters i n depth, about a s mean depth of 213 meters. The various channels of the record are i d e n t i -f i e d i n the same way as before. Temperature increases upwards and the maximum excursions i n t h i s s e c t i o n of record are approximately 0.25°C. Time, again, advances from l e f t to r i g h t , but each v e r t i c a l d i v i s i o n t h i s time represents 10 seconds i n s t e a d of 5. C y c l i n g time i s about 50 seconds. The 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 f i g u r e , w i t h the peaks of the t r a c e representing maximum depth. 33 For more than 15 minutes (or more than one k i l o m e t e r ) before the beginning of the s e c t i o n of record shown, the water i s almost p e r f e c t l y i s o t h e r m a l and, although the towing winch i s i n the c y c l i n g mode, the temperature traces are very n e a r l y s t r a i g h t . About one minute from the l e f t margin of the f i g u r e , the lowest thermistor touches colder water at the bottom of a c y c l e . Each c y c l e t h e r e a f t e r penetrates the c o l d e r water more deeply u n t i l , three c y c l e s l a t e r , the upper t h e r m i s t o r enters i t f o r the f i r s t time, and, by about the center of the f i g u r e , a l l thermistors remain i n the underlying body of cold e r water a l l the time. The boundary between the two bodies of water i s very sharp, and, w h i l e the warm upper water i s q u i e t , the water below the boundary i s s t r o n g l y t u r b u l e n t and contains intense thermal m i c r o s t r u c t u r e . One suspects that there must be v e l o c i t y shear across the boundary, but, u n f o r t u n a t e l y we have not yet been able to measure shear. Turbulent i n t e n s i t i e s below t h i s boundary are the highest so f a r observed below the thermocline. (Note f i r s t entry i n Table I ) . A p i c t u r e of the ocean begins to take form then, c o n s i s t i n g of f a i r l y e xtensive regions of uniform gradients corresponding more or l e s s to e a r l i e r ideas of the s t r u c t u r e of the ocean below the thermocline. In t e r s p e r s e d between or w i t h i n these uniform or " 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 one-half of the 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 regions which I describe 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 regions e x h i b i t an i r r e g u l a r temperature s t r u c t u r e , q u i t e unrelated to the mean gradients i n the area. They may vary i n thickness from a few meters to a few tens of meters and i n h o r i z o n t a l extent up to tens of k i l o m e t e r s and perhaps more. 34 The a c t i v e regions 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 centimeters to a few meters i n t h i c k n e s s , separated by t h i n boundary regions of r e l a t i v e l y steeper temperature gradients often exceeding 0.01 °C cm \ These l a y e r s and i n t e r - l a y e r boundaries may be 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 " and "sheets" as observed at shallower depths i n the Mediterranean. 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 t h a t , without compensation by other f a c t o r s , the s t r u c t u r e would be g r a v i -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 be q u i t e intense - sometimes 0.2 or 0.3°C w i t h i n a few centimeters. Scattered throughout the a c t i v e regions we f i n d patches of turbulence and thermal m i c r o s t r u c t u r e , u s u a l l y much sma l l e r (by a f a c t o r of 10 to 100) 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 patches, and u s u a l l y l o c a t e d i n or adjacent to the steeper temperature gradients of the boundary regions between l a y e r s . Comments by Stommel and Federov (1967) w i t h respect to the "patchiness" of turbulence i n the ocean reported by Grant, M o i l l i e t and Vogel (1968) are c e r t a i n l y v a l i d . More oft e n than not, i t seems, the l a y e r s (and boundaries) are d i s t o r t e d v e r t i c a l l y by what appear to be i n t e r n a l waves, and a h o r i z o n t a l sampling technique as used by Grant, et a l could obviously l e a d to i n c o r r e c t conclusions as regards patch ^ s i z e and d i s t r i b u t i o n . The turbulence we observe i s nevertheless patchy and i n t e r m i t t e n t , and a s t a t i s t i c a l examination of patch c h a r a c t e r i s t i c s and d i s t r i b u t i o n would be a rewarding study i n i t s e l f . I have not under-taken such an a n a l y s i s i n any q u a n t i t a t i v e d e t a i l . 35 F o s s i l Turbulence I have made the statement that turbulence i s always accompanied by temperature microstructure but that the reverse i s frequently not true. I have suggested further that the existence of temperature microstructure may be taken as an i n d i c a t i o n that, although there may be no measurable turbulence present, the region must have been turbulent i n the recent past, - otherwise the thermal structure would have decayed by conduction. Batchelor (1959) has constructed a theory describing 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 turbulent f l u i d , and the a p p l i c a t i o n of t h i s theory to the ocean environment has received s u b s t a n t i a l support from Grant, Hughes, Vogel and M o i l l i e t (1968) . Consider a turbulent s i t u a t i o n i n which the spectrum of tempera-ture f l u c t u a t i o n conforms to Batchelor's theory, and suppose that, at some stage, the turbulent mixing ceases. The smallest scales of micro-structure w i l l quickly die away by conduction, while the larger scales w i l l p e r s i s t for longer periods. The e f f e c t on the temperature spectrum w i l l be a progressive drooping at the upper end, s t a r t i n g f i r s t at the highest wavenumbers, and reaching farther back with time to lower and lower wavenumbers. The temperature structure l e f t behind a f t e r the turbulence has disappeared has been re f e r r e d to as " f o s s i l turbulence" or the "footprints of turbulence", - the l a t t e r term a t t r i b u t e d by Stewart (1969) to Markovin of Johns Hopkins U n i v e r s i t y . The two power spectra of temperature fluctuations p l o t t e d i n Figure 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 . Both spectra are taken from Operation F-l-69 while i n the cycl i n g mode i n a region containing many thin layers with sporadic patches of turbulence. The length 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. The two spectra are identified as coming from Tape 16 at 0300:10 hours and Tape 13 at 2141:20 hours, respectively. The sample from Tape 16 contained strong turbulence, as may be seen from the short section of the original record reproduced also in Figure 13, with differentiated channels of temperature and velocity indicated. The sample from Tape 13 contained no detectable turbulence. So far as I am able to t e l l , the velocity signal seen on the record i s entirely due to vibration. The spectral form predicted by Batchelor's theory is lai d over the spectrum from Tape 16, and the f i t is as good as we have any reason to expect. The f l a t portion at the high wavenumber end of the spectrum is due to electronic noise, and the sharp peak at log k = 1.3 is an artifact of the electronic equipment. The minor deviation from the theore-t i c a l curve before the spectrum flattens off into pure noise, i s probably also due to the presence of some noise mixed with the signal. The spectrum from Tape 13 has been shifted upwards by 0.24 in 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 characteristic at the high end that we would expect in a case of " f o s s i l turbulence", i f the ideas I have expressed above are valid. From the separation of the two curves and the thermal diffusivity of water, we can calculate a time - about half-an-hour in this case - since the region ceased to be turbulent. Having made the point I must admit that I am not really convinced that Figure 13 illustrates a genuine case of fossilized turbulence. The theory predicts a horizontal shift of the whole pattern 37 along the log k a x i s , according to the r a t e , e , of d i s s i p a t i o n of energy i n the t u r b u l e n t f i e l d , - and my s p e c t r a , because of the shortness of the samples, are not 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 at the high end and h o r i z o n t a l s h i f t of the whole curve. Perhaps Figure 13 simply i l l u s t r a t e s one sample co n t a i n i n g r e l a t i v e l y strong turbulence, and another i n which the turbulence, though s t i l l a c t i v e , i s at a l e v e l below our t h r e s h o l d of d e t e c t i o n . I b e l i e v e , however, that w i t h longer samples from which smoother s p e c t r a could be generated, i t should be p o s s i b l e to i d e n t i f y f o s s i l turbulence by the method I have described. Density S t r u c t u r e I t becomes a matter of some i n t e r e s t at t h i s p o i n t to examine the e f f e c t s of 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 "Instrumentation" t h a t the c o n d u c t i v i t y sensor should have a response e s s e n t i a l l y f l a t and un d i s -t o r t e d up t o about 5 Hz (at normal towing speeds) and i t i s c l e a r from the records t h a t the response does indeed extend w e l l beyond 10 Hz, although perhaps not p r e c i s l y f l a t . From the geometry of the sensing head and flow path, one would expect i t to begin dropping o f f s e r i o u s l y at something l i k e 30 Hz. No d e t a i l e d a n a l y s i s of the response of t h i s instrument has been undertaken because unf 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 other f a c t o r s i n the present a p p l i c a t i o n . As mounted on the towed body, the e f f e c t i v e center of the 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 centimeters l o n g i t u d i n a l l y and 33 centimeters l a t e r a l l y from the center t h e r m i s t o r which i s used to 38 provide temperature i n f o r m a t i o n f o r computing de n s i t y . Knowing the mean v e l o c i t y of advance, a c o r r e c t i o n f o r the l o n g i t u d i n a l displacement, to an accuracy of 10 percent or b e t t e r , can be inc l u d e d i n the computa-t i o n . In the presence of unknown h o r i z o n t a l s t r u c t u r e however, and reco g n i z i n g the p o s s i b i l i t y of some s m a l l "bank" angle of the body, there i s no way of c o r r e c t i n g f o r the l a t e r a l displacement. In computati of s a l i n i t y or density t h e r e f o r e , no r e l i a n c e should be placed 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 than perhaps f i v e times the spacing of sensors, or some 150 centimeters i n the l o n g i t u d i n a l d i r e c t i o n , corresponding to about 50 centimeters v e r t i c a l l y ( i n the c y c l i n g mode) or a frequency of about 1 Hz at our normal towing speed. For computation of density 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 operation a two-stage process which derives f i r s t a value 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 the ta b l e s p u b l i s h e d by the U.S. Navy Hydrographic O f f i c e i n H.O. P u b l i c a -t i o n No. 619 (1956). For t h i s s t e p , = G-28.3-0.8(T-4)  J U 0.839+0.02233(T-4) ' K J i n which T i s temperature i n °C S i s s a l i n i t y i n °/oo G i s c o n d u c t i v i t y i n m i l l i m h o s , gives a value f o r S accurate to ±.1% f o r a temperature range of 4—9°C and s a l i n i t y from 31-34 °/oo, which i s s u f f i c i e n t f o r a l l of our measure-ments. For the second stage a qu a d r a t i c f i t t o the t a b u l a t e d values i n H.O. P u b l i c a t i o n No. 615 (1952) leads to the f o l l o w i n g expression f o r a^: a = 23.8395-0.0921(T-4)-0.00584(T-4) 39 2 + (S-30) [o. 7395-0.00256 (T-4)^| , (26) i n which a , i n the usual oceanographic sense, i s defined 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 at speci-s,t,o s,t,o f i e d temperature, t , s a l i n i t y , s, and atmospheric pressure. R e s u l t i n g values f o r a are accurate to ±0.1% over the same range of temperature and s a l i n i t y . Combining (25) and (26) and rounding o f f the c o e f f i c i e n t s to the extent p o s s i b l e without l o s s i n o v e r a l l accuracy we get f i n a l l y 0.7935G-0.00256GL-0.10729L-.00491L2-.00013L3-2.4547, (27) a t 0.839+0.02233L i n which L = T-4. I t i s t h i s formula that I have used f o r a l l c a l -c u l a t i o n s of a . t Figure 14 shows a s e r i e s of p l o t s of a c a l c u l a t e d from the same s e c t i o n of record as shown i n Figure 10. Successive p l o t s , s t a r t i n g from the l e f t , correspond to s e q u e n t i a l h a l f c y c l e s i n depth, 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 to the r i g h t by 0.1 i n a from the previous one. The values shown f o r a are appropriate only to the f i r s t (incomplete) h a l f c y c l e at the l e f t . Since the u s e f u l r e s o l u t i o n of density f l u c t u a t i o n s i s l i m i t e d by the se p a r a t i o n of the temperature and c o n d u c t i v i t y sensors , most of the meaningless high frequencies have been removed by f i l t e r i n g . S t i l l , the s m a l l e s t s c a l e of f l u c t u a t i o n s i n Figure 14 and the 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 the body passes through steep gradients of temperature and/or s a l i n i t y , are probably unreal and should be ignored. o to CM cn CD i —< LO i cn u_ O J o i 2 O O CM *-> CM I — o cr CC U J Ln o UJ CE Q_ UJ cr CO t — oi * fie i 02'Ofil (Sb313W) H l d 3 0 oe *9fti ofi'2si os'esi 0 9 *Ti9I OL'Ol I cr z: aa <otn (13 00 'OfrTi 00'09h 00*08*1 00*005 00*029 (133J) Hld3Q OO'OfiS 00*09^ Figure 15. A r t i f i c i a l a profile corresponding to the f i f t h trace of Figure 14 but without the influence of salinity. 40 I b e l i e v e any features extending over 50 centimeters or more i n depth to be r e a l . The e f f e c t s of the steep gradients of temperature of Figure 10 are n o t i c e a b l y subdued i n the density p r o f i l e , being compensated l a r g e l y but not always completely, by corresponding gradients of s a l i n i t y . A few regions of minor i n s t a b i l i t y , amounting to some 0.02 or 0.03 i n a , remain uncompensated. I am confident that these are r e a l and indeed, 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 which I have computed p r o f i l e s of t h i s type. None i n my experience so f a r has exceeded 0.05 i n 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 density p r o f i l e , I have reproduced i n Figure 15 an a r t i f i c i a l a curve corresponding to the f i f t h t r a c e of Figure 14 as i t would 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 that 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 at the bottom). I t w i l l be observed that o c c a s i o n a l l y i n Figure 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. These r e v e r s a l s represent occasions on which, because i t was not i n proper adjustment, or because of excessive sea s t a t e , the servo c o n t r o l on the towing winch allowed the body depth to f l u c t u a t e momentarily. Some-times the traces overlap q u i t e n e a t l y . At other times, because of h o r i z o n t a l gradients or more l i k e l y because of i r r e g u l a r body motion when the servo loses c o n t r o l , the record shows a marked d i f f e r e n c e i n shape each time the depth increment i s r e t r a c e d . Beyond n o t i n g t h e i r existence I do not f e e l that any importance should be attached to these i r r e g u l a r i t i e s . 41 I t i s i n t e r e s t i n g to note t h a t w h i l e the temperature p r o f i l e may be very 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 , bearing no apparent r e l a t i o n to the mean temperature gradient i n the area, the mean slope of the density p r o f i l e i n a l l cases that I have examined corresponds q u i t e c l o s e l y ( b e t t e r than a f a c t o r of 2) to the mean density gradient as derived from oceanographic s t a t i o n s . I cannot make any more exact comparison i n t h i s r e s p e c t , because oceanographic s t a t i o n s were taken only once or twice a day during the experiment, and there may be a lapse of s e v e r a l hours (and tens of k i l o m e t e r s ) between the time of any p a r t i c u l a r sample and the time of the c l o s e s t s t a t i o n . I t has so f a r not been p o s s i b l e to r e l a t e the p r o b a b i l i t y of occurrence or the i n t e n s i t y of turbulence to any outstanding feature of the density s t r u c t u r e . 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 to occur i n s t r o n g l y s t a b l e , n e u t r a l or unstable regions. As already noted, however, temperature m i c r o s t r u c t u r e shows a strong preference f o r regions where the mean temperature gradient i s steep ( e i t h e r p o s i t i v e or negative) and turbulence, when d e t e c t a b l e , tends to occur where the temperature m i c r o s t r u c t u r e i s most i n t e n s e . Quite contrary to Woods' (1966-67) observation that turbulence i s of vanis h i n g 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 of occurrence of turbulence i n our s i t u a t i o n i s much great e r and maximum turbu 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 occur w i t h i n the steep temperature gradients between l a y e r s . I t i s f r e q u e n t l y i m p o s s i b l e , however, to i d e n t i f y these steep gradients of temperature on the density p r o f i l e s . 42 V e l o c i t y Spectra I have computed power s p e c t r a from a number of samples of v e l o c i t y f l u c t u a t i o n s recorded during Sea Operations F-ll-67 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 to work w i t h reasonably uniform samples of as long a d u r a t i o n as p o s s i b l e . There are, however, many hazards to be encountered i n the c o l l e c t i o n of data. Turbulence occurs i n patches w i t h i n l a y e r s - and there 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 next patch w i l l be. Many good samples are l o s t because of i n a p p r o p r i a t e gain s e t t i n g s , or gain changes made too e a r l y or too l a t e . Probe washes are necessary from time to time and may s p o i l an otherwise u s e f u l s e c t i o n of record. Any appreciable change i n ship's speed during recording w i l l d i s t o r t the r e s u l t i n g spectrum. When one compounds these inherent problems w i t h the g e n e r a l l y uncooperative nature of w i n t e r weather i n the north 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 mechanical f a i l u r e , operator e r r o r or other m i s f o r t u n e , one i s l e f t w i t h very few s u i t a b l e samples of any length to choose from. During Operation F-ll-67 we accomplished some 32 hours of recording i n two weeks at sea and i n Operation F-l-69 about 35 hours out of three weeks. From these raw data there are perhaps 20 or 25 samples, varying i n length from ten seconds t o two minutes, from which meaningful s p e c t r a might be derived. In the c y c l i n g mode, w i t h the t u r b u l e n t patches u s u a l l y confined to 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 three unusual cases. In the constant depth mode the chance of encountering a t u r b u l e n t l a y e r at a l l is lower than when cycling, but when one is 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 typical 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 latter at 2027:40 on 4 February 1969. The sample of Figure 16 was recorded in the cycling mode at a mean depth of 210 meters. Figure 17 comes from a constant depth run at 215 meters. The solid line in each case is the spectrum as computed from the raw signal. As noted earlier in the section on instrumentation, a considerable amount of low frequency noise i s generated by ship motion and vibration in the towing system. This i s the source of the large peaks of energy at low wavenumbers. At high frequencies, also where the spectral 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 is no detectable signal. This noise spectrum is then subtracted from the original and the resultant "noise-free" spectrum is plotted in small circles on the same axes, as in Figure 17. The technique works reasonably well in the high frequency range, but not so well at the low frequencies where the vibration tends to be 44 sporadic and noise l e v e l s vary g r e a t l y from moment to moment and wave to wave. The missing p o i n t s at the low frequency end of the c o r r e c t e d spectrum are o f f - s c a l e at the bottom of the page, representing occasions on which the noise l e v e l approached very 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 place no r e l i a n c e on the s p e c t r a l shape below about log k = -1 or k = 0.1, corresponding to an eddy s i z e of some 60 centimeters. The dashed curve drawn i n by hand i n each case (heavier dashed curve i n Figure 16) i s the " u n i v e r s a l curve" f i t t e d to the o r i g i n a l spectrum i n Figure 16 and to the n o i s e - c o r r e c t e d spectrum of Figure 17, by the method of Stewart and Grant (1962)(see Page 10). The kinematic 2 -1 v i s c o s i t y of the water i s taken as 0.0142 cm sec and the l i n e of slope +1 i s drawn through the p o i n t (v = 1.386, v~^ 4 = -2.31). A few p o i n t s have been allowed to 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 probable that the s c a t t e r , towards the low frequency end of the spectrum, i s due to the r e l a t i v e shortness of the sample and/or inadequate noise c o r r e c t i o n , and does not represent the t r u e s p e c t r a l l e v e l . N e i t h e r spectrum shows a c l e a r l y defined i n e r t i a l subrange w i t h -5/3 slope as p r e d i c t e d by theory, but i t i s easy to b e l i e v e that such a region e x i s t s i n both. For Operation F-l-69 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 devices were developed, and the spectrum from that operation i n p a r t i c u l a r , being somewhat cleaner i n the mid—frequencies, shows something very close to the p r e d i c t e d slope of -5/3 f o r a range of perhaps h a l f a decade i n k; 45 Energy D i s s i p a t i o n For 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 Equation (10) w i t h the f o l l o w i n g r e s u l t s : e(ergs sec '''cm 3) U n i v e r s a l Curve Equation (10) Figure 16 2.75 x 10~ 3 2.94 x 10~ 3 Figure 17 1.74 x 10~ 4 2.52 x 10" 4 ' I t i s obvious why the value of £ derived from Equation (10) i s l a r g e r i n each case. While the s p e c t r a f i t the u n i v e r s a l curve reasonably w e l l through the higher wave number region of what appears to 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 begin to deviate before the peak of the d i s s i p a t i o n curve i s reached (where the slope of the energy spectrum on t h i s l o g - l o g p l o t i s -2) and at higher wavenumbers l i e w e l l above the u n i v e r s a l curve. This has been the p a t t e r n i n most of the turbulence s p e c t r a from the open sea, 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 inshore waters as reported by Grant, Stewart and M o i l l i e t (1962) and Grant, Hughes, Vogel and M o i l l i e t (1968), many of which match the u n i v e r s a l curve 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 searching f o r a b e l i e v a b l e e x p l a nation of the d i f f e r e n c e , without f i n d i n g any c l e a r answer. There are, 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 , which to preserve c o n t i n u i t y of argument here, I s h a l l leave f o r d i s c u s s i o n i n a separate s e c t i o n . In the meantime i t i s not unreasonable to regard the d i s s i p a t i o n values derived from the f i t of the u n i v e r s a l o r H c O • H U cd W T 3 cu 4-> U CU u u o a cu CD • H o 53 4-1 o cu Cu cl PS ca ^ ! <U 4J 4-) A, a) cu e CO i d r H 4J O a CO u g e m ca cu co 0) > a cd co u CU > • r l B cu CU cd n CO CO CO CO i r o 1 o> !• <-1 CM 1 r~-l a» I* vo VO m co m • • • • • • r H CN CM CO - 3 -CO I oo I I CTi CM CO CO I I O CO o r -C M i - l I C M CM CO ( i • <- CO 1 • CO i 1 O i n 1 <N 1 r H 1 CO 11 r H 1 CT\ 1 m 1 r H 1 r H m r H CO m CM a\ m • • • • • • • • • • • i—1 CM VO CO CM CM r H r H CM CM CO CO CO oo oo <f CM CM CM CM r H r H CM CM r H r H r H m m m m r H t H <r oo oo CM CM CM t H r H CM CM CM r H r H r H r H VO vO VO 00 00 O C M C M m C M i n C M m CM m C M C M m m m o r H C M m C M m C M m CM m CM m o m i n o O m O o m o o 00 O CO m o O o o r H m CO o <r CM r H o CM O co r H CO m oo oo O CO o • H r^. m oo r~~ a\ CO CO CO CO CO CM CM CM m o ;o r H o o CM CO <r CO CO CO o r H o o o CM CO CO CO o o o r H r H o o o CM CM CM CM CM o o o O r H r H r H r H r H vO vo C M C M C M C M VO CM CM vo <N C M vo CM CM VO C M Ov vO C M av VD C M CTv VO C M m cy> v o C M m vo C M m vo C M m vo C M m <7> vo C M m vo C M m C M vo r H 00 C M vO r H 00 TABLE I: Energy D i s s i p a t i o n Rates 46 curve and from Equation (10) as lower and upper l i m i t s , d i f f e r i n g by a factor ranging from s l i g h t l y greater than 1 to ij.ust over 2, which a f t e r a l l i s not a large f a c t o r , compared to the many other uncertainties of t h i s game. For most of the s u i t a b l e samples a v a i l a b l e I have obtained d i s s i p a t i o n rates by f i t t i n g the universal curve. In a few cases I have gone through the procedure of correcting for background noise, but noise l e v e l s through the range of maximum d i s s i p a t i o n are usually such that the correction makes only a small difference to the value obtained for e. For those samples for which there i s not too much sca t t e r of points i n the c r i t i c a l part of the spectrum I have, as above, obtained a second value for E from Equation (10). The r e s u l t s are summarized i n Table I, where for convenience I have w r i t t e n 1.90 x 10 , for example, as 1.90-2. The values shown are arranged i n chronological order, except the l a s t two which come from one of the deepest submarine runs of Operation F-ll-62 and are included here for comparison only. To make some sort of estimate of mean and t o t a l turbulent d i s s i p a t i o n of energy, I have, using the computed values of Table If as a guide, v i s u a l l y scanned a l l the paper records from Operations F - l l - 6 7 and F-l-69, estimating the t o t a l percentage of time (which I i n t e r p r e t as a per-centage of the volume) that turbulence was present, arid have divided the t o t a l percentage i n t o three categories on the basis of i n t e n s i t y -high, medium and low. T o t a l percentages are p l o t t e d i n Figure 18 as a function of depth, with each point representing one run - the o o ox «8 ro o o X v -O CM OO oo X X XX XX X X o xo o x X X o o x o x ^Xo X O X o o X i X X X o CO cr UJ o i -00 Ld 2 I r-Q. o CM o (0 _L_ L o CD o o CM Figure 18. Percentage of ocean volume that is turbulent, as a function of depth. The circles are for F-ll-67 runs and the crosses for F—1-69 runs. Estimated Turbulence Level Percentage F-ll-67 Turbulent F-l-69 Dissipation ^ (ergs cm sec ) 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 of volume that i s turbulent and estimated d i s s i p a t i o n rates. 47 duration of a magnetic tape or approximately one hour. The circles are for F-ll-67 and the crosses for F-l-69. Then, for each operation separately, I have taken percentages, averaged over a l l runs for each of the three levels of intensity. The results are set down in Table IT with estimated dissipation 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 particularly in 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, Moilliet and Vogel (1968) but I have not included these data because, as I have suggested, the mechanism of generation i s probably quite different in this region. The method is admittedly rough and subjective i n certain aspects, but I believe the results to be valid within about 20 percent. The crosses of F-l-69 in Figure 18 seem to indicate a decrease in the total percentage of turbulence with increasing depth. The circles 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 significant trend with depth. Looking at the two sets of data together i t is probably safe to say that there is some decreasing trend with increasing depth. In any case I cannot with these data, confirm the apparent increase in the occurrence of turbulence between 250 and 350 meters reported by Grant, Moilliet 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 criticism. Nevertheless I thought i t 48 might be amusing to 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 of t i d a l energy took place p r i m a r i l y through bottom " f r i c t i o n " i n shallow areas, and come to the conc l u s i o n that t h i s 19 -1 process alone cannot account f o r more than 10 ergs sec . A s t r o -19 -1 nomical observations c a l l f o r a t i d a l d i s s i p a t i o n of 3 x 10 ergs sec and they p o s t u l a t e that perhaps "the energy of the surface t i d e s i s e f f e c t i v e l y converted i n t o i n t e r n a l wave motion and then d i s s i p a t e d w i t h i n the ocean volume." Using the values from Table II as r e p r e s e n t a t i v e of the deep oceans of the w o r l d , and making the assumption that the average d i s s i p a t i o n decreases by a f a c t o r of two f o r each 300 meter i n t e r v a l of depth, we get f o r the p e r i o d of Operation F - l l - 6 7 a t o t a l worldwide 19 -1 d i s s i p a t i o n r a t e of j u s t 2 x 10 ergs sec which, s u r p r i s i n g l y enough, i s e x a c t l y the d i f f e r e n c e we are lo o k i n g f o r between Munk and MacDonald's estimate of the maximum d i s s i p a t i o n i n shallow seas and the t o t a l r e q u i r e d . The observations of F - l l - 6 7 were taken during a p e r i o d of moderate s p r i n g t i d e s . S i m i l a r l y the f i g u r e s from Operation F - l - 6 9 , during a p e r i o d of t i d a l d e c l i n e from s p r i n g to neap, lead to a t o t a l 19 -1 d i s s i p a t i o n of 1.3 x 10 ergs sec . The answers seem to be e n t i r e l y c o n s i s t e n t and of the r i g h t order of magnitude although, as I have pointed out, they are 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 observation which may help us to b e l i e v e that at l e a s t some of the energy of the turbulence may be of t i d a l o r i g i n . During the p e r i o d of data recording i n F - l l - 6 7 there was no apparent trend 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 amplitudes were approximately constant. During F-l-69 on the other hand, there was 49 a n o t i c e a b l e decay i n turbulence l e v e l s at a l l depths as t i d a l a mpli-tudes d e c l i n e d from s p r i n g to neap. Having made the poi n t I must q u i c k l y go on to say that I do not t h i n k much importance should be attached to i t - n o t , at l e a s t , u n t i l f u r t h e r experimental evidence i s a v a i l a b l e . I t i s , a f t e r a l l , based on only two observations and may be q u i t e c o i n c i d e n t a l . Furthermore there were other f a c t o r s which tend to complicate the p i c t u r e . F i r s t l y , the l o c a l e of the experiment changed by some 200 k i l o m e t e r s during the p e r i o d that t u r b u l e n t i n t e n s i t i e s were observed to decrease i n the l a t t e r part of F-l-69, and there may be a geographical v a r i a t i o n i n v o l v e d . Secondly, there was a moderate storm on 3-4 February 1969 w i t h winds of 40 knots and over. Heavy seas b u i l t up and no measurements were p o s s i b l e . The storm was followed by three days of l i g h t winds ( l e s s than 10 knots) and the experiment was resumed l a t e on 4 February. At that stage r e l a t i v e l y high l e v e l s of turbulence were observed at a l l depths, and i t was during the f o l l o w i n g three days of r e l a t i v e calm that the l e v e l decreased s t e a d i l y and q u i t e conspicuously throughout the volume as the sea s t a t e died down - w h i l e at the same time t i d a l amplitudes were decreasing. I t seems u n l i k e l y that even q u i t e v i o l e n t s urface disturbances could produce turbulence by d i r e c t mixing a c t i o n at depths as great as 300 meters. I t may be p o s s i b l e , however, that surface a c t i o n could generate i n t e r n a l waves at such depths, and i f we suggest then t h a t , under appropriate circumstances, these i n t e r n a l waves might break (as has been observed and photographed by Woods (1966-67) at shallower depths i n the Mediterranean) we might expect to produce the s o r t of 50 s p o r a d i c a l l y o c c u r r i n g patches of turbulence t h a t we observe along a boundary between l a y e r s . Our observations seem to be c o n s i s t e n t w i t h ideas of turbulence generation by i n d i r e c t a c t i o n of surface winds and a l s o by conversion of t i d a l energy. Perhaps both mechanisms c o n t r i b u t e . Each supposes an intermediate stage during which the energy i s contained 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 the presence of i n t e r n a l waves i n and below the thermocline. For example the short h o r i z o n t a l bars on Figure 14 mark the upper l i m i t of an almost v e r t i c a l s e c t i o n near the center of each density p l o t . 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 wave w i t h an amplitude of about 5 meters and apparent wavelength of 700 or 800 meters. No r e l i a b l e estimate of r e a l wavelength can be made, si n c e the d i r e c t i o n and v e l o c i t y of propagation w i t h respect to the ship's course and speed are not known. The wave-like p a t t e r n , however, continues f o r some distance i n both d i r e c t i o n s beyond the l i m i t s of Figure 14. I t i s probable a l s o that shear v e l o c i t i e s e x i s t between la y e r s (again t h i s has been observed by Woods (1966-67) i n the Medi-terranean) and we may speculate that i n s t a b i l i t y occurs from time to time and from place to place 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 the a c t i o n of i n t e r n a l waves, and the l o c a l Richardson's number becomes unstable. U n f o r t u n a t e l y , as I have s a i d , although our v e l o c i t y probe has the re q u i r e d s e n s i t i v i t y , i t has so f a r not been p o s s i b l e to measure shear between l a y e r s because of excessive noise l e v e l s at low frequencies. The F i t of 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 explanation of the f a c t that none of our deep sea s p e c t r a f i t the " u n i v e r s a l curve" at high 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 considered 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) Intermittency of the turbulence s i g n a l . (d) V a r i a t i o n s i n speed during r e c o r d i n g . (e) Contamination 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 considered together. The theory behind the u n i v e r s a l curve assumes a high Reynolds number and i s o t r o p i c turbulence. Below the thermocline we have found that turbulence occurs i n patches, 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 probably accommpanied by (and d r i v e n by) v e l o c i t y shear. One would not expect the Reynolds number t o be high and, i n the l a r g e r s c a l e s at l e a s t , one would not expect i s o t r o p y . According to current ideas of the mechanism of turbulence however, pressure forces i n the f l u i d (see Batchelor (1953), page 88), tend to e q u a l i z e the d i r e c t i o n a l components and thus erase 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 forces act to d r i v e the "cascade" of energy from low wavenumbers to higher wavenumbers. We should t h e r e f o r e approach more and more c l o s e l y to i s o t r o p y as we move upwards i n wavenumber and, i f our spectrum was to f i t the u n i v e r s a l curve at a l l , the region of best f i t should be at 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 widening 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 fit t e d the universal curve properly arid that i t should be shifted up to the position of the lighter 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 experi-menters - in particular Stewart and Townsend (1951). Looked at in this way, our spectra show none of the established characteristics of low Reynolds number turbulence and my conclusion, without going through the analysis in detail, is that we cannot explain away our d i f f i c u l t y in this manner. "Intermittency" (c) is one of the well known characteristics of turbulence. Even in a fully developed turbulent f i e l d there tend to be regions of activity interspersed with regions of quiescence, and the energy associated with the larger wavenumbers is unevenly dis-tributed in space. Grant, Stewart and Moilliet (1962) have discussed the effect of intermittency on the shape of the energy spectrum and point out that the result should be some reduction in curvature at the "knee" - the transition region between the i n e r t i a l subrange and the region of viscous dissipation - and this in fact is what we observe. They conclude, however, that the degree of intermittency in their samples, recorded in in-shore t i d a l waters has a negligible effect on the shape of their spectra. We might speculate that, for some reason which is not immediately clear, the degree of intermittency in our off-shore, deep-water samples is much greater and the effect correspondingly magnified. To check this possibility, I have taken two 52 second samples, one from 20 r-UJ o z UJ CC cc O o o u. o cc UJ GO 3 16 81 100 200 300 ' 400 PERCENTAGE OF MEAN 500 (a) Sample F-6-67 Tape 2 1513:30 10 June 1967 30 r— c/> 25 UJ o z Ul cc 20 CC o o o u. o 15 5 10 m 100 200 300 PERCENTAGE OF MEAN 400 500 (b) Sample F-l-69 Tape 19 1005:00 5 February 1969 Figure 19. Distribution of turbulent dissipation densities for successive short intervals within two 52 second samples. 53 an e a r l i e r in-shore operation (F-6-67) which f i t s the un i v e r s a l curve very c l o s e l y , and the other from F-l-69, with an extreme m i s f i t . I have divided each i n t o 64 sections and computed a value of e for each section. The d i s t r i b u t i o n of e as a percentage of the mean i s shown f o r the two samples i n Figure 19 (a) and (b). The two d i s t r i -butions are s i m i l a r and the grouping i s even a l i t t l e b i t closer for our F-l-69 sample than for the other. I am not quite sure how one defines intermittency quantita-t i v e l y , but i f what I have done i s a r e l i a b l e method of estimating the degree of intermittency i n a q u a l i t a t i v e or comparative way, then i t seems clear that intermittency i s not the cause of our problem. Variations i n towing speed (d) during the length of a sample w i l l have a s i m i l a r e f f e c t on the shape of the spectrum p l o t t e d on log-log axes. Towing speed determines the p o s i t i o n of the spectrum on the log k axis, and changes i n speed w i l l cause i t to s h i f t back and fort h without changing shape. The shape of the average spectrum w i l l , however, be a l t e r e d , and the e f f e c t again w i l l be a reduction of curvature i n the t r a n s i t i o n region. Even i f the ship's speed i s held constant there may be an appreciable v a r i a t i o n i n speed of the towed body, depending on sea st a t e . The winch i s designed to maintain constant depth and i n doing so can introduce fluctuations i n forward v e l o c i t y -an e f f e c t which would not be present, or would at least be much smaller, for e a r l i e r measurements taken i n protected coastal waters. I have examined speed v a r i a t i o n s over the length of three samples which show major deviations from the univer s a l curve at high wavenumbers. In these three samples the v a r i a t i o n never exceeded 10 percent of the mean speed and might produce an e f f e c t j u s t barely v i s i b l e on our spectra. I t could not by a large f a c t o r produce the Ii Figure 20. Velocity and temperature spectra from cycling run at 213 meters depth, il l u s t r a t i n g possible effects of buoyancy forces on spectral shape. Figure 21. V e l o c i t y and temperature s p e c t r a from constant depth run at 64 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 forces~'bn s p e c t r a l shape-.-'' 54 e f f e c t observed. There i s always the p o s s i b i l i t y of error (g) i n my procedure (using a version of the Fast Fourier Transform) for computing power spectra. I have, however, checked a l l steps very c a r e f u l l y and I am able to reproduce p r e c i s e l y spectra which have been computed indepen-dently arid by quite d i f f e r e n t methods. I do not bel i e v e the discrepancy i s due to error or improper technique. I have already discussed the question (e) of 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, and concluded that the e f f e c t would be n e g l i g i b l y small through the wavenumber range of maximum d i s s i p a t i o n . At higher wavenumbers the magnitude of the e f f e c t i s i n some doubt. Two p a i r of spectra - v e l o c i t y and temperature - are p l o t t e d on common log k axes i n Figures 20 and 21 for samples as indicated from Operations F - l l - 6 7 and F-l-69 re s p e c t i v e l y . The u n i v e r s a l curve i s f i t t e d to the noise-corrected v e l o c i t y spectra by the method described e a r l i e r and the t h e o r e t i c a l spectrum of temperature fl u c t u a t i o n s (heavier dashed l i n e ) derived by Batchelor (1959) i s f i t t e d to the experimental temperature spectra as described by Grant, Hughes, Vogel and M o i l l i e t (1968). The sharp r i s e at the high end of the temperature spectra i s due to e l e c t r o n i c noise i n the system, but before the r i s e there i s a noticeable deviation from the Batchelor curve, - and we notice a s i m i l a r deviation i n most of the oceanic temperature spectra published by Grant, et a l (1968). I f we bel i e v e that the spectrum r e a l l y follows the t h e o r e t i c a l curve and that the deviation i s the r e s u l t of noise, then i t i s clear that the temperature fl u c t u a t i o n s 55 are d i s s i p a t i n g much too f a s t to cause the observed d i f f e r e n c e between the u n i v e r s a l curve and the v e l o c i t y spectrum at the highest wavenumbers. I f , on the other hand, the d e v i a t i o n i s r e a l and the temperature spectrum i n f a c t does not drop o f f as f a s t as p r e d i c t e d by theory '(and again we might blame i n t e r m i t t e n c y i n the 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 that temperature contamination could be the cause of the discrepancy i n the v e l o c i t y s p e c t r a at the hi g h e s t wavenumbers (or could at 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 ) but no t , as I have s a i d , i n the v i c i n i t y of the peak of the 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 at my present stage of a n a l y s i s . We are l e f t to consider ( f ) , the p o s s i b l e e f f e c t s of buoyancy f o r c e s . I f by some means which need not be s p e c i f i e d , turbulence i s generated i n a s t a b l e density g r a d i e n t , some work must i n i t i a l l y be done against g r a v i t y , and energy w i l l be e x t r a c t e d from the turbulence at s m a l l wavenumbers. At some l a t e r stage i n the mixing process, s m a l l 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 the region and buoyancy forces w i l l tend to d r i v e a secondary mechanism to r e s t o r e s t a b i l i t y . One may speculate that at high wavenumbers the 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 the true t u r b u l e n t v e l o c i t i e s . Or, t a k i n g another view, we develop a somewhat more co m p l i -cated model. I t i s not uncommon to f i n d a v e r t i c a l s t r u c t u r e i n which compensating temperature and s a l i n i t y gradients r e s u l t i n n e u t r a l or ne a r - n e u t r a l 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 there 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 of heat and s a l t , however, d i f f e r by some two orders of 56 magnitude, and i n due course the temperature fluctuations w i l l die away by conduction at the higher wavenumbers, leaving the more p e r s i s t a n t s a l i n i t y f l uctuations with corresponding i n s t a b i l i t i e s and restoring forces. For a f i e l d i n which small density fluctuations e x i s t , the v e l o c i t y of p a r t i c l e s subject to buoyancy forces w i l l be very small and for the sort of order-of-magnitude c a l c u l a t i o n which I propose to undertake I be l i e v e i t i s safe to ignore accelerations i n the upper wavenumber range with which we are concerned, where the turbulence Reynolds number i s known to be low. Any p a r t i c l e of f l u i d then w i l l be i n equilibrium under the influence of two equal and opposite accelerating forces, one due to gravity and the other to v i s c o s i t y . I f we represent by <j>(k), ^ ( k ) , and i(>(k) s p e c t r a l density functions of v e l o c i t y , density 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 sense that density fluctuations described by f2(k) , corresponding to a temperature f i e l d defined 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 defined by <j>(k), i t can be r e a d i l y shown that V(k) -£&|4 , (28) k v p i n which g i s the acceleration of gravity and p i s the mean density of the medium (which I s h a l l take as unity for sea water, as a reasonable approximation for the purpose of t h i s a n a l y s i s ) . The three spectrum 3 -2 functions w i l l i n a l l cases be i n units of cm sec for v e l o c i t y , gm^cm for density and °C 2 cm for temperature, but to avoid frequent r e p e t i t i o n i n the next few paragraphs I w i l l quote only numerical va l u e s . Consider f i r s t the p o s s i b i l i t y that the density f l u c t u a t i o n s are due s o l e l y to v a r i a t i o n s i n temperature. The temperature depen-dent v a r i a t i o n i n density i s approximately 0.1 i n a per °C, or «(k) = 10" 8Kk), (29) Now i n Figure 21, f o r example, i f we take <j>(k) as d e s c r i b i n g the excess of the measured v e l o c i t y spectrum over the u n i v e r s a l curve (the d e v i a t i o n which we are attempting to e x p l a i n ) then at log k = 0 (or k = 1, corresponding to a s c a l e of about 6 centimeters) <f>(l) _3 i s approximately 2 x 10 . From the temperature spectrum, ijj(l) i s -4 roughly 2.2 x 10 and from (28) and (29) t h i s would give us a _2 cf)(l) of 1 x 10 - which i s more than we r e q u i r e to e x p l a i n the v e l o c i t y excess, by a f a c t o r of 5. S i m i l a r l y at l o g k = 0.5 (k - 3 and a s c a l e of about 2 -4 centimeters) $(3) = 2.7 x 10 . The corresponding tj>(3) i s about 2.8 x 10 which by the same argument would produce a <j>(3) of 1.7 x 10 - which i s too s m a l l . We may however, at t h i s stage, invoke the i d e a of d i f f e r e n t i a l d i f f u s i v i t i e s of heat and s a l t . By Batchelor's theory the value of k at which 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 -mining 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 propor-t i o n a l to the square root of the d i f f u s i v i t y . I have attempted to approximate t h i s e f f e c t by s l i d i n g Batchelor's curve outwards along i t s i n i t i a l slope of -1 to p o s i t i o n the "knee" one decade f a r t h e r out i n k - the l i g h t e r dashed curve i n Figures 20 and 21. Now, from a water 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 density f l u c t u a t i o n s 58 l e f t behind a f t e r the 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 of the 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 of temperature alone, i f there had been no s a l i n i t y s t r u c t u r e . I t seems safe then, f o r the present purpose, to consider t h i s extended Ba t c h e l o r curve as s t i l l r e presenting temperature f l u c t u a -t i o n s , but of a more p e r s i s t a n t k i n d . In t h i s case, s t i l l at log k = 0.5 we get i^(3) = 8 x 10 and t h i s should give us a <J>(3) of 5 x 10 ^, which again 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 . Again at log k = 1 (k = 10 and a s c a l e of 0.5 centimeters) cj)(10) = 2.8 x 10 and (from the extended curve) ip(10) = 2.2 x 10 l e a d i n g to a <J)(10) of 1 x 10 which i s much too s m a l l . For two reasons I do not f i n d i t d i s t u r b i n g that t h i s r a t h e r crude approach i n d i c a t e s an over-coi?rection at lower values of k. F i r s t l y , the c a l c u l a t e d v e l o c i t i e s due t o buoyancy forces 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 our experiments 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 of convective c e l l s w i l l of course be set up by the 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 which one would expect to be sm a l l e r i n general (and probably w i t h a d i f f e r e n t s p e c t r a l shape) than the v e r t i c a l v e l o c i t i e s which d r i v e the convection. How much s m a l l e r , I have not attempted to estimate. Secondly, I have assumed (a) that temperature was the only c o n t r i b u t i n g f a c t o r at log k = 0 and (b) tha t a l l the temperature s t r u c t u r e had decayed at lo g k = 0.5. In 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 combination of temperature and s a l i n i t y , and there i s obviously some temperature component l e f t at l o g k = 0.5. I t i s not d i f f i c u l t , then, to b e l i e v e that the e f f e c t could be r e a l and that i t 59 could produce the observed difference 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 large wavenumbers, where the a v a i l a b l e correction seems to be too small, i s less s a t i s f a c t o r y . To produce the observed value of <K10) = 2.8 x 10~6 would require, from (28) ft(10) = 5.6 x 10~ 1 2 —6 or fluctuations of 7.5 x 10 i n density. I am w i l l i n g to b e l i e v e that density f l u c t u a t i o n s of t h i s magnitude and scale might e x i s t , but i t i s d i f f i c u l t to explain how they could a r i s e , on the basis of the data we have on hand. Without including the numbers here, a p a r a l l e l analysis of the example of Figure 20 y i e l d s s i m i l a r r e s u l t s but with a somewhat larger under-correction at high wavenumbers. Further examination of t h i s phenomenon ( i f i t i s real) should be the subject of a separate study. For the present, although i t does not appear to be a complete answer, there seems to b.e a good basis on which to suggest that a secondary convective process, driven by buoyancy forces, may be the primary cause of the discrepancy between our v e l o c i t y spectra and the u n i v e r s a l curve through some mid-range of wavenumbers. My best guess at t h i s time i s that the temperature s e n s i t i -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 contributing factor at higher wavenumber, l i f t i n g the v e l o c i t y spectrum even higher than can be explained by buoyancy forces alone. The fact that spectra from in-shore waters have usually not shown t h i s e f f e c t - at least not to the same degree - i s not incon-s i s t e n t . Those experiments were c a r r i e d out generally i n w e l l mixed waters with a higher l e v e l of turbulence and r e l a t i v e l y lower temperature 60 and density g r a d i e n t s . Both temperature contamination of the 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 forces should the r e f o r e be l e s s apparent. In f a c t i t has not been uncommon f o r v e l o c i t y s p e c t r a to show some excess over the u n i v e r s a l curve at h i g h wavenumbers. F i n a l l y , a re-examination of some 1967 data (Operation F-6-67) from in-shore waters , w i t h high t u r b u l e n t i n t e n s i t i e s and low "noise" l e v e l s , r e v e a l s that s e v e r a l very " 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 at high wavenumbers. While I have not yet had an opportunity 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 that some of the phenomena which I have discussed i n the l a s t few pages may have been e f f e c t i v e to some minor degree i n many of the ocean turbulence s p e c t r a which have been processed i n the p a s t , i n c l u d i n g those from in-shore waters (see Grant, Stewart and M o i l l i e t (1962), Stewart and Grant (1962), Grant, Hughes, Vogel and M o i l l i e t (1968), G r a n t , M o i l l i e t and Vogel (1968)) and, i n p a r t i c u l a r , i n the data from which the present u n i v e r s a l curve was d e r i v e d . I f we can assume the theory of " u n i v e r s a l e q u i l i b r i u m " to be v a l i d there seems to be no a l t e r n a t i v e c o n c l u s i o n . I have suggested s e v e r a l p o s s i b l e reasons (and there may be others) why an experimental spectrum might appear f l a t t e r at high wavenumbers than the t h e o r e t i c a l curve, but I see no way t o e x p l a i n a steeper s l o p e . With t h i s argument i n mind I have ( f o l l o w i n g the procedure of Stewart and Grant (1962)) produced a new approximation to Kolmogoroff's u n i v e r s a l . f u n c t i o n . Figure 22 shows t h i s "new" u n i v e r s a l curve i n comparison to the o l d one which has been accepted by t h i s l a b o r a t o r y Figure 22. A new empirical approach to Kolmogoroff's universal spectrum function for isotropic turbulence. Earlier version due to Stewart and Grant C1962) is 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 together i n the low and mid-range of wavenumbers th a t I have found i t convenient to d i s p l a c e the o l d one (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 v e r t i c a l l y so that the shapes may be compared more r e a d i l y . The new curve ( p l o t t e d w i t h a slope of e x a c t l y - 5/3 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 than a l i n e width 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 sharper i n the "knee"; then crosses and f a l l s below the o l d curve, reaching a slope very c l o s e t o -7 at the extreme outer end. The new curve i s a composite derived from three separate samples, one of 95 seconds and two of 175 seconds d u r a t i o n , from Operation F-6-67. For each, a d i s s i p a t i o n r a t e obtained by i n t e g r a t i o n (as i n Equation 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 together to produce the curve of Figure 22. I have shown only a few of the computed po 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 sampling procedure designed simply t o give a reasonably uniform d i s t r i b u t i o n of p o i n t s along the curve. In 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 together t h a t they could not be shown sep a r a t e l y and I have p l o t t e d only 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 to i l l u s t r a t e the s c a t t e r , b u t , to avoid undue c l u t t e r on the diagram, I have l e f t the others unmarked. The new curve leads to a value of the one-dimensional Kolmogoroff constant, K' = 0.56, - somewhat l a r g e r than most p r e v i o u s l y reported r e s u l t s . In 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 that 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 which the new 62 curve has been derived show n o t i c e a b l y lower l e v e l s of thermal micro-s t r u c t u r e (by f a c t o r s of 3 to 10 i n s p e c t r a l l e v e l ) than those f o r other samples from the same area during the same o p e r a t i o n , but f o r which the v e l o c i t y s p e c t r a do not show such a steep slope at high wavenumbers. Lower temperature m i c r o s t r u c t u r e probably i n d i c a t e s a w e l l mixed body of water w i t h correspondingly 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 clo s e to the t r u t h then, 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 to be high - t h i s spectrum might come clos e to the u n i v e r s a l form p r e d i c t e d by theory. My new " u n i v e r s a l curve", i n f a c t , shows a very c l o s e match at high wavenumbers to some of the e a r l y s p e c t r a by Stewart and Townsend (1951) i n a wind t u n n e l , and comes c l o s e r than the o l d one to more recent r e s u l t s by Pond (1965) i n the atmosphere. Turbulent Heat Flux 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 heat by tu r b u l e n t mixing 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 analysed s i x samples i n t h i s way - three from F - l l - 6 7 and three from F-l-69. S u i t a b l e samples ranging i n length from p a r t of a depth c y c l e to s e v e r a l c y c l e s are s e l e c t e d from records taken i n the c y c l i n g mode. Primary c r i t e r i a f o r s e l e c t i o n are ( i ) reasonable u n i f o r m i t y 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 major 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 gradients of temperature as s m a l l as p o s s i b l e , ( i v ) no gain changes or other disturbances. 63 The differentiated signal from the temperature probe, suitably f i l t e r e d to remove as much as possible of the noise, is f i r s t processed through an analogue circuit designed to compensate for the frequency response of the probe. From the corrected signal, a mean square value is computed, and, with application of calibration factors and adjustment for recording gain settings, the result may be designated 2 Q 2 2 vj~^ ") (see Page 13) . From t h i s we would l i k e to estimate (V6) , ,3 6 2 The ocean tends to be horizontally 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 — ) . If we assume a uniform o x 3 y structure in the horizontal plane however, there w i l l be an optimum angle .(to the horizontal) at which to make a one-dimensional measurement 2 to give a best approximation to (V9) . This angle would weight the >3 0 2 horizontal component of G—) by a factor of 2 with respect to the piS vertical component, and turns out to be just over 35°. In our cycling mode the angles of ascent and descent are usually slightly less than 30°, which is a l i t t l e b i t low, but 2 nevertheless close to the optimum, I shall therefore take (V9) 0,3 9* 2 as 3(~) . The depth range is then determined from the depth record and the mean temperature range from one of the thermistors. For samples having a low signal-to-noise ratio 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 signal sample being processed, and have made appropriate correction to the value 5 0 2 of C^~) • Resulting values of vertical turbulent heat flux, with and without noise correction, are summarized in Table III. The last column vO o CM co r H o\ CM St m co m r H m VD co cn in oo oo 00 m oo o S t m vO r - cn s r cn st- cn cn o a\ r H s t CM r H cn oo 00 O O o CM o> s t VO •n 00 VO oo co cn CO CM o r H s l - r H CM 00 S T m vo CTv o VD CM CO CO CM m o m m VO o o r H r H r H r H CO 00 00 00 00 CO vO CM CM r H CM r H r H H r H CM o CO o CM o s t 00 in r- vO s t CO CO CO O oo m m co m r H r H sr m o r H CM CM r H oo o o r H m co CO CO oo oo m m r H o o o o o CM vo CM CM vo co CM v o co CM v o CM CM vO CM vO CM CM CO m TABLE I I I : V e r t i c a l heat flux 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 . 64 shows the e f f e c t i v e eddy c o e f f i c i e n t of d i f f u s i v i t y ( n o i s e - c o r r e c t e d where a p p l i c a b l e ) f o r each sample. Samples 4 and 5 were taken from regions of q u i t e intense temperature s t r u c t u r e , r e p r e s e n t a t i v e of only 1 or 2 percent perhaps of the volume of ocean covered by our experiments. The other samples are more r e p r e s e n t a t i v e of commonly o c c u r r i n g i n t e n s i t i e s which might be found throughout 25 t o 30 percent of the volume. Compensation f o r noise by the method used probably over-c o r r e c t s , because there i s almost c e r t a i n l y some r e s i d u a l temperature s i g n a l i n the s e c t i o n of noise used f o r c o r r e c t i o n . The c o r r e c t e d f i g u r e , f o r samples 2 and 3 i n p a r t i c u l a r , where the c o r r e c t i o n s are l a r g e , should be regarded w i t h some s u s p i c i o n . The r e s u l t s may probably be r e l i a b l y regarded as lower l i m i t s . My r e s u l t s are too few and the s c a t t e r too great to estimate a r e l i a b l e mean value f o r heat f l u x or eddy c o e f f i c i e n t f o r the re g i o n . 2 -1 The average of the l a s t column i n Table I I I i s 1.12 cm sec which i s 2 -1 cl o s e to the value of 1 cm sec suggested by Munk (1966) and others. However, my r e s u l t s are from s e l e c t e d samples and each covers only a l i m i t e d range i n depth. My estimate (which I cannot support q u a n t i -t a t i v e l y ) from v i s u a l examination of the records , i s that a mean value f o r the volume of ocean covered by our experiments would be sm a l l e r 2 -1 by a f a c t o r of about 5 - something l i k e 0.2 cm sec This 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 reported by Osborn (1969) from measurements of the v e r t i c a l component of temperature gradient i n the San Diego Trough i n August 1968. His value f o r v e r t i c a l heat flow 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 -1 i n the range 0.02 to 0.06 cm sec , depending on the r e l a t i o n s h i p between a n c ! (V9) . Since h i s measurements were taken v e r t i c a l l y , i n the d i r e c t i o n of maximum g r a d i e n t s , the f a c t o r should probably 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 of 0.04 cm sec "*". His measurements were made over a much greater range of depth than ours and the r e s u l t i s t h e r e f o r e more l i k e a mean value f o r the area. On t h i s b a s i s h i s r e s u l t seems to be lower again than mine, by another f a c t o r of 5. 66 DISCUSSION There are not many s p e c i f i c conclusions to be drawn. I have presented data which I hope w i l l contribute i n some useful way to our meager store of knowledge on the turbulent structure of the ocean, and I have discussed 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 turbulence we observe. In some respects i t seems to f a l l i n t o the pattern predicted by current theories of i s o t r o p i c turbulence, and i n other respects i t does not. We have discovered that, throughout the volume of ocean covered by our experiments, turbulence e x i s t s i n a patchy structure w i t h i n r e l a -t i v e l y t h i n layers and there i s probably v e l o c i t y shear between and perhaps throughout the layers. We would not r e a l l y expect the turbulence to be i s o t r o p i c , and perhaps the pattern we observe resembles more c l o s e l y the two dimensional s i t u a t i o n described by Kraichman (1967), but for which the theory i s not yet w e l l developed. I have estimated the t o t a l , world-wide, turbulent d i s s i p a t i o n on energy, but, based on so few observations over such a small volume, the r e s u l t i s of doubtful value. We would l i k e to know much more about the c h a r a c t e r i s t i c s of turbulent patches and t h e i r d i s t r i b u t i o n throughout the world oceans, and for t h i s we simply require more of the sort of observations that have already been made. From such a continued programme of observation we could also learn more about the v e r t i c a l transport of heat, momentum, s a l t and other dissolved or suspended materials which are of i n t e r e s t to the marine e c o l o g i s t s . I t appears that s a l i n i t y and density structure may have important e f f e c t s on the mechanism of ocean turbulence. To develop 67 a b e t t e r understanding of these 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 features of s a l i n i t y and d e n s i t y . I t should not be d i f f i c u l t to improve our r e s o l u t i o n by an order of magnitude, and perhaps more, without s a c r i f i c e of accuracy. In order to cast some l i g h t on the question of i s o t r o p y (or l a c k of i t ) i t would be very v a l u a b l e , a l s o , to be able to measure a cross-stream component of v e l o c i t y . In p r i n c i p l e t h i s 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 plankton. A s o l u t i o n w i l l be d i f f i -c u l t but perhaps not impossible. We would l i k e to be able t o measure shear, and thereby o b t a i n l o c a l Richardson number, as a f u r t h e r c o n t r i b u t i o n to our under-standing of the nature of the turbulence and the mechanism of generation. T h i s , a l s o , i s a d i f f i c u l t t a s k , but probably not i m p o s s i b l e . Throughout the progress of the work, although I have not s t r e s s e d the p o i n t , I have had a nagging s u s p i c i o n that there 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 turbulence. I have not yet made any attempt to d i s t i n g u i s h between the two types of motion, but there are a number of ways that one might go about i t . Perhaps the f i r s t to t r y would be to 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 angle between them. My predecessors have e s t a b l i s h e d a b a s i s on which to b e g i n , and have pointed the way. I have taken a s m a l l step forward. Much remains to be done. 68 BIBLIOGRAPHY Batchelor, G.K. 1953: Homogeneous Turbulence. Cambridge University Press Batchelor, G.K. 1959: Small Scale V a r i a t i o n of Convected Quantities l i k e Temperature i n Turbulent F l u i d (Part 1). J . F l u i d Mech. _5, 113. Fabula, A.G. 1968: The Dynamic Response of Towed Thermometers. J . F l u i d Mech. 34, 449. Grant, H.L., Stewart, R.W. and M o i l l i e t , A. 1962: Turbulence Spectra from a T i d a l Channel. J . F l u i d Mech. 12, 241. Grant, H.L., Hughes, B.A., Vogel, W.M. and M o i l l i e t , A. 1968: The Spectrum of Temperature Fluctuations i n Turbulent Flow. J. F l u i d Mech. 34, 423. Grant, H.L. , M o i l l i e t , A. and Vogel, W.M. 1968: Some Observations of the Occurrence of Turbulence i n and above the Thermocline. J. F l u i d Mech. 34, 443. Hinze, J.O. 1959: Turbulence. McGraw-Hill Book Company, New York. von Karman, T. 1937(a): On the S t a t i s t i c a l Theory of Turbulence. Proc. Nat. Acad. S c i . Wash. 23, 98. von Karman, T. 1937(b): The Fundamentals of the S t a t i s t i c a l Theory of Turbulence. 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 of Turbulence Proc. 5th Int. Congr. App. Math. 347. Kolmogoroff, A.N. 1941: The Local Structure of Turbulence i n Incompressib Viscous F l u i d for very large Reynolds Numbers. C.R. Acad. S c i . U.R.S.S. 30, 301. Monin, A.S. and Yaglom, A.M. 1967: S t a t i s t i c a l Hydrodynamics (Vol 2). Nauka. Munk, W.H. 1966: Abyssal Recipes. Deep-Sea Res. 13, 707. Munk, W.H. and MacDonald, G.J.F. 1960: The Rotation of the Earth. Cambridge University Press. Osborn, T.R. 1969: Oceanic Fine Structure. Doctoral D i s s e r t a t i o n . University 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. Cambridge University Press. 69 Pond, S. 1965: Turbulence Spectra i n the Atmospheric Boundary Layer over the Sea. Doctoral D i s s e r t a t i o n , University of 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 Correlations i n Is o t r o p i c Turbulence. Proc. 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 Science 4^, 1269. Stewart, R.W. arid Townsend, A.A. 1951: P h i l . Trans. A. 243, 359. Stewart, R.W. and Grant, H.L. 1962: Determination of the Rate of Di s s i p a t i o n of Turbulent Energy near the Sea Surface i n the Presence of Waves. J. Geophys. Res. 6^ 7, 3177. Stommel, H. and Federov, K.N. 1967: Small scale Structure i n Temperature and S a l i n i t y near Timor and Mindanao. Tellus 19_, 306. Taylor, G.I. 1921: D i f f u s i o n by Continuous Movements. Proc. Lond. Math. Soc. 20_, 196. Taylor, G.I. 1935: S t a t i s t i c a l Theory of Turbulence. Proc. Roy. Soc. A, 151, 421. Turner, J.S. and Stommel, H.: A new Case of Convection i n the Presence of V e r t i c a l S a l i n i t y and Temperature Gradients. Proc. Nat. Acad. S c i . j>2, 49. Woods, J.D. and Fosberry, G.G. 1966-67: The Structure of the Thermocline. Underwater Association (of Malta) Report 1966-67. - - - 1952: Tables for Sea Water Density. U.S. Navy Hydrographic O f f i c e , H.O. P u b l i c a t i o n No. 615. - - - 1956: Tables f o r Rapid Computation of Density and E l e c t r i c a l Conductivity of Sea Water. U.S. Navy Hydrographic O f f i c e . H.O. Pub l i c a t i o n No. 619. P o s i t i o n s Held: 1947-present Defence S c i e n t i f i c S e r v i c e O f f i c e r Defence R e s e a r c h B o a r d of Canada 1947- 48 D i r e c t o r a t e of E l e c t r o n i c s R e s e a r c h . 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. 1948- 50 P a c i f i c N aval L a b o r a t o r y . R e s e a r c h i n underwater a c o u s t i c s and oceanography. 1950-53 Graduate Studies (Physics) at U B C on 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 Titanate". 1953-58 Head Seaward Defence Section, P N L . R e s e a r c h i n underwater a c o u s t i c s and low frequency magnetics r e l a t e d to detection of submarine s. 1959- 63 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 and Deputy S c i e n t i f i c A d v i s o r to Chief of Naval 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 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 ) . 1963-66 Deputy Chief, Canadian Defence R e s e a r c h Staff, Washington, D. C. and Deputy Defence R e s e a r c h Attache, Canadian Embassy, Washington, D. C. 1966- 67 D i r e c t o r of P h y s i c a l R esearch, DRB/HQ. 1967- 70 Defence R e s e a r c h E s t a b l i s h m e n t P a c i f i c and Institute of Oceanography, UBC. R e s e a r c h on oceanic turbulence. Note: Wartime s e r v i c e with the Canadian A r m y and p r i o r s e r v i c e with the National R e s e a r c h C o u n c i l of Canada have not been included. P u b l i c a t i o n s : P r o g r e s s R e p o r t o n R e s e a r c h o n T i t a n a t e s . U n c l a s s i f i e d . D R B 5 2 / 1 1 8 5 8 . U B C 1 9 5 2 . P i e z o e l e c t r i c E f f e c t s i n P o l a r i z e d T i t a n a t e s . U n c l a s s i f i e d . D R B 5 3 / 9 5 1 7 . U B C 1 9 5 3 . T h e F e r r o e l e c t r i c P r o p e r t i e s o f B a r i u m T i t a n a t e . M . A . T h e s i s , U B C 1 9 5 2 . T h e F l u c t u a t i o n P r o b l e m s i n U n d e r w a t e r S o u n d . N a v a l P a p e r I V : D R B F i f t h S y m p o s i u m 1 9 5 3 . C o n f i d e n t i a l . D R B 5 4 / 6 6 3 8 . W a t e r T e m p e r a t u r e S t r u c t u r e a n d i t s E f f e c t o n t h e P e r f o r m a n c e 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 V i c t o r i a H a r b o u r s . P N L I n t e r i m R e p o r t P I R - 6 , 1 9 5 4 . C o n f i d e n t i a l . D R B 5 4 / 8 2 1 1 . S u r v e y o f t h e S t a t e o f D e v e l o p m e n t o f L F a n d V L F S o u n d S u r v e i l l a n c e S y s t e m s . P N L 1 9 5 5 . T h e D e s i g n o f I n d i c a t o r L o o p S y s t e m s f o r D e t e c t i n g S m a l l a n d S l o w l y M o v i n g T a r g e t s . P N L R e p o r t 1 0 . 1 9 5 5 . S e c r e t . D R B 5 5 / 1 5 6 6 8 . S o m e C o n s i d e r a t i o n s i n t h e D e s i g n o f M a g n e t i c I n d i c a t o r L o o p S y s t e m s f o r t h e D e t e c t i o n o f S l o w T a r g e t s . S e c r e t . U . S . N a v y H a r b o u r D e f e n c e a n d C o u n t e r m e a s u r e s B u l l e t i n , 1 9 5 6 . 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 a t P N L . P N L 1 9 5 7 . A P r e l i m i n a r y S t u d y o f I n d i c a t o r L o o p s i n D e e p W a t e r . P N L T e c h n i c a l M e m o r a n d u m 5 7 - 1 , 1 9 5 7 . S e c r e t . D S I S 5 7 / 2 7 3 6 . G e o g r a p h i c a l V a r i a t i o n s i n G e o m a g n e t i c M i c r o p u l s a t i o n s . P N L T e c h M e m o 5 8 - 6 , 1 9 5 8 . U n c l a s s i f i e d . D S I S 5 9 / 1 4 3 3 0 . S u b - A u d i o S p e c t r a o f M a g n e t i c S t o r m s a n d S o l a r W h i s t l e r s . J o u r n a l o f t h e A m e r i c a n P h y s i c a l S o c i e t y , 1 9 5 8 . S u b - A u d i b l e G e o m a g n e t i c F l u c t u a t i o n s . N a t u r e , 1 9 5 8 . U n c l a s s i f i e d . D S I S 5 8 / 1 3 6 6 3 . M a r i t i m e R e s e a r c h f o r D e f e n c e i n C a n a d a . S e c r e t . D M R S t a f f P a p e r , 1 9 6 1 . T h e N e w R C N R e s e a r c h S h i p A G H 1 7 1 . R C N N a v a l T e c h n i c a l R e v i e w , F i r s t Q u a r t e r 1 9 6 2 . 

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