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The turbulent fluxes of momentum and sensible heat over the open sea during moderate to strong winds Large, William George 1979

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THE  TURBULENT FLUXES OF MOMENTUM  SENSIBLE HEAT OVER THE OPEN MODERATE  AND  SEA DURING  TO STRONG WINDS.  by WILLIAM GEORGE B. A. S c . ,  University  LARGE  of British  A THESIS SUBMITTED IN PARTIAL THE  Columbia,  FULFILMENT OF  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  THE  FACULTY OF GRADUATE STUDIES DEPARTMENT  OF PHYSICS  INSTITUTE OF OCEANOGRAPHY  We a c c e p t to  THE  this  t h e s i s as c o n f o r m i n g  the required  standard  UNIVERSITY OF BRITISH August, ©  William  1972  COLUMEIA  1979  George L a r g e ,  1979  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  an a d v a n c e d  degree at the U n i v e r s i t y  the L i b r a r y  s h a l l make  I  it freely  of B r i t i s h  available  scholarly  thesis  It  for financial  i s understood that gain shall  written permission.  Department  of  The U n i v e r s i t y  nrrawnCTAPHv of British  Columbia  2075 Wesbrook P l a c e Vancouver, Canada V6T 1WS  Date  I agree  NOVEMBER  1. 1Q7Q  that  and s t u d y .  copying of this  thesis  p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t  by h i s r e p r e s e n t a t i v e s . this  Columbia,  f o r reference  f u r t h e r agree that permission f o r e x t e n s i v e  for  of  f u l f i l m e n t o f the requirements f o r  or  c o p y i n g o r p u b l i c a t inon  n o t be a l l o w e d w i t h o u t my  ii ABSTRACT Two s y s t e m s of  momentum,  strong and  sensible  heat  winds a r e d e s c r i b e d .  the  and  moisture  other t h e Reynolds  flux  non-linear  operating region,  sensors  turbulent  are  found  from  conditions of the flux  results  o f an e x p e r i m e n t  platform  moored  i n 59m o f water  Spectra,  cospectra,  coefficients temperature reported  data  and  values.  from  found  to  Simultaneous  The dynamic  comparison dissipation essentially  were d e p l o y e d on t h e of  ship  system, an  and  about  2.18x10  - 3  that  the  actual  statistics the Reynolds be  a r e presented. and  flux  comparable  dissipation  a stable  transfer  v e l o c i t y and  to  previously  and R e y n o l d s  flux  h e a t f l u x e s i n up t o  agreement.  o f a second  weathership  experiment CCGS  where  Quadra.  tower  drag  coefficients  from  demonstrates  that  the  tower  open ocean  between  in  10 km o f f s h o r e ,  site.  Bedford  The n e u t r a l  CDN, i s f o u n d , on a v e r a g e , t o be n e a r l y winds  sensor  responses  on t h e B e d f o r d t o w e r ,  m/s w i n d s a r e shown t o be i n e x c e l l e n t  systems  drag  constant  No v a r i a t i o n  with  A the i s  coefficient, at  4 a n d 10 m/s a n d t o i n c r e a s e a l m o s t a t 26 m/s.  A  measurements.  Also presented are the r e s u l t s  to  method.  b e h a v i o r and a v o i d s i t s  e s t i m a t e s o f b o t h t h e momentum and s e n s i b l e  for  method  component,  measurements  turbulence  are calculated  velocity  i s derived.  The  the  d u r i n g moderate t o  o r eddy c o r r e l a t i o n  accounts f o r the p r o p e l l e r ' s non-cosine  20  fluxes  One e m p l o y s t h e d i s s i p a t i o n  a method o f r e s o l v i n g t h e v e r t i c a l  of t h e  air-sea  G i l l p r o p e l l e r - v a n e anemometer i s t h e v e l o c i t y  modified and  f o r remote measurements o f t h e  1.14x10  -3  linearly  either  fetch  iii  (greater than 10 km) estimates  of  the  or  stability  sensible  c o n d i t i o n s a r e presented. CTN,  i s found,  on  The  average,  stable s t r a t i f i c a t i o n increase  heat  is flux  neutral to  t o 1.08x10-  3  observed. from  a  Dissipation wide range of  transfer  coefficient,  vary from about 0.69x10 in  the  unstable  case.  -3  in An  i n CTN with i n c r e a s i n g wind speed i s suggested by only  some of the data. Time additional  series  of  sources  the  of  fluxes  are  used  to  v a r i a t i o n i n the t r a n s f e r  investigate coefficients.  T h e i r s t a t i s t i c a l v a r i a b i l i t y about a running mean i s seen t o be about  10%.  Evidence i s presented that i n d i c a t e s t h a t  departures from conditions.  CDN  average  i s observed  average, during r i s i n g a change i n wind  values  are  related  to  t o be s i g n i f i c a n t l y  persistent  sea  surface  s m a l l e r , on  winds than during f a l l i n g winds or  direction.  after  iv  TABLE OF CONTENTS Page ABSTRACT  . .. i i  TABLE OF CONTENTS  »  iv  LIST OF TABLES  vi  LIST OF FIGURES  vii  ACKNOWLEDGEMENT  -  CHAPTER 1  INTRODUCTION  . . . .  CHAPTER 2  EXISTING THEORY AND EXPERIMENTAL RESULTS  rr  P  xi 1  2.1  Air-Sea I n t e r a c t i o n  4  2.2  Monin-Obukhov S i m i l a r i t y Theory  9  2.3  Bulk Aerodynamic  2.4  The Reynolds Flux Method  19  2.5  The D i s s i p a t i o n Method  21  2.6  E s t i m a t i n g The S t a b i l i t y Parameter Z/L  31  CHAPTER 3  P a r a m e t e r i z a t i o n s .............  THE INSTRUMENTATION  13  AND EXPERIMENTAL PROGRAM  3.1  Introduction  37  3.2  The Sensors  3.3  The Reynolds Flux System  46  3.4  The D i s s i p a t i o n System  52  3.5  Sensor Response  3.6  The Experimental Program  „  i.........  38  56 63  V  CHAPTER 4  REYNOLDS FLUX MEASUREMENTS THE BEDFORD STABLE TOWER  4.1  Introduction  4.2  The S t a b i l i t y  4.3  Turbulence  Spectra  4.4  Turbulence  Statistics  4.5  The F l u x e s  Of Momentum  CHAPTER 5  FROM 69  P a r a m e t e r Z/L  70  And C o s p e c t r a  72 87  And S e n s i b l e Heat . . . . . . .  92  INTERCOMPARISON OF THE REYNOLDS FLUX AND DISSIPATION METHODS  5.1  Introduction  101  5.2  The Momentum F l u x  103  5.3  The S e n s i b l e  117  CHAPTER 6  Heat F l u x  DISSIPATION MEASUREMENTS FROM STABLE TOWER AND CCGS QUADRA  THE BEDFORD  6.1  Introduction  6.2  Bulk Aerodynamic Momentum F l u x  Parameterization  Bulk  Parameterization  6.3  Aerodynamic  Sensible  CHAPTER 7  REFERENCES  APPENDIX  122 Of The 126  Heat F l u x  SUMMARY AND CONCLUSIONS  . ...  THE INTERCOMPARISON RESULTS  Of The 150  166  172  177  vi LIST OF TABLES TABLE  TABLE  I  II  TABLE I I I  TABLE TABLE TABLE  IV V VI  TABLE VII  TABLE VIII  TABLE  TABLE TABLE  IX  X XI  TABLE XII  TABLE XIII  TABLE XIV  Summary of possible errors i n the v e l o c i t y measurement and t h e i r e f f e c t s on the Reynolds f l u x method  43  Turbulent v e l o c i t y statistics 196 Reynolds f l u x runs  88  from  the  Standard d e v i a t i o n s o f the t u r b u l e n c e statistics about their stability band means p l o t t e d i n f i g u r e 18. .................  89  Comparison integrating  of the d i f f e r e n t methods o f t h e u,w cospectrum. .............  93  Comparison of the d i f f e r e n t methods o f i n t e g r a t i n g the w,t cospectrum. .............  95  Ratio of d i s s i p a t i o n t o Reynolds f l u x estimates of the momentum f l u x band averaged over 2 m/s wind speed i n t e r v a l s .  ...  113  Ratio o f d i s s i p a t i o n t o Reynolds f l u x estimates of the momentum f l u x band averaged over s t a b i l i t y ranges. .............  114  V a r i a t i o n of the n e u t r a l drag c o e f f i c i e n t with fetch f o r winds between 4 and 10 m/s  128  The s t a b i l i t y dependency of the drag coefficients from the 4 < U10 < 10 m/s data of t a b l e VIII  130  Mean 10 CDN of wind speed d i f f e r e n t wind c o n d i t i o n s .  bands  140  Mean 10 CDN o f wind d i f f e r e n t months.  bands f o r  3  3  speed  in  142  Parameterization of the s e n s i b l e heat flux by band averaging 0 AT over ranges of <wt> Averaged neutral Stanton number function of wind speed in s t r a t i f i c a t i o n only.  .  as a stable  Averaged n e u t r a l Stanton number as a function of wind speed i n u n s t a b l e s t r a t i f i c a t i o n only.  158  161  .  162  vii LIST OF FIGURES FIGURE  FIGURE  FIGURE  FIGURE  FIGURE FIGURE  FIGURE  FIGURE  FIGURE  1:  2:  Stability adjustments of the dissipation methods o f e s t i m a t i n g momentum f l u x .  four the  Stability adjustments dissipation methods of s e n s i b l e heat f l u x . .  two the  of the estimating  28  30  3 A: The G i l l t w i n p r o p e l l e r - v a n e anemometer. B: The HAT s e n s o r h o u s i n g . C: D e f i n i t i o n o f a n g l e s used i n r e s o l v i n g the velocity components and c a l c u l a t i n g the t i l t a n g l e 6 4:  5: 6:  S i g n a l p r o c e s s i n g i n t h e Reynolds flux system, showing t h e s a m p l i n g scheme and all parameters considered in the analysis. > ..  47  Signal system.  53  processing  i n the  dissipation  D e t e r m i n a t i o n o f the d i s t a n c e c o n s t a n t s from t h e 0.8 : 1.6 Hz band-pass f i l t e r r a t i o s of A: t h e G i l l - u h o r i z o n t a l p r o p e l l e r , B: t h e G i l l - w t i l t e d p r o p e l l e r , <=<= 59.5°.  7:  8:  40  58  D e t e r m i n a t i o n o f t h e microbead t h e r m i s t o r response from t h e 0.8 : 1.6 Hz band-pass f i l t e r ratios.  60  R a t i o s o f <uw> c a l c u l a t e d from d i f f e r e n t p a i r s o f band-pass f i l t e r s as a function of wind speed  62  9 A: The B e d f o r d tower s i t e near H a l i f a x Nova Scotia. B: The i n s t r u m e n t a t i o n on t h e B e d f o r d tower.  FIGURE 10 A: Ocean Weather S t a t i o n "PAPA", 50°N, 145°W, and t h e r o u t e o f t h e w e a t h e r s h i p s . B: The i n s t r u m e n t a t i o n on t h e f o r e m a s t o f CCGS Quadra  ...  64  67  Vlll  FIGURE 11  FIGURE 12  Comparison of the most complete expression f o r the s t a b i l i t y parameter Z/L(u*,<wt>) t o : A: an a p p r o x i m a t e e x p r e s s i o n Z / L ( U * , A T ) . B: t h e b u l k e s t i m a t e Z / L (AT) . •  71  Normalized spectra of the downstream velocity component from averages of f ^ u ( n ) / u * from: A: 108 u n s t a b l e r u n s B: 88 s t a b l e r u n s  75  2  FIGURE  13:  FIGURE 14  The horizontal velocity spectrum, f ( f ) / averaged o v e r 4 r u n s from CCGS Quadra i n 22 m/s w i n d s .  Normalized v e r t i c a l v e l o c i t y s p e c t r a a v e r a g e s o f f "rw (n) / u * o v e r : A: 108 u n s t a b l e r u n s B: 88 s t a b l e r u n s  78  from  2  FIGURE  15:  The n o r m a l i z e d t e m p e r a t u r e averages o f f *rt(n)/(o*t) temperature runs  2  FIGURE  16:  80  spectrum from . over a l l 60 82  Normalized u n s t a b l e (A) and s t a b l e (B) u,w cospectra from averages of f ^uw(n)/u* . Integration under the s o l i d c u r v e s g i v e s E f o r t h e 13 method. .....  84  N o r m a l i z e d w,t c o s p e c t r a f r o m a v e r a g e s o f f ^wt(n)/<wt> in (A) u n s t a b l e and (B) s t a b l e c o n d i t i o n s . I n t e g r a t i o n under the s o l i d curves gives E f o r t h e 13 method  86  Non-dimensional t u r b u l e n c e s t a t i s t i c s as functions of s t a b i l i t y . See t a b l e I I I for standard deviations about plotted means.  90  The n e u t r a l drag coefficient speed f o r t h e 196 R e y n o l d s f l u x runs  97  2  FIGURE  FIGURE  FIGURE  17:  18:  19:  FIGURE 20:  vs wind momentum  <wt> v s . U10(TSFC-T10) for the t e m p e r a t u r e r u n s w i t h |AT| > 0 . 5 ° C  52 .  99  ix  FIGURE 21:  FIGURE 22  FIGURE 23  FIGURE 24  Comparison o f u* i n m/s from t h e n e u t r a l d i s s i p a t i o n method a n d t h e R e y n o l d s flux method f o r a l l 192 s i m u l t a n e o u s B e d f o r d tower runs .. Investigation of the "near momentum f l u x r e g i m e f o r ; A: 61 r u n s w i t h 0.0 <Z/L< 0.5 B: 70 r u n s w i t h -0. 1 <Z/L< 0.0 .  Comparison runs t o A: d i s s i p a t i o n B: d i s s i p a t i o n  stable  Reynolds  106 flux  method 2 method 3.  108  I n t e r c o m p a r i s o n o f u* from the "best" d i s s i p a t i o n method (2) and t h e "best" Reynolds flux method (13) f o r a l l 192 simultaneous runs  FIGURE 26:  FIGURE 28  88  neutral"  C o m p a r i s o n o f 104 u n s t a b l e R e y n o l d s flux runs t o A: d i s s i p a t i o n method 2 B: d i s s i p a t i o n method 4. .......................  FIGURE 2 5:  FIGURE 27  of  104  Comparison o f u* from the dissipation system and from t h e BIO eddy c o r r e l a t i o n s y s t e m s f o r 20 r u n s on t h e B e d f o r d t o w e r .  112  ...  Comparison of the 60 simultaneous s e n s i b l e heat f l u x c a l c u l a t i o n s i n °Cm/s. A: <wt>DISS1 v s . <wt>FLUX B: <wt>DISS2 v s . <wt>FLUX. The neutral drag coefficient as a f u n c t i o n o f wind s p e e d from A: 1086 h o u r l y averages from t h e Bedford tower B: 505 h o u r l y a v e r a g e s f r o m t h e CCGS Quadra.  FIGURE 29: FIGURE 30:  Comparison (triangles)  116  118  ...  of ship (pluses) and tower neutral drag c o e f f i c i e n t s . ......  The n e u t r a l drag coefficient as a function o f wind speed. L i n e s show a C h a r n o c k r e p r e s e n t a t i o n w i t h <=<•=• 0.0 144, K= 0.41 (dashed) and e g u a t i o n s 6.1 (solid). ......  110  125 127  132  X  FIGURE 31:  FIGURE 32:  FIGURE 33: FIGURE 34: FIGURE 35: FIGURE 36:  FIGURE 37: FIGURE 38: FIGURE 39:  Time s e r i e s o f t h e momentum f l u x f r o m r u n D33C. Time i s from 4:40 GMT December 7, 1976.  .  138  Time s e r i e s o f t h e momentum f l u x from r u n D29D. Time i s from 17:00 GMT September 26, 1976.  145  Momentum f l u x t i m e s e r i e s f r o m r u n D31F. Time i s f r o m 4:00 GMT O c t o b e r 20, 1976.  147  Momentum f l u x time s e r i e s f r o m r u n D38B. Time i s f r o m 16:00 GMT March 12, 1977  148  Parameterization of the sensible heat f l u x (°Cm/s) i n u n s t a b l e s t r a t i f i c a t i o n . ....  151  Time series o f t h e s e n s i b l e heat f l u x d u r i n g r u n D33C (figure 31) . Time i s f r o m 4:40 GMT December 7, 1976.  153  Parameterization of the s e n s i b l e heat f l u x i n °Cm/s f o r s t a b l e s t r a t i f i c a t i o n  156  The n e u t r a l S t a n t o n number as a of s t a b i l i t y ...  159  function  Sensible heat f l u x t i m e s e r i e s from r u n D38B ( f i g u r e 3 4 ) . T i m e i s f r o m 16:00 GMT March 12, 1977  164  xi ACKNOWLEDGEMENT I s h o u l d l i k e t o e x p r e s s my thanks t o t h e many persons have  contributed  initiated  by  continually  t o t h e s u c c e s s o f t h i s work.  Dr. S. Pond,  provided  great deal  i s owed  designed  the  who,  as  of  The p r o j e c t was  research  supervisor,  h i s e f f o r t s , guidance and enthusiasm. t o E. Meyer  electronics  {Meyer  and  made  developed much o f t h e mini-computer efforts  who  Systems  them  Inc.),  work.  software.  I  A who  B. Walker applaud t h e  D. E n g l i s h , P. Merchant, H. H e c k l and o t h e r s of the  IOUBC s t a f f i n b u i l d i n g and d e p l o y i n g t h e i n s t r u m e n t s . Throughout his  air-sea  Institute and  interaction  and  others  at the  often  serviced  operations.  of  CCGS  Quadra  was  Bedford  E. Anderson  t h e i n s t r u m e n t a t i o n i n my  The c o - o p e r a t i o n o f C a p t a i n Dykes,  crew  from  group  p r o v i d e d b o t h l o g i s t i c and moral s u p p o r t .  D. Hendsbee  absence. the  the Bedford tower experiment Dr. S. D. Smith and  essential  the o f f i c e r s  and  t o t h e weathership  Some s e r v i c i n g was p o s s i b l e a t PAPA, thanks t o a i d  Dr. M. Miyake  and  his staff  (IOS P a t r i c i a Bay) and from  T. Neuhaus (Seakem Oceanography) . The p r o j e c t was g e n e r o u s l y s u p p o r t e d by t h e U n i t e d Office  of  Naval  Research  0C014-76-C-0446 under  States  ( C o n t r a c t s N 00014-66-C-0047 and N  Project  083-207)  Research C o u n c i l of Canada (Grant A8301).  and  by  the  National  I personally received  p o s t g r a d u a t e s c h o l a r s h i p s from NRC and a f e l l o w s h i p from UBC.  1 CHAPTER 1  INTRODUCTION  This  thesis  d e s c r i b e s an e x p e r i m e n t a l program d e s i g n e d t o  measure the t u r b u l e n t exchanges between t h e open ocean atmosphere i n moderate t o s t r o n g of  (5-50 m/s) winds.  and t h e  Measurements  the most i m p o r t a n t exchanges have been t h e s u b j e c t o f r e c e n t  r e v i e w s , i n which transfer  they  are parameterized  coefficients.  Recent  by  non-dimensional  d e t e r m i n a t i o n s of  the drag  c o e f f i c i e n t , which i s used t o e x p r e s s t h e momentum f l u x i n terms of the sguare o f t h e mean wind Garratt,  1977.  The  speed,  sensible  p a r a m e t e r i z e d by F r i e h e and  heat  have and  Schmitt,  been  reviewed  moisture  by  fluxes are  1976, i n terms  o f the  s u r f a c e - a i r temperature and h u m i d i t y d i f f e r e n c e s , r e s p e c t i v e l y and  the mean wind speed.  There a r e s e v e r a l o b s t a c l e s t h a t make  open ocean measurements i n h i g h winds d i f f i c u l t and therefore,  restricted  onshore p l a t f o r m s . fluxes,  have,  the m a j o r i t y t o low winds and t o near o r  The most common  t h e Reynolds  that  flux  methods  of  obtaining  (or eddy c o r r e l a t i o n ) and p r o f i l e ,  work b e s t on s t a b l e p l a t f o r m s w i t h m i n i m a l f l o w d i s t o r t i o n , these  conditions  their  and  high  winds,  cause  towers  to  many s e n s o r s e i t h e r t o f a i l c o m p l e t e l y or t o l o s e  calibration. The a i r - s e a energy exchanges a r e i n v o l v e d i n a  important  processes,  development to  and wave g e n e r a t i o n .  t h e open  number  of  including the large scale c i r c u l a t i o n s of  the ocean and atmosphere and, a t  set  but  a r e n o t easy t o s a t i s f y d u r i n g storms a t s e a .  Adverse c o n d i t i o n s accompanying collapse  the  ocean  smaller  scales,  thermocline  By e x t e n d i n g t h e e x i s t i n g data  and t o  higher  wind  speeds,  this  2 experimental  program should be r e l e v a n t t o the  study  of  these  processes. Modelling  and  p r e d i c t i n g l a r g e s c a l e f e a t u r e s r e q u i r e the  f l u x e s , which a r e t o o d i f f i c u l t and c o s t l y t o on  measure  directly  t h i s s c a l e , t o be c a l c u l a t e d from e a s i l y measured q u a n t i t i e s  through  parameterizations  observations.  For  based  this  on  purpose,  t r a n s f e r c o e f f i c i e n t s t o 20 m/s  relatively extension  few  of  direct  t h e measured  ought t o s u f f i c e , because h i g h e r  winds r a r e l y c o n t r i b u t e very much t o the f l u x e s averaged over month  or  more  about 25 m/s of  the  (Fissel  e t a l . , 1977).  A further extension  s h o u l d c l e a r l y r e v e a l any wind  coefficients.  speed  m/s  and  Banke, 1975,  wind  wind  At p r e s e n t t h e r e i s an o p i n i o n t h a t , i n  speed i s a p p r o p r i a t e  speed.  and  The  others f i n d average  a  about  trend  significant  increase  typical  degree.  of t u r b u l e n c e  deal  of  because  The  large  amount  of  measurements, s u g g e s t s , t h a t i n  stability,  it  would  the  be  wave  possible field  v a r i a b i l i t y i n the t r a n s f e r c o e f f i c i e n t s statistical  of  sea,  a  data from a l l p o s s i b l e c o n d i t i o n s a r e r e q u i r e d .  With a l a r g e data s e t effects  of  i s , a t most, s m a l l , but the c u r l of t h e wind s t r e s s  o r d e r t o a r r i v e at a r e p r e s e n t a t i v e p i c t u r e of the open great  with  s t r e s s computed from e i t h e r t y p e  c o u l d be a f f e c t e d t o a g r e a t e r scatter,  a  (Stewart, 1974), w h i l e Smith  drag c o e f f i c i e n t f o r m u l a t i o n s h o u l d be n e a r l y the same, the  to  dependencies  view of the s c a t t e r , a c o n s t a n t drag c o e f f i c i e n t up t o 14  a  and apart  to  examine  the  o t h e r sources from  the  s c a t t e r and s y s t e m a t i c i n s t r u m e n t a t i o n e r r o r s .  of  real  3  Continuous  records  over  a  long  period  i n c l u d e a v a r i e t y of l o c a l and s h o r t - l i v e d frontal  passages,  not be a p p l i c a b l e . appropriate  operate  in  histories  be  f o r which a l a r g e s c a l e p a r a m e t e r i z a t i o n  may  coefficients  the  simpler  be  possible  to  i n others d i r e c t  approach.  The  find stress  capability  40  m/s  should allow the e n t i r e  (winds, temperatures  and  f l u x e s ) of most storms to  followed.  above  and  phenomena,  should as  In some cases i t may  winds  time  such  transfer  e s t i m a t e s may  of  Such  time  series  should  be  useful  to time be  for  the  i n v e s t i g a t i o n of many small s c a l e processes. A modified  Gill  p r o p e l l e r - v a n e anemometer proved  very s u i t a b l e v e l o c i t y sensor f o r t h i s study. and  The  to  and  humidity  enclosures.  The  microbead  spray  and  contaminated  high winds and fluxes  were  recorded,  sensors  were  thermistors  housed were  a  momentum f l u x  drag c o e f f i c i e n t were s u c c e s s f u l l y measured i n 26 m/s  Temperature  be  winds.  in protective  often  broken  by  by s a l t , however they d i d s u r v i v e some  heat t r a n s f e r c o e f f i c i e n t s corresponding to l a r g e obtained.  because  of  No  useful  humidity  data  were  ever  the f a i l u r e of s e v e r a l types of sensors.  For open sea work a s h i p i s the most convenient  p l a t f o r m and i t s  motion and flow d i s t o r t i o n can be t o l e r a t e d by  the  dissipation  1978) .  T h i s method  method was  of measuring f l u x e s (Pond and Large,  first  t e s t e d on a s t a b l e o f f s h o r e p l a t f o r m where i t s r e s u l t s  compared f a v o u r a b l y to the Reynolds f l u x method. employed  designed  operating  was  on a s h i p , a l l o w i n g open sea data t o be c o l l e c t e d .  order t o gather as much data as was  It  possible,  the  then In  instrumentation  to r e c o r d c o n t i n u o u s l y f o r a month or more, while  remotely.  4  CHAPTER 2  2.1  MISTING THEORY AND  EXPERIMENTAL RESULTS  Air-Sea I n t e r a c t i o n Exchanges between the atmosphere and ocean are most  measured  in  the  atmospheric  easily  s u r f a c e l a y e r where the t r a n s f e r  processes are dominated by t u r b u l e n c e .  Viscous  and  diffusive  molecular t r a n s f e r s are n e g l i g i b l e i n t h i s l a y e r , which begins a few  centimeters  above  the  surface  and extends  up to a l e v e l  where the e a r t h ' s r o t a t i o n and the g e o s t r o p h i c pressure g r a d i e n t become important. the  layer  may  Yaglom, 1965 1977,  D e t a i l e d treatments  be found i n Lumley and Panofsky,  and  1967,  are s p e c i f i c a l l y  turbulent  the  scalar  1964,  and Kraus,  1972. . T h i s chapter and  concerned  with  the  theory  theory  is  guantity,  R.  extended  Following  t o any  passive  Reynolds'  Busch,  related  the momentum f l u x are t r e a t e d also  in  Monin and  f l u x measurements and t h e i r i n t e r p r e t a t i o n .  s e n s i b l e heat f l u x and and  of the t u r b u l e n t flow  to  Here the explicitly  atmospheric  convention,  the  t u r b u l e n t p r o p e r t i e s are p a r t i t i o n e d i n t o a mean ( < > denotes a time  average)  and  a  fluctuation  (lower  case symbols).  The  components of the i n s t a n t a n e o u s wind v e c t o r , V = Oi+Vj+Wk, where i,  j , and  become  k are u n i t v e c t o r s  U=<U>+u,  V=<V>+v and  of  an  x-y-z  W=<W>+w.  The  the axes puts k v e r t i c a l l y up and i along wind  vector  such  components, <V> 1967).  that  and <W>,  S i m i l a r l y any  temperature  T=<T>+t  d e f i n i t i o n <u>,  <v>,  the  mean  are both  coordinate  usual o r i e n t a t i o n of the  mean  cross-stream zero  system,  (Burling  horizontal  and  vertical  and  Stewart,  s c a l a r f i e l d R becomes <R>+r (and the a i r and  <w>,  the <t>  air and <r>  pressure  P=<P>+p).  are a l l z e r o .  By  5  It  i s the fluctuating  vertical  velocity  t r a n s p o r t s f l u i d p r o p e r t i e s up and down,  giving  which rise  bodily to  the  Reynolds f l u x e s d e f i n e d by:  TT _ _^ < >  Momentum f l u x  where  uw  S e n s i b l e heat f l u x  Hs = ^ Cp <wt>  any s c a l a r f l u x  Hr =  ^  (2. 1)  <wr> ,  i s t h e mean a i r d e n s i t y and Cp i s t h e s p e c i f i c heat at  constant pressure.  S i n c e , <W>=<w>=0, t h e f l u c t u a t i n g  quantities  i n 2.1 can be r e p l a c e d by t h e i r i n s t a n t a n e o u s v a l u e s U, T and R. I n t h i s c o o r d i n a t e system <vw> s h o u l d tend t o zero w i t h enough flux.  averaging  period,  wind  on a  unit  area  (positive  Hs i s a  also  turbulent  substituting  S i m i l a r l y gas f l u x e s such a s carbon  be c o n s i d e r e d .  the  heat  u p ) . The m o i s t u r e f l u x , a l s o an i m p o r t a n t  a i r - s e a exchange, i s expressed by s i m p l y h u m i d i t y f o r R.  of  o f underlying surface, 77 i s a l s o  r e f e r r e d t o as t h e R e y n o l d s s t r e s s . transfer  long  so ~~C r e p r e s e n t s t h e t o t a l momentum  Since i t gives r i s e t o a f o r c e i n t h e d i r e c t i o n  mean  a  absolute  d i o x i d e may  Often t h e terms momentum f l u x and s e n s i b l e  heat f l u x r e f e r t o t h e k i n e m a t i c f l u x e s <uw> and <wt>. The Reynolds f l u x e s a r i s e i n t h e e q u a t i o n of motion and i n scalar  c o n s e r v a t i o n e q u a t i o n s where t h e i r s u r f a c e v a l u e s become  i m p o r t a n t boundary c o n d i t i o n s f o r both t h e atmosphere and ocean. I n the e q u a t i o n f o r <D> i n t h e boundary  layer,  force  due t o t h e c r o s s - s t r e a m  zero.  The e q u a t i o n s f o r t h e mean f l o w and mean  the  surface  the Coriolis  component, V, i s , on average, temperature  in  l a y e r , assuming h o r i z o n t a l l y homogenous t u r b u l e n c e  6  (Busch, pp 74 and 75) , but r e t a i n i n g terms w i t h  the l a r g e s t mean  horizontal gradients, are:  =  P _<_>  3t  d<T> 3t  +  ^jF -  _<_>  <H> __<T> dx  +  3z  <3x  where RT i s t h e v e r t i c a l heat t r a n s f e r due t o negligible  horizontal  (2.2)  _d (Hs_+_ET) = 0 , dz ~£ Cp  pressure,  horizontal  radiation. temperature  v e r t i c a l r a d i a t i v e f l u x g r a d i e n t s and a s t e a d y mean turbulent  Hith and  state,  f l u x e s a r e constant throughout the l a y e r .  the  I t i s then  p o s s i b l e t o measure t h e s u r f a c e f l u x e s above wave i n f l u e n c e s a  convenient  height,  r o t a t i o n and t h e l a r g e  Z. scale  However,  away  horizontal  from  the  gradients  at  surface, eventually  become i n f l u e n t i a l . In s t e a d y f l o w , t h e measured s t r e s s , T"(Z) , i s l e s s t h a n t h e surface  s t r e s s , ~Co.  I f t h e d i f f e r e n c e a t a h e i g h t , he, i s 10%  (Lumley and P a n o f s k y , 1964, a r b i t r a r i l y use 20%), below  can  be  stress" layer.  t h e n the  regarded as b e i n g a " c o n s t a n t f l u x " o r " c o n s t a n t E f f e c t i v e l y , he i s t a k e n t o be the upper  of  t h e atmospheric s u r f a c e l a y e r .  the  s u r f a c e l a y e r a r e governed by t h e g e o s t r o p h i c b a l a n c e ,  f  Ug  =  1/£  In mid-latitudes  limit  winds above  d<P>/ dn ,  where f i s t h e C o r i o l i s parameter (about 1x10-* s geostrophic  flow  _ 1  ) , Ug i s t h e  wind and n i s a h o r i z o n t a l c o o r d i n a t e p e r p e n d i c u l a r  to t h e Ug d i r e c t i o n .  O b s e r v a t i o n s have shown  Ug  t o be  about  7 1.3 <U>  and  1973). first  about  S u b s t i t u t i n g , d<P>/ dx =  steady  flow  0.1  i 3 7 7 + 1.3  S  5t  so  a 10% r e d u c t i o n  T(Z)  To -  he  i s found  =  1.3  1x10 , <U>=5 order  over  m/s.  the sea more  at  than  1977), s e t t i n g  In  rising  when  <0>  s i n 16°  Z ,  unsteady  = 2790 s e c o n d s <uw>. <D>  10m  10—  3  have <U>  (2.3)  a l m o s t a l w a y s shown (drag  coefficient  he r i s e s ,  o f h e , when  3<0>/ d t c a n e a s i l y  be t h e same  flow,  2.2.  enhanced  factor  of  relative  because a s m a l l e r On t h e f a l l i n g  2 despite the neglect  surface  They serve  stress*  wind  than t h e surface  than  situtaion  falling  out  that,  height  he may be  good  of h o r i z o n t a l advection  t h e measured  during  gradient  with  are possibly  t o point  On  i ssufficient to  wind t h e l o s s o f f l u x  These a r g u m e n t s  t o 3<P>/dx.  rising  stress gradient  by t h e d e c e l e r a t i o n a n d i n t h i s lower.  >  14m a s a l o w e r l i m i t  w i n d t h e a c c e l e r a t i o n i s down t h e p r e s s u r e  considerably  the  the  o f m a g n i t u d e a s (1.3 f <U> s i n 16°) = 0.13 <0> / h o u r .  balance  same  into  "£b/^  i  Garratt,  - 3  f  = _ 0 j <uw> 1.3 f <U> s i n 1 6 °  <uw>/<U> t o a v e r a g e  is  (Deacon,  f <D> s i n 1 6 °  ^ 5z  =  Measurements  and  d<P>/ 3 n ,  s i n 16°  To  the  of the i d i r e c t i o n  o f 2.2 y i e l d s .  cku>  In  16° t o t h e r i g h t  to  a  terms,  with  the  10m s t r e s s may be g r e a t e r on w i n d s , when i t c o u l d  s t r e s s by 5 t o 10%.  be l e s s  8  The h e i g h t t o which t h e s e n s i b l e heat f l u x 10%  remains  of i t s s u r f a c e v a l u e i s not o b v i o u s and i t may  below u s u a l measurement h e i g h t s .  Since c-<T>/dx  within  sometimes be  is  not  simply  r e l a t e d t o the l a r g e s c a l e p r e s s u r e g r a d i e n t , i t i s not p o s s i b l e to s c a l e the v e r t i c a l divergence done  for  the  Reynolds  of Hs t o a C o r i o l i s term as  stress.  Neglecting  change i n Hs i s found a t a h e i g h t he g i v e n  he  =  0.1  <wt>  (fiT/fit)-*  radiation, a  divergence,  ,  d u r i n g a time i n t e r v a l  the sea show t h a t <wt> i s of Schmitt,  1976),  order  10~  3  fit.  vertical  heat  Measurements over  <U>  AT  (Friehe  and  where AT i s t h e temperature d i f f e r e n c e between  the sea s u r f a c e and atmosphere. <0>  10%  by  where 6T i s the change i n t e m p e r a t u r e due t o the flux  was  To  keep  he  above  10m,  with  AT as low as 10 °Cm/s r e q u i r e s  6T/  which  may  fit  <  0.36  °C/hour,  not n e c e s s a r i l y be s a t i s f i e d .  sea i s l a r g e , contributor  presumably with  ,  h o r i z o n t a l advection  6T/ fit h o p e f u l l y  temperature i s steady <D>  When a <T>/o t over  remaining  3<T>/3x must b a l a n c e  ,  is  the  the  major  small.  When t h e  dHs/c-z  in  2. 2,  giving  he  and  implying  =  10-*  that  AT  he  ( 3<T>/dx )-»  is  only  above 10m  when the h o r i z o n t a l  9 temperature g r a d i e n t i s r a t h e r s m a l l , l e s s than 0.01 °C/km f o r a AT of 1°C.  A further complication  i n f r a r e d absorption divergence  that  (Busch, 1977). when  height  anywhere  tends  to  This e f f e c t  cause  Hs  to  i n c r e a s e with  enhances t h e p o s i t i v e f l u x  height  gradient  but reduces the l o s s of s e n s i b l e heat f l u x  when AT i s p o s i t i v e .  i n the "constant  equivalent  when  by water vapour may produce a r a d i a t i v e f l u x  _.T i s negative,  with  a r i s e s during low winds  It will  be  assumed  that  Hs  s t r e s s " l a y e r over a temperate sea i s  t o the s u r f a c e f l u x t o w i t h i n  the  accuracy  o f the  measurement.  H o p e f u l l y , t h i s assumption i s t r u e on average, but  verification  would  require  a  d i r e c t measurement o f Hs at two  levels.  2.2  Monin-Obukhov S i m i l a r i t y Theory The  layer and  understanding  of  the  turbulent  atmospheric  surface  i s l a r g e l y due t o Monin-Obukhov s i m i l a r i t y theory  Yaglom, p  425  characteristics  ff).  The  theory  assumes  that  (Monin  turbulent  depend only on a few p h y s i c a l parameters,  f a c i l i t a t e s the a p p l i c a t i o n of dimensional  analysis.  which  Above  the  d i r e c t i n f l u e n c e of the bottom boundary the important parameters are  the  height  horizontally turbulent  (the only s p a t i a l v a r i a b l e l e f t i n the assumed  homogenous  transports  turbulence),  the  and the s t a b i l i t y of the a i r column*  supposed height  independence o f t h e f l u x e s  the  scales  following  a i r density,  naturally  leads  the The to  which i n c o r p o r a t e the t r a n s p o r t s through  the l a y e r and t h e d e n s i t y :  10 friction velocity  u*  =  (Ib/^>) */  =  temperature s c a l e  t* =  -<wt>/ /<u*  scalar scale  r* =  -<wr>/ Ku* ,  2  where von Karman's c o n s t a n t , K, i s i n c l u d e d  |-<uw>|*/  2  (2.4)  to  simplify  later  equations, but other s c a l e s  T* = -<wt> / u* and  are sometimes used. obtained  from  E* = -<wr> / u*  An a p p r o p r i a t e s t a b i l i t y  parameter, Z/L, i s  the r a t i o o f the c o n v e c t i v e or buoyant  turbulent  k i n e t i c energy, B, produced i n a n o n - n e u t r a l a i r column, t o the purely mechanical production i n t h e e q u i v a l e n t n e u t r a l case, Po. It  w i l l be seen i n s e c t i o n 2.5, t h a t  B  where  Tv,  =  g <w Tv> / To  the  and  =  u * V KZ ,  (2.5)  v i r t u a l temperature i n degrees K e l v i n , accounts  f o r the f l u c t u a t i n g temperature and the  Po  moisture  contributions  to  f l u c t u a t i n g d e n s i t y , g i s g r a v i t a t i o n a l a c c e l e r a t i o n and To  i s t h e l o c a l average v i r t u a l temperature.  The  important  scale  i s the Monin-Obukhov l e n g t h , L, whose magnitude gives the height at which Po = |B|, thus  -Z L  In  neutral  =  B_ Po  and  stratification  L  =  - u * _To_ . K g <w Tv>  <w Tv>  3  and  (2.6)  Z/L go t o zero w h i l e L  11  approaches i n f i n i t y positive  in  and the s i g n i s chosen t o  stable  conditions.  make  L  L  should  group, Z/L. and  a  be  frequency, f , possible,  f u n c t i o n s of t h e only  to  the problem.  making  but  a  further  because  of  dimensionless  natural  substituted.  Normalized  of  both  the  u*, r *  dimensionless  2  2  scale  Ose of s p e c t r a i n t r o d u c e s a  difficulty  frequency  n  (cru) = <u > and ( e f t ) 2  possible  dimensionless  the  n  =  group,  fZ/u*,  i n obtaining  fZ/<U>  s p e c t r a and c o s p e c t r a  as non-dimensional t u r b u l e n t functions  Z,  Note t h a t each a d d i t i o n a l s c a l a r adds both a  dimension  Z/L  Dimensional a n a l y s i s p r e d i c t s  t h a t a l l t u r b u l e n t f u n c t i o n s non-dimensionalized by and  and  is  u* the usually  can be regarded  f u n c t i o n s and t h e r e f o r e  should  be  and Z/L, whereas t h e i r i n t e g r a l s such as  = <t > should  depend only  2  on  Z/L.  With  important parameters common t o a l l s u r f a c e l a y e r f l o w s , the  s t r u c t u r e of the t u r b u l e n c e , always  be  "similar",  according  to  this  theory,  must  with any dependencies cn Z/L and n being  universally applicable. An  important  logarithmic  consequence  profile  of  Dimensional c o n s i d e r a t i o n s  XZ_ u*  _<0> dz  =  0m  the  of  similarity  mean  wind  and  theory mean  i s the scalars.  l e a d d i r e c t l y t o t h e forms:  (Z/L) ( 2  and  Z_ d<R> r * l>z  =  9r(Z/L)  where von Karman's constant has  already  ^r(0)=1.  been  included  Measured v a l u e s  *7)  ,  s e t s ^m=1 a t n e u t r a l in  the  of K vary  definition  stability  and  of r * so that  between about 0.35 and  0.42  12 (Busch, 0.40  1977), so a t l e a s t a 5% e r r o r i n i t s customary v a l u e of  must  be  relationships.  allowed. Dyer,  In  a  review  of  flux-profile  1974, suggests t h a t t h e best forms o f t h e  u n i v e r s a l f u n c t i o n s are  0 -1.0  < Z/L < 0.2:  r*m = r>r = 1 + 5 Z/L  < Z/L <  fm = (1 - 16 Z/L)-i/*  0 :  r*r  where t h e u n s t a b l e provided  by  =  the  case i s  (1 -  16  Z/L)-i/2  Businger-Dyer  Dyer and H i c k s , 1970.  ,  representation  The mean v a l u e s a t a h e i g h t  Z, UZ and EZ, a r e found by i n e g r a t i n g 2.7, (Paulson, 1970),  OZ = ( U * / K)  • [ l n ( Z / Z o ) - Ym(Z/L)  ]  EZ = BSFC + r * [ l n ( Z / Z o r ) - Y r (Z/L)  where  Viz/L) = stable:  unstable:  J^\^  ' *  (£)  3 /£  ],  (2.8)  ^  "Ym(Z/L) = Yf (Z/L) = -5 Z/L  Ym (Z/L)  = 2 ln[(1 + X)/2] -  2 tan-iX  + ln[  (1+X2)  /2 ]  + 7T/2  Yr(Z/L) = 2 l n [ ( 1 + X 2 ) / 2 ]  with  X = ( 1 - 1 6 Z/L) i / *  .  At n e u t r a l s t a b i l i t y t h e i n t e g r a l The  constants  of  integration  Zo  vanishes,  leaving  V(0) = o  and Z o r , assumed t o be much  13 s m a l l e r than Z, are the roughness l e n g t h s , which f u l l y  describe  the s u r f a c e as "seen" by the t u r b u l e n c e , but they are not simply related  to  sea  temperature.  surface  They  parameters  need  to  be  such  as  included  in  wave height and the  dimensional  a n a l y s i s only near t h e s u r f a c e where they s e t the magnitude, but not the s t r u c t u r e , o f the turbulence throughout  2.3  Bulk Aerodynamic P a r a m e t e r i z a t i o n s The f l u x e s are parameterized  sea  the l a y e r . .  surface-air  temperature  i n terms of the mean wind, t h e  difference  and  s u r f a c e - a i r mean  s c a l a r d i f f e r e n c e , AR, with t h e bulk aerodynamic  Z~/£  =  u*  2  <uw>  =  CD <D>2  formulae:  Hs/^Cp  = - K u* t * =  <wt>  =  CT <0> AT  Hr  = - K u* r * =  <wr>  =  CE <D> AR,  (2.9)  with -AT=TSCF-TZ and AR=RSFC-RZ, where TSFC and RSFC a r e the mean surface  temperature  non-dimensional  and  scalar  transfer  coefficient  and  Stanton  coefficient  of  moisture  coefficients number  CD  while  transport,  T h e i r dependence on s t a b i l i t y , from  values,  respectively.  and CT a r e t h e drag the  corresponding  CE, i s the Dalton number.  roughness and height  i s evident  2.8, but Zo over the sea has a complicated f u n c t i o n a l  (Burling determined  and  Stewart,  1967).  experimentally  bulk q u a n t i t i e s  and  such  from  However, 2.9  calculated  The  they  can  form  also  be  using measured f l u x e s and coefficients  provide  a  14 convenient  means  of comparing f l u x measurements.  To e l i m i n a t e  the v a r i a t i o n with height they are commonly e v a l u a t e d at 10m a s :  C10  = -<uw> / (U10)  2  CT10  =  <wt> / [D10 (TSFC-T10) ]  (2.10)  CR10  =  <wr> / [D10 (RSFC-R10) ] . .  Equation 2.8 shows the wind speed, temperature and s c a l a r  means  a t 10m (U10, T10 and R10) t o be:  D10 = DZ - (u*/ X) [ I n (Z/10m) -"Vm(Z/L)  For  + Yin (10m/L) ]  T10 = TZ - t * [ln(Z/10m)  - VI (Z/L) + "Vi (1 Om/L) ]  R10 = RZ - r * [ln(Z/10m)  - Y t (Z/L) + "Vr (10m/L) ] .  comparative  purposes  i t i s convenient  t o e l i m i n a t e the  s t a b i l i t y dependence by e v a l u a t i n g t h e roughness 2.8  and  using  (2.11)  lengths  from  them t o f i n d the c o e f f i c i e n t s i n the e q u i v a l e n t  n e u t r a l case at 10m from:  The  CDN  =  Kz  / [ln(10m/Zo) ]  CTN  =  X  2  / [ In (10m/Zot) • ln(10m/Zo)]  CRN  =  X  2  / [ln(10m/Zor) • ln(10m/Zo)] .  neutral  homogeneous as constant. Zo,  should  be  (2.12)  constants  over  t e r r a i n where the roughness l e n g t h s can be regarded T h i s p r e d i c t i o n has been v e r i f i e d over land  f o r example,  vegetation.  coefficients  2  where  i s e x c l u s i v e l y determined by topography and  I t i s n o t unreasonable t o expect  this  concept  to  15 work  even  surface. (1977)  better  over t h e sea where t h e r e i s o n l y one t y p e o f  However, are  direct  very  measurements*  scattered  reviewed  by  Garratt  and i n d i c a t e t h a t t h e n e u t r a l drag  c o e f f i c i e n t v a r i e s w i t h wind speed and i s much s m a l l e r than t h a t found over l a n d . important  parameters  surface. is  This r e s u l t implies that there are a d d i t i o n a l of  the sea  An o b v i o u s d i f f e r e n c e between a l a n d and sea  boundary  surface  gravity  determining  waves,  the  roughness  so i t seems a p p r o p r i a t e t o add t h e  a c c e l e r a t i o n due t o g r a v i t y , g, t o t h e problem. the Charnock (1955) d i m e n s i o n l e s s  Zo  where  g / u*2  =0.0144  This  leads  to  group f o r f l o w near t h e waves,  = <=<-  (2.13)  i s suggested by G a r r a t t (1977).  n o t e s t h a t f o r winds below 10 m/s  Stewart,  t h e Charnock  1974,  representation  w i t h °<- c o n s t a n t p r e d i c t s a more r a p i d i n c r e a s e i n CDN w i t h wind speed  than  i s indicated  Kriiggermeyer  (1970)  G a r r a t t ' s review. parameters Stewart  may  and  this  be  important the  waves),  which  of  Brocks  i s also  therefore,  that  roles  of  and  present more  surface  in  surface  t o t h i s aspect of turbulent  the length  i s proportional  results  feature  possible  e x c i t e d waves, t h e wave s l o p e force  the  I t appears,  discusses  (capillary  by  flow.  tension  and phase speed of t h e l o n g e s t  and to  the (wind  total speed  wind  generation  - wave speed).  K i t a i g o r o d s k i i and Z a s l a v s k i i , 1974, c o n s i d e r t h e phase speed o f the dominant wave and a p u r e l y v i s c o u s momentum and  Stewart,  v a r i o u s moments  1967, of  examine the  wave  flux.  Burling  the i m p l i c a t i o n s of dependency on spectrum.  With  the  roughness  16 lengths  p o s s i b l y depending on many parameters i t appears that a  r a t h e r d e t a i l e d knowledge of the sea s u r f a c e would before  be  required  the t u r b u l e n t f l u x e s over the sea could be found from Zo  and Zor. The p a r a m e t e r i z a t i o n s can a l s o formulae.  An  experimental  c o e f f i c i e n t s at 10m, to  be  estimated  (AT = TSFC-TZ),  2.12,  be  regarded  formulation  f o r example*  as  of  empirical  the  would allow  neutral  the  fluxes  from mean or bulk q u a n t i t i e s , UZ, TZ and TSFC  with  Z/L,  i f  known,  providing  a  stability  correction. The momentum f l u x can be found from 2.9 by f i n d i n g the drag coefficient  at  the  measurement height, Z, the wind speed, OZ,  and the s t a b i l i t y , 2/L, from CDN.  E l i m i n a t i o n of Zo  and 2.8 and s u b s t i t u t i o n i n t o 2-9  CD = CDN  where  ln(Z/10m)  {1+ CDN / K 1  2  - 1  as  a  s h i f t e d t o 10m Substituting for  2.12  leaves,  (In (Z/10m)-Ym (Z/L) ) } , -2  (2.14)  and Yin (Z/L) d e s c r i b e the v a r i a t i o n of the drag  c o e f f i c i e n t with h e i g h t and s t a b i l i t y , given  from  function before a  of  the  drag  10m  2  I f CDN  wind* then DZ must f i r s t  coefficient  u*/UZ = CD*/ = C10V 2  respectively.  can  be  is be  determined.  010/DZ, i n t o 2.11  and s o l v i n g  UZ/010 l e a v e s ,  DZ/010 = 1+ C10V  2  K~ l  [ln(Z/10m)-Vin(Z/L)+Yln(10m/L) ].  The term i n square b r a c k e t s , K(Z,Z/L), i s u s u a l l y  dominated  by  17 ln(Z/10m), larger  which,  with  C10 / / 1  this  height  range n e g l e c t  K(Z,Z/L) i n t r o d u c e s an e r r o r <Z/L<  0.08,  additional ignored.  however  6%  =  2  Z/L=0.2, t a k i n g  error,  of  ranges  UZ  itself  [1  from  depend on 010,  than  portion  2%  for  of  -1.0  010  by a b o u t  Z/L=0.1,  so  i t  a t Z=10m, so 2.14  1 a t Z/L=  is  an not  gives  -1 t o about  b r a c k e t s t o be  -1 a t  1.0  introduces  i s within usual  measurement  OZ,  CDN  and  Z/L  using  K-  K{Z,Z/L)]~i.  2.15  may  1  2  respectively.  decreases  at  which  + CDN*/  27m,  10%  2  t h e term i n c u r l y  =  of l e s s  from about  1% i n 010,  and  about  CDNi/ Ym (10m/L) } ~ i .  l  2  when i t i s c a l c u l a t e d  CDN  3%  makes 010  of the s t a b i l i t y  i t  {1 - K~  CDN*/  only  010  Should  Z=27m  i s e q u i v a l e n t t o CD  Ym(10m/L)  error  at  i n 010  w i t h Z/L=0.2 and  C10  C10V  an  0.1,  o r s m a l l e r t h a n UZ f o r a Z o f 3.7m  Throughout  Since  =  2  (2.15)  have t o be s o l v e d  with  an i t e r a t i v e t e c h n i q u e . If unknown  the s t a b i l i t y and  inaccurate because  assumed  010,  CDN  Banke,  and  associated  the  be  finding  neutral, CDN  f o u n d f r o m 2.15  1975,  0.000075 U10, CDN  in  to  from  <Z/L<  errors 010  0.2, arise  and  s h o u l d be l e s s t h a n  r e p o r t a drag c o e f f i c i e n t  s o a 10% e r r o r momentum  with d i r e c t  i n 010  flux,  at 20  which  measurements.  is  but  is  from  an  through  i s not s h i f t e d t o t h e proper s t a b i l i t y .  e r r o r i n 010's and  i s i n t h e r a n g e -1.0  The  10%.  2.14, total Smith  e q u a l t o 0.00061 +  m/s, less  r e d u c e s t o 7% than  With Y i n (Z/L)  in  the  error  ranging  from  18 1.0 the  to  -1.0, t a k i n g i t t o be z e r o c o u l d l e a d t o a 20% e r r o r i n  momentum f l u x .  Only i n t h e range -0.25 <2/L< 0.1  does t h e  t o t a l e r r o r i n assuming n e u t r a l s t a b i l i t y remain l e s s than 10%. I f CD and CDN a r e a v a i l a b l e , t h e analogous procedure can be followed  t o f i n d t h e s e n s i b l e heat f l u x from TZ, TSFC, and 0Z,  u s i n g 2.9. of  CTN,  The Stanton number, CT, i s e x p r e s s e d a s  CDN,  a  function  CD, and Z/L, by e l i m i n a t i n g Zo and Zot from 2.12  and 2.8, then s u b s t i t u t i n g i n t o 2.9:  CT  =  CTN [ 1 + CTN K- 1  (CD/CDN) */ . CDN-*/ ( l n (Z/10m)-"Vl (Z/L) ) ] 2  2  The major e r r o r comes from t h e u n c e r t a i n t y in  CDN  and CD due t o U10 c a n c e l  CDN and CTN i n t r o d u c e s Yt(Z/L)  i  sn  o  t very  a 2% e r r o r  i n CTN.  The  assumption  errors  i n (CD/CDN) and a 10% e r r o r i n i n t h e denominator.  d i f f e r e n t from Yin (Z/L) , assuming  s t a b i l i t y causes about t h e same e r r o r i n CT as i n CD. this  (2.16)  Since neutral However,  i s never needed, because a means o f e s t i m a t i n g  Z/L from OZ and AT, which a r e r e q u i r e d i n 2.9, i s developed i n section  2.6.  The  uncertainty  o f t h i s e s t i m a t e ( s e c t i o n 4.2)  s h o u l d r e s u l t i n about a 5% e r r o r i n CT and CD. The s e n s i b l e heat f l u x i s sometimes p a r a m e t e r i z e d as  where  a  stability  <wt>  =  a  010  and  b  are experimentally  and wind speed.  (TSFC-T10)  +  b ,  determined  functions  of  The a i r t e m p e r a t u r e a t 10m, T10, c a n  be found as f o l l o w s ; from 2.11  19 TZ - T10  =  t * [ In (Z/10m) -  (Z/L) + > t ( 1 0 m / L ) ] ,  where t h e term i n s q u a r e b r a c k e t s , t o be denoted behaves  as  Kt(Z,Z/L),  as K(Z Z/L) and the s t a b i l i t y c o n t r i b u t i o n can a g a i n be r  i g n o r e d i n near n e u t r a l c o n d i t i o n s .  Substituting for  t * using  2.9 g i v e s  T10 = TZ • (CT/CDi/ ) Kr 2  2.4  1  (TSFC-TZ) K t ( Z Z / L ) .  (2.17)  f  The Reynolds F l u x Method The  Reynolds  flux  o r eddy c o r r e l a t i o n method i s t h e most  d i r e c t measurement o f t h e f l u x e s and has been employed over sea and  by  Pond  others.  either  u  et a l . ,  the  1971, H i c k s , 1972, Smith and Banke, 1975,  I t involves i n t e g r a t i n g the cospectra  of  w  and  o r r t o o b t a i n t h e c o v a r i a n c e s and hence f l u x e s .  The  s p e c t r a l forms of t h e c o v a r i a n c e s a r e :  <uw>  = JVuw(f)  df  <wt>  = J^wtff)  df  <wr>  = _/>vr(f)  df.  (2.18)  I n p r a c t i c e t h e c o s p e c t r a a r e determined by d i g i t a l f a s t F o u r i e r t r a n s f o r m t e c h n i q u e s , which g i v e intervals  values  of  f ( f ) at  o f f such t h a t f(f) A f g i v e s t h e c o v a r i a n c e i n a band  centered a t f of width Af. Nyquist  discrete  frequency,  The h i g h e s t frequency  computed, t h e  f n y , i s s e t by t h e d i g i t i z a t i o n p e r i o d At:  20 (fny=1/2_t) . allowed  to  Contributions alias  back  from  below  higher  described  in  can  fny so t h a t the e f f e c t i v e  l i m i t of the i n t e g r a t i o n i s i n c r e a s e d system  frequencies  section  ( to about 2  3.3).  fny  only  a  few  per  cent  of  upper  in  the  The c o n t r i b u t i o n s to the  c o v a r i a n c e s from n a t u r a l f r e q u e n c i e s , n=fZ/<0>, g r e a t e r are  be  the t o t a l .  than  With 20 m/s  measurements at 10 m w i l l t h e r e f o r e i n c l u d e  most  of  winds,  the  high  frequency c o n t r i b u t i o n s i f A t i s no longer than Z/<0>, about seconds. of  0.5  The lowest c a l c u l a t e d frequency, f 1 , i s the r e c i p r o c a l  the  duration  of  the  c o v a r i a n c e down to f1 /2.  measurement  and  ^ ( f 1 ) i n c l u d e s the  Some c o s p e c t r a are s t i l l non-zero  n=0.001, so i n order to be a b l e t o measure f l u x e s i n 5 m/s at  1  at  winds  10 m the samples must be taken f o r about Z/(0.002<0>) =  seconds  or  about  statistically  15  minutes.  However  ^(f1)  is  1000  not  a  w e l l determined q u a n t i t y and i n p r a c t i c e a t l e a s t  3 s e q u e n t i a l d e t e r m i n a t i o n s need to be averaqed,  requiring  the  d u r a t i o n of a f l u x run t o be at l e a s t 45 minutes. U n f o r t u n a t e l y , measurements cannot be extended t o more than about  1  hour  because  s t a t i o n a r i t y begins t o be l o s t as a new  flow s i t u a t i o n develops. f l u x e s are o f t e n not method.  It  is  The low frequency c o n t r i b u t i o n s to the  well  also  established  clear  <uw>  estimate  the  Reynolds  flux  t h a t another disadvantage to t h i s  method i s the l a r g e amount of data sinqle  by  required.  For  example,  from a 45 minute run with _t=0.5 seconds  r e q u i r e s about f i v e thousand d i g i t i z a t i o n s of each v a r i a b l e . course the s p e c t r a of the measured q u a n t i t i e s may from  the  a l s o be  same data and are o f t e n a great advantage  sensor performance.  a  Of  found  i n checking  The s e n s i t i v i t y of the Reynolds f l u x method  21 to  instrument  buoys,  orientation i s  whose  covariances. anemometer 1968).  motion A  one  a  and  great  mean  degree  handicap  tilt  error  in  on  effect the  ships  the  mean  and  measured  tilt  cf  an  may induce e r r o r s i n <uw> i n the order of 10% (Pond,  It i s possible to  measure  the  instantaneous  platform  motion and to c o r r e c t t h e v e l o c i t i e s point by p o i n t (Mitsuta and Fujitani,  1974),  requirements  but  this  and i s not a  greatly  very  l a r g e amounts of open sea f l u x The  Reynolds  methods  are  calculated transfer  2.5  practical  the  recording  of  obtaining  means  measurements.  f l u x method i s not very a p p l i c a b l e t o remote  open sea o p e r a t i o n , but i t has other  increases  compared  become either  the  standard  directly  or  to  through the  coefficients.  The D i s s i p a t i o n Method F o l l o w i n g Deacon's, 1959, s u g g e s t i o n the d i s s i p a t i o n  has been employed i n open sea c o n d i t i o n s by Pond Wucknitz,  1976,  Denman  measurement  and Miyake, 1973, and o t h e r s .  tolerated. uncertainty assumptions.  an  1971,  It isa explicit  of the v e r t i c a l v e l o c i t y * a l l o w i n g moving p l a t f o r m s  be used and reducing measurement  distortions  method  et a l . ,  very a t t r a c t i v e method because i t does not i n v o l v e  to  which  that  would  errors.  In  various the  addition,  flow  hinder c o v a r i a n c e measurements, can be  Instead, the major sources of of  In  cited  constants studies  error  and  in  arise the  i t s results  in  the  necessary have  been  22 compared  to  direct  Reynolds  f l u x measurements up t o moderate  winds, but f u r t h e r comparison  at  high  wind  speeds  is  still  necessary. In  the  case  of t h e momentum f l u x t h e method stems from a  c o n s i d e r a t i o n of the balance o f unit  mass,  flow  e  =  (u + v 2  2  turbulent  kinetic  energy  per  + w ) / 2 , i n h o r i z o n t a l l y homogeneous 2  (Busch, 1977),  cke> = u * dt  2  d<0> + g <w_Tv> dz To  £ -  P  € -  +  B  -  3 [<we> + 1, <wp>]  5z  £  D ,  (2. 19)  where Tv i s the v i r t u a l temperature i n degrees K e l v i n and To i t s l o c a l average and p fluctuations the  i s the  fluctuating  pressure.  a r e c h i e f l y produced by mechanical i n t e r a c t i o n s of  Reynolds s t r e s s with t h e mean flow r e p r e s e n t e d by the  term,  p=u*  2  3<U>/dZ  d i s s i p a t i o n , £.  From  and  lost  Lumley  at  and  small  Panofsky,  1964  as the l o s s o r gain due t o buoyancy  s e c t i o n 2.2.  D i s t h e sum  first,  work  <wp>/g.  done  per  vertical  referred  B is to i n  divergences: the  u n i t area by the f l u c t u a t i n g  These are r e f e r r e d t o as  transports  of  kinetic  divergence term has been  height  two  p95,  of the t u r b u l e n t k i n e t i c energy f l u x <we> and the second,  the  1975.  of  first  s c a l e s t o molecular  recognizable  of  Turbulent  energy,  the  turbulent  respectively.  investigated  by  McBean  pressure,  and  pressure  The  complete  and  Elliot,  In t h i s work <we> and <wp> were measured over land at one for a  0.12 gave  range  o f Z/L v a l u e s .  A f i t between -0.31 <Z/L<  23 <wp> /  u* )  =  3  2.3 Z/L  -  0.20 .  T h e i r <we> r e s u l t s were p l o t t e d w i t h t h o s e o f G a r r a t t , 1972, and Banke and S m i t h , 1973.  In view  of the s c a t t e r  i t i s not  unreasonable t o assume a r e l a t i o n  <we> / u *  3  =  -2.3 Z/L  +  constant.  E x t e n s i v e measurements over l a n d o f the t u r b u l e n t t r a n s p o r t  term  have been made by Wyngaard and Cote", 1971, over a wider range o f stabilities.  In unstable  conditions  their  results  c a n be  expressed as  <we> / u *  3  =  -2.5 Z/L  +  constant.  The combined e x p e r i m e n t a l e v i d e n c e i n t h e range  -1  <Z/L<  0.1  suggests t h a t t o a v e r y good a p p r o x i m a t i o n  <we>  +  <wp>/^  =  a constant  D i f f e r e n t i a t i o n by z i m p l i e s t h a t on average, t h e k i n e t i c gained  through  p r e s s u r e t r a n s p o r t n e a r l y b a l a n c e s t h a t l o s t by  turbulent transport, that conclude  that  i s , D=0-  the e f f e c t s  Wyngaard  and Cote  also  of h o r i z o n t a l i n h o m o g e n e i t i e s and  n o n - s t a t i o n a r i t y are n e g l i g i b l e magnitude,  energy  t h a t i s , d<e>/dt = 0.  by  more  than  two o r d e r s o f  24 Combining  2.6  and  the p r o f i l e  e q u a t i o n s , 2.7, w i t h t h e  r e m a i n i n g terms i n 2.19 r e s u l t s i n t h e s i m p l e s e t of e q u a t i o n s :  where  P  =  B  =  - ( * 3 / jcz)  6  =  Po  Po,  (u*  / KZ)  0m (Z/L)  =  Po  Z/L  =  -Po  Z/L  2.2,  is  the  U  i n section  i n the e q u i v a l e n t  s i m p l y expressed  3  fm(Z/L)  [ 0 m (Z/L) - Z/L ]  introduced  production  u*  3  neutral  case.  mechanical  Thus u* can be  as a f u n c t i o n o f € and Z/L:  = < Z € / [ 0 m (Z/L) - Z/L] .  (2.20)  I n a s i m i l a r f a s h i o n t h e problem o f e v a l u a t i n g r * and t h e scalar  fluxes  c a n be  simplified  to finding  d i s s i p a t i o n r a t e of s c a l a r f l u c t u a t i o n s , N r . 2.19  The  =  2  -<wr> d<R> 6z  -  Nr  -  f o r temperature.  of  1977),  J. d<wr > . 2 bz 2  (2.21)  study of flyngaard and Cote (1971) i n v e s t i g a t e s t h i s  thoroughly  and t h e  analogue  i s t h e s i m p l e r s c a l a r v a r i a n c e budget, (Busch,  1 _<r > 2 dt  The  u*  The v e r t i c a l d i v e r g e n c e  equation  term t u r n s  out t o be an o r d e r o f magnitude s m a l l e r than t h e p r o d u c t i o n term and the time  rate  negligible. straightforward  of  change  Substituting relationship  and  inhomogeneities  f o r d<E>/3z  from  2.7  are  again  gives the  25 r*z  =  Nr  Z / [K u* f r ( Z / L ) ] .  (2.22)  D i r e c t measurements of 6 and Nr are d i f f i c u l t involve  centimeter  scales  (frequencies  However, they c a n be i n f e r r e d  well  because  they  beyond 100 Hz).  from t h e s p e c t r a o f  the s c a l a r s ,  ^ r ( f ) , and downstream v e l o c i t y , ^ u ( f ) , a t f r e q u e n c i e s , f , i n t h e -5/3  region where t h e Kolmogoroff  where  ^U(f)  =  K' 62/3  ^r(f)  =  Br' Nr € " V  Taylor's  is  also  based  Kolmogoroff but  they  /<0>)-2/3 f-5/3  (27T  hypothesis  r a d i a n wavenumber with on  (27r/<0>) - 2 / 3  (2TC f/<0>) .  dimensional  f-sfc ,  a r e n o t , as  f o r both  Pond, 1971 and Busch,  The form of these  analysis  yet, well  temperature a  equations  so the 1-dimensional stability,  enough e s t a b l i s h e d f o r any  Reasonable  1977), with  (2.23)  t o r e p l a c e t h e downstream  c o n s t a n t s K' and Br* may be f u n c t i o n s of  Br' = 0.80  terms  3  i s used  dependency t o be observable. and  hypothesis p r e d i c t s  values  a r e K' = 0.55  and moisture  possible  10%  (Paquin and error-  In  o f the n a t u r a l frequency, n=fZ/<D>, the -5/3 r e g i o n has  been found t o be w e l l  developed  by  n=1  so  that  dissipation  estimates may be obtained from r e l a t i v e l y low f r e q u e n c i e s (about 2 Hz, f o r 20 m/s winds a t 10m h e i q h t ) . Several  methods  of  calculating  measurements of 6 and Z/L a r e f e a s i b l e . used by Denman and Miyake, of 2.20  the momentum  flux  from  The s i m p l e s t , method 1,  1973, i s t o employ t h e n e u t r a l  form  26 <UW>DISSI  This  z  ( K  =  e  3  equation i s a l s o v a l i d i n non-neutral c o n d i t i o n s p r o v i d i n g  t h e r e i s an o v e r a l l balance between the  (2. 24)  ) z/  buoyant  mechanical  production  and  production.  The  the v e r t i c a l  the s t a b i l i t y experimental  divergences,  m o d i f i c a t i o n of t h e evidence  suggests  that  the sea.  Method 2, t h e r e f o r e , assumes o n l y  over  land  t h e complete form of 2.20 s h o u l d be t e s t e d over that  the v e r t i c a l  d i v e r g e n c e s b a l a n c e and uses  <uw>DISS2  This  =  i s t h e method  Wucknitz,  the l a t t e r  uses  a  Eichardson  of  order  Banke,  1975),  with  a  pressure  -Z/L t o a r r i v e a t 2.25. I t has o f t e n been  assumed t h a t l o c a l p r o d u c t i o n , P, and  number  and t h e former assume a b a l a n c e , f o l l o w i n g Wyngaard  and Cote, of buoyancy and t u r b u l e n t t r a n s p o r t transport  (2.25)  used by K h a l s a and B u s i n g e r , 1978, and by  1976, but  formulation  ( K Z € ) 2/3 • ( l _ (Z/L) - Z/L)-2/3  balances  dissipation  (Smith  i m p l y i n g an o v e r a l l b a l a n c e between t h e two  d i v e r g e n c e s and buoyancy.  T h i s i s the assumption  of  method  3,  which s t a t e s  <uw>DISS3  Pond  et a l . ,  =  {K  Z 6)2/3  1971, found  that  •  [^m(Z/L) ]-2/3 .  i n unstable  momentum f l u x from t h e d i s s i p a t i o n  and  Eeynolds  (2.26)  c o n d i t i o n s the flux  methods  were i n t h e b e s t agreement i f they assumed t h a t t h e r e d u c t i o n i n mechanical  production  due  to  stability  modification  of the  27 profile  was compensated by t h e net gain i n t u r b u l e n t energy from  vertical  t h a t i s , 6 = Po + B.  divergences,  This  fourth  method  i s expressed by  <uw>DISS4  The general  The  (1 - Z/L)-2/3.  (K Z 6 ) /  Method 1  F1  =  1  Method 2  F2  =  [ ^m(Z/L) - Z/L ]~ /  Method 3  F3  =  [ ^m (Z/L) l " /  Method 4  F4  =  £1 - Z / L ] - / .  2  FX,  likely  •  FX  2  2  2  are to  3  3  p l o t t e d i n f i g u r e 1 over t h e range of  be  encountered  I t i s apparent  be  valid  range there  the most a p p r o p r i a t e , Equations  (2.28)  3  3  that  over  over  should  an  the  sea  at  a reasonable measure of  i s important t o a l l but method may  (2.27)  o f t h e four d i s s i p a t i o n methods i s  =  mid-latitudes.  stability  •  <uw>DISS  stabilities  methods  6 )^  (n  expression  functions,  stability  =  1.  any  individual  one  o f the  run, but over any  be one d i s s i p a t i o n method  that  is  on average.  2.23 and  2.28 i n d i c a t e t h a t <uw> from a l l t h e  d i s s i p a t i o n methods i s p r o p o r t i o n a l t o  [  K Z ] / K'-i 2  3  ( f S i ( f ) <0>~ / ).  Even with no e r r o r i n t h e measurement u n c e r t a i n t i e s i n K,  2  of  (2.29)  3  ^u (f)  59S, i n the measurement heiqht  and  <D>,  the  Z, say 0.5m i n  28  29 10m  and  <uw>.  in  K',  10%,  c o u l d combine t o produce  a 15% e r r o r i n  assumption  likely  These e r r o r s and  somewhat  systematic,  the Reynolds measurements  but  errors  are  to  be  f o r t u n a t e l y they are not the same i n  f l u x method.  Intercomparisons with  Reynolds  flux  are t h e r e f o r e e s s e n t i a l , i n order to e s t a b l i s h the  "best" d i s s i p a t i o n method and to ensure t h a t there are no  major  systematic e r r o r s . There  are  fewer  ways  a r r i v e a t Nt, and only two heat  flux  vertical of  are  methods of c a l c u l a t i n g  practical.  At  profile,  <wt>DISS1  the  the  stability  experimental  sensible  modification  method 1, gives  [ K u* Nt Z ]i/2 .  =  to  n e u t r a l s t a b i l i t y and when the  divergence term i s balanced by  the temperature  Again  of " j u g g l i n g " the terms of 2.21  (2.30)  evidence over l a n d suggests using  2.22  from which method 2 assumes  <wt>DISS2  [ K  =  u* Nt Z ] i /  [ ft (Z/L) ]~ I .  •  2  1 Z  (2.31)  The g e n e r a l form of c a l c u l a t i n g the s e n s i b l e heat f l u x i s simply  F1  and  [ K u* Nt Z]*/  <wt>DISS  =  Method 1  F1  =  1.0  Method 2  F2  =  [ ^ t (Z/L) ] - i / .  F2  considerably  are  shown  2  •  FX (2.32)  2  in  figure  2.  even near n e u t r a l s t a b i l i t y ,  The  methods  differ  t h e r e f o r e , the "best"  FIGURE 2  Stability adjustments of the methods of e s t i m a t i n g the s e n s i b l e  two dissipation heat f l u x .  31 method should be easy t o e s t a b l i s h , depending the  s t a b i l i t y measurements,  since  method  on the accuracy of  2  i s sensitive  to  e r r o r s i n Z/L. Equations  2.32, 2.23 and 2.20 i n d i c a t e t h a t <wt> from both  d i s s i p a t i o n methods i s p r o p o r t i o n a l t o  ( K Z)2fr _ [ Bt» K ' ]7/2 Again u n c e r t a i n t y i n K,  [ 0 t 0U]l/2  <U>"2/3 .  Z and the Kolmogoroff c o n s t a n t s t o g e t h e r  c o u l d produce a 15% e r r o r i n <wt>DISS. possible  to  (2.33)  substantially  reduce  However,  systematic  i t should errors  be  through  Reynolds f l u x i n t e r c o m p a r i s o n s .  2.6  Estimating In  section  characterized fundamental  of  Tv  and  by  a  the  =  - KJL g u* 3  To,  i t from  the  of  parameter,  i t is difficult  The complete  Z/L  stability  stability  estimating  investigated.  Z L  2.2,  Parameter  r o l e i n the theory and  Unfortunately, means  The S t a b i l i t y  the  a i r column  Z/L,  measurement to  is  which p l a y s a  of  turbulence.  o b t a i n with 2.6, so t h r e e  incomplete  data  will  now  be  e x p r e s s i o n from 2.6 i s ,  < w_T v> . To  instantaneous  and  local  average  temperatures, a r e d e f i n e d as t h e temperatures r e g u i r e d  virtual to  give  32 dry  a i r the  pressure..  same  density  as  Lumley  and P a n o f s k y ,  =  (1 + 0.61 mj ,  Tv  T  actual  moist  1964, show  a i r a t t h e same  that;  where Tv and t h e a i r t e m p e r a t u r e ,  T, a r e i n d e g r e e s K e l v i n  is  and  specific  approximate  humidity. the v i r t u a l  <w Tv>  where  TZ  Lumley  is  =  temperature  (p  96)  also  f l u x by  <wt> + 0.61 TZ <wm> ,  the  mean  a i r temperature  c o n v e r s i o n t o a b s o l u t e h u m i d i t y , Q, with  Panofsky  and m  in  a t the height  g/m , 3  is  Z.  The  accomplished  ( P h e l p s , 1971),  so  Over  Q  =  1298  Tv  =  T  temperate  by l e s s  To Z L  [1 + To Q  seas  l a r g e temperature differ  at  Z  gradient  / To) m 1.72 x 10-*] .  more t h a n a b o u t  and t h e v i r t u a l  10m t h e r e i s n o t a  and a i r  temperatures  t h a n 2%, making  = <Tv> =  (273°K  =  - K Z g u* 3  TZ  +  TZ  2  QZ  <wt> • [1+ T o To  reasonable approximations.  1.72 x 10~6 2  1.72x10-6  <w_> ] <wt>  (2.34)  33 Over  temperate seas t h e m o i s t u r e c o n t e n t o f t h e atmosphere  and t h e a t m o s p h e r i c p r e s s u r e , a f f e c t t h e a i r d e n s i t y by about 1% and 5% r e s p e c t i v e l y . enough  to  For  dynamic  flux  calculations,  i ti s  only i n c l u d e the a t m o s p h e r i c p r e s s u r e , PA i n JcPa, by  c a l c u l a t i n g t h e d e n s i t y from  £  =  1.29  (273/TZ) (PA/101) .  (2.35)  Very o f t e n t h e a b s o l u t e h u m i d i t y and m o i s t u r e are  unknown  and  sensible  <wQ>,  Z/L must be approximated from measurements of  u*, <wt> and t h e mean a i r and s u r f a c e t e m p e r a t u r e s . of  flux,  The  ratio  heat f l u x t o l a t e n t heat f l u x , t h e Bowen r a t i o , G,  can be used t o g i v e  <w£> <wt>  =  p_Cp_ L G  =  0.534 G  (273/ TZ)  i n g/m /°C, where t h e p r e s s u r e  and  density  P h e l p s and Pond, 1971, r e p o r t a  3  have  been  neglected.  moisture  effects  v a l u e of 0.24 f o r G from t h e i r San Diego r e s u l t s .  on t h e  Substituting  i n t o 2.34 g i v e s  Z L which  =  shows  - K_Z g u* 3  that  <wt> • [ 1 + 0.001 T o ] , To  the moisture  flux  o n e - t h i r d as much t o t h e s t a b i l i t y as flux.  may  does  contribute  about  the sensible  heat  34 An  in  situ  aerodynamic  G  Bowen  ratio  can  be e s t i m a t e d from the b u l k  p a r a m e t e r i z a t i o n s , s e c t i o n 2.3, v i z :  =  £_Cj} L  <wt> <wQ>  =  p_Cp_ L  <0>_CT <0> CE  The Stanton number, CT, and D a l t o n number, been  found  to  be  nearly  the  humidity  is  QSAT (T)  C1  =  be  CE  and  30%  lower  various  C1  temperatures  errors,  CT  will  be  and  assumed  so  humidities  that  QSAT(TSFC).  the  This expression i s a over  pure  water  at  s u r f a c e h u m i d i t y over s a l t  I n o r d e r t o reduce  systematic  a r e l a t i v e h u m i d i t y o f 75% w i l l be assumed, which i s i n  middle of t h e h u m i d i t y range e x p e c t e d over humidity  contributes  only  about  30%  temperate to  assumption s h o u l d i n t r o d u c e a random e r r o r i n Z/L of at  CE.  exp(C2/ T)  saturation  w a t e r , QSFC, i s 0.98  Since  than  as  = 6.4038 x 10» and C2 = -5107.4.  f i t t o a t a b l e of  the  sometimes  The s a t u r a t i o n h u m i d i t y as a f u n c t i o n of t e m p e r a t u r e , i s  g i v e n by Hertzman e t a l . , 1974,  with  have  n o t t h e major c o n t r i b u t o r t o Z/L  because of the l a r g e e r r o r i n AQ, equal.  CE,  e q u i v a l e n t (Pond et a l . , 1971), but  Francey and G a r r a t t , 1978, f i n d CT t o Because  AT . AQ  worst  and  d i f f e r e n c e , AQ,  usually  of l e s s than 10%.  Z/L, about  seas. this 20%  The s e a - a i r h u m i d i t y  and hence a Bowen r a t i o , can now be  found  from  TSFC and TZ u s i n g  G (AT) = (p Cp/L) AT  [0.98 QSAT(TSFC) -0.75 Q SAT (T Z) ] ~ i .  35  S u b s t i t u t i n g i n t o 2.34 e s t i m a t e s Z/L from u * , <wt>, TZ and TSFC:  - X_Z g  Z(u*,<wt>) = L  In  u*  To  G (AT)  (2.36)  cases where <wt> i s a l s o unknown, b u l k p a r a m e t e r i z a t i o n  r e p l a c e s i t w i t h CT OZ AT. 1978,  <wt> • [1 + To 2.5x10-* 1  3  indicates  that  The r e v i e w by CT  s t r a t i f i c a t i o n and about  i s  0.86x10  about  Friehe 1x10~  i n stable.  -3  3  and  Schmitt,  in  unstable  Therefore,  a  s i m p l e r e s t i m a t e of Z/L i s g i v e n by  Z/L (u*,AT) = - KJL g CT OZ__T [1 + To 2.5x10-* 1. u* To G (AT) 3  Following u*  3  D e a r d o r f f , 1968, t h e b u l k f o r m u l a , 2.9, r e p l a c e s  w i t h CD / OZ 3  determined  2  (2.37)  3  so t h a t a s t a b i l i t y  parameter Z/L (AT)  s o l e y from t h e b u l k parameters,  c a n be  OZ, TZ, and TSFC.  p o r t i o n o f t h e Z/L e x p r e s s i o n i s i d e n t i f i e d as a b u l k  A  Eichardson  number  E i (AT) so  = -g _Z OZ  Z/L (AT) =  K  2  CT CD  AT (1 + To 2_5x_10-*], To G (AT) E i (AT) . CD*/ " 2  A r e a s o n a b l e average CD i s 1.25 x 1 0 ~ ( G a r r a t t , 1977), so 3  with  Z/L (AT)  =  11 E i (AT)  CT/CD  =  0.70  =0.80  (CT/ CD)  for  AT < 0 AT > 0  (2.38)  36 i s a very p r a c t i c a l estimate of the s t a b i l i t y differs  from  Deardorff's  final  form  u n s t a b l e c o n d i t i o n s , as i t r e f l e c t s more of  the  bulk c o e f f i c i e n t s .  parameter.  o f Z/L = 12 E i (AT) recent  for  determinations  However, i t ought t o be compared t o  the more e x a c t e x p r e s s i o n , 2.36, whenever <wt> and u* available*  This  are  both  37 CHAPTER 3  3.1  THE INSTRUMENTATION AND EXPERIMENTAL PROGRAM  Introduction In  order  t o c o l l e c t t h e d e s i r e d amount o f h i g h wind  d a t a a Reynolds f l u x system and a d i s s i p a t i o n system designed  f o r unattended o p e r a t i o n .  have  speed been  A d d i t i o n a l a s p e c t s o f both  systems i n c l u d i n g e r r o r a n a l y s i s , d e s i g n  criteria,  and  sensor  response r e q u i r e m e n t s a r e g i v e n i n Pond and L a r g e , 1978, and the detailed et a l . ,  analysis 1979.  consumption  of  The  and  a  the v e l o c i t y measurement i s a l s o i n Pond  essential large  considerations  recording  a r e low  capability  to  power  keep t h e  s e r v i c i n g p e r i o d l o n g and s e n s o r s a b l e t o f u n c t i o n i n t h e hoped for  30-40 m/s winds and accompanying s p r a y .  hostile  environment  electronics possible  f o r long  are l i k e l y  the important  periods  to f a i l  When o p e r a t i n g i n a  of  time,  periodically,  measurements  s e n s o r s and  so  whenever  a r e e i t h e r d u p l i c a t e d or  t h e i r sensors are c a l i b r a t e d i n s i t u . The r e s u l t s from two f i e l d o p e r a t i o n s a r e t o be in near  this  study.  Halifax  platform  Nova  to allow  The  f i r s t was conducted on t h e Bedford tower  Scotia,  which  also  provided  a  stable  enough  m e a n i n g f u l Reynolds f l u x measurements t o be  used t o " c a l i b r a t e " the d i s s i p a t i o n are  presented  system.  Intercomparisons  p o s s i b l e w i t h t h e a i r - s e a i n t e r a c t i o n system from t h e  Bedford I n s t i t u t e of Oceanography, BIO, which was a l s o i n s t a l l e d on t h e tower.  I n a p r e l i m i n a r y experiment on Sable  systems  found t o be c o m p a t i b l e when o p e r a t i n g on t h e same  platform.  were  Island a l l  The r e s u l t s o f t h a t i n t e r c o m p a r i s o n and o f a p r e v i o u s  38  BIO experiment on t h e i s l a n d a r e r e p o r t e d i n Smith e t a l . , and  Smith  and  measurements  Banke,  were  1975,  respectively.  The  1976,  dissipation  extended t o h i g h e r wind speeds and more open  sea c o n d i t i o n s i n a second experiment conducted  from  the  CCGS  Quadra d u r i n g i t s p a t r o l s a t ocean weather s t a t i o n "PAPA".  3.2  The The  Sensors velocity  measurements  p r o p e l l e r - v a n e anemometer (R.M. are  carefully  are  Young  based Co.),  whose  the  propellers  air  (Baynton,  1970).  number was checked i n a wind t u n n e l and found t o be  2% of t h e f a c t o r y c a l i b r a t i o n . propeller to propeller ablation  of  the  and  leading  within  T h i s a c c u r a c y i s m a i n t a i n e d from  is  not  edge.  a x i a l wind f a l l s below about 1 friction  Gill  c o n s t r u c t e d h e l i c o i d s t h a t t u r n a p r e c i s e number  o f r e v o l u t i o n s f o r each meter of p a s s i n g This  on  affected  by  considerable  A problem does a r i s e when t h e  m/s,  because  the  b e g i n t o produce a n o n - l i n e a r o u t p u t .  inertia  and  Another problem  i s t h a t when the wind v e c t o r makes an a n g l e -9- (angle of  attack)  g r e a t e r than about 20°, t o t h e p r o p e l l e r a x i s t h e apparent a x i a l velocity  component  is  l e s s than the e x p e c t e d c o s ( ^ ) t i m e s t h e  magnitude of the wind, by a f a c t o r between  35  approximated by Large,  1978).  and  75  degrees,  /3[$r)  this  -  For angles  non-cosine  -1. 1 03-0.27 -0-, f o r -9- i n Although  these  problems  pose  attack  behavior  radians  d i f f i c u l t i e s i n d e t e r m i n i n g the h o r i z o n t a l v e l o c i t y they  of  (Pond no  is and  serious  components,  c o m p l i c a t e the measurement o f the v e r t i c a l v e l o c i t y .  W is  derived  from a p r o p e l l e r , G i l l - w , whose a x i s  angle, °<=60°,  to  the  axis  horizontal  average wind speed g r e a t e r  component  enough of the The  of  the  tilted  axes  and  of  fully  references  3C  vane  and  in  and  publications.  the The  c i t e d , so only an  following Gill-w  this  way  the  corrections  outline  follows.  notation  (taking the  i n t o i t s c a l i b r a t i o n ) and  regime.  are kept i n  anemometer of f i g u r e 3 i s  v e l o c i t y components are r e s o l v e d figure  m/s  for  possible.  twin p r o p e l l e r - v a n e  i n the  4  non-linear  f i g u r e 3B i s always maintained and  the non-cosine behavior are The  its  i n s t a n t a n e o u s wind v e c t o r  e s s e n t i a l l y the same plane by the geometry  than about  p r o p e l l e r always c o n t a i n s  h o r i z o n t a l wind t o avoid  propeller  an  at a s m a l l angle 8 from the  ( f i g u r e 3) . axial  at  propeller,  tilted  the  tilted  of a standard, G i l l - u ,  which i s g e n e r a l l y At an  is  The  described  of  how  defined  the  angles of  conform to these  previous  ncn-cosine behavior at •d=°<  G i l l - U s i g n a l s from the Reynolds  flux  system supply the v e l o c i t i e s :  Gill-u and  -e  Q  8 - tan-  and  w  are  contribution  from  the  v a r i a t i o n s i n the G i l l - u closely,  1  w sin 8  (w/Q)  the  components, r e s p e c t i v e l y .  very  +  G i l l - w = V2 = £Q cosH+fi)+w s i n (*<+ S) }•£ 1-0..27 (6- t a n -  with  where  = V1 = Q cos 8  providing  ,  horizontal and a  and  vertical  contains wind,  Gill-w signals check  (w/Q) ) ] (3.1)  horizontal Because V2  1  that  a  the track  velocity  considerable low  frequency  one  everything  another  i s working  40  FTGORE  3 A: The G i l l t w i n p r o p e l l e r - v a n e anemometer. B: The HAT s e n s o r h o u s i n g . C: D e f i n i t i o n o f a n g l e s used i n r e s o l v i n g t h e v e l o c i t y components and c a l c u l a t i n g t h e t i l t a n g l e o.  properly. be  angle 8 needs t o be evaluated before  The t i l t  removed  from t h e G i l l - w s i g n a l and w c a l c u l a t e d .  Since the  average v e r t i c a l v e l o c i t y must e v e n t u a l l y go t o z e r o , estimate  of 8  i s that  c a l c u l a t e d <W> e x a c t l y period.  angle  0,  where  a  <  >  denotes  the averaging  8 i s measured over a t l e a s t 15 minutes t o  An average  Assuming  good  of r o t a t i o n needed t o make t h e  g i v e good averages o f the r a t i o Y = <V1>/<V2> from which derived.  Q can  t a n - * (w/Q)  <V1> = <Q> cos 8  i t  is  = w/Q and <w>=0,  and  <V2> = <Q> {cos(<x+S) [1-0.27 5/^(^0 ] +<w2> <Q>-2 s i n « + S )  are  correct  t o second  order.  0.27/ /${<<) }  The term i n <w > <Q>-2 i s only 2  about 0.2% of t h e p r e v i o u s term, l e a v i n g  Y= {1-0.27 8/ /3{c<)} [cos<=< - s i n K  which, assuming  tan 8 ] ,  8 - t a n 8, gives a q u a d r a t i c i n 8.  It i s  the  negative square root o f the q u a d r a t i c formula that i s needed, so • 8 i s estimated from  8 = b - { b2+  /0.27)  (Y-coso<) /sin°< }  b = 0.5 [ c o t ^ + / ^ ( ^ 0 / 0 . 2 7 ] .  This  expression  shows  that  (3.2)  o f f s e t e r r o r s , which e n t e r Y, and  e r r o r s i n °< and the/3 r e l a t i o n produce apparent t i l t s  t h a t can  seriously  Now  affect  Reynolds  stress  measurements.  some  42 s t r a i g h t forward algebra y i e l d s :  V2-YV1=Bw  + (A/V1) w 2  A = £0.27/^(00  ]  sin«+6)  cos 6  (3.3)  B = cos(«x+5) 0.27/^x) + {1-0.27 £//£(*)} s i n <x/cos S,  where Q has been r e p l a c e d by V1/cos & and a and  terms  of  order  (w/Q)  have  3  p l a t f o r m t h e instantaneous t i l t  (Pond  and  Large,  actually  1978).  i n <w >/<Q> 2  been n e g l e c t e d .  d i r e c t i o n , but the use o f t h e "average" error  term  depends  2  On a f i x e d  on  the wind  6 i n t r o d u c e s very  little  The q u a d r a t i c i n w i s solved  u s i n g t h e p o s i t i v e square r o o t of the q u a d r a t i c formula, t o give an estimate of w f o r each p a i r values  i n the  of  averaging p e r i o d .  v e l o c i t y components a r e then found  recorded  Gill-w  and  The instantaneous  Gill-u  horizontal  from:  Q = V1/cos £ - w t a n 8 0 = Q cos (an)  (3.4)  V = v = Q s i n (an) ,  where t h e instantaneous wind d i r e c t i o n , AN, eguals the  mean  direction,  <AN>,  i s chosen  such  cross-stream v e l o c i t y <V> = <Q sin(an)> =0. associated summarized  with  resolving  i n table  together with t h e i r drag  coefficient.  0,v w #  and  Q  I (reproduced from  <AN>+an  and  t h a t t h e average  The p o s s i b l e e r r o r s in this  manner are  Pond and Large,  1978) *  e f f e c t s cn the c a l c u l a t e d momentum f l u x Some  errors  should  tend  to  and  cancel,  h o p e f u l l y t h e r e i s no more than a ±10% e r r o r i n the average  so  CD.  43 r  j  —-  — -  T"  SOUECE  I °< e r r o r  o f ±1°  |<uw>|  i  -  |  ±5%  I  CD ±5%  ±2% ± U  | |  ±3% ±2%  ±4%  I  ±1%  ±3%  I  ±3%  -r  a t 5m/s  |errors  at  10m/s  I±2% i n c a l i b r a t i o n  !  relation | S  ii  | 8=0  I r e s p o n s e o f |£=±10° •  IV I  1  propeller|  1 1  1  I  TABLE  I  I  ±1% ±10%  I I  I  |Offset e r r o r s p a r t l y ! |cancel r a t h e r than | |add giving about | |1/2 t h e e f f e c t s |  I  I  Summary o f p o s s i b l e errors i n the velocity measurement and t h e i r e f f e c t s on t h e E e y n o l d s f l u x method.  platform,  because  the 8  from t h e i n s t a n t a n e o u s t i l t calculated  from  this  i s practicable  on  vane's  signal.  needed t o f i n d w.  type  system does g i v e  an  The  0  measurement  moving  different  i s also  not  o f d a t a because i t i s not a simple  Gill-u  average  signal  V1/cos £  i s removed v e c t o r a l l y )  of Q (and 0, s i n c e  a  d e r i v e d from Y may be v e r y  matter t o s e p a r a t e t h e wind e f f e c t from t h e p l a t f o r m  velocity  | | | |  I F o r | S\ < 2-3° e r r o r | | i s s i m i l a r t o 6=0. | |For |6| =5° i t i s | | l i k e l y w i t h i n ±5%. |  ±1% ±10%  I  Only t h e d i s s i p a t i o n method  the  |  1i  i i Negligible I Negligible  fluctuations  |Non-cosine  —i  COMMENTS  i1 | The °< e r r o r is |believed to be |within ±.5° with |2-3% e f f e c t s  j I Offset  -  |  <Q>=1.005 <0>) .  motion i n  from t h e d i s s i p a t i o n  (from  which  a  ship's  and approximate average v a l u e s I n t h i s method t h e  i s not t h e major s o u r c e o f e r r o r  velocity  ( s e c t i o n 2.5). A  44  + 2% c a l i b r a t i o n e r r o r o n l y l e a d s t o 2.7% |<uw>|  and  -1.3%  errors  in  and CD r e s p e c t i v e l y and a t 5m/s t h e y a r e a f f e c t e d by t h e  o f f s e t e r r o r by o n l y 0.3% and 1.3%.  However,  only  frequencies  above those c o n t a m i n a t e d by t h e p l a t f o r m motion may be u t i l i z e d . The G i l l - w s i g n a l f u n c t i o n s as a check t h a t t h e G i l l - u and  electronics  propeller  a r e working p r o p e r l y and, i f n e c e s s a r y , as an  i n p u t t o t h e d i s s i p a t i o n method. The e n c l o s u r e , HAT, of f i g u r e shield  and  temperature  offers  protection  3,  serves  against  as  a  radiation  r a i n and spray f o r t h e  and h u m i d i t y s e n s o r s t h a t a r e mounted i n i t .  Glass  c o a t e d microbead t h e r m i s t o r s ( V i c t o r y E n g i n e e r i n g Corp.) measure both  the  mean  and f l u c t u a t i n g a i r temperature w h i l e g l a s s rod  t h e r m i s t o r s p o t t e d i n epoxy measure both t h e sea temperature and a mean a i r t e m p e r a t u r e . .  A l l these  transducers  form  part  of  s i m i l a r b r i d g e c i r c u i t s whose n o n - l i n e a r i t y b a l a n c e s t h a t o f t h e thermistors,  making  d e t e c t o r l i n e a r over initially  t h e output about  a  of  25°C  an  operational amplifier  range.  A l l probes  were  c a l i b r a t e d i n a water b a t h a g a i n s t a s t a n d a r d mercury  thermometer b u t l a t e r t h e r o d t h e r m i s t o r calibration  check  of  the  microbead.  provides The  two  an  in  situ  temperature  measurements s h o u l d not d i f f e r by more than 0.1°C, when both t h e rod and microbead a r e w o r k i n g p r o p e r l y . Although no l a t e n t heat f l u x data a r e a s y e t a v a i l a b l e , brief  description  of  t h e attempted  humidity  follows.  On S a b l e I s l a n d t h e humidity f l u c t u a t i o n s  with  aluminium-oxide  an  a r r a y (Thunder  sensor  a  measurements were  taken  ( P a n a m e t r i c s Corp.) and a Brady  S c i e n t i f i c C o r p . ) , but t h e s e f a i l e d  because  the  45  s e n s o r s d e t e r i o r a t e d i n the s a l t a i r environment. less  This pccurred  r a p i d l y i n the case o f t h e Brady so an attempt was made on  the Bedford tower t o p r o v i d e an i n s i t u c a l i b r a t i o n by r e p l a c i n g the a l u m i n i u m - o x i d e probe w i t h a second Brady covered with a micron  stainless  steel sintered f i l t e r .  The c a l i b r a t i o n  drift  was much r e d u c e d , but s t i l l s e r i o u s , making  both  unsuitable  For up t o a week or  for  l o n g unattended o p e r a t i o n .  two the d r i f t of the f i l t e r e d Brady was not calibration  was  complicated  by  what may  e f f e c t s and temperature s e n s i t i v i t y . of  an  too  Brady  60  arrays  bad,  but i t s  have been h y s t e r e s i s  In a d d i t i o n , the  open Brady i s m a r g i n a l at best (Smith e t a l . ,  t h e r e f o r e seemed b e s t t o abandon t h e Brady a r r a y and  response 1976). to  It  regard  a l l the data from i t as u n r e l i a b l e . For  the  ship  o p e r a t i o n s where power r e g u i r e m e n t s a r e not  r e s t r i c t i v e a Lyman-alpha  humidiometer  ( E l e c t r o m a g n e t i c Research  Corp.) has been employed t o g i v e t h e f l u c t u a t i n g h u m i d i t y , w h i l e a Cambridge Systems (Model 2000) dewpoint system p r o v i d e d t h e i n s i t u c a l i b r a t i o n and average .  The l a t t e r worked  properly  over a month b e f o r e needing s e r v i c i n g and i s p r o m i s i n g . gives  an  microbead.  aspirated The  mean  a i r temperature  Lyman-alpha,  however,  for  I t also  checking  reguired  for  the  constant  a t t e n t i o n as i t s windows q u i c k l y became so d i r t y t h a t i t s s i g n a l went o f f s c a l e b e f o r e p r o v i d i n g any u s e f u l d a t a .  46 3.3  The Reynolds F l u x System This  system  includes  the s e n s o r s , an e l e c t r o n i c s package  and 6 d i g i t a l c a s s e t t e tape r e c o r d e r s t o sample, record  digitize,  t h e data needed t o determine t h e t u r b u l e n t f l u x e s by t h e  Reynolds f l u x method, s e c t i o n 2.4channels  i n t h e same  illustrates converting  t h e data  manner flow  I t p r o c e s s e s each o f  as  and  shown  i n figure  parameters  Although  i t s6  4, which  considered  in  s t o r e d data back t o t h e o r i g i n a l p h y s i c a l q u a n t i t i e s  sensed by t h e t r a n s d u c e r s (V1,V2,AN,R, where R i s any  scalar).  t h e d a t a p r o c e s s i n g i s , f o r c o n v e n i e n c e , shown f o r t h e  s p e c t r a , i t i s a c t u a l l y performed from  and  which  on  the F o u r i e r  t h e s p e c t r a and c o s p e c t r a a r e d e r i v e d .  f l u x r e c o r d c o n s i s t s o f NG s e q u e n t i a l g r o u p s , sampling  coefficients  first  each  A Reynolds formed  by  t h e p r e w h i t e n e r , Vp, a t 3Hz, NF t i m e s , then t h e  low-pass  f i l t e r , VL, a t 1/SSP,  period,  SSP, i s made a s l o n g a s p o s s i b l e t o c o n s e r v e power and  tape. the  times.  The  The h i g h f r e q u e n c y v a r i a n c e and c o v a r i a n c e low-pass  filter  f a s t subsamples. as  NS  6  prevents f u l l  lost  sampling  because  a l i a s i n g i s r e c o v e r e d by t h e  The 3 Hz r a t e i s f i x e d because i t i s as  of  thumbwheel  record length, frequency  space  NF,NS,NG and SSP a r e programmed  switches  t h e subsampling covered  scheme  and  the p o r t i o n s of  by each s a m p l i n g r a t e .  o r d e r t o prevent t h e c a s s e t t e s f i l l i n g wind  speed  limit  can  be  by  and t o g e t h e r they determine t h e  An a d d i t i o n a l  s w i t c h s e t s t h e time i n t e r v a l between t h e s t a r t of r e c o r d s .  a  fast  c h a n n e l s can be r e c o r d e d by a p a i r o f p a r a l l e l r e c o r d e r s ,  each r e c e i v i n g 3 c h a n n e l s . means  slow  w i t h low wind speed  In data,  s e t by a n o t h e r s w i t c h so t h a t a  s c h e d u l e d r e c o r d i s not taken i f t h e average wind speed  i n the  47  | ENVIRONMENT | I D v w R fuvwr (f) | V1 V2 AN R  r*2 (f)  Transducer and P r e a m p l i f i e r | Gain=C Offset=B | Transfer F u n c t i o n Hs (f) | i  Vs=  B + C (V1,V2,AN,R)  4»s (f) =C  ,  VP  !Hp(f) |  | Hs (f) | 2  •  1  | Low-Pass F i l t e r I dc gain=1 Offset=BL | T r a n s f e r Function HL(f)  J  <rp(f)= <rs(f)  <f>2 (f)  i  | Prewhitener I | dc gain=0 Offset=Bp | | T r a n s f e r Function Hp(f) |  i  2  i  VL=Vs+BL  2  I | |  *L(f) = ^s (f) IHL(f) |  2  Sample And Hold  3 Hz  1/SSP  Multiplexer A To D Converter 12-bit Words NF Samples / Group  NS Samples / Group  | A pair of d i g i t a l cassette j | tapes s t o r e NG groups per | | f l u x record. j  FIGURE  4:  Signal processing i n t h e Reynolds f l u x system, showing the sampling scheme and a l l parameters considered i n the a n a l y s i s .  48 previous  six  minutes  is  l e s s than the s e t l i m i t .  The  system  c o n t i n u e s t o c o l l e c t d a t a u n t i l t h e t h r e e p a i r s of c a s s e t t e s are full. The low  frequency  s p e c t r a ^uvwr ( f ) ,  are  u,v,w  available  low-pass f i l t e r s have a 1 function,  HL (f)  and r  second  Nyguist  almost  the  to  fL,  so  n e a r l y c a n c e l one a n o t h e r .  coefficients  and  slow samples.  The  from  the  time  constant  (3db down at fL= 0.16  s e t t o 3 seconds, g i v i n g a equal  Fourier  Hz).  and  transfer  SSP has always  frequency  fsn,  (1/6  been Hz),  f i l t e r l o s s and a l i a s i n g  should  The s e n s o r t r a n s f e r f u n c t i o n ,  Hs(f),  i s i g n o r e d because i t i s t y p i c a l l y 3db down a t more than 5 times fsn.  A f a s t Fourier transform  spectra, ^ L ( f ) ,  of  the  samples  which must be n e a r l y e q u i v a l e n t t o C  f< f s n , where t h e g a i n , C, i n c l u d e s t h e from p h y s i c a l u n i t s t o v o l t a g e . the  slow  dimensional  produces r*2(f) f o r  2  conversion  Because of t h e n o n - l i n e a r i t y i n  w c a l c u l a t i o n , the v e l o c i t y data must f i r s t be c o n v e r t e d t o  V1, V2 and  AN = C - i (VL-BL-B) and  equations  3.3  and  the ^uvw(f) s p e c t r a . group  of  slows  3.4,  then  before  to  12.8  set  Hz  to  fns  v a r i a n c e and c o v a r i a n c e from 0.00065 Hz t o 0.167 the  high  and and  to  w  obtaining  256,  so  frequency  cofficients  and  contain  responses  are  explicitly  involved.  c i r c u i t s behave as time d i f f e r e n t i a t o r s a t increase  the  signal  levels  one  low  the  Hz. from  the  samples i s more c o m p l i c a t e d because the p r e w h i t e n e r . Hp (f) , sensor  with  minutes and i t s F o u r i e r c o f f i c i e n t s  o c c u r a t f r e q u e n c i e s from 0.0013  Finding  v  transforminq  NS has always been  lasts  U,  The  and  prewhitener  frequencies  and e l i m i n a t e s p e c t r a l  fast  to  distortion  49  from non-sampled f r e q u e n c i e s , t h e n filters  a t the higher  roll  frequencies.  o f f as  R-C  By d e s i g n t h e i r response i s  maximum and n e a r l y f l a t a t t h e f a s t s a m p l i n g Nyquist 1.5  Hz,  so  that  aliasing  c o n t r i b u t i o n s below a few Hz. f a s t samples ( c o r r e s p o n d i n g  7*2 (f)  With  ^p(f) [ C  the v e l o c i t y  channels,  transformed  occurs  without  much  loss  of  of the  are e a s i l y converted t o  |Hs(f)|  | H p ( f ) | ]-2 .  t h e 02(f)  are inverse  Fourier  and a dc l e v e l i s added t o make t h e l a s t f a s t sample  of V1, V2 and AN e q u a l t o t h e f i r s t slow sample of 0,  frequency,  The F o u r i e r c o e f f i c i e n t s  t o f*p (f))  =  low-pass  each  group.  v, and w a r e t h e n c a l c u l a t e d u s i n g t h e mean c o o r d i n a t e s  as determined by  t h e slow  coefficients  t h e s e t i m e s e r i e s t h a t a r e used t o produce t h e  of  d e s i r e d high frequency the  non-linear  performed  and  references.  the  has  only  possibility always  one  i t i s the  cospectra. transform  i s discussed  Without need  i n the  be  cited  0.0234 Hz, so a l l t h e v a r i a n c e and c o v a r i a n c e  of  bands a r e a l r e a d y  i n t h e slow samples.  F l u x e s t i m a t e s and s t a t i s t i c a l  quantities  are c a l c u l a t e d  runs of NG RP s e q u e n t i a l groups o f a r e c o r d .  t i m e i s used as t h e a v e r a g i n g coordinate  Fourier  been s e t t o 128 making t h e l o w e s t  lower 6 and p a r t o f t h e seventh frequency  contained  from  and  0uvw(f) s p e c t r a and  calculation  this  NF  f a s t frequency  w  samples,  axes  determination.  period i n the  calculation  and  The group s p e c t r a and c o s p e c t r a a r e  averaged t o g e t h e r over t h e r u n . the o v e r l a p p i n g frequency  8  The t o t a l r u n  An attempt has been made t o use  bands t o  adjust  t h e high  frequency  50 p o r t i o n , however, t h i s has not been s u c c e s s f u l because the 6  estimates  from  the  f a s t samples are not s t a t i s t i c a l l y  c e r t a i n and  often r a d i c a l l y  the  high  other  at  does  not begin  f= 0.1715 Hz  estimates.  0.167  Hz,  resulting  to simply  is,  to  frequency, <0>  and  this  flux  observations. first  freguency  186  from  with  value  interpolating  eighth values. point  f=  this  spectra The  0.00065  method:  could  give  second,  rise  the  s t a t i s t i c a l l y c e r t a i n as one a  frequency  and  first,  cospectra the  11  Hz.  first,  method, sum,  There the  are  that  are  lowest  two  natural  n= fZ/<0>, i n c l u d e d i n the i n t e g r a t i o n decreases with  dependencies;  over  low  m u l t i p l y each value by i t s bandwidth and  integrate  disadvantages  128  i s formed by  i n t e g r a t e d i n three d i f f e r e n t ways. is  The  from  Hz so an i n t e r m e d i a t e  (bandwidth 0.009 Hz)  very  another and  but the e i g h t h high  u n t i l f= 0.176  between the seventh and The  d i f f e r e n t from one  frequency  values span 0.00065 <f< band  lower  problem  run  could  to  lowest  apparent frequencies  would l i k e and  speed  are  f a i l u r e to  not  as  converge  c r e a t e a great d e a l of v a r i a b i l i t y i n  A second i n t e g r a t i o n method, 1 2 , by  wind  alleviates  i n c l u d i n g the v a r i a n c e and c o v a r i a n c e  the  c f the  i n d i v i d u a l group means about the o v e r a l l mean of  a  run.  This  e f f e c t i v e l y adds a f u r t h e r NGBP samples at a 13.5  minute p e r i o d ,  which c o n t a i n the c o n t r i b u t i o n s from 0.00062/NGEP to 0.00062 Hz. However,  the  statistical  c o n t r i b u t i o n i s very h i g h , Note  that  present  a  small  uncertainty enhancing  s p e c t r a l gap  i n the 12 i n t e g r a t i o n ,  the  this  second  additional 11  problem.  from 0.00062 to 0.00065 Hz i s  because  suspended during the f a s t sampling.  in  The  the  slow  sampling  13 method always  is  begins  51 its  integration  the  spectral  a t the same n a t u r a l frequency, n= 0.004, where  values  are  reasonably  well  established.  The  i n t e g r a l i s then m u l t i p l i e d by a constant f a c t o r E t o compensate for for  the  excluded  low freguency c o n t r i b u t i o n s .  each q u a n t i t y i s  cospectrum,  NT* (n) ,  found  from  which  is  the  plotted  against  log{n)  u n i v e r s a l form, depending calculated to be  a  for  normalized  determined  averaqes over a l l a v a i l a b l e runs^  The value of E  The  in  spectrum  s e c t i o n 4.3 from  non-dimensional  convenience,  only on Z/L.  In  or  should  (n),  display  section  4.3,  a  E  is  from the normalized wt and uw c o s p e c t r a and i s found function  of  stability.  Although  the  implied  low  frequency c o n t r i b u t i o n may not be exact, the r e s u l t s should g i v e representative  averages  and be s u b j e c t t o minimal  variability.  The t h r e e methods a r e expressed by: f~ CO  11 = /  ^(f)  df  J.00065  (~. 00062  1 2 = 1 1 + J  J  r-  (3.5)  OO r*(f)  df  f=.004<D>/Z  0 The  ^ (f) df  .00062/NGEP  N^(n)  d(logn)  /  j N^(n) d ( l o g n ) . 70.004  13 method i s the most a t t r a c t i v e and i s  others  in  applicable.  section  4.5  to  determine  i f  compared it  is  with  the  universally  52 3.4  The D i s s i p a t i o n  System  T h i s system employs the same sensors and p r e a m p l i f i e r s , but has  i t s own  recorders.  electronics It  calculations  and  two  digital  cassette  p r o v i d e s t h e estimates of 6 and Nr f o r the f l u x  (section  temperatures,  package  2.5)  humidity  and  and  the  mean  sea  and  air  wind f o r p a r a m e t e r i z a t i o n ( s e c t i o n  2.3) and s t a b i l i t y c a l c u l a t i o n s ( s e c t i o n 2.6). The a r c h i t e c t u r e of the data flow i s shown i n f i g u r e intervals Hz,  of  5.  Dt, each band-pass f i l t e r  Between  recording  at  output i s sampled a t 20  d i g i t i z e d , squared and summed NI times.  The sums are s t o r e d  i n i n t e r n a l memory u n i t s u n t i l they are w r i t t e n onto a c a s s e t t e , at which time a l l the low-pass f i l t e r channels are a l s o and  recorded.  while s t i l l start  of  Switches  proqram NI t o be as l a r g e as p o s s i b l e  a l l o w i n g the summation t o be a  tape  sampled  write.  completed  before  the  Dt i s u s u a l l y s e t t o 4 or 5 minutes,  making t h i s r e c o r d i n g system very economical  of tape.  The low-pass f i l t e r s a r e s i n g l e pole E-C c i r c u i t s with a 25 second  time c o n s t a n t ,  amplifier,  hence  followed  they  are  by  a  unity  £  calculation  These averaged  and  operational  w e l l s u i t e d f o r p r o v i d i n g the mean  v e l o c i t y and s c a l a r values over t h e averaging the  gain  velocity  period  computations  r e s u l t s may be combined t o g i v e  used  for  of s e c t i o n 3. 1. the  means  over  l o n g e r time i n t e r v a l s i f d e s i r e d . The  band-pass  f i l t e r s c o n s i s t of double pole high and low  pass stages centered nominally at fc= 0.4, 0.8 and 1.6 Hz. prewhitener  is a  The  d i f f e r e n t i a t o r a t low f r e q u e n c i e s t h a t r o l l s  o f f as a s i n g l e pole R-C f i l t e r  above 10-15 Hz.  The two f i l t e r s  53 | ENVIRONMENT |,. D v w R T*uvwr (f) V1 V2 AN R  | |  •2 ( f )  I Transducer and P r e a m p l i f i e r | I dc gain=C Offset=B | | T r a n s f e r F u n c t i o n Hs (f) I 1  Vs = B + C  .  (V1,V2,AN,R)  I Prewhitener | dc gain=0 Offset=Bd | T r a n s f e r F u n c t i o n Hd(f)  I H*|  1  ^s(f)=C2 <^2(f)  -M  |Hs(f) | 2  |  Low-Pass F i l t e r d c gain=1 Offset=EL | T r a n s f e r F u n c t i o n HL (f)  = ^ s ( f ) |Hd (f) | 2  Vd  | .4Hz | I Band-Pass | I F i l t e r H4(f) I  . 8Hz J Band-Pass | I F i l t e r H8 (f) |  VL=  Vs+BL  I  1.6Hz | | Band-Pass | | F i l t e r H16 (f) |  1  ±  20Hz  1/Dt  Multiplexer  I  A To D C o n v e r t e r  | Square, sum and s t o r e t h e | J Band-Pass c h a n n e l s | Total  Power P D i g i t a l cassette, records the | sum o f NI s q u a r e s and t h e | Low-Pass samples e v e r y Dt |~ seconds. |  I  FIGURE  5:  Signal  processing i n the d i s s i p a t i o n  system.  ±  54 together form band-pass  filters  r e p r e s e n t e d by combined  transfer  f u n c t i o n s He (f) with center f r e q u e n c i e s at about 0.55, 2.1  Hz.  Since the i n p u t spectrum f a l l s  f r e q u e n c i e s of g r e a t e s t power output are The stored data words d i v i d e d passing  through  off rapidly near  the  1 .05  ( f / ) the - 5  fc  3  values.  by NI g i v e the average power,  each band-pass  filter.  A -5/3  for a l l selected  <P>  =  with the  <r (fc)  RHO  = C  j ( f / f c) -s/3  2  |Hs(f)|  | He (f) 1  2  the i n t e g r a l taken over the range of f r e q u e n c i e s passed by filters.  Because  RHO  contains  Hs (f) ,  a  function  of  0  speed  each band-pass f i l t e r channel. Equation  2.23  fluctuations,  Nr,  one-dimensional of s c a l a r s  relates the  0 ( f c ) t o the d i s s i p a t i o n of s c a l a r  molecular  dissipation,  €,  Kolmogoroff c o n s t a n t s , Br' and K*.  and  the  In the case  0 r ( f ) = 0 2 ( f ) and  Nr =  <P> RHO  €__ Br'  (2TT/<0>) / 2  i s a v a i l a b l e from each s c a l a r band-pass determined.  Calculating  €.  from  3  fcS/  introduces  some  w  into  (3.6)  3  filter  once 6  has  been  the v e l o c i t y s i g n a l s i s more  complicated because V2 always contains some tilt  df  2  ( s e c t i o n 3.5), the i n t e g r a l must be evaluated at each wind for  each  channels from  RHO  where  <P>,  spectrum a c r o s s  He i s assumed i n order to get a d i s c r e t e s p e c t r a l value at fc  and  V1 as w e l l .  w  and  a  non-zero  Some e r r o r i s thus  55  i n t r o d u c e d i n t o EHO  because a t t h e f r e q u e n c i e s  r  utilized  only  0u(f), and n o t 0w (f) , i s expected t o be p r o p o r t i o n a l t o f ~ / and 5  hence  neither  V1  nor V2 s h o u l d have e x a c t l y a -5/3 spectrum.  S i n c e t h e s p e c t r a l v a l u e s o f the h o r i z o n t a l are  nearly  3  velocity  component 0u(f),  e q u a l t o t h o s e o f t h e downstream component,  (Pond and L a r g e , 1978), 3.1 q i v e s  02(f)  =  A  = cos  f o r t h e V1 s i g n a l  S(6,f) = [ 1 + t a n S 2  0u(f) S (8,f)  A  2  8  ^w(f)/^u(f)  +2tan8 0uw (f)/0u(f)  S (8,f) s h o u l d r e a l l y be p l a c e d i n s i d e t h e i n t e g r a l expression  t h e RHO  and i n t e g r a t e d over t h e band-passed f r e q u e n c i e s , but  0w(f)/0u(f) and 0uw(f)/0u(f) can o n l y be approximated,  because they  of  ].  a r e taken  t o be  constants  outside the i n t e g r a l to give inertial  subrange  an  0w(f)/0u(f)  =  over each f i l t e r and p l a c e d  approximate  S'(8).  In the  4/3, but t h i s b e h a v i o r i s n o t  observed near t h e f c ' s and i n s t e a d i t i s t a k e n t o be 0.81, 1.11 and  1.29  a t f c = 0.4, 0.8 and 1.6 Hz r e s p e c t i v e l y .  s i m p l y t h e averages o f 14 Sable  Island  which  at  8=-5° and  0.98  anemometer  i s only a small c o r r e c t i o n  a t 8= + 5°) ,  o u t t o be  T h e r e f o r e , S'(8) random.  (about  but not a c c o u n t i n g  i n t r o d u c e s a s y s t e m a t i c e r r o r , which on a turn  o b s e r v a t i o n s from  a l s o show 0uw(fc)/^u(fc) t o average -0.11,  S» (8)  -0.16 and -0.15.  sonic  These a r e  leaning  tower  1.03  for could  a f u n c t i o n o f wind d i r e c t i o n and hence f e t c h .  i s a p p l i e d t o reduce t h e e r r o r and make i t more  The c o r r e c t i o n i s l a r g e r and t h e e r r o r more s e r i o u s i n  i t  56 the  V2 case where 3-1 g i v e s  A =  [ cos  ^ ( ^ / ^ ( X ) ]2  S(6,f) ={1+tan K + £ )  0w(f)/^u(f)+2tan (<<+£) ^uw ( f ) / ^ u (f) }  2  An  approximate  S'(6)  again be used, b u t -O' = £+ °< must be  can  assumed s i n c e t h e data t o c a l c u l a t e t h e i n s t a n t a n e o u s a n g l e attack  at  each  digitization  i s not  whenever p o s s i b l e i t i s f a r more dissipation  from  available.  desirable  calculate  the  velocity  With  band  pass  gives: €  =  z / 3  (27T/<0» / 2  A K•  3.5  Therefore,  the G i l l - u r a t h e r than t h e G i l l - w data.  these a p p r o x i m a t i o n s and r e s e r v a t i o n s each filter  to  <P>  3  fcf/l  (3.7)  S • (B)  RHO  Sensor Response When  c a l c u l a t i n g € and Nr, s e n s o r response c o r r e c t i o n s a r e  e s s e n t i a l and t h e y a r e o f some i m p o r t a n c e t o t h e Reynolds measurements. means  of  conditions filter or  of  Fortunately,  establishing encountered.  Hs (f)  the  d i s s i p a t i o n system p r o v i d e s a  under  Assuming  the  actual  turbulent  the s e n s o r s behave as an R-C  (3db down a t f o : H s ( f ) = (1 + j f / f o ) - * ,  6 v a l u e s from any two band-pass  an a p p r o p r i a t e c h o i c e o f f o .  flux  j=/ T ), either r  Nr  f i l t e r s can be made e q u a l by  Of c o u r s e random d e p a r t u r e s of t h e  i n p u t spectrum from i t s average -5/3  slope  create  scatter  in  t h e s e f o ' s , but on average n e a r l y t h e same response i s i n d i c a t e d  57 by  a l l three p a i r s of f i l t e r s  (the 0.4 and 0.8 Hz, t h e 0.4 and  1.6 Hz and t h e 0.8 and 1.6 H z ) . establishes  that  the  The s u c c e s s o f t h i s  assumption  of  an  E-C  response i s  a p p r o p r i a t e and t h a t t h e r e i s a c o n s i s t e n t average throughout  technique  -5/3  region  t h e range of f r e q u e n c i e s passed by the t h r e e f i l t e r  combinations. The response propellers,  of  mechanical  i s characterized  sensors,  by  such  as  The  E-C  filter  more i m p o r t a n t t o e s t a b l i s h response  i s poor.  i s plotted  change i n  analogue g i v e s 2ix fo=<U>/D. f o during  low winds  where t h e  t h e 2 7Tfo  required  to  make  the  c a l c u l a t i o n s o f € from t h e 0.8 and 1.6 Hz f i l t e r s e q u a l . D  were  truely  a  constant  through t h e o r i g i n o f s l o p e D. m/s,  improve  Gill-u Now i f  t h i s p l o t would be a s t r a i g h t The data  imply  that  line  below  even  more  A t h i g h e r speeds t h e response appears than  expected  (D  decreases)  i n c o r p o r a t e d by u s i n g t h e s o l i d l i n e o f f i g u r e 0/(0-1.Om/s). three  this  12  band-pass  particular  different  weight  filter  and t h i s i s D  =  0.56m  (19cm,  2-bladed)  The r e s p o n s e changes only s l i g h t l y  anemometer,  used  o u t p u t s over t h e e n t i r e t i m e t h a t  anemometer-propeller  of t h e p r o p e l l e r .  construction,  6A,  to  The l i n e i s a f i t , f o r 0> 4m/s, t o comparisons o f  c o m b i n a t i o n was i n use. a  speed  D i s about 0.65m, a s i g n i f i c a n t l y b e t t e r response than the  quoted v a l u e o f 0.8m.  all  It i s  I n f i g u r e 6, t h e h o u r l y averaged wind  against  Gill  a distance constant, D = the  wind passage r e q u i r e d f o r a 63% r e c o v e r y from a s t e p velocity.  the  with  but depends s t r o n g l y on t h e type and Heavier  propellers  of  similar  on S a b l e I s l a n d , g i v e D = 1.0m 0/(0-0.7m/s)  and 19cm 4-bladed ones show D = 0.79m 0/(0-1.8m/s).  58  o CM  1  1  fi:  CD  1  1  [  GILL-U  i— i — I — I — I — I — I — I — I — I — I — I  0.  5.  1  CM  B:  10.  15.  1 — I — I — r  20.  25.  I I  30.  T  35  1 — I — r  GILL-W  +++  +  o.  —i—i—i—r  FIG DEE  6:  5.  10  ~ i — i — i — i — r 15.  20. 25 2TTf (HZ)  30.  35  B  D e t e r a i n a t i o n of the d i s t a n c e constants 0.8 t 1.6 Hz band-pass f i l t e r r a t i o s of A: t h e G i l l - u h o r i z o n t a l p r o p e l l e r , B: t h e G i l l - w t i l t e d p r o p e l l e r , °< = 59.5°.  from  the  59 The data o f f i g u r e s 6A and periods,  but  evidently  (longer d i s t a n c e responds.  more  constant,  This  may  DT=1.22 D  for°<=60 ,  forms  from  the  the t i l t e d  useful  line  speeds  of  because  Gill-w  data  are l e s s  figure  so  the w  i t seems  the distance constant of the t i l t e d  (1975),  6B  and  spectrum  whose  results  This  means  p l e n t i f u l a s w e l l a s more  Such an approach t u r n s out t o l i e between Gill  propeller  a l a r g e p a r t o f t h e i n p u t s i g n a l , V2, i s no l o n g e r  u n c e r t a i n than t h a t of t h e G i l l - u , take  time  t h e n o n - c o s i n e b e h a v i o r , because  -5/3 throughout the G i l l - w 0.8 Hz band-pass f i l t e r . that  same  i s an a c c e p t a b l e f i t f o r 0<12 m/s.  The t e c h n i q u e f a i l s a t h i g h e r which  before  the s o l i d  which  o  come  a i r must pass i n t h e h o r i z o n t a l  DT)  reflect  assuming DT=D//5?(°<) g i v e s  6B  for a  preferable  p r o p e l l e r as Hicks  60°  to  D//3{<K).  (1972 B)  and  angle of attack give  DT=1.41 D and 1.15 D, r e s p e c t i v e l y . A s i m i l a r p r o c e d u r e was response  of  each  microbead  used  to  establish  thermistor  the i n  mounted  situ  i n t h e HAT.  R e g r e t t a b l y , i t had t o be based on v e r y l i t t l e d a t a because each bead worked f o r only a recorded  relatively  short  time  and  a  l o t of  d a t a has been r e j e c t e d because of c a l i b r a t i o n  problems  and s u s p e c t e d s a l t c o n t a m i n a t i o n o f t h e microbead. reliable  t e m p e r a t u r e d a t a from t h e Bedford tower i s i n c l u d e d i n  f i g u r e 7, i n which t h e h o u r l y averaged against the  0.8  Clearly of  Most o f the  wind  speed  i s plotted  t h e sensor response r e g u i r e d t o make Nt c a l c u l a t e d from and  1.6  Hz  temperature  band-pass  t h e r e s p o n s e improves w i t h wind speed.  s l o p e 0.90m, i s an a c c e p t a b l e f i t t o a l l t h e  filters,  equal.  The s o l i d data,  line,  implying  t h a t t h e microbead r e s p o n s e , i n winds up t o a t l e a s t 20 m/s, can  FIGURE  7:  Determination of the microbead t h e r m i s t o r response from the 0.8 : 1.6 Hz band-pass f i l t e r r a t i o s . The s o l i d l i n e has slope 0.90m.  61  a l s o be d e s c r i b e d as an E-C f i l t e r w i t h a d i s t a n c e c o n s t a n t , DB. Miyake  e t a l . (1970 B)  a  26  Hz  microbeads a t an a i r c r a f t speed o f  70  m/s  about 0.4m). indicated  quote  fiqure  7.  constant  I t i s s u s p e c t e d , however, t h a t t h e  response i s l i m i t e d by the HAT  air  (distance  The lower wind speeds may q i v e t h e p o o r e r r e s p o n s e  by  distance  response f o r s i m i l a r  itself  and  the success  c o n s t a n t d e s c r i p t i o n i s a consequence  needed t o f l u s h t h e e n c l o s u r e .  of a  of t h e amount of  A c c o r d i n g l y * t h e data  from  i n d i v i d u a l microbeads agree w i t h a DB o f 0.90m t o w i t h i n ±5%. If  t h e response  i s b e i n g t r e a t e d p r o p e r l y , t h e Eeynolds  s t r e s s d e r i v e d from each o f t h e t h r e e band-pass f i l t e r s on  should,  average, be e q u a l . . In f i g u r e 8 the r a t i o s of € zl 3 (from 3.7)  and e q u i v a l e n t l y function  (from e q u a t i o n 2.28)  o f wind  Evidently  ratios  are plotted  as a  speed f o r t h e same data a s used i n f i g u r e 6.  t h e chosen  individual  <uw>  response  differ  from  is  reasonable.  Very  few  1.0  by more than 10%. At t h e  l o w e r winds t h e averages o f a l l t h r e e r a t i o s a r e n e a r l y 1. 0 and in  the c a s e  of  the 0.8/1.6 r a t i o , t h i s i s t r u e up t o 20 m/s.  Between 12 and 20 m/s, t h e 0.4 Hz band-pass have  about  expected.  5%  smaller  T h i s may  filter  appears  to  s t r e s s v a l u e s ( l e s s output power) than  reflect  a  deviation  from  a  purely  E-C  r e s p o n s e , but more l i k e l y i t i s e v i d e n c e o f t h e lower p o r t i o n of the  filter  l y i n g , on a v e r a g e , below t h e f - / f r e q u e n c i e s d u r i n g  t h e s e h i g h e r winds.  5  3  At 16 m/s t h e d i s t a n c e c o n s t a n t f o r m u l a t i o n  g i v e s D= 0.6m, but i f i t were t a k e n t o be a c o n s t a n t observed  0.4/0.8 r a t i o would be even l e s s , because t h e response  c o r r e c t i o n a t 0.8 Hz i n c r e a s e s f a s t e r t h a n response  0.65m t h e  i s made  poorer.  at  0.4  Hz  as the  The c o r r e c t i o n i s h i g h l y n o n - l i n e a r  FIGURE  8:  Ratios of <uw> c a l c u l a t e d from d i f f e r e n t p a i r s of band-pass f i l t e r s as a f u n c t i o n of wind speed. The s o l i d l i n e of f i g u r e 6fl g i v e s the sensor response*  63 w i t h wind speed Because  and  very  different  from  filter  the r a t i o s of f i g u r e 8 v a r y so l i t t l e ,  mean wind speed, i t i s response  will  dependencies. feasible  produce  any  on a v e r a g e , with  errors  major  in  the  spurious  sensor  wind  both the 0.4 and 0.8 Hz band-pass  entirely  spectrum.  that  filter.  speed  A s i m i l a r check on t h e microbead response i s  because  often not  unlikely  to  The  in  the  -5/3  region  of  filters  the  not are  temperature  i n e v i t a b l e presence of contaminated d a t a adds a  further complication.  3.6  The E x p e r i m e n t a l Program The Bedford tower experiment l a s t e d from September 1976  to  A p r i l 1977.  A d e s c r i p t i o n of the tower and t h e r e s u l t s from t h e  BIO  can  system  be  found  in  Smith,  1979.  The tower was a  f l o a t i n g s p a r buoy moored i n 59m of water, which makes the essentially  a  deep  water  wave  regime  (Smith,  l o c a t i o n and a photogragh o f t h e tower a r e shown The  shortest  fetch  to  The  thermistor. find  the  conditions  extend  over  The G i l l  and HAT a r e a t  the  Z  a  very  the BIO t h r u s t and aerovane anemometers and The t i d e t a b l e s f o r H a l i f a x phase  harbour  9.  170°  are  top  microbead used  to  and a m p l i t u d e (assumed e q u a l t o h a l f the t i d a l  range) a t t h e b e g i n n i n g of each r u n , from which the height  figure  e l e c t r o n i c s packages can be seen on the main deck,  about 3m above t h e s e a . alongside  in  The  t h e tower s i t e i s from the west and i s  about 10 km, w h i l e open f e t c h range.  1979).  site  measurement  i s c a l c u l a t e d assuming a p u r e l y M2 t i d e , which i s the  FIGURE  9 A: T h e B e d f o r d t o w e r s i t e n e a r H a l i f a x Nova S c o t i a . B: The i n s t r u m e n t a t i o n on t h e B e d f o r d t o w e r .  65 predominant t i d e i n t h i s a r e a . tied  to  the  tower  about  The sea t e m p e r a t u r e  10m  sensor  below mean sea l e v e l .  was  Surface  meteorological observations, i n c l u d i n g the atmospheric pressure, PA, f o r a i r d e n s i t y c a l c u l a t i o n s , were r o u t i n e l y r e c o r d e d a t t h e Shearwater "A"  land  station  of  the  Atmospheric  Environment  S e r v i c e , l o c a t e d about 15 km n o r t h o f t h e tower s i t e While  on  the tower, t h e Reynolds f l u x system r e c o r d e d t h e  t h r e e anemometer s i g n a l s p l u s a microbead Brady  humidiometer  and  a  filtered  thermistor,  Brady  s w i t c h s e t t i n g s of s e c t i o n 3.3 were employed of  either  3  or  4  an  open  from t h e HAT. so t h a t  flux  The runs  groups c o r r e s p o n d i n g t o 40.5 o r 54 minutes  r e s p e c t i v e l y , can be p r o c e s s e d . began  (figure 9).  From September 15 a new  record  e v e r y hour, b u t on t h e 23rd t h e i n t e r v a l was i n c r e a s e d t o  3 hours and t h e lower wind speed l i m i t was s e t t o October  4  the  limit  was  10  m/s.  On  changed t o 8 m/s, then i n c r e a s e d t o  12m/s on October 6 and put back t o 10m/s on F e b r u a r y 15 where i t remained  until  dissipation  t h e end  system  of  t h e experiment.  Meanwhile  ( f i g u r e 5) sampled and r e c o r d e d t h e low-pass  d a t a from t h e same s i x s i g n a l s p l u s a r o d t h e r m i s t o r HAT  and t h e sea t e m p e r a t u r e .  from  of  summations,  NI,  the  The G i l l - u , G i l l - w , microbead and  open Brady s i g n a l s were s e l e c t e d t o be band-pass f i l t e r e d . number  the  The  was s e t t o 4500 t o comply w i t h a 4  minute Dt, which enabled t h e p a i r of c a s s e t t e s t o l a s t f o r 52.5 days.  66 The  weather  ship  experiment i n c l u d e d the f o u r p a t r o l s o f  CCGS Quadra between J u l y 1977 and A p r i l 1978. and  fourth  third  p a t r o l s a s i n g l e p r o p e l l e r G i l l anemometer was  with the G i l l - u s i g n a l Gill-w  D u r i n g the  signal.  also  being  processed  as  the  used  missing  The t y p i c a l mode o f o p e r a t i o n of the s h i p when  a t "PAPA" ( f i g u r e 10) was t o d r i f t w i t h the wind then r e t u r n station  by steaming i n t o t h e wind a t l e s s t h a n 4 k n o t s .  to  During  the l a t t e r o p e r a t i o n the g r e a t b u l k o f good data were c o l l e c t e d , but some u s e f u l data were a l s o c o l l e c t e d as t h e s h i p steamed 7  to  12  knots  while  en  route  to  "PAPA" ( f i g u r e 10).  l o c a t i o n of t h e s e n s o r s on the s h i p ' s f o r e m a s t i s shown photograph  of  figure  10.  over the bow  base  of  is  not  in  the  the  mast.  With  winds  the measured t i l t a n g l e s a r e t y p i c a l l y o n l y  about +7°, i n d i c a t i n g t h a t t h e s h i p ' s flow  The  C a b l e s were r u n t o the e l e c t r o n i c s  packages two decks below t h e coming  at  distortion  of  the  enough t o upset the d i s s i p a t i o n method.  winds more than 30° t o s t a r b o a r d or 60° t o p o r t  were  mean  However, found  to  have g r e a t l y p e r t u r b e d h i g h f r e q u e n c i e s , which proved t o be very unfortunate winds. of  because  the  ship  drifted  f o r many hours i n such  In a d d i t i o n the foremast l o c a t i o n r e c e i v e d a g r e a t  spray  so  that  the  microbeads  broke  and t h e lyman-alpha  windows became d i r t y soon a f t e r t h e f i r s t e n c o u n t e r seas.  As  a  consequence  very  humidity data are a v a i l a b l e caused  a  propellers, subsequent  great which  deal  of  they  experiment  pitting  (JASIN  mounted f o r w a r d of t h e bow  with  heavy  l i t t l e temperature d a t a and no  from  can  deal  the  ship.  The  spray  also  i n the l e a d i n g edges o f t h e  fortunately 1978),  the  of the FS Meteor  tolerate. same so  In  sensors  that  the  a were wind  FIGUEE  10 A: Ocean Weather S t a t i o n "PAPA", 50°N, 1 4 5 ° w , and the r o u t e o f the w e a t h e r s h i p s . B: The i n s t r u m e n t a t i o n on t h e foremast o f CCGS Quadra.  68 carried  t h e spray away and a g r e a t d e a l o f both temperature and  h u m i d i t y d a t a were c o l l e c t e d . While on filtered rod  and  CCGS  QUADRA,  the dissipation  low-pass  and r e c o r d e d t h e s i g n a l s from the f o l l o w i n g s e n s o r s : a two  anemometer,  microbead  thermistors  were  from  t h e HAT,  the  Gill  a Lyman-alpha humidiometer and t h e dewpoint system.  The two G i l l v e l o c i t y , the two signals  system  microbead  and t h e Lyman-alpha  a l l band-pass f i l t e r e d * . Dt was s e t a t 5 minutes,  a l l o w i n g NI t o be 5800 and up t o 56 days o f d a t a t o be s t o r e d on the  two c a s s e t t e s .  provide  velocity  The Reynolds f l u x and  system  scalar spectra.  signals.  included  to  I t was s e t up a s on the  tower, but t h e Brady a r r a y s were r e p l a c e d by Lyman-alpha  was  t h e dewpoint  and  The wind speed l i m i t was always s e t t o a t  l e a s t 8 m/s so t h a t f l u x r e c o r d s were taken throughout most o f a patrol.  With t h e s e s w i t c h s e t t i n g s i t was p o s s i b l e t o t u r n  systems  on  upon  return  temperature  the  p r i o r t o s a i l i n g and t o r e t r i e v e t h e d a t a c a s s e t t e s seven  weeks  later.  A  sea  surface  "bucket"  and t h e a t m o s p h e r i c p r e s s u r e a r e a v a i l a b l e from t h e  ship's three hourly meteorological observations.  69 CHAPTER 4  REYNOLDS FLUX MEASUREMENTS FROM THE  4.1  BEDFORD STABLE TOWER  Introduction The Reynolds f l u x data s e t from the Bedford tower  of  196  momentum  flux  runs  with  winds  up t o 20 m/s and the  majority of s t a b i l i t i e s i n the range -0.4 <Z/L< cases  the  fetch  consists  0.1.  In  most  i s u n l i m i t e d , but winds from a l l d i r e c t i o n s ,  except those which put t h e sensors i n t h e wake of the BIO t h r u s t (from t h e e a s t ) , are a l l o w e d , so some f e t c h e s a r e as 10 km.  The  runs  which  propeller i n i t s  i n each  linear  operating  a l s o ensures that the measurement h e i g h t , Z = 13 m,  i s i n the "constant f l u x " l a y e r . that  as  are r e s t r i c t e d t o t h e 5 m/s or g r e a t e r winds  necessary t o keep the t i l t e d range,  short  I t i s very g r a t i f y i n g t o  find  case where simultaneous d i s s i p a t i o n data e x i s t s ,  192 runs, the band-pass  data confirm the  r e g i o n i n the v e l o c i t y s p e c t r a .  existence  of  a  Other runs a r e r e j e c t e d  -5/3  because  the G i l l - w and G i l l - u s i g n a l s do not t r a c k each other p r o p e r l y . All  196  runs  have been c o n s i d e r e d f o r s e n s i b l e heat f l u x  c a l c u l a t i o n s , because even 5 m/s winds a r e s u f f i c i e n t the  HAT.  However,  during  very  cold  flush  many of these runs the temperature  data are not a v a i l a b l e , because e i t h e r t h e microbead or  to  a i r drove i t s s i g n a l o f f s c a l e .  was  broken  A few runs are  a l s o r e j e c t e d because t h e mean a i r temperatures from the r o d and microbead addition  thermistors many  do  not  agree  to  within  ±0.1°C.  In  more runs have not been processed due to what i s  b e l i e v e d t o be the s e n s i t i v i t y o f a s a l t  contaminated  microbead  70 to  humidity  fluctuations  as r e p o r t e d by S c h m i t t e t a l . ,  1978.  T h i s b e h a v i o r i s r e c o g n i z e d by r e l a t i v e l y l i t t l e v a r i a n c e i n the temperature spectrum below n=0.01 and i n many but  not  these  cases,  a l l , t h e d i s s i p a t i o n d a t a r e v e a l t h a t t h e temperature  spectrum i s not f a l l i n g as s t e e p l y as -5/3. runs  of  have  been  Only 60 of t h e  196  found t o s a t i s f y c r i t e r i a f o r temperature f l u x  calculations. A l l t h e Reynolds f l u x r e s u l t s a r e t a b u l a t e d i n t h e Appendix and are r e f e r r e d t o as runs T1 t o T196.  4.2  The S t a b i l i t y Parameter A s t a b i l i t y parameter  2.38  the  i s calculated  Z/L(AT)  f o r each of t h e 196 runs.  i s approximated by probe,  Z/L from  equation  The s u r f a c e t e m p e r a t u r e , TSFC,  dissipation  system's  sea  temperature  TSEA, which i s assumed t o have f a l l e n l i n e a r l y over a 16  hour p e r i o d t h a t was n o t recorded (runs T90-T93). The mean a i r temperature,  TZ,  at  the  measurement h e i g h t , Z, u s u a l l y  comes  from the r o d t h e r m i s t o r of t h e d i s s i p a t i o n system, b u t over unrecorded  gap  and d u r i n g p e r i o d s when t h e rod's s i g n a l  the  either  has e r r a t i c b e h a v i o r (runs T47-T55, T74-T85 and T138-T149) or i s o f f s c a l e , t h e f l u x system's used.  Unfortunately,  recordings  during  runs  of  the  microbead  are  T102-T110,  T117-T122  and  T131-T133 n e i t h e r t e m p e r a t u r e sensor was o p e r a t i o n a l and necessary Shearwater.  to  use  the  In f i g u r e 11B,  meteorological Z/L(AT)  i t is  observations  from  i s p l o t t e d against the  more  71  8"0  t7*0  K 0  (IV )  (jv  FIGURE 11  1/Z  t7'0-  0*0  O'O  • Xfl)1 / Z  Comparison of t h e most complete e x p r e s s i o n f o r t h e s t a b i l i t y parameter Z/L ( u * <wt>) t o : A: an a p p r o x i m a t e e x p r e s s i o n Z / L ( u * A T ) . B: the b u l k e s t i m a t e Z/L (AT) . r  #  72  exact  Z/L(u*,<wt>) ( e q u a t i o n 2.36) f o r t h e 60 temperature runs.  The two c a l c u l a t i o n s tend t o agree on averaqe and seldom by  more  than  substantial  ±0.05,  but occasionally  the difference i s  (more than 0.2). S i n c e u* i s c a l c u l a t e d f o r a l l t h e  runs i t c a n be used, i n s t e a d o f <0>, t o c a l c u l a t e parameter  differ  Z/L(u*,AT) from e q u a t i o n 2.37.  a  stability  However t h i s e s t i m a t e  does n o t agree as w e l l w i t h Z/L(u*,<wt>) as shown i n f i g u r e 11A, where s y s t e m a t i c d e p a r t u r e s from a 1:1 r e l a t i o n s h i p a r e e v i d e n t . S i n c e <wt> i s o n l y a v a i l a b l e from t h e t e m p e r a t u r e runs i t must  be approximated by CT <D> AT, but e v i d e n t l y t h e a s s o c i a t e d  e r r o r i s p a r t i a l l y compensated with  often  CD <0> . 2  The  bulk  by t h e e r r o r  estimate  i n replacing  Z/L ( AT)  i s t o be  e x c l u s i v e l y , because i t i s t h e b e s t e s t i m a t e o f s t a b i l i t y  u*  2  used that  i s always a v a i l a b l e , even though i t may n o t be v e r y a c c u r a t e f o r an i n d i v i d u a l r u n .  4.3  Turbulence Spectra And Cospectra The  spectra  of  the  fluctuating  v e l o c i t y components and  f l u c t u a t i n g temperature, f * ( f ) , provide a means o f e v a l u a t i n g t h e performance of the Reynolds f l u x system  ( s e c t i o n 3.3).  To f i n d a value of E f o r each q u a n t i t y method, eguation 3.5, normalized s p e c t r a are  established  by  s p e c t r a l v a l u e s and n=fZ/<0>  averaging their  over  and  by the 13  cospectra,  (n),  a l l a v a i l a b l e runs. A l l  corresponding  (186 per r u n ) , are f i r s t  integrated  natural  calculated*  frequencies,  The f(n) are then  73  multiplied log (n). u*  by  f  t o produce a v a r i a n c e p r e s e r v i n g p l o t  Next t h e f 0(n) a r e n o n - d i m e n s i o n a l i z e d  i n t h e case of v e l o c i t y  2  temperature Finally,  spectra  and  <wt>  the d i s c r e t e normalized  a particular stability A l o g (n)  and  by d i v i d i n g by:  cospectra,  =-Xu*t*  deviation,  l o g (n)  should,  cr, f o r e a c h to  band.  2  integrating  0uw,  and  2  0t  <wt>  are  n, such  plot  i s  a  great  in that  of  NT (n) 1  theory, display a  The n o r m a l i z i n g f a c t o r s found  f o r each  run  by  a n d 0 w t f r o m n=0.004 and a r e t h e r e f o r e a s  much a s 10% s m a l l , b u t t h e e r r o r i s i n d e p e n d e n t o f There  cospectra.  t o be N 0 ( n ) , and  A  similarity  u n i v e r s a l f o r m , d e p e n d i n g on s t a b i l i t y . u* =-<uw>, < t t > = ( a t )  for  2  s p e c t r a l v a l u e s from M runs  r a n g e a r e band a v e r a g e d o v e r  according  (at)  f o r w,t  r e m a i n s c o n s t a n t , g i v i n g a mean, t a k e n  a standard vs.  spectra  against  wind  speed.  deal of s c a t t e r i n the 0 ( f ) ' s , not only  from  run  t o r u n , b u t b e t w e e n n e a r b y f r e q u e n c i e s o f t h e same r u n , due  to  the  latter  inherent  variability  of the Fourier c o e f f i c i e n t s .  e f f e c t i s r e d u c e d by a v e r a g i n g  over  t h e NG  groups  The of  f l u x r u n . However, i t i s n o t reduced f u r t h e r , by a v e r a g i n g Fourier  bands,  which should  because  be k e p t  as narrow a s  where t h e r e a r e o n l y  a c o n s e q u e n c e , or i s e x t r e m e l y variability  of  the  mean,  i n d e p e n d e n t , crm-oy/F i s t a k e n deviation  of  statistics,  which should  runs,  that  and  the  mean.  the  over  t h i s g r e a t l y i n c r e a s e s t h e band-width, possible  in  N0 (n) r e p r e s e n t a t i v e o f i t s n a t u r a l f r e q u e n c y , frequencies  a  l a r g e and n o t N0 ( n ) .  especially  indicative  Since  the  a s an e s t i m a t i o n o f This  and  to  keep a t low  a few p o i n t s i n e a c h b a n d .  estimation  be a p p r o a c h e d w i t h a  mean  order  cr a r e  good  M  As  of  the  runs  are  the  standard  assumes  Gaussian  large  number  measures  of  cf the  74  population s t a t i s t i c s ,  which r e q u i r e s that  p o i n t s i n a band, be much l a r g e r than M. is  not  NP,  the  This l a t t e r  remain  nearly  approximation.  Gaussian  with  the  o"m=o/'vM  S i m i l a r l y , when NP becomes  less  each  statistics  a  r  of  assumption  s t r i c t l y s a t i s f i e d as NP approaches M, but because  run continues t o c o n t r i b u t e a t l e a s t one p o i n t , should  number  reasonable  than  M,  each  p o i n t comes from a d i f f e r e n t run and oti=o/v/NP~ i s assumed. In  the  f o l l o w i n g normalized p l o t s N^(n) from each band i s  p l o t t e d i n the middle of the log(n) band and shown by a  diamond  with  In  vertical  bars  extending  l o g a r i t h m i c p l o t s the means lines  of  up  and  (sguares)  - 2 / 3 slope, i n d i c a t i n g  are  1 o"m.  plotted  and - 5  The runs are sometimes s p l i t i n t o  groups  which  stable  and  are averaged and p l o t t e d s e p a r a t e l y .  attempt to average over s m a l l e r majority  the solid  f (f) p r o p o r t i o n a l t o f / , are  drawn.  large  down  stability  unstable  There i s no  ranges  of runs span only a narrow  3  because  the  range and because of  the l a r g e u n c e r t a i n t y i n Z/L (AT) .  V e l o c i t y Spectra The  normalized  component,  spectra  of  the  N^u (n), are shown i n f i g u r e  dependence on s t a b i l i t y .  downstream  velocity  12 and there i s a marked  The peak of the spectrum of the s t a b l e  runs* f i g u r e 12B, occurs at a  natural  frequency  more  decade higher than t h a t of the unstable runs ( f i g u r e  than  a  12A), whose  spectrum i n turn has a g r e a t e r p r o p o r t i o n c f i t s energy a t lower frequencies.  The  spectral  h i g h e s t wind speed runs  and  points their  below n=10~ average  3  over  come from the the  natural  75  O'O  »OT  FIGDRE 12  i-OI  Q'Z  Normalized spectra of the downstream velocity component from averages o f f 0u(n)/u* (pluses from slow samples o n l y ) . Solid l i n e has slope -2/3. V e r t i c a l l i n e s are ± 1 o*m. B: 88 s t a b l e runs. A: 108 u n s t a b l e runs, 2  76  f r e g u e n c y band, l o g ( n ) = -3.21 stable  and  unstable  t o -3.00  case.  i s about 0.75  i n both the  I t does appear, t h e r e f o r e , t h a t a  s p e c t r a l gap i s emerging between t h e f l u c t u a t i n g motion and mean  flow.  Some  e v i d e n t i n the averaging  platform  spectra,  over  large  motion  perhaps  the  i s e x p e c t e d , but i t i s not  because  i t is  bands.  The l o g - l o g p l o t s of  freguency  obscured  by  f i g u r e 12 d i s p l a y a s i m i l a r shape and s t a b i l i t y dependence as do the  over  land  measurements  spectra over  of  McBean,  1971.  In  contrast,  the  l a n d of K a i m a l e t a l . , 1972, suggest s h a r p e r  peaks. C o n t r i b u t i o n s t o the bands between from  n=0.1  and  n=0.4  come  both the slow and the f a s t samples depending on wind  speed  and t h e s m a l l p l u s e s on f i g u r e 12A r e p r e s e n t the using  only  t h e slow samples.  averages  These a r e p l o t t e d a t the average  v a l u e of l o g (n) and not a t t h e band c e n t e r as  the  overall  the f a s t sampled  spectrum  on a v e r a g e , match t h e more s t a t i s t i c a l l y c e r t a i n  spectral  averages. does,  band  I n t h i s range  (0.1 <n<  0.4)  v a l u e s found from t h e slow samples. aliasing  is  no  evidence  of  i n the slow samples c o r r o b o r a t i n g t h e argument t h a t i t  i s compensated by the 1 second time Similar  There  are  matching  is  constant  low-pass  filter.  not done i n f i g u r e 12B because the p o i n t s  f a l l near t h e peak of t h e spectrum. I t happens t h a t a l l t h r e e G i l l - u band-pass f i l t e r s utilized "PAPA". stable  under  unstable  about a n a t u r a l  be  a l l c o n d i t i o n s encountered a t the tower and a t  The l o g a r i t h m i c p l o t s o f f i g u r e 12 show t h a t and  may  s p e c t r a b e g i n t o d i s p l a y a -5/3  freguency  n=0.2.  Above  n=1.0,  the  both  the  region at Nyguist  77  frequency  when <0>=18 m/s, t h e N 0 u (n) f a l l above t h e -2/3 l i n e s  ( f a l l l e s s r a p i d l y t h a n - 5 / 3 ) , r e f l e c t i n g t h e expected distortion the  due  to aliasing.  F i g u r e 8 s u g g e s t s t h a t , a t Z=13m,  output o f t h e 0.4 Hz band-pass f i l t e r  below the  t h e -5/3  Hz.  However,  average,  fiqure  8  also  (0.2  indicates  i s only  12m/s/ 13m)  5%  about  Therefore, u t i l i z i n g a l l three  lower,  filters  on  f o r winds to  find  s t r e s s s h o u l d i n t r o d u c e a s y s t e m a t i c e r r o r l e s s than 2% and r e t u r n improve the s t a t i s t i c a l  The  effective  low  frequency  certainty  of  the estimate.  c u t - o f f of t h e 0.4 Hz f i l t e r and  p r e w h i t e n e r c o m b i n a t i o n i s n <0>/Z = (0.2 20m/s/ 13m) = 0 . 3 the  3db  down  frequency  of H c ( f ) .  wind  always  =  below  (0.3Hz  22m/ 0.2)  d i s s i p a t i o n c a l c u l a t i o n s always use band-pass  plus  33 m/s,  the  data  ship  speed  therefore, from  cannot be used i n t h e d i s s i p a t i o n method  velocity  spectrum,  f 0Q(f),  average of f o u r Reynolds f l u x r e c o r d s taken and  the  a l l three  they pass f r e q u e n c i e s c o n t a m i n a t e d by t h e s h i p ' s motion.  seas  is  filters.  Of c o u r s e , f i l t e r s  horizontal  Hz,  The tower winds a r e always  l e s s than 20 m/s and a t "PAPA", t h e  if  =  that the stress  t h a n t h a t c a l c u l a t e d from t h e o t h e r f i l t e r s ,  up t o 20 m/s. the  freguencies  range w i t h 12 m/s and h i g h e r winds, which s e t s  c a l c u l a t e d from t h e 0.4 Hz f i l t e r  in  contains  low f r e q u e n c y c u t - o f f o f Hc(f) a t about  0.2  spectral  of  figure  during  s l i g h t l y u n s t a b l e c o n d i t i o n s a t "PAPA".  The  13, i s an very  rough  The s p e c t r a l  v a l u e s a r e averaged over bands o f l o g ( f ) i n t h e manner d e s c r i b e d for  the n o r m a l i z e d s p e c t r a .  The number o f r u n s , M, i s 4, so the  v e r t i c a l b a r s extend ±1 ffm deviation  about  o/2,  where  <r i s t h e s t a n d a r d  t h e mean f f*Q(f) o f a l o g (f) band.  The 22 m/s  78  pro  o O  i O  r  r*si  -67  t o  T o  2'T FIGURE 13  8'0  O'O  The h o r i z o n t a l v e l o c i t y spectrum, f 0Q (f) i n Hz and (m/s) , averaged over 4 runs from CCGS Quadra i n 22 m/s winds. V e r t i c a l bars extend ±1 e s t i m a t i o n of the standard d e v i a t i o n of t h e mean. 2  79 winds make n and f very n e a r l y e q u i v a l e n t and the accordingly, to  spectrum  is,  n e a r l y the same as f i g u r e 12A except between  0.3 Hz where  the  motion  of  CCGS  Quadra  is  f=0.1  conspicuous.  T h a n k f u l l y , even under such extreme c o n d i t i o n s , very l i t t l e motion  should  be  passed  prewhitener combination. s h i p i s always Figure N0w(n). 3Hz  by  the  0.4  Hz  band-pass  N o n e t h e l e s s , i t s output  ship filter  while  cn  a  checked.  14 shows the n o r m a l i z e d v e r t i c a l v e l o c i t y  spectrum,  The peaks, near n e q u a l s 1, a r e b a r e l y reached w i t h the  f a s t s a m p l i n g r a t e , but t h e r e appears t o be  a  shift  to  a  h i g h e r frequency i n the s t a b l e c a s e , which i s i n a c c o r d w i t h t h e over  land  studies  previously cited.  the peaks must be d i s t o r t e d by large  amount  of  high  the  frequency  i n e v i t a b l y l o s t because t h e r e i s sensor response. At  The s p e c t r a l shapes near  aliasing variance,  only  partial  of  a  some  correction  low f r e q u e n c i e s am i s v e r y s m a l l and t h e low s p e c t r a l  other  been  the  Gill-w  levels  found  consistent  In  with  the  (0.8Hz 13m/12m/s) -0.9, and  logarithmic  plots  of  f o r example, t h e 0.4,  0.8  m/s,  8 m/s  and  16 m/s,  On  and 1.6 Hz o u t p u t s should  d e f i n i t e l y not be used when the wind speed exeeds (0.3 =4  14.  Gill-w  band-pass f i l t e r o u t p u t s are used i n the d i s s i p a t i o n method. tower,  -5/3 this  figure  T h e r e f o r e , some r e s t r i c t i o n s have t o be imposed when t h e  1.0)  in  section  response i n v e s t i g a t i o n suggested t h a t t h e  range o f 0 w ( f ) b e g i n s above n=  the  for  s t u d i e s , i n d i c a t i n q that the h o r i z o n t a l v e l o c i t y i s being  p r o p e r l y removed from t h e t i l t e d p r o p e l l e r s i g n a l .  is  of which i s  Again t h e r e i s no e v i d e n c e of p l a t f o r m motion.  and the observed s t a b i l i t y dependence have a l s o  3.5  relatively  respectively.  Hz  13m/  80  w  CO ZD  o  • H  a  =- O .—1  CC  LE  —  DD CE  • •  -  —  =-  T  ^  —  CO  -  2:  ZD CO O  0 1—1  .—1  i-OT  FIGURE 14  j-01  8'0  wy>  I M  Normalized v e r t i c a l v e l o c i t y s p e c t r a from of f f w ( n ) / u * over: A: 108 unstable runs B: 88 s t a b l e runs. V e r t i c a l l i n e s are ±1 crm. 2  averages  81 The Temperature The N 0 t (n),  Spectrum  normalized  spectrum  of t h e temperature f l u c t u a t i o n s ,  from a l l 60 t e m p e r a t u r e r u n s , i s  shown  in  figure  15.  I n d i v i d u a l p l o t s f o r a v e r a g e s over the 27 u n s t a b l e and 33 s t a b l e runs  a r e not p r e s e n t e d because t h e y a r e not v e r y d i f f e r e n t  w i t h so few r u n s , n o t v e r y s t a t i s t i c a l l y majority  of  runs  have  |Z/L|  <  r e p r e s e n t a t i v e o f "near n e u t r a l " the  spectral  shape  is  very  0.1,  et a l . ,  freguency. band  much  like  a  deviation*  mean  supports would  available. averages  indicates  a  figure  sharper  of the  emerge  0.15,  more  spectrum  peak  of  1524  and  runs,  or  due  be  near of  at a higher frequency  of high  a  spectral  wind  gap  speed  that  r u n s were  The two p l u s e s p l o t t e d near n=0.2 and n=0.3 a r e  the  402 p o i n t s , r e s p e c t i v e l y , from t h e slow  f r e q u e n c y p l u s may be a consequence to  a  frequency  portion  The r i s e of the h i g h e r  of combining t h e s t a b l e  little  microbead i s s u s p e c t e d of r e s p o n d i n g the  may  which, d e s p i t e a l a r g e standard  existence if  the  Accordingly,  temperature  the temperature spectrum q u i t e w e l l .  unstable  15  McBean's (1971)  samples o n l y and t h e i r average f i t s the h i g h of  However,  An average over t h e l o g ( n ) = -3.25 t o -3.0  gives  seemingly  1972,  so  stratification.  n e u t r a l c a s e , however the g e n e r a l i z e d Kaimal  certain.  and,  to  and  aliasing,  b u t when the  humidity  fluctuations  peak of t h e spectrum i s found above n=0.1  and t h e i n c l u s i o n  of  o n l y a s m a l l amount of such d a t a c o u l d l i k e l y be  of  this feature.  the  source  82  o  I  o  60  RUNS  •  •  • •  E n  I 111 n i | — r r r lO"  FIGOEE 15  2  IO"  1  FXZ/<U>  The n o r m a l i z e d temperature spectrum from averages of f ^t(n)/(ot) over a l l 60 temperature runs (pluses from slow samples only) . S o l i d l i n e has slope -2/3 and v e r t i c a l l i n e s extend ± 1 oTn. 2  83 The  logarithmic  plot  does  not e x h i b i t any e v i d e n c e c f a  -5/3 r e g i o n ,  which t h e San Diego r e s u l t s  1971,  to  show  begin  at  about  of  n=0.6.  Phelps  and  Pond,  Here t h e spectrum i s  d i s t o r t e d by a l i a s i n g b e f o r e i t can d e v e l o p , however one o f criteria  for  selecting  the  60  temperature  runs i s t h a t the  r a t i o s of the band pass f i l t e r s r e v e a l the e x i s t e n c e o f region  above  n=0.6.  p r e w h i t e n e r and filters  are  0.8 0.3,  and  1.6  Hz  0.55  and  1.0  the  temperature  i m p l i c a t i o n i s t h a t the use dissipation  method  manner: the 0*4  of  ought  to  tower and 10 m/s  (Z  0.55Hz/0.6)  =  12 m/s  on the s h i p .  data  from  the  check on t h e -5/3  The u w  Hz r e s p e c t i v e l y .  restricted  data  The  in  the  i n the f o l l o w i n g  on the tower and 20 m/s (Z 1.0Hz  /0.6)  U n l u c k i l y , a t the 1.6  m/s  on  = 20 m/s higher  on the Quadra on the tower wind  speeds  Hz f i l t e r a r e u s e f u l , so t h e r e i s no  region.  The n o r m a l i z e d u,w  cospectrum,  N0uw(n),  from  the  stable  i s s i g n i f i c a n t l y d i f f e r e n t from t h a t found i n t h e u n s t a b l e  c a s e , as shown by f i g u r e 16. McBean  band-pass  Cospectrum  x  runs  -5/3  on the s h i p , the 0.8 Hz t o speeds l e s s than  and the 1.6 Hz t o <0> below  only  be  temperature  Hz t o winds l e s s t h a n (Z 0.3Hz/0.6) = 6  the  and 37 m/s  a  The 3db down f r e q u e n c i e s of the combined  0.4,  about  the  and  excellent calculating cospectra  The  over  land  Miyake  (1972)  and  Kaimal  agreement  with  these  over  E  for  (page 5 1 ) ,  Alog(n) = 0.25.  the the  13  method  N0(n)  are  results  of  e t a l . (1972) sea  are  spectra.  o f i n t e g r a t i n g u,w averaged  over  F o r c l a r i t y , the bands i n f i g u r e s  both in When  and  w,t  bands  of  16 and 17 a r e  84  fl:  CO  108 UNSTABLE  RUNS  O  CXI  o  5°  —i  i iTiiii|—i -a  10 -4  1 0  B:  CQ  r Tvm\—i  io-  2  i 111 n i | —  io-» -FXZ/O  111 n i | — i  10°  r 111 in  10  8 8 STABLE RUNS  O  O  O  i  O  10" 4 FIGURE 16  i 111iity—1111111—i  10- 3  lO" 2  i i iini|—i  10" 1  -FXZ/<U>  i 1111111—i r TTTTT  10°  10  Normalized unstable (A) and s t a b l e (B) u,w cospectra ±1 Ola, from averages of f fuw(n) / u * . I n t e g r a t i o n under t h e s o l i d curves gives E f o r the 13 method. 2  85 0.40,  but  the  integrated. unstable  solid  curves  From i t s peak a t a cospectrum,  The  3  more  1%  out the approximate  natural  figure  f r e q u e n c i e s l e a v i n g about n=10- .  trace  16A, of  freguency  falls  the  steeply  total  n=1.  n=0.03  the  to  lower  covariance  below  gentle f a l l t o higher freguencies i s usual,  but h e r e , as i n f i g u r e s 12 and 14, a l i a s i n g d i s t o r t s above  areas  the  shape  The h i g h e s t f r e q u e n c y p o i n t i s p l o t t e d a t n=4,  band c e n t e r , but t h e average l o g ( n ) o f t h i s band  is  at  the  n=3. 2,  which i s near t h e h i g h frequency c u t - o f f of t h e i n t e g r a t i o n over the  Alog(n)  =  0.25  found t o be 1.06 cospectrum,  bands.  times  figure  The t o t a l a r e a under t h e c u r v e  the 16B,  area  from  n=0.004.  shows  more  covariance  f e g u e n c i e s w i t h a peak at about n=0.2on  average,  below  n=0.002,  There i s no  under the s o l i d c u r v e i s o n l y about  stable  at  higher  covariance,  1.005  times  The t o t a l area the  area  from  The r a t i o E, r e q u i r e d f o r the 13 method of i n t e g r a t i n g  the cospectrum, t u r n s out t o be Eu=1-06  The  but i n d i v i d u a l runs o f t e n d i s p l a y  s i g n i f i c a n t amounts, both p o s i t i v e and n e g a t i v e .  n=.004.  was  and  Es=1.005  are  a  function  realistic  cf  values  stability  and  f o r u n s t a b l e and  stable cases, r e s p e c t i v e l y .  The w^t The similar  Cospectrum normalized fashion  measurements.  as  wt F  N^uw  cospectrum, and  also  N^wt ( n ) ,  behaves  in  a  agrees w i t h t h e over l a n d  The u n s t a b l e cospectrum, f i g u r e 17A,  displays  a  broader peak at a s l i g h t l y lower f r e q u e n c y t h a n does the s t a b l e , figure  17B.  Again  there  is  a  greater  proportion  c o v a r i a n c e a t t h e lower f r e q u e n c i e s i n t h e u n s t a b l e c a s e ,  of  the where  o TTTTT  o  10" FIGURE 17  T T TTTTTTj  10"  a  10"  fXZ/<U>  10°  rrm 10  Normalized w,t c o s p e c t r a ±1 Cm, from averages of f ^wt(n)/<wt> i n (A) unstable and (B) s t a b l e conditions. I n t e g r a t i o n under- the s o l i d curves gives E f o r the 13 method.  87 the  total  area  under  amount from n=0. 004.. 1.04.  The  the s o l i d curve i s about  In the s t a b l e  only  this  ratio  the  33  stable  and  27  u n s t a b l e temperature  is difficult  Humidity s e n s i t i v i t y  w,t  (stable). runs these  as  s t a b l e case, f i g u r e  Turbulence  of  the  reflected  temperature  t o diagnose from the cospectrum,  r e s u l t s i n f fwt(n)/<wt>  4.4  only  l a r g e r e s t i m a t e s o f the standard d e v i a t i o n of the mean,  than found f o r N 0 u w . sensor  is  (unstable) and Es=1.04  c o s p e c t r a and i n t e g r a t i o n s have more u n c e r t a i n t y , by  times the  suggestion i s t h a t the 13 method of i n t e g r a t i n g  c o s p e c t r a ought t o use Eu=1. 10 With  case  1.10  being  very  similar  to  because i t  the  average  17B.  Statistics  The s p e c t r a and c o s p e c t r a from each run are i n t e g r a t e d f=0.00065  Hz  (the  11  method),  to  give  s t a t i s t i c a l q u a n t i t i e s oil, oV, oV, at and coefficient  r(uw)  = <uw>/(cru oV) .  estimates  the  u,w  the  correlation  The mean, standard d e v i a t i o n  and wind speed dependence of some of these normalized are presented i n t a b l e I I , however t h e r e may dependence i n these r e s u l t s .  of  from  be  quantities  some  stability  I t i s evident from f i q u r e 12  that  t h i s method of i n t e g r a t i n g 0 u (f) i s l i k e l y t o underestimate  oil by  more  than  13%  at  <0>=6  m/s.  This  effect  i n c r e a s i n g wind speed and accounts f o r observed  increase  expected  for  frequency  OV  in and  au/<0> 0"t,  contributions.  with <0>.  which The  at  also  mean  decreases  least  half  of  with the  A s i m i l a r behavior i s have  significant  low  and s c a t t e r of ov/<0> and  88 i  Means o f 196 runs  Standard deviation  1  Results cf Smith & Banke 33 runs  Linear regression  OTi/<U>  092  018  .061 + .0026<O>  094 ± .014  0"V/<U>  .080  .031  .036 + .0037<U>  084 ± .022  Cw/< U>  .042  .006  027 + .0013<U>  10  1.18+ .005 <0>  1. 24  ffW/U*  31  -r(uw)  TABLE  II  ,06  ov/u*  ± .07  T u r b u l e n t v e l o c i t y s t a t i s t i c s from t h e 196 Reynolds f l u x runs. The means ± 1 s t a n d a r d d e v i a t i o n from Smith and Banke, 1975, a r e shown f o r comparison. The v a l u e s  c f o"w/<U>  a r e r a t h e r l e s s than t h o s e o f Smith and Banke, 1975,  perhaps because corrected  the a l i a s e d  f o r sensor  frequencies are not completely  response.  Figure  16 shows t h a t t h e 11  method s h o u l d never underestimate CTuw by more than 5% the  loss  and  that  o f h i g h f r e q u e n c y c o v a r i a n c e s h o u l d be l e s s t h a n h a l f  the amount o f v a r i a n c e l o s t by tfw. The combined may,  ± .005  1. 47 ± .11 34  0"u/<U> a r e , t h e r e f o r e , q u i t e r e a s o n a b l e . and  .048  therefore,  error  i n otiw  be about h a l f t h e sum of t h e oru and o*w e r r o r s ,  which i s c o n s i s t e n t w i t h t h e c o r r e l a t i o n c o e f f i c i e n t r(uw)  being  s i m i l a r to previously reported values. Figure (?*=Kt*  18, shows  t h e means  of o*u/u*,  o"v/u* and o t / T *  i s used t o conform w i t h McBean, 1971) band averaged over  ranges of Z/L. averaging,  Only 39 o f t h e t e m p e r a t u r e r u n s a r e used i n t h e  because many r u n s a r e near n e u t r a l where l a r g e o t / T *  89 Standard d e v i a t i o n s about the p l o t t e d means S t a b i l i t y range mid Z/L ±0.01  Number of runs  -0.05  o"u/u*  tfv/u*  tfw/u*  13  0.30  0.79  0.12  -0.03  17  0.25  0.41  0.09  -0.01  22  0.43  0.51  0.06  0.01  25  0.58  0.69  0.10  0.03  28  0.34  0.26  0.08  0.05  16  0.47  0.45  0.09  TABLE I I I  Standard d e v i a t i o n s of the t u r b u l e n c e s t a t i s t i c s about the s t a b i l i t y band means p l o t t e d i n f i g u r e 18.  values occur as a r e s u l t of McBean.  With  so  few  the  "noise"  temperature  in  runs  ot  discussed  available  Z/L=0.077 i s p l o t t e d even though only 6 runs f a l l  in  ort/T* the  from  i n t o each band.  the  10  some standard d e v i a t i o n s  band averaging at s m a l l vaues of |Z/L|, are presented  in table I I I .  T y p i c a l l y , the standard d e v i a t i o n s about the mean  cTt/T* values i n f i g u r e standard  deviations  i n McBean's dependence  results.  18 are about 0.5.  The magnitude  i n t a b l e I I I are comparable o*w/u*  exhibits  the  of  the  to the s c a t t e r  smallest  stability  and the l e a s t s c a t t e r , perhaps because low freguency  contributions to plotted  For c l a r i t y ,  at  band.  Otherwise, the s t a b i l i t y ranges a r e s e l e c t e d so t h a t a t l e a s t runs f a l l  by  in figure  Cw  are  18 f a l l  minimal.  Almost  a l l the  averages  w i t h i n t h e s c a t t e r c f McBean's (197 1)  90  -0.3  FIGURE 18  Non-dimensional t u r b u l e n c e s t a t i s t i c s band averaged over stability. See t a b l e III for standard d e v i a t i o n s about p l o t t e d means.  91  p l o t s and t h e observed variances even  differences  a r e computed  smaller  CTu's,  a r e not unexpected.  a s i n t e g r a l s from n=0.01 t o 10, g i v i n g  but better  ow's  than  t h e 11  h i g h e r t h a n t h e c o r r e s p o n d i n g means i n f i g u r e  (<0>  method.  h i s o"u/u* v a l u e s t e n d t o be l o w e r and h i s 0*w/u*'s  Accordingly,  wind  His  18.  However, t h e  speed ranges o f t h e two s t u d i e s a r e c o n s i d e r a b l y d i f f e r e n t <8 m/s f o r  dependencies, comparison. integrals oV/u*  such  as  McBean s 1  shown  runs),  with  i n figure McBean.  18  dependence  wind  speed  are calculated Despite these  are generally  the from  problems,  in  excellent  Measurements o f t h e s e n s i b l e heat and  m o i s t u r e f l u x e s were used by McBean t o f i n d stability  any  I I , complicate  T*  different frequencies.  cft/T*  so  i n table  I n a d d i t i o n * both u* and over  and  agreement  a l l of  Z/L.  The  overall  o f a l l the s t a t i s t i c a l  q u a n t i t i e s i s very  s i m i l a r i n both s t u d i e s , which l e n d s credence  t o the b e l i e f that  Z/L(AT) i s , on  of  average,  a  good  estimate  the  stability  parameter. There  do  n o t appear  between t h e s t a t i s t i c a l loss  of  to  be any unexpected  q u a n t i t i e s and  previous  probably  and  system  fluxes.  <wt>.  In conclusion  serious  The  o"w  consequences  values  reliable  felt  the s e n s o r s and Reynolds  seem t o be p e r f o r m i n g as e x p e c t e d and  providing  The  t o o s m a l l , b u t because t h i s i s due t o f r e q u e n c i e s  above 1.5 Hz t h e r e s h o u l d be no <uw>  results.  low f r e q u e n c y c o v a r i a n c e can h o p e f u l l y be a v o i d e d w i t h  the 12 o r 13 methods o f i n t e q r a t i n g c o s p e c t r a . are  discrepancies  guite  capable  by flux of  e s t i m a t e s o f t h e momentum and s e n s i b l e heat  92  4-5  The F l u x e s Of Momentum And S e n s i b l e Heat Three methods o f i n t e g r a t i n g c o s p e c t r a over  low  the  uncertain  f r e q u e n c i e s were d i s c u s s e d i n s e c t i o n 3.3 and f o r m u l a t e d i n  e q u a t i o n s 3.5. samples,  12  11 adds  includes  a l l f r e q u e n c i e s from  contributions  from  the  the  slow  lower f r e q u e n c i e s  r e p r e s e n t e d by t h e group means and 13 i n t e g r a t e s from n=0.004 t o which a s t a b i l i t y dependent f a c t o r , E, i s a p p l i e d t o account f o r the  low f r e q u e n c i e s not i n t e g r a t e d .  different  methods  a r e averaged over 2 m/s  t a b u l a t e d i n t a b l e IV. systematically increases. m/s  to  The r a t i o s of <uw> from t h e  1.0  The 13:11 from  wind speed bands and  r a t i o i s expected t o  greater  v a l u e s as the wind speed  For the u n s t a b l e runs t h i s s h o u l d o c c u r a t about  13  when the i n t e g r a l from f=0.00065 Hz b e g i n s t o c o v e r a l l the  n a t u r a l frequency range of 16A).  the  normalized  cospectrum  With Eu=1.06 t h i s does o c c u r , but above 14 m/s  i s a g a i n g r e a t e r t h a n 1 p o s s i b l y because t h e s e r u n s to  converge  neutral  (figure the r a t i o  are  nearer  c o n d i t i o n s than the average and r e q u i r e a l o w e r Eu.  However* the o v e r a l l average o f 1.00  s u g g e s t s t h a t Eu s h o u l d  be  i n c r e a s e d t o r e f l e c t t h a t t h e 11 method sometimes does miss some of  the  covariance.  The  uncertainty  in  Z/L makes s t a b i l i t y  adjustments t o Eu i m p r a c t i c a l , but t h e s e would a f f e c t by  much l e s s than t h e measurement e r r o r .  r e a s o n a b l e and t h e o v e r a l l 12:13 using  this  factor  includes  r a t i o of  the  flux  Keeping Eu=1.06 seems 0.99  average  downward momentum f l u x as shown by 11:12  indicates  that  c o n t r i b u t i o n t o the  c o v a r i a n c e from the group means, which i n f a c t the  the  usually >1.0.  reduces  93 108 unstable runs Eu=1.06  Wind speed  12:13 13:11  P o i n t s 11:12  ±1 m/s  88 s t a b l e runs Es=1.005  13  1. 10  0. 97  1.02  17  1. 03  1. 00  0.98  10  18  1. 00  1.01  12  21  0. 98  14  12  16 18  P o i n t s 11:12  12:13 13:11  1.02  0.92  1.18  15  1.01  0.79  1.04  0.99  21  1.05  0.95  1.02  1.06  0.99  21  1.03  0.96  1.02  1.04  0. 94  1.03  11  1.02  0.99  1.00  14  1. 03  0. 96  1.03  1.01  1.00  0.98  11  1. 03  0. 95  1.02  1.01  1.04  0.96  1. 03 . 15  0.99 . 14  1 .00 .07  1.03 .22  0.94 .31  1.03 . 14  overall average ±1o-J.U  TABLE  IV  At  Comparison of the d i f f e r e n t methods of the u,w cospectrum. 0=11  m/s  the  e n t i r e s t a b l e normalized averaged  method begins t o i n t e g r a t e over the  u,w  cospectrum  over a l l runs above 11 m/s  the 12:13 r a t i o lower  11  speeds  0.98, the  showing Es=  13  method  the 13:11  1.005  does  (figure  t o be  not  12:13  <1.  These  positive  When  r a t i o i s 1.00  and  appropriate.  At  making  contributions  balanced i n the normalized cospectrum by n e g a t i v e (downward flux)  16B).  i n c l u d e low freguency  c o n t r i b u t i o n s which reduce the downward f l u x , and  integrating  from the higher wind speed runs.  to  13:11  >1  -<uw> were  contributions One  particular  94 run  i n the 6  m/s  band  g i v e s 13:11 = 2.13 and t h e r e a r e n o t  enough o t h e r runs t o b a l a n c e i t o f f . the  band  13:11  gives  would  13:11  be  averaging.  reduced  One  stable  positive contribution integral,  <1.  <uw>,  this  i f more  runs  were  available  13:11  from  for  r u n i n t h e 8 m/s band has such a l a r g e  from  becomes  t h e group positive  means  that  the  w i t h 12:13= -1.56.  average  and  total  Without  overall  average  t o 0.96, so t h a t most o f t h e c o v a r i a n c e from t h e group  means i s , on a v e r a g e , i n c l u d e d i n t h e 13 method. of  run  I t i s l i k e l y then t h a t t h e o v e r a l l  t h i s one run both t h e 12:13 band increase  Excluding  with  The  decrease  wind speed i n t h e s t a b l e c a s e , s u g g e s t s t h a t i f  more runs and a b e t t e r measure o f Z/L were a v a i l a b l e  Es  should  be made a f u n c t i o n o f s t a b l i l i t y . The d i f f e r e n t methods o f i n t e g r a t i n g t h e w,t cospectrum a r e compared  i n table  unstable  band  contribution,  V.  The  a r e caused -0.018  strange  by  results  r u n T111  i n the 12 m/s,  whose  group  °Cm/s, i s l a r g e r i n magnitude  o p p o s i t e s i g n t o t h e 11 i n t e g r a l , 0.015 °Cm/s.  mean  than and o f  I f t h i s one run  i s e x c l u d e d , t h e band average and o v e r a l l average 11:12 become a more  reasonable  1.06  and  0.94, r e s p e c t i v e l y ,  with  the  c o r r e s p o n d i n g 12:13 r a t i o s going t o 0.99 and 1.11.. F o r t h e low speed u n s t a b l e r u n s , 11:12 l e s s t h a n one, suggests t h a t t h e r e i s a s i g n i f i c a n t c o n t r i b u t i o n t o the w,t c o v a r i a n c e a t f r e q u e n c i e s below  f=0.00065  as  do t h e r e s u l t s of McBean and Miyake, 1972.  Without h i g h wind speed runs i t i s not p o s s i b l e normalized  cospectrum  s t i l l f a i r l y large.  (figure  to  extend  the  17A) below n=0.001, where i t i s  The cospectrum was made t o drop o f f t o 0 a t  n=0.0002 so t h a t Eu=1.10, which i s a compromise.  The McBean and  95 27 u n s t a b l e runs Eu=1. 10  Wind speed  33 s t a b l e runs Es=1.04  T  ±1m/s  Points  Points  11:12 12:13 13:11  .79  1.36  1.01  1.08  1.04  96  1 .06  1.05  .52  6. 28  10  99  1.00  1 .01  1.19  0.95  1.03  12  -. 14  80  1 .06  1.06  0.92  1.03  14  1.03  0.91  1.06  16  96  1.07  C.99  18  73  52  1.0 1  99 47  1.22 1.89  1.03 .09  11  Overall average  .92 f-  V  .68 1.37  1.06 .39  1.04 . 12  Comparison of the d i f f e r e n t methods of i n t e g r a t i n g the w,t cospectrum.  Miyake r e s u l t s i n d i c a t e a more r a p i d drop, but the o v e r a l l r a t i o of-1.06 h i n t s t h a t Eu should be l a r g e r . during unstable c o n d i t i o n s to  1. 17  ++  ±\<r  TABLE  11:12 12:13 13:11  —i  integrate  The  wind  12:13 speeds  were always too low f o r the 1 1 method  over t h e e n t i r e normalized cospectrum making  >1 a t a l l speeds and the o v e r a l l average  1.04.  13:11  96 At a l l wind speeds the 11 method i n c l u d e s the e n t i r e s t a b l e cospectrum, f i g u r e 17B, systematic the  and  a c c o r d i n g l y the 13:11  trend with wind speed and  existence  of  random  low  r a t i o shows no  i t s variability  frequency  attests  c o n t r i b u t i o n s to the  s e n s i b l e heat f l u x which are smoothed by the 13 method. suspected  that  more  runs  average r a t i o of 1.0,  at  the  to  It  lower speeds would g i v e  an  Again there  are  some very anomalous runs with l a r g e group mean c o n t r i b u t i o n s  as  shown by the 12:13 runs  the same as above 15 m/s.  is  band averages o f 0.52  and  6.28.  Without such  the 13 method again accounts f o r most of the average group  mean c o n t r i b u t i o n . f i g u r e 17B,  In view of the  u n c e r t a i n t y i n t a b l e V and i n  caused by the l a c k o f runs,  a value  of  Es=1.04  is  acceptable. Tables  IV  and  V  exhibit  evidence  c o n t r i b u t i o n s t o the f l u x e s from the u n c e r t a i n causing  a  the 11 and  great  of low  large  frequencies  d e a l of s c a t t e r i n the f l u x e s c a l c u l a t e d from  12 methods.  To avoid the r e s u l t i n g s c a t t e r ,  method w i l l be adopted as the means of i n t e g r a t i n g the of  all  and  for 0wt  they  are  the  runs.  The  choices f o r 0uw  of Eu=1.10 and reasonable  s i g n i f i c a n t systematic w i l l be  denoted  random  by  Es=1.04 have  compromises and  of Eu=1.06 and some  and  parameters by u*FL0X, t*FL0X and so  Es=1.005  do not appear to cause  <wt>FL0X on.  and  13  cospectra  uncertainty,  e r r o r s or apparent t r e n d s . <uw>FL0X  the  but any  The i n t e g r a l s the  derived  97  i  1 Z  FIGURE 19  1  r  o  NOG O O O I  The n e u t r a l drag c o e f f i c i e n t vs wind speed from the 196 Reynolds f l u x momentum runs. T r i a n g l e s are the s t a b l e runs and p l u s e s the u n s t a b l e .  98 The  Reynolds  f l u x r e s u l t s a r e p r e s e n t e d i n f i g u r e s 19 and  20 and compared w i t h t h e d i s s i p a t i o n method more  complete  i n Chapter  the  A  view o f t h e b e h a v i o r of t h e f l u x e s i s o f f e r e d i n  Chapter 6 by t h e more e x t e n s i v e d i s s i p a t i o n data s e t . present  5.  measured  wind,  OZ,  <uw>FLUX, <wt>FL0X and Z/L(AT)  temperatures,  For the  TZ  and TSFC,  have been put i n t o e g u a t i o n s  2.4  and 2.8 t o g i v e t h e roughness l e n g t h s , Zo and Z o t , and i n t o 2.11 and a  2.10 t o g i v e a wind speed, 010 an a i r t e m p e r a t u r e , T10, and drag  coefficient,  coefficient,  CDN,  C10,  at  10  meters.  A  neutral  drag  i s d e r i v e d from Zo w i t h e q u a t i o n 2-12.  The  p l o t of CDN v s . 010, f i g u r e 19, l o o k s i d e n t i c a l to t h e BIO tower r e s u l t s i n S m i t h , 1979, from which neutral  C10  values  a  i s nearly  of  120  near  on 010, g i v e s 0.44 + 0.063 U10 = 103C10 as  compared t o 0.46 + 0.069 010 = 103CDN there  regression  from  figure  19.  an e q u a l p a r t i t i o n between s t a b l e  Since  (triangles)  and u n s t a b l e (crosses) runs i n f i g u r e 19, a r e g r e s s i o n o f C10 on 010, 0.43 + .069 010 = higher  coefficients  at  103C10, the  i s not higher  very  wind  different.  speeds a r e commonly  o b s e r v e d , b u t o v e r a l l these v a l u e s a r e d i s t i n c t l y those  at  similar  wind  f i g u r e 19 t h e s t a b l e  stability  range  smaller  speeds i n G a r r a t t ' s , 1977, r e v i e w .  ( t r i a n g l e s ) and u n s t a b l e (pluses)  not s e p a r a t e i n t o d i s t i n g u i s h i n g p a t t e r n s . found  The  data  than In do  Throughout t h e s m a l l  over t h e s e a , average s t a b i l i t y  effects  appear t o be s m a l l . In f i g u r e 20 <wt>FL0X i s p l o t t e d a g a i n s t 010(TSEA-T10) f o r the  52  temperature runs w i t h |AT| > 0-5°C, so t h a t a l i n e from  any p o i n t t o t h e o r i g i n has a 2.10.  slope  equal  to  CT10, e q u a t i o n  The s o l i d l i n e r e p r e s e n t s t h e p a r a m e t e r i z a t i o n of F r i e h e  99  1  1  o  1  CD  X X  O CvJ  CD  <x x<$£ •  x  X  ZD  a  CD  i  X X  o o 1  (S/WGo) FIGURE 20  1  1  1  <1M>  <wt> vs. U10 ( T S F C - T 1 0 ) i n ° C and m/s f o r t h e 52 temperature runs with | A T | >0.5°C. S t a b i l i t y ranges: A , z / L >0.05; X , -0.1 <Z/L< 0.05; + , -0.2 <Z/L< -0.1; <J>, Z/L <-0.2. S o l i d l i n e i s from F r i e h e and Schmitt (1976).  100  ana  Schmitt,  25°Cm/s. range, and  1976,  which  fits  quite  The data do not support which  Friehe  and Schmitt  well  f o r -10  an i n c r e a s e i n CT10 above t h i s suggest on the b a s i s of Smith  Banke's, 1975, measurements on the beach  The  BIO tower r e s u l t s  (Smith,  at  Sable  Smith  or  figure  20,  Island.  1979) span | <0> A T | < 150°Cm/s and  i n d i c a t e s l i g h t l y higher CT10 values than do e i t h e r Schmitt  <U10 AT<  i n both the unstable  Friehe  and s t a b l e  and  cases.  (1979) f i n d s 10 <wt>= 3.2+ 1.10 010 A T , f o r AT>0 and -0.1 + 3  0.83 010 AT, f o r AT <0, from r e g r e s s i o n s of <wt> on 010 A T . A l l three s t u d i e s show t h e s t a b l e c o e f f i c i e n t CT10  in  scatter during  unstable  stratification.  to  be  smaller  There i s not a great d e a l of  i n f i g u r e 20, except from two runs ( p l o t t e d as sguares), which  conditions  very  warm  a i r moved  over  a  cold  data i s presented. crosses,  are  Such  Near n e u t r a l runs  dissipation  (|Z/L| <0.05), p l o t t e d  as  much the same as the more s t a b l e ( t r i a n g l e s ) , but  more u n s t a b l e  <Z/L)  sea.  g r e a t l y i n f l u e n c e the average s e n s i b l e heat f l u x and  are discussed i n s e c t i o n 6.3, when the corresponding  the  than  ( p l u s e s , Z/L 0.05 t o 0.25 and  diamonds,  0.25  seem to g i v e s m a l l e r CT10s, however t h e r e are f a r t o o few  data t o be c o n c l u s i v e as there a r e wind speed, f e t c h e f f e c t s to consider.  and  other  101 CHAPTER 5  INTERCOMPARISON  OF  THE  REYNOLDS  FLOX AND DISSIPATION METHODS  5-1  Introduction The  Bedford  opportunity  to  tower  experiment  establish,  provides  an  excellent  by comparison w i t h both the Reynolds  f l u x and BIO r e s u l t s , a d i s s i p a t i o n method t h a t i s v a l i d over wide  range  of  open  sea  recorded data during temperature  runs  conditions.  The d i s s i p a t i o n  four  and  6  methods  and  the  r e s u l t s a r e t a b u l a t e d with those of  eguation <wt>DISS  and  manipulating  velocity  i s obtained  stability  effect  on  the  profile, both  the  by  turbulent  eguations including  the  stability,  kinetic 2.28.  and  energy  Similarly  excluding  the  temperature p r o f i l e , equations 2.32.  The "best" momentum and s e n s i b l e heat f l u x are  The  a u*DISS = (<uw>DISS) 1/2 from each of the  give  of  system  192 Reynolds f l u x momentum runs and a l l 60  t h e i r corresponding f l u x runs i n the Appendix. Z/L (AT),  a  dissipation  methods  to be determined by comparison with u*FL0X and <wt>FL0X from direct  dissipation independent,  eddy and  correlation  Reynolds  because  flux  measurements. systems  are  However, not  they share t h e same s e n s o r s .  entirely  In order to  complete the i n t e r c o m p a r i s o n of  the  checked  measurements c f u* from the BIO  system.  with  eddy  correlation  methods,  the  u*DISS  is  also  102 I t i s e s s e n t i a l to the intercomparison t h a t the runs be nearly  simultaneous  as  possible.  chosen t o begin between 0 and flux  run  and  in  most  The  dissipation  runs are  4 minutes before the s t a r t of  cases t h e s t a r t s are w i t h i n 2  the  minutes.  They l a s t f o r 56 minutes i f the f l u x run c o n s i s t s of f o u r , minute,  consecutive  averaging p e r i o d s , < >. average  eguation average found  the run.  power, <P>,  3.7.  The  The d i s s i p a t i o n , €,  is  taken  in  only  p r o p o r t i o n a l to € / 2  values  never  runs.  With  both  (fu(fc)  10% and u s u a l l y by l e s s than 7%.  fc / )  and  3  values by  the  average  dissipation.  €  should  Values  of  l i e entirely  o f t e n an average may  the  differ  fc / )  dissipation  -5/3  of  5  3  line  molecular temperature  using only f i l t e r s  r e g i o n of f t ( f ) .  Thus, Nt i s  of only 1 or 2 s e p a r a t e estimates and t h e r e f o r e  not be as r e l i a b l e  (ft(fc)  as  6.  In  order  for  the  calculated  f c / ) v a l u e s to agree with i n d i v i d u a l band-pass f i l t e r s 5  3  to w i t h i n 10%, the individual 2.33  in  2  The d e v i a t i o n i n (fu(fc)  f l u c t u a t i o n s are c a l c u l a t e d from eguation 3.6 that  u*  than  be a good measure of the the  is  less  i s probably due t o t h e spectrum's f l u c t u a t i o n s about a -5/3 and  their  10%  5  from those d e r i v e d from a s i n g l e band-pass f i l t e r  into  than  (eguation 2.23), t h e i r average  3  the  substituting  d i f f e r from  15% and a d i f f e r e n c e of more  10  as  from each G i l l - u band-pass f i l t e r ,  separate  by more than  cases  These times become the  of the three i n d i v i d u a l values obtained by  the average  13.5  groups and f o r 44 minutes i n the few  t h a t o n l y three groups comprise  as  average,  Nt,  estimate by more than  shows t h a t 10% d e v i a t i o n s i n  must 10%  not  differ  from  (eguation 2.23).  both  f t (f)  produce a 10% d e v i a t i o n i n the c a l c u l a t e d <wt>.  and  each  Equation  fu(f)  will  103 5.2  The Momentum F l u x At  neutral  equivalent simply of  stability  a l l f o u r momentum f l u x methods a r e  and i n n o n - n e u t r a l c o n d i t i o n s  methods  2  3  r  and  4  a d j u s t t h e n e u t r a l a p p r o x i m a t i o n , method 1, by a f u n c t i o n  Z/L,  fiqure  1.  u*DISS1,  c a l c u l a t i o n and i t i s p l o t t e d There  equation  2.24, i s t h e s i m p l e s t  against  u*FLUX  i n figure  21.  i s g e n e r a l l y good agreement between t h e two c a l c u l a t i o n s  from the 192 s i m u l t a n e o u s r u n s , f o r which Z/L i s u s u a l l y between -0.45  and 0.20.  A 20% d e v i a t i o n i n the u*  estimations  from  a  1:1 r e l a t i o n s h i p i s i n d i c a t e d by t h e dashed l i n e s , which s a t i s f y the  equation  |x-y|  with  / [ (x + y) /2] =  x=u*FLUX  and  0.2 ,  y=u*DISS.  In  (5. 1)  view  o f t h e e r r o r s i n both  methods, d e v i a t i o n s o f t h i s magnitude a r e e x p e c t e d . the  higher  Points  at  u* v a l u e s r a r e l y f a l l o u t s i d e t h e dashed l i n e s .  It  appears, t h e r e f o r e , t h a t t h e n e u t r a l d i s s i p a t i o n method p r o v i d e s a v e r y good e s t i m a t e u * = 0.16 2  The  of  momentum  fluxes  greater  than  ( m / s ) , which occur a t wind speeds above about 11 m/s. 2  smaller fluxes  span  a  greater  stability  range  and t h e  c l u s t e r of p o i n t s l y i n g above t h e upper dashed l i n e , w i t h m/s,  come  from  t h e most  stable  runs.  s t a b l e c o n d i t i o n s , which tends than u*FL0X.  to  make  u*<0.4  Apparently,  assumptions o f d i s s i p a t i o n method 1, cause a s y s t e m a t i c  greater  about  u*DISS1  the  error i n  significantly  104  FIGURE 21:  Comparison of u* i n m/s from the neutral d i s s i p a t i o n method and the Reynolds f l u x method f o r all 192 simultaneous Bedford tower runs. Dashed l i n e s i n d i c a t e a 20% d e v i a t i o n fiom the solid 1:1 line.  105 Method  1  should  be  v a l i d over  s t a b i l i t i e s where the buoyancy and  two  a range of "near n e u t r a l " v e r t i c a l divergence  o f the t u r b u l e n t k i n e t i c energy equation on  the  and  v e l o c i t y p r o f i l e are e i t h e r s m a l l or tend t o c a n c e l The  extent  grouping  the  simultaneous runs a c c o r d i n g t o  of  such  over what range u*DISS1 and stable  side  f i g u r e 22A.  it The  <Z/L<  than  reqime  u*FL0X agree  is  on  solid triangles, are s t i l l  u*FL0X and  a stability  about  10%.  calculations and  22B  u*DISS1  the  On  c o r r e c t i o n t h a t reduces  < Z / L < -0.1  -0.05  The  range are not i n c l u d e d  tends t o be s m a l l e r than u*FL0X by an average of  However,  in  more  unstable  again tend t o agree.  g i v e s a very good e s t i m a t e  conditions  knowledge  of  the  the  two  A combination of f i g u r e s 22A <Z/L<  of the momentum f l u x  stability.  Extension  This  0.05, without of  the  little  i s a u s e f u l r e s u l t , because open ocean c o n d i t i o n s  o f t e n w i t h i n t h i s range and because an accurate Z / L available. in  down  (solid  error.  perhaps  u*DISS  i s acceptable. < Z / L <  For than  shows that  l i m i t down to a t l e a s t Z/L=-0.4, i n t r o d u c e s very  always  with  more  unstable  are  the  runs  by  shows t h a t i n a "near n e u t r a l " regime, -0.1  an e x p l i c i t  by  seeing  agreement.  often  use of the n e u t r a l eguation  Runs i n the -0.3  U*DISS1  and  average.  showing reasonable  agreement i s e v i d e n t i n the runs with -0.1  because  Z/L{AT)  On the unstable s i d e , f i g u r e 22B  Z / L =-0.10  triangles).  investigated  representing  run g i v e s u*DISS1 g r e a t e r ,  i s necessary. to  a  one  observed to extend t o Z/L=0.05 as shown by  is  0.05,  Z/L>0.10 every 20%,  Z/L  the e f f e c t s o f  another.  0.04  terms  very  It  is  i s only i n r a t h e r s t a b l e , Z/L>0.0 5,  unstable  stratification,  approximations cause a p p r e c i a b l e e r r o r s .  that  the  not and  neutral  106  8'0  9'0  I9SIQ  2"0  W O  0*0  m CO  8'0  9"0  t7* 0  issia m  2*0  O'O  Investigation of t h e "near n e u t r a l " momentum f l u x (u* i n m/s) regime f o r ; 61 s t a b l e runs ( s o l i d t r i a n g l e s 0.04 <Z/L< 0.05). 70 u n s t a b l e runs ( s o l i d t r i a n g l e s -0. K Z / K - 0 . 0 5 ) .  107  F o r t u n a t e l y , e s t i m a t e s of Z/L(AT) are a v a i l a b l e f o r a l l t h e simultaneous  runs.  Under s t a b l e c o n d i t i o n s the buoyancy term o f  the t u r b u l e n t k i n e t i c energy e g u a t i o n is  actually  more  a l o n e and the Another  production  larger  production  gives  larger  u*  estimates.  method  2  dominating. u*DISS2>  in  both,  stable  as  u*DISS3,  is  with  adjustment. plotted  so  The  against  only u*  clearly  methods  shown  3 and  estimates  u*FLUX  for  the  conditions,  observed t h a t i n the s t a b l e runs u * D I S S 1 u*FLUX,  profile,  so  t h e e f f e c t on the  (2.26)  does  (2.25)  Thus,  velocity  that  the  from  u*DISS4>  by  tends  equation  2.19  to  be  these  smaller  balance,  is  observations.  and  its  greater  local  being  by  proper  methods  are  production  small.  agreement,  nearly and  However, its  eguals buoyancy  method 2 i s adjustment  a s s u m p t i o n , t h a t the two divergence  supported  It is  a l l 8 8 s t a b l e runs i n f i g u r e 2 3 .  p r e f e r r e d because i t does account f o r buoyancy, is  U*DISS1>  2 can p r o v i d e the both  effect  f i g u r e 1.  d i s s i p a t i o n , on average, w i t h both the d i v e r g e n c e of  u*  profile,  profile  Both d i s s i p a t i o n methods appear t o g i v e e q u a l l y good establishing  the  Method 4 (eguation 2 . 2 7 ) i n c o r p o r a t e s  the buoyancy term and method 3  terms  there  e f f e c t of s t a b l e s t r a t i f i c a t i o n i s t o reduce the amount  e s t i m a t e s become s m a l l e r .  than  i s a s i n k , so  than i s l o s t through d i s s i p a t i o n  of f l u x a s s o c i a t e d w i t h a g i v e n  while  (2.19)  McBean  and  Elliot's,  terms 1975,  Comparison of 88 s t a b l e Reynolds f l u x runs to d i s s i p a t i o n method 2 (u* i n m/s) d i s s i p a t i o n method 3 (u* i n m/s).  109  During  unstable  conditions  s t a b i l i t y modified p r o f i l e , reversed,  with  on  the r o l e s of buoyancy and the  the  dissipation  u*DISS3> u*DISS1> u*DISS4.  l e s s than U * D I S S 1 .  it  At about Z / L = - 0 . 4 ,  by l e s s than  i s the only method t h a t p r o v i d e s  refinements.  Method  more u n s t a b l e cases.  3 clearly  the  24.  The  indicates  Because  throughout profile  of  et a l . ,  as  method  suggested  u*DISS1  also  - 0 . 4 <Z/1< 0 . 0 5 , the  must  runs,  stability  methods 4 and 2  are  unstable runs i n  2 i s e x c e l l e n t and the the  1:1  line.  This  t h a t the divergence terms a l s o tend t o c a n c e l  i n unstable c o n d i t i o n s findings.  becomes  gives f a r t o o l a r g e a u* i n the  s c a t t e r i s very evenly d i s t r i b u t e d about result  source  the  appropriate  The u* e s t i m a t e s from  agreement  to  and g u a l i t a t i v e l y  10%  p l o t t e d a g a i n s t u * F L 0 X f o r the 1 0 4 simultaneous figure  down  u*DISS2  Throughout t h e u n s t a b l e range of  d i f f e r s from U * D I S S 1  u*DISS2  dominates  when the buoyancy f i n a l l y becomes an important  of t u r b u l e n t k i n e t i c energy.  are  F i g u r e 1 shows t h a t  i n method 2 the e f f e c t on t h e p r o f i l e s t i l l Z/L=-0.1,  estimates  nearly  balance  by  gives effect  the  McBean  and  a reasonable of  buoyant  Elliot's estimate  stability  on  production.  1 9 7 1 , c a l c u l a t e d u* up to 0 . 3 m/s u s i n g method 4 ,  the Pond which  i s seen t o be a c c e p t a b l e , but not a p p l i c a b l e t o higher u*values.  FIGOEE 24  Comparison of 104 u n s t a b l e Reynolds f l u x runs t o A: d i s s i p a t i o n method 2 (u* i n m/s) B: d i s s i p a t i o n method 4 (u* i n m/s).  111 Whenever  Z/L  s t a b i l i t y range of "best"  estimates  i s available the  i n t e r c o m p a r i s o n , method  from  f i g u r e 21  the  192  illustrates  correction..  In  2  gives  the  o f u*, h e n c e f o r t h u*DISS and <uw>DISS w i l l be  c a l c u l a t e d using t h i s method. u*FLDX  i t i s e v i d e n t t h a t , over the  F i g u r e 25 i s a p l o t of u*DISS  vs  simultaneous  runs and a comparison with  the  effect  overall  of  the  stability  t h e r e g i o n 0.15 <u*FL0X< Q.Hm/s, the r e d u c t i o n  of u*DISS  from  the  most  stable  runs  greatly  improves  the  agreement,  but u*DISS s t i l l tends t o be g r e a t e r than u*FLUX.  As  a consequence, t h e average o f r e g r e s s i o n s o f u*DISS and u*FL0X,  u*DISS  has  a  ratio, The  =  positive  0.96  offset  u*FL0X  +  0.025 m/s,  the o v e r a l l average U * D I S S : u * F L U X  and  1.03 (standard d e v i a t i o n 0.10),  two  techniques  differ  i s greater  20%  error  i n <uw>DISS  scatter  and a non-compensating  <uw>FL0X g i v e a 20% d e v i a t i o n i n u* e s t i m a t e s . that  the  u*  agreement  expected.  20% e r r o r i n  It  is  would be so good i f a major  i s of fundamental importance t o  u*FL0X.  Conversely,  propellers Reynolds  is a flux  potential  source  measurements*  e s t i m a t e s , thus the good agreement being  treated  properly.  behavior  of  but  freguency c o v a r i a n c e s a r e being handled  of  substantial  not  to  indicates  Similarly,  because  but only secondary t o  u * D I S S ,  t h e non-cosine  doubtful  systematic  e r r o r had a r i s e n from t h e p r o p e l l e r response c o r r e c t i o n it  1.00.  by at most 28% and u s u a l l y by l e s s  than 20% i n u*, which i s about the amount of A  than  the that  the error  Gill in  dissipation i t too i s  i t appears as i f the low satisfactorily.  112  FIGURE 25:  Intercomparison o f u* i n m/s from the " b e s t " dissipation (2) and the " b e s t " Reynolds f l u x (13) method f o r a l l 192 simultaneous runs.  113 <uw>DISS <uw>FLUX Wind speed range (m/s)  1  Number of points  T  Mean  Standard deviation  Minimum  Maximum  6 - 8  27  1- 10  0. 14  0.82  1 .42  8 - 1 0  25  1.02  0. 21  0. 68  1 .49  10  -  12  54  1. 14  0. 23  0. 68  1 .58  12  -  14  32  1.05  0. 16  0.79  1 .34  14  -  16  18  0.97  0. 13  0.76  1 .23  16  -  18  17  1.00  0.09  0.79  1.10  18  -  20  1.01  0. 14  0.83  1 .36  1.05  0.17  0. 68  1 .48  Overall 4 - 2 0  182 XL  TABLE  VI  Eatio of dissipation the momentum f l u x speed i n t e r v a l s .  t o Reynolds f l u x e s t i m a t e s of band averaged over 2 m/s wind  The momentum f l u x and drag c o e f f i c i e n t a r e p r o p o r t i o n a l <uw>,  so t r e n d s i n the <uw>DISS:<uw>FL0X r a t i o are i n v e s t i g a t e d  by averaging the r a t i o over wind speed and tables are  to  VI  and V I I , r e s p e c t i v e l y .  stability  In order that  bands i n  the band  not unduly weighted by i n d i v i d u a l runs with a t y p i c a l  means  ratios,  only those runs whose r a t i o s f a l l w i t h i n ±2 standard  deviations  about  the means,  a  complete band  average a r e used t o c a l c u l a t e  standard d e v i a t i o n s and ranges i n t a b l e s VI,  the  overall  In  table  average o f 1.05 and standard d e v i a t i o n ,  tr, of  0.17, a r e g u i t e a c c e p t a b l e .  A ar of 17%  VI and VII.  i s comparable  t o the  114 <UW>DISS <UW>FLUX  Number of points  Stability range Z/L -.45  -.30  -.30  -.15  -.15  I-  i  r Standard deviation  Mean  Maximum  Minimum  .j 1.08  0.23  0.77  1. 48  15  0.97  0.14  0.72  1-31  74  1.04  0. 17  0.68  1.36  0  0.05  59  1.06  0. 17  0.76  1. 40  C.C5  0.10  18  1.16  0.17  0.92  1.53  0.10  0.20  1.34  0.33  0.87  1.65  JL L.  TABLE VII  expected  R a t i o o f d i s s i p a t i o n t o Reynolds f l u x e s t i m a t e s o f the momentum f l u x band averaged over s t a b i l i t y ranges. error  in  each  method  and the mean i s l e s s than  g r e a t e r than the d e s i r e d o v e r a l l average of large  ratios  that  i t s g r e a t e s t range.  1.00,  with  wind  1.00.  speed.  At  the  T h e r e f o r e , i t seems l i k e l y  be  higher  to  decrease  speeds  where  should always be near n e u t r a l the band means are about that any wind speed  o f ' t h e drag c o e f f i c i e n t observed i n also  has  Otherwise t h e r e i s no systematic trend with seems  stability  the  occur during lower winds when s t a b i l i t y  wind speed, although the range of the r a t i o increasing  despite  o/3  found  dissipation  dependency  results  would  i n corresponding eddy c o r r e l a t i o n measurements.  T a b l e VII shows t h a t , as expected, the s t a b l e runs  produce  largest  switching to  average  ratios.  Figure  1  shows  that  d i s s i p a t i o n method 3 would not g r e a t l y a l t e r t h i s r e s u l t  (4%  the  in  1 15  the  0.10  <Z/L<  r a t i o s are method.  0.20  caused  band).  by  i s p o s s i b l e t h a t the higher  underestimating  <uw>FL0X  with  13  the  As Z/L i n c r e a s e s , the p r o p o r t i o n of c o v a r i a n c e a t high  f r e q u e n c i e s and,  hence,  sensor  corrections  response  should not exceed on  It  average,  5%.  the  amount also  lost  through  increases,  incomplete  but  the e f f e c t  I t has been shown i n s e c t i o n  Es=1.005  treats  the  low  4.5,  frequency  that,  covariance  adequately, but the f o u r runs that give such a l a r g e average the  most  (runs  s t a b l e band of t a b l e VII occurred n e a r l y s e g u e n t i a l l y  T174,  T175,  neccessarily  T176  reflect  underestimating Z/L order  and  T178),  average  f l u c t u a t i n g temperature  In  so  the  conditions.  data from  band  does  not  Since there are no  these r u n s , Z/L (AT)  could  depend  to complete  on  be  and causing o v e r e s t i m a t e s of u*DISS. the i n t e r c o m p a r i s o n of methods i t i s  important t o show t h a t the observed agreement of f i g u r e 25 not  to  using  the same sensors.  Dr. S.D.  does  Smith of the  Bedford I n s t i t u t e of Oceanography has k i n d l y allowed some of h i s eddy c o r r e l a t i o n measurements (Smith,  1979)  measurements.  to  be  of  compared  u*, to  u*BI0,  The runs o v e r l a p as do the Reynolds 44 minutes i n d u r a t i o n .  thrust  operated from  anemometer  simultaneous is  excellent  considering  u*DISS runs and the  is  plotted  scatter  addition  of  The  tower  dissipation f l u x runs  BIO  against  is  u*BI0  for  6.4 1976.  all  20  On average, the agreement no  larger  calibration  s e p a r a t i o n of the anemometers by about  and  mark  October 7 t o December 8,  from t h i s p e r i o d . the  the  simultaneous  are t y p i c a l l y about  In f i g u r e 26,  from  2m.  than errors  A direct  of u*FLUX and u*BIO values i s not p o s s i b l e , because  expected and  the  comparison  simultaneous  116  FIGUBE 26:  Comparison of u* i n m/s from the d i s s i p a t i o n system and from the BIO eddy c o r r e l a t i o n system from 20 runs on the Bedford tower.  117 measurements a r e r a r e , however t h e gives  a favourable  i n d i r e c t one.  dissipation  intercomparison  These c o n c l u s i o n s  ought t o be  g u a l i f i e d by n o t i n g t h a t t h e r e a r e disagreements w i t h winds  from  the  mean  l a t e r BIO data which a r e s t i l l t o be r e s o l v e d .  The  u* comparison o f t h e s e data shows  u*DISS  to  be  greater  than  u*BIO ( o f t e n by more than 20%) i n 28 o f 30 r u n s .  5.3  The S e n s i b l e Heat F l u x The  sensible  heat  flux  i s estimated  using  t h e two  d i s s i p a t i o n methods f o r the 60 s i m u l t a n e o u s temperature r u n s and t h e s e a r e compared t o <wt>FLUX i n f i g u r e 27. satisfy  5.1  with  deviation  of  <wt>DISS,  the  more n e g a t i v e rather  large  x=<wt>FL0X  the  actual  neutral  The  lines  and y=<wt>DISS, i n d i c a t i n g a 20%  fluxes  from  approximation,  the  solid  1:1  line.  i s c l e a r l y , on a v e r a g e ,  t h a n <wt>FL0X ( f i g u r e 27A). . Method correction  dashed  2  applies  a  f o r t h e i n f l u e n c e of s t a b i l i t y on t h e  temperature p r o f i l e , but f i g u r e 2 shows t h e adjustment t o be i n the  proper  sense  i n both  s t a b l e and u n s t a b l e  conditions.  A  r e g r e s s i o n o f <wt>DISS2 a g a i n s t <wt>FL0X ( f i g u r e 27B) g i v e s  <wt>DISS2  with a  =  correlation  remarkably  good  1.04 <wt>FLUX,  coefficient  of  0.99.  The  agreement i s  c o n s i d e r i n g the e r r o r s i n both methods and t h e  s e n s i t i v i t y of <wt>DISS2 t o t h e r a t h e r u n c e r t a i n Z/L(AT). results  suggest  that  the  turbulent  transport  term  These i n the  118  frO'O  O'O  t 7 Q ' o-  <lrt>  i  1  t?0'0  1  O'O  TSSIQ FIGITBE 27  1  r  t70'0-  <ltt>  Comparison o f t h e 60 simultaneous s e n s i b l e heat f l u x c a l c u l a t i o n s i n °Cm/s. A: <wt>DISS1 vs. <wt>FLUX B: <wt>DISS2 vs. <wt>FLUX.  119  temperature  variance  budget i s i t s e l f s m a l l and t h a t i t cannot  compensate f o r changes i n t h e l o c a l variance  due  to  stability.  1  could  be  used  to  w i t h o u t an an e x p l i c i t Z/L.  of  temperature  I n t h e range -0.03 <Z/L< 0.05 t h e  c o r r e c t i o n t o <wt>DISSl i s l e s s method  production  than  10%  estimate  and,  i f necessary,  t h e s e n s i b l e heat f l u x  However, method 2 g i v e s t h e t e t t e r  e s t i m a t e and w i l l always be used t o c a l c u l a t e <wt>DISS.  The two  p o i n t s i n t h e f o u r t h guadrants o f f i g u r e s 27A and 27B i l l u s t r a t e an  inherent  difficulty  d i s s i p a t i o n method.  i n finding  small  fluxes  <wt>DISS i s c a l c u l a t e d frcm  with  eguation  the 2.32  and t h e s i g n of t h e sguare r o o t i s chosen so as t o f o r c e <wt> t o have  the  same  sign  as AT = TSFC-TZ.  However, i t i s commonly  observed i n eddy c o r r e l a t i o n measurements t h a t <wt> i s between 0 and very  +0.0 5 °Cm/s when .AT i s s l i g h t l y n e g a t i v e . few  sea, but magnitude  measurements the excellent of  the  flux  of  There  have  been  l a r g e s e n s i b l e heat f l u x e s over the  agreement  i n figure  27B,  when t h e  i s l a r g e , s t r o n g l y suggests that  this  measurement may be done using t h e d i s s i p a t i o n method. The the  low and h i g h freguency t e m p e r a t u r e f l u c t u a t i o n s  sensible  heat  f l u x c a l c u l a t i o n s i n t h e same manner as t h e  v e l o c i t y v a r i a t i o n s a f f e c t t h e momentum f l u x . regarding  both  t h e Reynolds  performing properly With  no  S i m i l a r arguments  non-cosine b e h a v i o r , s e n s o r response and low f r e g u e n c y  covariance lead to the conclusion of  affect  large  flux  t h a t t h e temperature  and  dissipation  errors  i n evidence,  <wt>FLUX should both be g i v i n g r e p r e s e n t a t i v e s e n s i b l e heat f l u x .  systems must be  i n o r d e r t o a c h i e v e t h e observed  systematic  elements  agreement. <wt>DISS and  estimates  o f the  120 As  previously  processed  because  microbead. filters  noted  In  of  a  many  temperature runs have not been  suspected  salt  contamination  few of these cases the temperature  unexpectedly d i s p l a y a -5/3 drop  band-pass  filter  insufficient because  of  check  test  behavior.  dissipation  band-pass  within  i s , therefore,  for this  i t restricts  to  10%.. The  a  necessary, but  This  i s unfortunate  temperature measurements to  p e r i o d s when the temperature spectrum can be obtained Reynolds  flux  system.  A  possible  problem would be t o average filter of  means  output  of  from  the  of overcoming  this  another  band-pass  centered at about n=0.02 f o r comparison with the outputs  the f i l t e r s  note  the  the  that  i n the -5/3 range.  <wt>DISS  It  i s also  interesting  and <wt>FLUX are i n good agreement  unstable contaminated r u n s , a l b e i t  both  seem  to  be  to  i n some somewhat  high. It the  c o n s t a n t s and t h e assumptions.  major the  i s expected t h a t the l a r g e s t d i s s i p a t i o n e r r o r s are i n  persistent  errors,  a r e no errors i n  T h i s i s supported by e g u a t i o n s  and 2.33 which show <wt>DISS to be p r o p o r t i o n a l t o  ( KZ ) 1/3  If,  suggests t h a t t h e combined  c o n s t a n t s i s not very l a r g e .  2.29  The f a c t t h a t t h e r e  f o r example,  error,  u*DISS  (Bt')-V  2  u*DISS .  the Kolmogoroff c o n s t a n t , Bt', was would  be  expected  be  calculations.  r e s u l t s , f i g u r e s 25 and 27B, do not support  S i m i l a r l y , K and Z appear t o be  with  a c c u r a t e than  in  this.  agreement  more  in  <wt>DISS and hence, The  better  to  greatly  Reynolds  reasonable.  Of  flux  course  121 there  could  be major o f f s e t t i n g e r r o r s , or the c o n s t a n t s may  h i g h l y v a r i a b l e , but  it  seems  assumptions  are  the  which  d i s s i p a t i o n method. scatter  i n the  Reynolds f l u x On nearly both  u* and  uncertain  probable  Reynolds f l u x and  dissipation  and  as expected.  most s t a b l e cases by  also  that  it  is  the  aspect  of  the  much  of  the  that  <wt> intercomparisons o r i g i n a t e s with  the same momentum and the  <wt>,  is  most  likely  s e n s i b l e heat f l u x e s . Reynolds  With the  (Z/L>  d i s s i p a t i o n methods  .05),  systematic  errors.  confidence  in  the  It  is,  In  addition,  p o s s i b l e exception of u* the  give  f l u x systems appear to  estimates  both techniques, should be r e l i a b l e and  ship where the  the  values.  average, the  functioning the  It  more  be  therefore,  of  <uw>  f r e e of  possible  to  d i s s i p a t i o n system when i t i s operating  Reynolds f l u x method i s not  practicable.  be  from and major have on a  122 CHAPTER 6  DISSIPATION MEASUREMENTS FROM THE BEDFORD STABLE TOWER AND CCGS QUADRA  6.1  Introduction The d i s s i p a t i o n system has p r o v i d e d a g r e a t d e a l more  data  from t h e Bedford tower than t h e Reynolds f l u x system, because i t continuously  records  and  has  proved t o be more r e l i a b l e .  a d d i t i o n , a c o n s i d e r a b l e amount o f  dissipation  collected  1086 hours of momentum f l u x  at  "PAPA".  In total  measurements from t h e tower and 505 hours from  data  has  In been  the weathership  are found t o s a t i s f y a v a r i e t y o f c r i t e r i a f o r d a t a r e l i a b i l i t y . Only  237  hours o f tower d a t a and 23 hours from CCGS Quadra a r e  found t o be s u i t a b l e f o r s e n s i b l e heat f l u x c a l c u l a t i o n s . a r e s e v e r a l l o n g p e r i o d s of c o n t i n u o u s r e c o r d i n g which possible  There  make i t  t o i n v e s t i g a t e t h e time h i s t o r i e s o f t h e f l u x e s , winds  and t e m p e r a t u r e s . Only d a t a from t h e h o r i z o n t a l * G i l l - u ,  propeller  t o f i n d t h e d i s s i p a t i o n , € , and hence momentum f l u x . the  greater  moderate propeller  uncertainty,  wind  speed  that  speeds  measurements  are a v a i l a b l e  greater  than  used  Because o f  i t i s not w o r t h w h i l e i n c l u d i n g t h e  horizontal propeller f a i l e d . wind  are  from  from  the t i l t e d ,  Gill-w,  t h e few p e r i o d s when t h e  The tower a n a l y s i s i s l i m i t e d 4.0 m/s.  to  At l o w e r winds t h e G i l l - u  p r o p e l l e r i s s t i l l i n i t s l i n e a r regime, b u t t h e s e n s o r response c o r r e c t i o n s become v e r y l a r g e and i t i s not i m p o s s i b l e thickness  of  the "constant  anemometer h e i g h t .  flux"  On CCGS Quadra  layer  f o r the  to f a l l  below t h e  t h e measurement  height i s  123 n e a r l y twice as h i g h , so the l i m i t i s s e t a t 8.0 m/s. r e s t r i c t i o n r e q u i r e s the s t a b i l i t y 0.15.  At  Z/L=0.15  t o be i n the range -0.6 <Z/L<  dissipation  require a correction f o r s t a b i l i t y This  adjustment  i s supported  A further  momentum of  flux  about  mainly  by  calculations  25% the  (figure  1).  Reynolds  flux  i n t e r c o m p a r i s o n , where Z/L i s g r e a t e r than 0.15 f o r only runs, and a l s o by McBean and E l l i o t t ' s ,  three  1975, measurements, t h a t  i n c l u d e only t h r e e s t a b l e runs with the h i g h e s t at Z/L=0.12. I t is,  therefore,  dangerous  t o e x t r a p o l a t e these f i n d i n g s beyond  Z/L=0.15, where the c o r r e c t i o n unstable and  side  becomes  even  larger.  t h e r e a r e 21 runs i n the McBean and E l l i o t  104 runs i n the s e c t i o n 5.2 i n t e r c o m p a r i s o n , with  unstable  at  Z/L=-0.3 and -0.45, r e s p e c t i v e l y .  s t a b i l i t y adjustment i s s t i l l right  to  extend  l e s s than  flux  calculations,  because  they  Z/L=0.15 ( f i g u r e 2) and although  are s t r o n g l y supported consists  intercomparison rejected  the  most  10% so i t should be a l l  limits require  of  of  sensible  of  section  from  Z/L=-1.1  5.3.  to  The  and  0.75  Cote,  Z/L=0.4,  Temperature  i f t h e r e i s any evidence of s a l t  t o w i t h i n ±0.1°C.  heat  these are s u b s t a n t i a l , they  by t h e work of Wyngaard and  runs  This  € from G i l l - u .  data  not  1971, and the  are  contamination  microbead or i f the rod and bead t h e r m i s t o r s do average,  study  At Z/L=-0.6 the  s t a b i l i t y c o r r e c t i o n s t o <wt>DISS a r e 1.8 a t Z/L=-0.6  which  the  d i s s i p a t i o n method 2 at l e a s t t h i s f a r .  c r i t e r i o n e f f e c t i v e l y s e t s the outer  at  On  also  of the  agree,  on  124 In  p r o c e s s i n g a d i s s i p a t i o n momentum [ t e m p e r a t u r e ] r u n from  either  the ship  or  tower,  20  minute averages of a l l G i l l - u  [ t e m p e r a t u r e microbead] band-pass f i l t e r s i n t h e -5/3 r"u(f)  [ft(f)]  dissipation  a r e used of  fluctuations] are  turbulent  of  t h e momentum  flux  of t h e  [temperature  These i n d i v i d u a l v a l u e s [ N t ] necessary  [sensible  f o r the  heat f l u x ] from  However, i f any s e p a r a t e band-pass  value  criterion  ensures  used  that  fall  the spectral  values  at  the  w i t h i n 10% o f t h e average -5/3 s l o p e o f  i n p u t spectrum and t h a t f l u x e s  calculated  from  individual  f i l t e r s a r e w i t h i n 10% of t h e v a l u e found from t h e a v e r a g e . 20  minute  employed  because  i t i s felt  hourly  obtain  In  order  t h e h o u r l y averages, t h r e e s e g u e n t i a l 20 minute  e s t i m a t e s a r e averaged and then used t o c a l c u l a t e parameters. dissipation referred  averages  t h e longer averaging time  i n c r e a s e s t h e r e l i a b i l i t y o f t h e d i s s i p a t i o n method. to  The  averages c o u l d be used t o produce time s e r i e s o f t h e  f l u x e s and r e l a t e d parameters, but i n p r a c t i c e are  of  from 6 [ N t ] by more than 15% [ 1 0 % ] t h e r u n i s r e j e c t e d .  frequencies the  the €  values  energy  from e q u a t i o n 3.7 [ 3 . 6 ] .  e g u a t i o n 2.28 [ 2 . 3 2 ] . differs  independent  kinetic  averaged t o g e t h e r t o g i v e  calculation  This  to find  range  Hereafter, system  will  these not be  hourly  the  averages  specifically  flux  related  from  denoted,  the but  t o s i m p l y as <uw>, <wt>, u* t * , CD, CT and so on. F o r  dynamic f l u x c a l c u l a t i o n s  the a i r density  equation  t h e atmospheric  2.35,  using  £  i s found  pressure  from  m e t e o r o l o g i c a l o b s e r v a t i o n s from Shearwater and CCGS Quadra.  from the  125  B:  CCGS QUADRA  CM  + + +  +  CD LJ CD CD' CD  CD  2  ~i 10  10  FIGOEE 28  i  U10  U10  i 14  14  i  r 18  (M/S)  22  26  18  (M/S)  The n e u t r a l drag c o e f f i c i e n t as a f u n c t i o n of speed from: A: 1086 h o u r l y averages from the Bedford tower. B: 50 5 h o u r l y averages from t h e CCGS Quadra.  wind  126 6.2  B u l k Aerodynamic P a r a m e t e r i z a t i o n Of The Momentum F l u x Hourly averages o f u* and UZ and Z/L a r e used t o c a l c u l a t e  U10  from  eguation  from 2.8 and 2.12. and  ship  and  2.11 and t h e n e u t r a l drag c o e f f i c i e n t , CDN, These a r e p l o t t e d s e p a r a t e l y f o r  data i n f i g u r e 28.  most p o i n t s a r e obscured  CDN v a l u e . only  a  few  a  mean  Between U10 =4 t o 11 m/s t h e s c a t t e r i s u n i f o r m  with  by t h e c o n c e n t r a t i o n about  few v a l u e s of 10 CDN o u t s i d e t h e range 0.65 t o 1.5. At 3  appears points,  conditions. a two  very  tower  There a r e v e r y few extreme v a l u e s  h i g h e r wind speeds a tendency f o r h i g h e r there  the  to so  be l e s s s c a t t e r .  these  data  may  values  develops  and  Above U10=20 m/s t h e r e a r e not  fully  reflect  average  F o r t u n a t e l y , i n t h e r e g i o n 8 <010< 18 m/s, t h e r e i s  good o v e r l a p o f tower and s h i p r e s u l t s which a l l o w s t h e  s i t u a t i o n s t o be compared. In f i g u r e 29, CDN i s averaged over 2 m/s i n t e r v a l s of  provided  there  are a t  l e a s t 10 runs i n a band, and t h e means  p l o t t e d with v e r t i c a l b a r s e x t e n d i n g deviation.  up  F o r c l a r i t y , tower r e s u l t s  t h e l e f t of band c e n t e r and t h e s h i p right.  Over  t h e range  and  points  from  t h e tower  introduced  (pluses)  by  to the  less  than  one  1/2 o") from t h e other  to  i n moving  CCGS Quadra.  agreement a l s o e s t a b l i s h e s t h a t t h e tower representative  standard  No s y s t e m a t i c e r r o r s , such as i n t h e c h o i c e of  Z, appear t o have been system  1  8.5 <010< 20.5 m/s, t h e band averaged  d e v i a t i o n (but u s u a l l y l e s s than  p l a t f o r m ' s mean.  down  (triangles) are j u s t to  CDN's from one p l a t f o r m a r e seen t o d i f f e r standard  U10,  of  open  the  dissipation  The drag  coefficient  site  i s ,in  fact,  s e a c o n d i t i o n s , a t l e a s t up t o 20 m/s  127  FIGURE 29  Comparison of the ship (pluses) and tower (triangles) neutral drag c o e f f i c i e n t s . Vertical bars extend ± 1 o" about p l o t t e d band averages.  128 winds.  T h i s a l l o w s the tower and s h i p r e s u l t s  to  be  combined  i n t o a s i n g l e d a t a s e t of n e a r l y 1600 hours from about 16 months of o p e r a t i o n between  September  1976 and A p r i l  1978.  Fetch E f f e c t s The tower d a t a of f i g u r e 28A i n c l u d e some r u n s from l i m i t e d fetches,  whose  justified.  inclusion  in  the  Up t o about 10 m/s,  CDN  overall  data  to  investigate  coefficient.  The  the  results  influence are  n e u t r a l drag c o e f f i c i e n t , CDN,  1  | 1  Fetch (km)  |  10-20  shown  of  this  fetch  range  on  the  from measurements about 13m  •  are drag  i n t a b l e V I I I , where t h e  T — — — T • Number | Mean 10 CDN | | of | ±1 s t a n d a r d | 103CDN | 10 CDN Min | Max hours | deviation | 1 T  must be  from t h e tower does not vary  a p p r e c i a b l y w i t h wind speed, t h e r e f o r e data i n used  set  -  3  3  above  x — 1 | Azimuthall | range | I (° True) |  |  200  | 1.14 ±.18  J  0.75  |  2.03  | 253 - 393|  I |  54  | 1.10 ±.22  I  0.73  |  1.87  | 246 - 253| | 33 - 65 |  |  85  | 1.13 ±.24  |  0.64  |  1.76  | 235 - 246|  | Unlimited | | tower | i i i i | Unlimited | I tower+shipl | Tower | | a l l fetches| • «  263  | 1.13 ±.22  |  0.62  |  1.75  |  291  | 1-14  |  0.62  |  1.75  590  | 1. 13 ±. 21  j  0.62  |  2.03  i  •  I | 20 - 100 I | 100 - 200  TABLE V I I I  j  67 - 235| i 1  i ±-21  •  1  I  | •  j 0 - 360| •  V a r i a t i o n of t h e n e u t r a l drag c o e f f i c i e n t f e t c h f o r winds between 4 and 10 m/s.  with  129  the s e a , does n o t e x h i b i t any dependency on f e t c h e s g r e a t e r than 10 km and, i n view of t h e o v e r a l l s c a t t e r , t h e means consistent.  This  conclusion  depends  very  on u s i n g CDN, s i n c e t h e  mean C10 from t h e 10-20 km f e t c h range i s 17% l a r g e r the  are  than  from  u n l i m i t e d f e t c h r u n s , presumably because t h e o f f s h o r e winds  tended t o be more u n s t a b l e . below  10  m/s,  fetch  The i n d i c a t i o n i s , t h a t  effects  a r e not i m p o r t a n t  f o r winds  i f t h e aspect  r a t i o , Z / f e t c h , i s a t l e a s t as s m a l l as 1 0 ~ . There i s a l s o 3  indirect  implication  that  t h e s u r f a c e r o u g h n e s s , Zo, does not  depend s t r o n g l y on s u r f a c e wave parameters t h a t developed Wiegel  by  10  (1964,  km d u r i n g 10 m/s winds.  p  an  216), f o r fetch  are not  fully  The data c o m p i l e d by  limited  waves,  show t h e  s i g n i f i c a n t wave h e i g h t and t h e phase speed from a 1000 km f e t c h (fetch  g/<D> -10 ) 2  5  t o be, r e s p e c t i v e l y , 10 and 5 t i m e s  t h a n expected w i t h a 10 km f e t c h the  wind  speed  dependency  The n e c e s s i t y  greater  of e x t r a c t i n g  from CDN c o m p l i c a t e s e x t e n d i n g t h e  i n v e s t i g a t i o n above 10m/s, b u t a s t h e a s p e c t  ratio  stays the  same, t h e r e s h o u l d n o t be a sudden f e t c h dependency.  Tower data  from  a l l fetches  subseguent a n a l y s e s . additional effects.  are, therefore,  grouped  together  The b e t t e r s t a t i s t i c s r e s u l t i n g  in  a l l  from t h e  d a t a should more than compensate f o r any s m a l l f e t c h  130 Stability  Effects  E g u a t i o n 2.12 d e f i n e s CDN as a f u n c t i o n o n l y of Zo and implies  C10CDN  f o r Z/L<0,  neutral s t a b i l i t y . independent o f  C10<CDN  2.8  f o r Z/L>0 and C10=CDN at  T a b l e IX i n d i c a t e s t h a t CDN and hence Zo a r e  Z/L  i n the  unstable  values a r e c l e a r l y higher than the  case.  average,  At Z/L<-0.3, C10 but  reduction  to  n e u t r a l s t a b i l i t y g i v e s no s y s t e m a t i c t r e n d t o t h e mean u n s t a b l e CDN's,  which  a r e r e a s o n a b l y c o n s i s t e n t i n view o f t h e s c a t t e r .  Extraneous e f f e c t s seem t o i n f l u e n c e t h e s t a b l e runs t o a greater  degree.  When  reduced  t o n e u t r a l , t h e average s t a b l e  CDN * 1000 Z/L (AT) range  Number of hours  -.60  -.45  25  -.45  -.30  35  -.30  -.15  77  + T  much  T r  C10 * 1000  Mean ±1o~  Max Min  Mean ±1cr  Max Min  1.06 ±.12  0. 80  1.22 ±.14  0.91 1.52  1.12 ±.19  0.77 1.73  1.26 ±.22  0.86 1.98  0.98 ±.16  0. 67  1.07 ±.18  0.70 1.54  1. 31  1. 38  -. 15  0  166  1.09 ±.20  0.68 1.74  1.12 ±.21  0.68 1.83  0  +.05  104  1.19 ±.18  0.62 1.85  1.16 ±.18  0.60 1.81  +.05  +.10  122  1.21 ±.19  0.64 1.79  1.13 ±.17  0.60 1.64  +.10  +.15  61  1.23 ±.28  0.75 2.03  1.11 ±.24  0.68 1.80  + r  n  -i  TABLE  IX  J  The s t a b i l i t y dependency of t h e drag coefficients from t h e 4 < 010 < 10 m/s d a t a o f t a b l e V I I I .  131 CDN's are l a r g e r than t h e o v e r a l l mean and they seem t o i n c r e a s e with  stability.  responsible  However,  for  this  r a p i d changes i n wind sequence  of  the  feature  following  showing  the  suggest  that  coefficient i s well independent source  of  the  storm.  Such  and  of the t r e n d i n CDN  by  that  (figure  dependence  similarity  sea  a  important A  time  h i g h , low wind speed,  later  stability  described  Z/L  a  stratification.  development o f these  s t a b l e drag c o e f f i c i e n t s i s presented data  coefficients  p o s s i b l y i n f l u e n c e parameters  t o Zo and merely c o i n c i d e w i t h s t a b l e series  drag  are found t o be a s s o c i a t e d w i t h  direction  e v e n t s may  large  31).  The  the  drag  of  theory  with  Zo  surface c o n d i t i o n s are  the  w i t h Z/L  found i n t a b l e I X .  neutral  coefficients  Wind Speed Dependency In f i g u r e 30 t h e 1591 data 010  are  band averaged over 2 m/s  similar,  because  unstable runs. with  010  of  the  almost  A smooth curve  could  be  made  all  The  mean  equal  C10  values  described  p o i n t s show approximately  a  by  (concave up)  with CDN  to f i t these p o i n t s .  more  rapid  linear  from  a  constant. rise  of  10 t o 26 m/s.  t h i s b e h a v i o r , a l l 618  h o u r l y CDN  averaged  with U10>10 m/s  and  a l l 973  The CDN  ( c o r r e l a t i o n c o e f f i c i e n t 0.74).  values  are  numbers of s t a b l e and increasing  However, below  about 10m/s, the s l i g h t i n c r e a s e o f the average CDN's s h o u l d adequately  the  i n t e r v a l s and p l o t t e d at t h e ff).  mean ( v e r t i c a l bars show + 1  from  be  h i g h e r wind speed  with  U10,  that  is  I n o r d e r to g u a n t i f y with  U10<10  are r e g r e s s e d  m/s  against  A l l the band averages are  w e l l d e s c r i b e d by t h e r e s u l t i n g s o l i d l i n e of f i g u r e 30:  are 010 very  132  1  £  FIGURE 30  1  c!  1  NOG  1  T  \  OQOI  0  The n e u t r a l drag c o e f f i c i e n t averaged over wind speed bands. V e r t i c a l bars i n d i c a t e ± 1 or and the number of p o i n t s i n band i s shown below each average. L i n e s show the Charnock r e p r e s e n t a t i o n with °<= 0.0144, K= 0.41 (dashed) and eguations 6.1 (solid) .  133 IO3  CDN  103 C10 =  1.14  4 < U10 < 10  m/s (6. 1)  where  103  CDN  0.49  + .065  U10  103  C10  0.46  + .068  010  the  C10  numerical  10 < 010 < 27  m/s  r e s u l t s a r e i n c l u d e d f o r comparison.  values  of  6.1  depend  slightly  on  The e x a c t  the  somewhat  a r b i t r a r y c h o i c e of a lower wind speed l i m i t f o r the r e g r e s s i o n . Conveniently*  with  happen t o match. distinctly  The  <=<=0.016,  K=  of  10  of  CDN  m/s,  the l i n e  described  representation with  <=< =  0.0144,  as suggested by G a r r a t t  (1979) eddy c o r r e l a t i o n d a t a  s i t e extremely w e l l .  by  X=  (1977). from  the  For winds below 10 m/s,  runs  (1968-1969).  (1976-1978) between 6 and 22 m/s However,  3  (1975) are Island  the  8  Sea l o c a t i o n of  Kitaigorodski  Banks  Miyake  (1967), may  11  A r e g r e s s i o n of a l l 120 runs yields  higher,  Lake F l e v o a t 4 meters  site  from  0.44  +  0.063  010  =  suggesting  that  the  Sable  w i t h i t s s u r f zone and perhaps o t h e r s h a l l o w water  l o c a t i o n s : Lough Neagh a t 1972),  Bedford  Sable I s l a n d r e s u l t s of Smith and Eanke  significantly  site  (or  h i s average  near  10 C10.  is  Eguations  from 14 runs (1976-1978) and about 1.24  neutral  6.1  0.4 1  10 CDN i s 1.11 3  segments  from the dashed c u r v e o f f i g u r e 30, which  0.4),  6.1 f i t Smith's  choice  behavior  different  i s the Charnock  tower  the  of  to  15  meters  almost  et a l . ,  ( W i e r i n g a , 1974), the 10m Caspian et a l . (1973)  e t a l . (1970  a l l the  and  the  Spanish  A) and W e i l e r and B u r l i n g  not be r e p r e s e n t a t i v e of the open  Unfortunately,  (Sheppard  ocean  situation.  measurements above 14 m/s  (and  many a t lower s p e e d s ) , t h a t were a v a i l a b l e t c G a r r a t t came  from  134 these  shallow  water  locations.  A  number  of  open  sea  measurements c o n t r i b u t e d t o h i s 10 t o 11 m/s band average, which v e r y n e a r l y l i e s on 6.1.  I t a l s o seems  likely  that  excluding  the  r e s u l t s of Sheppard e t a l . would g i v e band averages i n t h e 3  to  7  the  range 7 t o 10 m/s, t h e band averages  run  about 20% ( l e s s than 1 ar) h i g h e r than e g u a t i o n s 6.1.  m/s  Open  range t h a t would be a d e q u a t e l y d e s c r i b e d by 6. 1.  ocean  measurements  b e t t e r agreement. to  used  by  Garratt  Garratt  generally  (1977) a r e i n  From t h e Argus I s l a n d t o w e r , a  site  similar  t h e B e d f o r d tower, the o v e r a l l average o f 69, near n e u t r a l ,  Reynolds f l u x CD's a t 7.5m i s 1.24x10~ to  of  In  10  3  f o r wind speeds  from  m/s (De L e o n i b u s , 1971).. The c o r r e s p o n d i n g v a l u e o f C10  i s about 1.17x10~ . 3  B r o c k s and Krugermeyer  (1970) p r e s e n t C10's  from 152, near n e u t r a l , 15 minute p r o f i l e s over t h e B a l t i c North  Seas  within  (1969).  Eguations  6.1  t h e s c a t t e r , b u t g e n e r a l l y l o w e r by 10 t o 15%. The  o v e r a l l average 10 C10 from Hoeber (5 t o 11  m/s)  3  and  and  and t h e E g u a t o r i a l A t l a n t i c measurements (787, near  n e u t r a l , 10 minute p r o f i l e s ) o f Hoeber are  4  i s 1.23±0.25  h i s band averages agree very w e l l w i t h those of f i g u r e 30,  except between 5 and 6 m/s where an average o f o n l y 11 p o i n t s i s 1.48.  With 2/3 of h i s p r o f i l e s u n s t a b l e , CDN may average a few  percent  less.  A v e r a g i n g t h e B a l t i c and N o r t h Sea d a t a (4 t o 12  m/s) g i v e s 10 C10 = 1.30±0.18, b u t t h e r e i s a s l i g h t t r e n d 3  wind  speed.  The Bass S t r a i t s i t e o f H i c k s (1972 A) ought t o be  r e p r e s e n t a t i v e o f t h e open s e a , reduced  by  with  u*  t o account  however  f o r surface  h i s wind drift.  speeds  are  I f t h e eddy  c o r r e l a t i o n drag c o e f f i c i e n t s a r e reduced by about 7%, t h e y then conform t o the CDN's o f f i g u r e 28 and t h e 30  values  between  3  135 and  8  m/s  then average 1 . 1 3 x 1 0 , however 6 r u n s from 8 t o 10 -3  m/s average about 1.4x10~ .  Garratt  3  correlation  runs  (3  to  also  uses  11 m/s) from Hasse  the  18  eddy  (197 0 ) , q u o t i n g an  average o f 10 C10 = 1.21 ±20%. 3  The two d a t a discussed  sets  by  Garratt  that  et al.  Because  of  flow  distortion  corresponding  eddy  correlation  (1971) , a r e e q u a l .  CDN i s expected t o be about 1 . 3 x 1 0 Accordingly, Paulson e t a l . f i n d appears  as  and  The l a t t e r data  to  FLIP,  i f the  between t h e data of f i g u r e 28  t h e average  (20 runs)  of Pond  give  an  4 and  The e g u i v a l e n t average  with  -3  from  i n winds between  3  m/s and s l i g h t l y u n s t a b l e c o n d i t i o n s .  It  due  measurements  average CD a t about 8 meters o f 1.52x10~ 8  t o be  (197 2) use an e m p i r i c a l c o r r e c t i o n f a c t o r chosen  so t h a t t h e i r average <uw> (from p r o f i l e s )  Si*  remain  a r e open sea s t u d i e s from B/V F L I P , however, t h e y a r e  not independent. Paulson  used  a  20%  variability.  10 CDN = 1.32 f o r 19 r u n s . 3  major and  s o u r c e o f t h e disagreement the  data  used  by  Garratt  (1977) i s t h a t t h e l a t t e r i n c l u d e s measurements from onshore and shallow  water  (less  than 15 meters) s i t e s .  c o n s i s t e n t w i t h most of the deep water drag  coefficients  to  within  E g u a t i o n s 6.1 a r e  (more  than  50  meters)  p o s s i b l e measurement e r r o r .  The  d i s c r e p a n c i e s suggest a s l i g h t l y h i g h e r drag c o e f f i c i e n t a t wind speeds below 10 hours)  m/s.  i n Bass S t r a i t  In  contrast,  (Antonia e t a l . ,  recent  measurements  (10  1978) i n winds between 5  and 10 m/s and -0.1 <Z/L< 0 g i v e an average 10 CD a t 5 meters o f 3  1.05 and 1.25 (about 0.9 and 1.1 a t 10 meters) from t h e Beynolds f l u x and d i s s i p a t i o n methods, r e s p e c t i v e l y .  Since  a  constant  136 CDN  i s a good f i t t o most i n d i v i d u a l data s e t s , i t i s l i J c e l y t o  remain a good d e s c r i p t i o n o f t h e o v e r a l l below  about  10  m/s.  open  ocean  situation  The " b e s t " c o n s t a n t t o use i s d e b a t a b l e ,  but i t s h o u l d be i n t h e range 1.1x10~  3  t o 1.3x10 .  The average  -3  10 C10's ( n e u t r a l o r near n e u t r a l ) from a l l t h e d i s c u s s e d 3  open  ocean; eddy c o r r e l a t i o n , d i s s i p a t i o n and p r o f i l e measurements i n winds  less  than  10 t o 12 m/s a r e a b o u t ; 1.17 (178 r u n s ) , 1.14  (626 hours) and 1.24 (958 p r o f i l e s , The  overall  188  hours),  respectively.  average i s 1.20, but o n l y 1.17 i f t h e r e s u l t s from  Hoeber and from B r o c k s and Kruggermeyer a r e weighted by 1/6 1/4, r e s p e c t i v e l y , t o make them comparable t o h o u r l y v a l u e s . the  higher  well  At  wind speeds, t h e vast m a j o r i t y o f t h e open s e a drag  c o e f f i c i e n t s come from Smith both  and  described  by  (1979) and  6.1.  figure  28,  which  are  I t i s an i n t e r e s t i n g f e a t u r e of  6.1, t h a t an e x t r a p o l a t i o n t o 50 m/s f i t s t h e h u r r i c a n e and wind flume data c o m p i l e d by G a r r a t t of  (1977) as w e l l as a  continuation  t h e Charnock l i n e o f f i g u r e 30.  The V a r i a b i l i t y Of CDN And Zo It  may  be  possible  to  d e s c r i b e t u r b u l e n c e and t h e drag  c o e f f i c i e n t s w i t h a v a r i a b l e Zo, a l t h o u g h t h i s i s expected t o be d i f f i c u l t and t h e r e a r e no measurements available.  The  of  surface  wind speed dependence o f CDN above 10m/s shows  t h a t a c o n s t a n t Zo i s n o t a p p l i c a b l e .  A Charnock  w i t h X = 0 . 0 1 2 3 (K=0.40) , passes w i t h i n +1 s t a n d a r d all  t h e band  means  of  the region  representation deviation  of  f i g u r e 30, but i t s p r e d i c t e d low wind  speed b e h a v i o r i s n o t observed. fits  conditions  A Charnock l i n e w i t h  <=< =0.008  from 010 = 11 t o 17 m/s f a i r l y w e l l , b u t then  137 f a l l s o f f much t o o q u i c k l y t o account f o r t h e v a l u e s m/s.  The  CDN's  about 0.016. <O10<  to  50 m/s i n G a r r a t t  CDN i s v e r y n e a r l y  a  t o 26  (1977), r e q u i r e °< t o be  constant,  10 m/s, a s i s t h e average o f C10.  up  0.00114,  for 4  T h i s b e h a v i o r may be a  consequence o f h i g h l y v a r i a b l e s e a s u r f a c e c o n d i t i o n s t e n d i n g t o make Zo i n c r e a s e w i t h d e c r e a s i n g wind speed average,  t h e tendency  of  and  balancing,  on  lower u* v a l u e s t o make i t s m a l l e r .  Above 10 m/s, t h e i m p o r t a n t parameters seem t o change c h a r a c t e r , so t h a t Zo v a r i e s w i t h wind speed, p r o d u c i n g the observed linear  r i s e i n CDN w i t h 010.  near  I t may be p o s s i b l e t o d e s c r i b e Zo  by a Charnock f o r m u l a t i o n w i t h °< an  experimentally  determined  f u n c t i o n o f v a r i o u s s u r f a c e parameters. To  explore  the influence  t u r b u l e n c e above i t , of  of  t h e sea  i t i s u s e f u l t o examine t h e t i m e  t h e winds and f l u x e s .  run D33C, f i g u r e 31.  average  CDN  over  a  few  hours  variability  i s only from  hour  i s also  6  to  accompanied  by  an  21.  In  The  falling  almost complete r e v e r s a l i n  drag c o e f f i c i e n t s a t low wind speeds.  the  high  The p i c t u r e o f lower than  drag c o e f f i c i e n t s on t h e r i s i n g wind and h i g h e r ones on  the f a l l i n g wind i s a l s o figures  a  i s seen t o behave v e r y d i f f e r e n t l y on t h e r i s i n g  d i r e c t i o n and i t i s t h i s s i t u a t i o n t h a t g i v e s r i s e t o  average  about  about 10%. The  wind than i t does when the wind speed i s d r o p p i n g . wind  histories  The drag c o e f f i c i e n t i s seen t o vary q u i t e  i n c r e a s e w i t h wind speed i s e v i d e n t addition,  on t h e  An example, w i t h h o u r l y a v e r a g e s , i s  smoothly w i t h t i m e , such t h a t the random running  surface  32 and 33.  supported  Denman and Miyake  by  runs  D29D  and D31F,  (1973) observed t h a t drag  c o e f f i c i e n t s tended t o i n c r e a s e on t h e l e a d i n g s i d e of a  storm.  138  —~t=>'  P  CM  T—r  1—1—r  i — r  1—r  o Q  ++++++ ++ +++  -I  CJ  +  +  + + + + +  +  i—1—r ++  +++  i — r  1—r  ++++++ ++  ++++  +++++  ++  T—r  1—r  m o'  +  + + +  ~i—r  1X1°. _ |  +  +s + ++++  J  +  V  a. r  1—1—1—r  i—1—1—1—1—r +++ •  UJ  0 FIGURE 31  ++"  -1—1—1—1—1—1—r 12  IB  24  30  TIME (HOURS)  36  1 — r  42  48  Time series o f t h e momentum f l u x from run D33C, s t a r t i n g a t 4:40 GMT December 7, 1976. Momentum f l u x e s a r e from t h e d i s s i p a t i o n ( p l u s e s ) , Reynolds f l u x (squares) and bulk ( s o l i d l i n e ) methods.  139 then  e i t h e r remain c o n s t a n t o r decrease s l i g h t l y .  T h i s i s also  a very apt d e s c r i p t i o n of the time s e r i e s i n f i g u r e s 31, 3 2 33.  The  scaling  arguments  of  section  2.1  p r e d i c t that the  d i f f e r e n c e between the 10m and s u r f a c e momentum f l u x greater  (giving  lower  coefficients),  Apparently the i n c r e a s e i n Zo i n t h i s enough  t o overcome t h i s l o s s .  on  and  the  situation  should  falling is  be  wind.  more  than  I t i s possible t o speculate that  Zo depends on s u r f a c e parameters t h a t , as the wind speed  falls,  remain near t h e i r " o l d " values produced by the p r e v i o u s l y higher winds.  I f °< were dependent  and hence 010-Cw  on t h e t o t a l wave generating  ( s e c t i o n 2.3), where Cw i s the component of the  wave speed i n the i d i r e c t i o n , i t would sudden  changes  force  in  be  very  sensitive  to  wind d i r e c t i o n , because these would tend to  make Cw s m a l l e r and perhaps even negative.  It  appears  likely  that some of the observed s c a t t e r i n drag c o e f f i c i e n t s i s due to the i n f l u e n c e of the past h i s t o r y of the wind as "remembered" by the sea s u r f a c e . (1973)  With access to wave s p e c t r a , Denman and  concluded t h a t the drag c o e f f i c i e n t  was dependent  Miyake on the  nature of the wave f i e l d t o the order of 20%. In order t o examine t h e i r i n f l u e n c e  on  the  average  tower data from v a r i o u s wind c o n d i t i o n s are presented X.  Unfortunately,  above  meaningful averages. direction"  are  respectively. category  m/s  there  Winds of "constant  allowed Data  15  used  to  have in  the  4  in  CDN, table  are too few data f o r speed"  m/s  "after  and  "constant  and 30 degree ranges direction  changes"  are from the s i x hours f o l l o w i n g a change i n d i r e c t i o n  of at l e a s t a 60 degrees i n l e s s than two hours. i n c l u d e d i n the r i s i n g  winds.  Peak winds are  The s u g g e s t i o n i s , t h a t e i t h e r  a  140 r a  WIND SPEED BANDS (M/S)  •1  •  | Wind | Eegression | | conditions j and | | (number of hours) |c o r r e l a t i o n |  4.5-7|  7-9  I  9-11 J  11-15|  J A l l tower data I (1086)  |- 79 +.043 010| J .59 |  1.11 | (176) |  1.13 | (264) I  1.17 | (259) |  1.33 (247)  | Constant speed J and d i r e c t i o n I (253)  |.71 + .049 010| | .60 | |  1.03 | (31) I  1. 13 I (68) I  1-14 I (79) |  1.31 (59)  I E i s i n g winds I (167)  |. 64 + .054 010| .70 | J  1.01 | (22) |  1.11 I (33) I  1-14 I (31) I  1.25 (49)  | E i s i n g wind |. 60 +.055 010| .67 | | steady d i r e c t i o n ! 1 (81) |  1.08 | (3) |  1.11 I (15) I  1-10 | (18) |  1.24 i (29)  |. 94 +.036 010| .51 | I  1.40 | (3) I  1.25 | (12) I  1.28 | (24) |  1.38 (49)  | F a l l i n g wind |1.05+.025 010| | steady d i r e c t i o n l .36 | I (80) |  1.31 | (2) I  1.28 I (8) I  1-29 | (18) |  1.34 (29)  I After direction | | changes | I (60) |  1.18 | (22) |  •  I  •  I F a l l i n g wind I (111)  L_.  TABLE  •  1  X  direction  1.34 (12) •  . J ,  i  i  Mean 10 CDN o f wind speed bands i n d i f f e r e n t wind conditions. Bracketted values a r e the number of hours contained i n an average o r r e g r e s s i o n of CDN a g a i n s t 010. 3  change or a f a l l i n g  average drag c o e f f i c i e n t s . observations  were  available  wind tends t o produce higher  Table only  X  also  during  indicates rising  constant d i r e c t i o n , as may be the case i n some average  i i 1.60 (16)  CDN  value  than given by 6 . 1 .  data  than  that i f  winds sets,  with the  f o r 7 <010< 11 m/s, would be about 4% lower The observations of CDN during r i s i n g  winds  141 show  a  s y s t e m a t i c r i s e w i t h wind speed and a r e g r e s s i o n of CDN  a g a i n s t 010 g i v e s 10* CDN= 0.64+ 0.054 010 coefficient one  of  0.7 0.  linearly  that  with  t h e average  i f data  direction  Similar  are included.  with  measurements be  coefficient  f o r a l l wind  constant  Such a  speed  and  e f f e c t s a r e expected a t t h e  h i g h e r speeds t o o , so i n order t o a r r i v e coefficient  drag  wind speed even below 10 m/s.  t r e n d may a l s o emerge even  drag  a correlation  Thus, i f o n l y t h e s e data were a v a i l a b l e  could e a s i l y conclude  increases  with  at  speeds  a  realistic  mean  i t i s imperative  made d u r i n g a l l l i k e l y wind c o n d i t i o n s .  that  It i s ,  t h e r e f o r e , p o s s i b l e t h a t drag c o e f f i c i e n t f o r m u l a t i o n s may with  location  vary  and time o f y e a r , w i t h t h e break from a c o n s t a n t  t o a l i n e a r l y i n c r e a s i n g CDN being q u i t e v a r i a b l e . The table  tower data i s a l s o s o r t e d  XI.  There  i s no  trend  into  monthly  i n t h e September data and t h e  average CDN's a r e lower than t h o s e o f t h e o t h e r i s a reasonably the  entire  wind  speed range.  conditions,  table  different,  throughout t h e year.  The  results  t h e year  possibly  seems  may,  either  t h e tower  throughout  of  to  reflect  experiments  therefore,  because wind c o n d i t i o n s  be vary  I t would be d e s i r a b l e t o i n c l u d e d a t a from  e v e r y month i n any drag c o e f f i c i e n t f o r m u l a t i o n . no measurements from  There  The h i g h CDN's a t low winds a r e  X.  conducted a t d i f f e r e n t t i m e s o f considerably  months.  s i g n i f i c a n t t r e n d i n t h e October data  e v i d e n t i n t h e December r e s u l t s , w h i l e March average  groupings i n  May or  through  August  Onfortunately,  are a v a i l a b l e  t h e w e a t h e r s h i p , but t h e h i g h wind speed  f o r m u l a t i o n s h o u l d n o t be a f f e c t e d as t h e s e a r e n o t t h e with t h e g r e a t e s t winds.  from  months  142 1  i  | r  WIND SPEED BANDS  r - i Wind | Regression | conditions I and | (number o f hours) | correlation |  (M/S)  |  -  5-7  |  7-9  |  9-11  11-15|  |  September (241)  11.05+.001 010| | .008  1.07 (94)  | |  1.04 | (79) |  1.05 | (47) |  1.06 (21)  October (131)  |.83 |  +.047 D10| .65  1.11 | (28) J  1.16 | (25) |  1.30 | (28) |  1.45 | (34) |  December (251)  |.78 |  +.044 O10| . 62  1. 14 | ("2) |  1. 14 | (53) |  1.33 | (73) |  March (271)  |.77 |  +.044 O10| .65  1. 18 | (49) |  1. 17 | (96) |  1.31 | (70) |  | I  I  l  I  1.22 | (20) |  i l  i  The  1 ,,  «  TABLE  XI  1.12 (24)  | |  •  J  Mean 10 CDN o f wind speed bands f o r d i f f e r e n t months. Bracketted values a r e the number of hours contained i n an average or r e g r e s s i o n o f CDN a g a i n s t 010. 3  i n v e s t i g a t i o n of the tower data has shown t h a t  stability effect  nor f e t c h  on  the  (greater than  average  10  km)  have  a  neither  significant  n e u t r a l drag c o e f f i c i e n t .  demonstrated t h a t much of the v a r i a b i l i t y i n CDN  I t has been measurements,  only between i n d i v i d u a l data p o i n t s , but between e n t i r e data  sets,  may  be  due  t o the i n f l u e n c e of t h e s u r f a c e  However, i t appears as surface  parameters  i f the  could  measurement  possibly  d i r e c t momentum f l u x measurements. can  •  E m p i r i c a l Drag C o e f f i c i e n t The  not  i  be p r a c t i c a l l y  formulation  incorporated  i s the wind speed.  be  more  of  wave f i e l d .  the  important  complicated  than  An important parameter  that  i n t o a n e u t r a l drag  coefficient  143 The of  e m p i r i c a l CDN f o r m u l a t i o n o f 6.1 g i v e s  t h e momentum  flux  from  bulk  estimates  t h e wind speed, OZ and s t a b i l i t y ,  Z/L(AT), f o l l o w i n g t h e procedure o u t l i n e d i n s e c t i o n i t e r a t i v e technigue  i s used t o s o l v e e g u a t i o n  2.3.  An  2.15 f o r 010. F o r  f i r s t pass 010«= OZ/ [1+ 0.1 K(Z,Z/L) ] i s assumed (CDN*/ / K  the  2  - 0 . 1 ) , g i v i n g a CDN' from 6.1. more  than  3)  010' i s found  On subseguent i t e r a t i o n s  (never  from 2.15 u s i n g t h e CDN' c f the  p r e v i o u s p a s s . u n t i l s u c c e s s i v e 010* v a l u e s change by  less  than  1%.  CDN' from t h e f i n a l pass i s s u b s t i t u t e d i n t o 2.14 t o g i v e a  CD,  which  g i v e s t h e momentum f l u x through 2.9. Bulk  estimates  are t o be compared t o d i r e c t e s t i m a t e s i n l a t e r time s e r i e s t h a t i n c l u d e data w i t h -1.0 <Z/L< 0.3. The s t a b i l i t y included of  need  n o t be  i n t h e 010 c a l c u l a t i o n , because t h e maximum s t a b i l i t y  the s h i p  stabilities  data  i s only  are higher,  0.08 and on  the reduction  the tower,  where  i s only from 13 t o 10  meters, t h e r e f o r e , ( s e c t i o n 2.3) t h e worst e r r o r i s l e s s t h a n 2% i n 010 and about 1% i n CD  and <uw>.  The e r r o r  i n Z/L (AT)  ( s e c t i o n 4.1) i n t r o d u c e s an e r r o r i n CD o f about 5%.. A 2% e r r o r in  0Z  becomes  4%  i n <uw>.  The l a r g e s t a n d a r d  f i g u r e 30 and t h e range o f p r e v i o u s measurements, any  CDN  combined  formulation error  has a t l e a s t  i n bulk  estimates 15% as  a from  deviations i n suggest  10% u n c e r t a i n t y . equation  therefore,  greater  than  are the errors  estimates.  Although  i n d i v i d u a l b u l k e s t i m a t e s may  2.9  that The are,  i n direct differ  from  d i r e c t d i s s i p a t i o n o r Reynolds f l u x measurements by 50% or more, there  should  necessary  be  averaging  reasonable  agreement  on average, a l b e i t t h e  p e r i o d may v a r y w i t h time and p l a c e .  144 Comparison Of Methods In a l l the time s e r i e s p r e s e n t e d , f i g u r e s momentum  f l u x or Reynolds s t r e s s ,  calculated Reynolds  from  ( i n N/m method  situation.  (pluses),  Run D29D, During  figure  the  32,  is a  typical  N-hr/m ,  which  2  i s 34%  dissipation calculations.  the  September  higher  momentum  than  found  input from  of the  Upon r e a c h i n g t h e peak winds t h e two  a r e i n much b e t t e r agreement and t h e d e v i a t i o n over the  whole r u n i s reduced D33C  from  u n s t a b l e c o n d i t i o n s o f t h e r i s i n g wind  (to hour 22) t h e bulk f o r m u l a g i v e s a t o t a l  methods  34, t h e  f l u x method (squares) and from t h e bulk f o r m u l a o f 6.1  (solid l i n e ) .  2.23  to  o r p a s c a l s . Pa) i s  2  the d i s s i p a t i o n  31  (figure  31)  t o 18%. A f r o n t i s p a s s i n g  t h e tower  in  and a s i m i l a r s i t u a t i o n o c c u r s , b u t w i t h t h e  r i s i n g and f a l l i n g wind e f f e c t s b a l a n c i n g , t h e o v e r a l l d e v i a t i o n i s o n l y 1%.  I n D29D t h e f a l l i n g  wind  and  changing  direction  e f f e c t s a r e not g r e a t enough t o make t h e average s t r e s s from the two  methods  equal.  I t would be expected  a r e s t r o n q l y f e l t a f t e r t h e passage because  as  centers  pass  A  low  pressure  low  after  which  earlier  winds  from  the east  i n s t r u m e n t a t i o n on t h e tower. neutral  they  drop o f f  33.  were  Stability  Unfortunately  obstructed  i s always  by other  very  nearly  o r s l i g h t l y s t a b l e and s h o u l d not have been a f a c t o r i n  c a u s i n g t h e l a r g e observed input  systems,  c e n t e r i s p a s s i n g t o t h e west of the  tower, from south t o n o r t h , i n D31F, f i g u r e the  pressure  t h e winds q u i c k l y f a l l , then r e g a i n  v e l o c i t y as the d i r e c t i o n changes slowly.  of  t h a t these i n f l u e n c e s  s t r e s s e s that give a  total  momentum  over t h e p e r i o d shown of 6.5 N-hr/m , which i s 12% h i g h e r  than g i v e n by t h e b u l k c a l c u l a t i o n s .  2  A  r u n from  March  1977,  145  Q CJ  •  <=>r-  1  i — r  co^-  ZD"  i—i—i—r  i—i—r  1  +++  ++  +  +++++++++++  i—i—r  i—i—i—r  i — i — r  i — i — i — i — i — i — i — i — r  i — i  CO LU  1  6  1  1  1  12  1  1  18  1  1  24  1  1  30  1  1  36  1  1  42  1 1  48  TIME (HOURS) FIGURE 32  Time s e r i e s o f the momentum flux from r u n D29D. Time i s from 17:00 GMT September 26, 1976, and symbols are t h e same as i n f i g u r e 31.  146 D38B, f i g u r e agreement  34 shows t h a t a l l t h r e e methods can be i n e x c e l l e n t  over  a  long  reasonably steady. cumulative  period  of  time  Over t h i s p e r i o d of  momentum  p r o v i d e d the wind i s  nearly  two  days,  the  i n p u t from t h e d i s s i p a t i o n c a l c u l a t i o n s i s  l e s s than 3% h i g h e r than t h a t found from the b u l k f o r m u l a . In  general  dissipation  the  calculations,  of run D29D, f i g u r e only  3  Reynolds  groups  32.  (40  flux  method  The f l u x r u n , T61,  minutes)  starting  i n t e r v a l t h e r e was a sudden 4 m/s h o u r l y a v e r a g i n g smooths.  does agree w i t h T61  is  15  an  average  minutes  of  a f t e r the  I n t h i s 15 minute  i n c r e a s e i n wind speed,  which  The s i m u l t a n e o u s d i s s i p a t i o n run  ( A p p e n d i x ) , i l l u s t r a t i n g t h a t i d e n t i c a l time  i n t e r v a l s are r e g u i r e d T112,  the  but an e x c e p t i o n i s found a t hour 28  b e g i n n i n g of t h e hour 28 d i s s i p a t i o n average.  the  verifies  for  intercomparisons.  The  flux  run,  a t hour 14 of run D33C ( f i g u r e 31) i s a l s o found t o be i n  much b e t t e r agreement  w i t h i t s s i m u l t a n e o u s d i s s i p a t i o n run than  w i t h the h o u r l y average.  Run D33C d i s c l o s e s a sampling  problem  a s s o c i a t e d w i t h the tower o p e r a t i o n of the Reynolds f l u x system. Most of the low wind speed runs were c o l l e c t e d i n September the  drag  coefficients  tend  to  be low.  v a r i a b l e winds seem t o produce some v e r y  when  L a t e r , when t h e more high  coefficients  at  wind speeds below 10 m/s,  t h e Reynolds f l u x system was prevented  from  wind  recording  by  the  speed  limit  Reynolds f l u x d a t a s e t ( f i g u r e 19) t e n d s small  CD's,  exhibit a  trend  measurements. m/s)  6.1  relative with Above  to wind the  6.1,  at  speed  to  setting. be  Thus t h e  biased  toward  t h e low wind speeds and t o range  of  maximum wind speed l i m i t s e t t i n g  (12  f i t s t h e data of f i g u r e  over  the  19 v e r y w e l l .  whole  147  _4  ol  CM  o  T  1  1  1  1  1  1  1  i — i  i — r  1  ++ ++ + +++ +++++++++  r\i"  +  +  i — r  i—r  i—i—i—r~ ++  + +  T—r  i — r  +++  + + + + +  i — r  rn .o"  i — r  i — r  1  1  ~1  1  1  -HH-+++-r+++++-H-  ++  co - i UJ  i — i — i — i — i — i — i — i — i — r  6  FIGURE 33  12  18  24  30  TIME (HOURS)  36  42  1  48  Momentum f l u x time s e r i e s f r c n run D31F. S t a r t i n g time i s 4:00 GMT October 20, 1976. The s o l i d l i n e r e p r e s e n t s the bulk e s t i m a t e s of T .  148  O  + +  ++.-*+++++ + ++++ ++++++ ++ + +  +++  ++  +  +  +  i — i — i — i — r  i—i—r  +  +  + + +  +  ++++  +  i—r  lo!£H +  ZD"  ++ + ++++ +  ++++  + + +  + + + +  T—i—r o" J  i — i  +++++++4.-,.+++++.*•++++++++,  +++++++++++++++++  y  H  a. i  i — i — i — r  i — i — r  + + + + + + + + + + + + + + + + + + + + +  CO  ++  + + + + + + + + + + + + + + + + + +  ++  + + + + +  H  -| 6  1  1 12  1  1 18  1  1 24  1  1 30  1  1 ?6  1  1 42  1  ) 48  TIME (HOURS) FIGURE 34  Momentum f l u x time s e r i e s from D38Bi Time i s from 16:00 GMT March 12, 1977 and symbols are the same as i n f i g u r e 31.  149  I t appears t h a t t h e estimates  of  the  p e r i o d s of a few if  bulk  total  aerodynamic  days or more.  The  bulk estimate  measured or approximated s t a b i l i t y c o n d i t i o n s  are  good  they  may  measures  to  which i s the more a c c u r a t e .  more of the d i s s i p a t i o n  a  estimates  day,  method's  from  methods,  I t i s conceivable  s y s t e m a t i c e r r o r s i n one  assumptions  However, i f t h i s occurred  and  causing  or the  i t i s l i k e l y t h a t the  o v e r a l l s c a t t e r of f i g u r e 28 would be g r e a t e r than in  included.  With comparable e r r o r i n both  t h a t the v a r y i n g winds are producing  discrepancies.  are  of the s t r e s s , but with more v a r i a b l e winds  estimates.  i s not obvious  good  should improve  winds the hourly bulk  c o n s i s t e n t l y d i f f e r , over p e r i o d s up  dissipation  gives  momentum i n p u t or average s t r e s s over  I t has been shown t h a t i n steady  it  method  the  scatter  drag c o e f f i c i e n t s c a l c u l a t e d from other methods, which i s not  observed.  It  is felt  t h a t , s i n c e at l e a s t some of the s c a t t e r  i n measured drag c o e f f i c i e n t s at the same wind dissipation  measurements,  although  ought to f o l l o w changes i n the r e a l bulk  estimates.  not be s t r i c t l y  A bulk formula  subject stress  speed  is  t o random e r r o r s , more  closely  winds.  layer  such  appropriate values with  cases,  a  switch it  may  f o r m u l a t i o n cabable minimal measurement  incorporating  may  a p p l i c a b l e t o short term phenomena, such as wave  following  In  than  based on long term averages  development during a r i s i n g wind or the deepening of an upper  real,  variable  inlet's  from down t o strong up be  possible  to  inlet  devise  an  o f p r o v i d i n g good hourly s t r e s s error.  A  possible  means  wind e f f e c t s would be t o allow the  c o e f f i c i e n t t o depend on the past h i s t o r y of the wind.  of drag  150  6.3  Bulk Aerodynamic  P a r a m e t e r i z a t i o n Of The S e n s i b l e Heat  The s e n s i b l e heat f l u x surface at  i s parameterized  - a i r temperature d i f f e r e n c e .  10m, T10, i s obtained from the  measurement  height,  i n terms  average  temperature  TZ, through eguation 2.11.  TSEA, measured about  exchanges  with t h e atmosphere  by  At the Bedford  of  the  3-hourly  by  a sea  radiation  and  may not be f o l l o w e d e x a c t l y .  On CCGS Quadra a s u r f a c e "bucket" temperature part  a t the  10m below the mean sea l e v e l ,  where t h e h e a t i n g and c o o l i n g of the s u r f a c e heat  cf a  The mean a i r temperature  tower the s u r f a c e temperature, TSFC, i s approximated temperature,  Flux  was  recorded  as  m e t e o r o l o g i c a l o b s e r v a t i o n s . These are  i n t e r p o l a t e d to give hourly TSEA values, which may be a problem, because  the  ship  was  steaming  through  large  sea  temperature g r a d i e n t s during the one run t h a t u s e f u l measurements  were  recorded.  surface  temperature  At any time then, TSEA may d i f f e r  s u b s t a n t i a l l y from a r e p r e s e n t a t i v e s u r f a c e temperature. precaution  that  the  As  a  Stanton number, CT (eguation 2.9), i s not  too a d v e r s e l y a f f e c t e d , data used i n the  p a r a m e t e r i z a t i o n are  r e s t r i c t e d to c o n d i t i o n s with |TSEA-TZ| > 1.0°C, even though the f l u x measurements may s t i l l Figure  35  be r e l i a b l e .  i s a p l o t o f <wt> a g a i n s t 010 .AT (AT=TSEA-T 10) ,  f o r a l l 129 hours of u n s t a b l e temperature data, and a r e g r e s s i o n line  (the average of <wt> a g a i n s t 010  <wt>).  The  23  AT  and  010  AT  hours of data from t h e weathership  pluses) show c o n s i d e r a b l e s c a t t e r , but no from the tower r e s u l t s  (triangles).  against  ( p l o t t e d as  systematic  The r e g r e s s i o n i s  departure  151  FIGURE 35  P a r a m e t e r i z a t i o n of the s e n s i b l e heat f l u x i n °Cm/s in unstable stratification. Triangles represent tower data and p l u s e s are from CCGS Quadra,.  152  <wt>  = 0.00100 U10 AT + 0.0029 °Cm/s  103 CT10 = 1.00 + 2-9(°Cm/s) / (U10 A T ) ,  with  a  correlation  coefficient  of  0.86.  (6.2)  This  is  almost  i d e n t i c a l t o the f o r m u l a g i v e n by F r i e h e and S c h m i t t * 1976, f o r 0<  010 A T  <25 °Cm/s o n l y .  data with  |<wt>|  eliminates  low  R e s t r i c t i n g the parameterization t o  >0.004°Cm/s, heat  flux  010  and  >4.0  m/s  value  | A T | >1°C  s m a l l U10 A T s i t u a t i o n s , but a  p o s i t i v e heat f l u x i s s t i l l p r e d i c t e d a t 010 A T the  and  =  0,  although  o f 0.002 °Cm/s g i v e n by F r i e h e and S c h m i t t , who used  mostly s m a l l h e a t f l u x d a t a , i s p r o b a b l y additional  data  more  realistic.  The  a t h i g h e r s e n s i b l e heat f l u x e s i n d i c a t e t h a t a  s i n g l e p a r a m e t e r i z a t i o n i s a c c e p t a b l e from 010 A T =0 t o p o s s i b l y more than 100 °Cm/s. BIO  tower  data  Again t h i s r e s u l t i s i n a c c o r d  with  the  o f S m i t h , 1979, but t h e average c o e f f i c i e n t i s  much lower than found by Smith and Banke (1975) from  a  limited  number o f Sable I s l a n d measurements. The  sensible  heat  f l u x t i m e s e r i e s from run D33C, f i g u r e  36, shows t h a t seemingly v e r y s m a l l Stanton numbers a r i s e d u r i n g a r a p i d i n c r e a s e i n a i r temperature, j u s t a f t e r negative. also  AT  first  F o r t u n a t e l y , Reynolds f l u x measurements (squares) a r e  available  over  t h i s p e r i o d and t h e i r qood agreement w i t h  the d i s s i p a t i o n method v e r i f i e s t h e t r e a t m e n t o f e q u a t i o n Temperature  spectra  from  the  <wt>  values  from  this  period  are  surface  values.  The  loss  of  that  reasonably accurate.  However, i t i s p o s s i b l e t h a t they are s i g n i f i c a n t l y their  2.21.  Reynolds f l u x r e c o r d i n q s do not  d i s p l a y any e v i d e n c e o f s a l t c o n t a m i n a t i o n , so i t i s f e l t the  goes  less  than  s e n s i b l e heat f l u x w i t h  153  ++  o  +  + + + +  + +  + +  i — i — i — i — i — i — i — i — i — i — i — i — r 24  0  +++++++++  +  k> o inn4  +  ++++  + +" in. i  1——i—i—i 24  0  +++ T — i — i — i — i — r + + +  0  +  CO  1  ^ r + "  +  r  +  24  . ++++++ ++  + + + +  "V.  +++  +  +  " ~ i — i — i — i — i — i — i — i — i — i — i — i — r 6 12 18 24 30 36 42  TIME FIGURE 3 6  (HOURS)  Time s e r i e s o f the s e n s i b l e heat f l u x from run D33C ( f i g u r e 3 1 ) . Time i s from 4:40 GMT December 7, 1976. Hs i s from t h e d i s s i p a t i o n ( p l u s e s ) , Reynolds f l u x (squares) and bulk ( s o l i d l i n e ) methods;.  154 h e i g h t was d i s c u s s e d heating  i n section  and  i f the  0.5°C/hour  were due s o l e l y t o t h e v e r t i c a l f l u x d i v e r g e n c e , then a  40% l o s s i n f l u x at 13m would be low  2.1  CTN  values  observed  expected.  Qualitatively  the  can be e x p l a i n e d by s p e c u l a t i n g t h a t  <wt> was measured above t h e " c o n s t a n t s e n s i b l e heat f l u x "  layer,  s i n c e i f t h i s were t h e c a s e , the percentage o f t h e  should  decrease  as  t h e magnitude  of t h e s u r f a c e f l u x i n c r e a s e s and no  l o s s s h o u l d be e v i d e n t a f t e r there  i s probably  a  are  other  <wt>'s  at  a  temperature.  less  loss  of  flux  with  a  great  degree  so  possibly  of  about  Another 10m  possibility  I n the 12 hours p r i o r t o run D33C t h e r e  little  and  of  temperature,  about  20°C.  was  I t appears  as  i f  the  very  surface  mixing  the  unstable It  and  water i s not  the  wind  column,  increased,  TSEA a c t u a l l y  impossible  that  the  h e a t i n g produced by t h e l a t e r h i g h a i r t e m p e r a t u r e s was  p r e v e n t e d from m i x i n g down t o the sea temperature probe then  that  TSFC, may have become much c o l d e r than TSEA d u r i n g  decreased from 3.9 t o 3.5°C. surface  is  t h e a i r t e m p e r a t u r e was below -15°C, g i v i n g a  t h i s t i m e , because as t h e a i r warmed presumably  the  i s not t r a c k i n g t h e s u r f a c e  temperature.  huge AT  height.  do n o t d i f f e r from t h e s u r f a c e f l u x by as much  depth  wind  However,  d e a l of h e a t i n g due t o h o r i z o n t a l  as t h e low CTN's would s u g g e s t . TSEA  peak  s i t u a t i o n s of r i s i n g temperature which do not  seem t o be a f f e c t e d t o such measured  the  great  a d v e c t i o n , which would mean There  loss  stable  upper  water column*  by  the  I n t h i s s i t u a t i o n TSEA c o u l d  become l e s s t h a n TSFC by enough t o produce t h e observed b e h a v i o r of D33C and t o upset t h e p a r a m e t e r i z a t i o n o f the flux.  There  sensible  heat  was o n l y one o t h e r s i m i l a r s i t u a t i o n a t the tower  155 and even lower Stanton numbers were c a l c u l a t e d , but were  rejected  on  the  basis  of abnormal temperature  Despite the preceding arguments, lower than may  occur  in  the  circumstances  i n c l u d e d i n the p a r a m e t e r i z a t i o n  Figure  and  data  spectra.  CT  values  but they a r e not  period of D33C i s not  analysis  of  the  stable  flux. 37  is  a p l o t of -<wt> a g a i n s t -010 (TSEA-T10) from  131 hours of s t a b l e s t r a t i f i c a t i o n p l o t t e d as c r o s s e s . and  average  described,  l i k e l y t o occur over t h e open sea, so t h i s  s e n s i b l e heat  these  -010 A T  with the suspect D33C r e s u l t s  The r e g r e s s i o n s of  against  -<wt>  for  the  -<wt> 123  against triangles  c o r r e l a t i o n c o e f f i c i e n t of 0.93 and when averaged  <wt>  =  103 CT10 =  0.00075 010 A T  have  a  yield  + 0.0020 °Cm/s  0.75 + 2.0(°Cm/s) /  which i s a l s o p l o t t e d on f i g u r e 37.  -010 A T  (010 A T ) ,  (6.3)  Again a p o s i t i v e heat  flux  of about 0.002 °Cm/s a t 0 AT=0 i s i n d i c a t e d even though t h e r e i s no data with |0 A T | < 5°Cm/s. lessens  the  slope  to  about  I n c l u s i o n of the suspect D33C data 0.00065.. F r i e h e and Schmitt only  considered data with 0 A T > -15°Cm/s and t h e i r suggested d i f f e r s from 6.3 by only 10% at 0 A T = -15°Cm/s. a  formula  There a r e only  few data p o i n t s beyond 0 A T = -35°Cm/s t h a t c o n t r i b u t e t o 6.3,  which, t h e r e f o r e , cannot be expected more  negative  0 AT's.  The  BIO  to tower  be  r e p r e s e n t a t i v e of  results  (Smith,  1979)  c o n t a i n more, l a r g e negative heat f l u x runs and suggest a l a r g e r CT10 of about 0.00083. 6.3 by about  Although the BIO r e g r e s s i o n d i f f e r s  13% at U A T = -100 °Cm/s, the data  points  from  overlap  156  FIGURE  37  P a r a m e t e r i z a t i o n of the s e n s i b l e heat f l u x (°Cm/s) in stable s t r a t i f i c a t i o n . Crosses are from D33C. S o l i d l i n e i s a r e g r e s s i o n of the t r i a n g l e s only*  157  very  well.  A s i n g l e p a r a m e t e r i z a t i o n o f t h e s e n s i b l e heat  in stable s t r a t i f i c a t i o n  should  adequately  describe  flux  a l l  the  measurements, but i t appears t o d i f f e r from t h e u n s t a b l e c a s e . It  i s felt  that  the u n c e r t a i n t y  q r e a t e r than i n <wt>, so band bands  of  averaqinq  i n U10 Al i s perhaps i s carried  out  over  <wt> and t h e r e s u l t s a r e t a b u l a t e d i n t a b l e X I I .  band averages a r e r e a s o n a b l y w e l l d e s c r i b e d by 6.2 and 6.3  The over  the e n t i r e range of measurement, thus l i n e a r f i t s t o t h e d a t a of figures  35  and  37 a r e a p p r o p r i a t e .  The r a t i o o f t h e averages  g i v e s a CT10 f o r each band and t h e u n s t a b l e v a l u e s higher  than t h e s t a b l e ones.  value  of  clearly  The i n d i v i d u a l p o i n t s a r e f a r t o o  few and s c a t t e r e d f o r any t r e n d s t o be seen. 103CT10  are  F o r example, t h e  1.21 i n t h e 0.05 t o 0.07 °Cm/s band, becomes  1.04 i f U10A.T i s i n c r e a s e d by o n l y 1/2 a s t a n d a r d d e v i a t i o n .  Stability The  Effects stability  dependence o f t h e n e u t r a l S t a n t o n number i s  examined i n f i g u r e 38, where a g a i n s t Z/L.  123  stable  which  respectively. base are  eguation  2.12,  The s o l i d l i n e s r e p r e s e n t t h e o v e r a l l  129 u n s t a b l e  about  CTN,  the  =  0.69  1 0 CTN  =  1.08 ,  3  3  standard  deviations  conclusions, independent  averages:  (6.4)  a r e 0.16  There i s n o t a g r e a t d e a l o f  definitive reasonably  1 0 CTN  i s plotted  data  and  on  0.36,  which  to  but i t appears as i f CTN and Zot of  Z/L  i n stable  and  unstable  158 r  Range o f <wt> i °Cm/s 0.C9,  Average <wt> T ±1 s t a n d a r d I Average 010AT d e v i a t i o n I ±1 s t a n d a r d | deviation .0,98 +.007 | 84.9 ±30  0.11  T~  -  -•r-  i  | 103 CT10| Number | | r a t i o of| of | | averagesi runs | | 1. 15 | 4 I  1  1 1  0.07,  0.09  l  .080  ±.007  |  79.0 ±16  |  1.01  |  7  1  0.05,  0.07  1  .058  ±.005  |  47.9 ±16  |  1.21  |  15  |  C.03,  0.05  1  .038  ±.007  |  35.5 ±13  |  1.07  |  38  |  0.01,  0.03  .023  ±.005  |  22.0 ±8.2  |  1.05  |  58  |  J  i  |  0.006, 0.01  l  .007  ±.0C1  I  9.86 ±1.7  |  0.71  |  7  |  l -.01, -.004  j I i  .008  ±.002  |  13.7 ±3.6  |  0.59  I  43  |  .014  ±.003  |  22.4 ±8.4  |  0.62  |  55  |  .025  ±.003  |  34.0 ±6.0  |  0.74  |  19  |  .035  |  50.3  |  0.70  |  3  I  .057  I  71.6  |  0.80  |  3  I  _  J.  i  -.02, -.01 -.03, -.02 -.05, -.03  i l  -.07, -.05  JL-  L  TABIE X I I  .J  •  P a r a m e t e r i z a t i o n o f t h e s e n s i b l e heat f l u x by a v e r a g i n g 0 AT over ranges o f <wt>.  stratification  separately.  mean CTN a t Z/L=0, i m p l i e s  However, a  parameter  that  dramatic  stability,  but t h a t  dependence  as  changes  change  character  otherwise  i s indicated  by  band  the d i s c o n t i n u i t y i n the  f e a t u r e c o u l d be i n c o r p o r a t e d i n t o t h e t h e o r y a  i  has very  i n Zot.  This  by r e l a t i n g Zot t o  abruptly little  at  neutral stability  t h e r e l a t i v e c o n s t a n c y of t h e  FIGURE 38  The n e u t r a l Stanton number as a f u n c t i o n of stability. Solid l i n e s r e p r e s e n t t h e mean i n both s t a b l e and u n s t a b l e s t r a t i f i c a t i o n .  160  average CTN away from Z/L=0. There i s a g r e a t d e a l o f s c a t t e r i n f i g u r e 38 and i t should be r e i t e r a t e d t h a t microbead could  only  be  contamination  by  salt  particles  checked a t t h e few, sometimes i n f r e g u e n t , times  f o r which s p e c t r a were a v a i l a b l e from t h e Reynolds f l u x  system.  I t i s t h e r e f o r e p o s s i b l e t h a t some contaminated data has escaped notice  and  Z/L<0.  i s responsible  Similarly,  oppositely  f o r some o f t h e high CTN v a l u e s a t  because  correlated  temperature  i n stable  and  humidity  s t r a t i f i c a t i o n , contaminated  d a t a may be r e s p o n s i b l e f o r some low CTN's a t Z/I >0. CT10  The  high  v a l u e s f o l l o w i n g hour 40 o f r u n D38B ( f i g u r e 39) a r e g u i t e  l i k e l y a r e s u l t of bead c o n t a m i n a t i o n , run  are  because a  Reynolds  flux  a t about hour 44 was r e j e c t e d on t h e b a s i s of a l a c k of low  f r e g u e n c y v a r i a n c e i n t h e t e m p e r a t u r e spectrum and  the run a t  hour 41 was a b o r d e r l i n e c a s e .  Win d Speed E f f e c t s Equation increase  with  counteract by  2.12 r e l a t e s CTN t o Zo, i n d i c a t i n g t h a t i t s h o u l d wind  speed  above  t h e i n c r e a s e i n Zo.  10  m/s,  i f Zot  The s i t u a t i o n may be  does  not  complicated  the observed dependency o f Z o t on Z/L, which c o r r e l a t e s with  wind speed.  The e f f e c t of wind speed on CTN i s i n v e s t i g a t e d f o r  the  and  stable  respectively.  unstable  case  to  tables  XIII  and  I n t h e s t a b l e case t h e r e i s no i n d i c a t i o n  i n c r e a s e i n CTN with wind speed. begins  in  increase,  t h a t CTN d e c r e a s e s .  there  XIV of an  I n f a c t above 10 m/s where CDN  i s a h i n t , a l b e i t not s i g n i f i c a n t ,  I n t a b l e XIV t h e means a r e s c a t t e r e d ,  but  161 Wind speed range (m/s) 6  to  8  8  to  10  Number o f runs  +-  T  Mean 10 CTN ±1 s t a n d a r d deviation 3  1  Minimum  19  0.71  ± .18  0. 43  1. 12  10  39  C.73  + .17  0.47  1.61  to  12  25  0.65  ± .14  0.36  0.98  12  to  14  26  0.69  ± .13  0. 44  0.88  14  t o 18.2  14  0.62  ± .20  0. 29  0. 88  TABLE X I I I  again  Averaged n e u t r a l Stanton number as a f u n c t i o n o f wind speed i n s t a b l e s t r a t i f i c a t i o n o n l y .  there  seems  to  be  no  obvious  wind speed dependency.  However, n e a r l y a l l of the data i n t a b l e XIV above 18 from  CCGS Quadra, which d i d not r e a l l y  lower wind speeds t o results.  There  fully  over  m/s  the  ship  and  shallow  Larger  water by Francey  CTN  values  by run D33C, f i g u r e 36, where t h e i n c r e a s e i n 0Z  13 m/s  +  3  10  from  (hours 7 t o 10) i s accompanied by a s h a r p r i s e i n  CTN from about 1.0 t o 1.4x10~ . above  010  The c o n t e n t i o n t h a t CTN i n c r e a s e s w i t h 010 i s a p p a r e n t l y  supported to  are  and G a r r a t t , 1978, who 3  10  tower  i s a s u g g e s t i o n i n t a b l e XIV t h a t t h e u n s t a b l e  f i n d an i n c r e a s e w i t h wind speed g i v e n by 10 CTN = 0.083 0.48.  come  y i e l d enough data a t the  intercompare  CTN i n c r e a s e s from U10 = 10 t o 18 m/s. reported  1  I Maximum  The  rise  i n CTN  with  winds  m/s appears t o be g r e a t l y p e r t u r b e d by the t r a n s i t i o n  to s t a b l e s t r a t i f i c a t i o n and a l t h o u g h t h e f o l l o w i n g s t a b l e are s u s p e c t , t h e  rise  seems  to  subsequently  continue.  data No  162 1  -  —  "  I I  Wind speed range (m/s)  1  5.5  1  8  1 I  to  "i— - — — _ | Maximum I Minimum  - T— Mean 10 CTN Number | +1 s t a n d a r d of r u n s | deviation  ,„ _  3  T  8  I  32  |  1.13  to  10  !  29  |  0.94  10  to  12  i  25  |  12  to  14  11  |  I  14  to  18 —!  13  |  1.31  ± .24  |  0.43  |  I  18  to  22  13  |  1.14  ± .28  |  0.78  I  |  22 t o  26  0.90  ± .06  |  0.85  |  |  0.56  |  2.28  ± .28  |  0.54  |  1 .47  1.06  ± .34  |  0.64  |  2.21  1.13  ± .24  |  0.71  |  1 .38  ± -47  i  — ii—  2.01  ...  i  ^  i•  1 .76  •  i ,  1 •  i  TABLE XIV  definite  •  conclusion  i s p o s s i b l e because of the l a c k of d a t a and  data  were  included  For example, i f t h e  i n the 14 t o 18.2 m/s  X I I I , t h e band average would d e c r e a s e g i v i n g a the  •  •  Averaged n e u t r a l S t a n t o n number as a f u n c t i o n of wind speed i n u n s t a b l e s t r a t i f i c a t i o n o n l y .  the s t r o n g i n f l u e n c e o f s t a b i l i t y . D33C  i  0.99  highest  suspect  range of t a b l e  smaller  CTN  at  speed, even though t h e s e a d d i t i o n a l CTN's i n c r e a s e  w i t h wind speed. These r e s u l t s do n o t , t h e r e f o r e , r u l e out that  CTN  follows  the  because t h i s t r e n d i s  wind not  speed dependency  supported  by  the  the  possibility  of Zo.  However,  Quadra  results,  because of the l i m i t e d amount of d a t a , some o f which i s p o s s i b l y contaminated not  fully  (run  D38B), and because the s t a b i l i t y e f f e c t s are  understood,  the  neutral  Stanton  number  is  not  163 formulated  as  observation  t h a t , on a v e r a g e , CTN  nearly  a  e g u a l t o CDN  Z o t - 0.0058 cm. 10  f u n c t i o n of wind speed.  m/s  with  f o r 4.0<  I t i s an i n t e r e s t i n g  f o r Z/KO,  010  <10  m/s,  0. 00 108,  is  very  0.00114, i m p l y i n g  I t i s p o s s i b l e t h a t Zot remains c o n s t a n t CTN  increasing  c o u l d be o b t a i n e d g i v e n from a CDN  due  t o Zo.  from an e x p e r i m e n t a l l y formulation,  Zo=  above  If this i s true,  determined Zot and  using e q u a t i o n  CTN a Zo  2.12.  Method Comparison The solid  b u l k e s t i m a t e s of the s e n s i b l e heat f l u x shown  lines  of  figures  s t a b i l i t y dependent CTN 2.3,  the  neutral  36  39,  g i v e n by 6.4.  Stanton  measurement h e i g h t ,  and  wind speed and  outlined  in  stability.  The  the  section  i s c o n v e r t e d t o a CT  e s t i m a t e s found from <wt> = CT OZ AT,  the  are c a l c u l a t e d from As  number  by  at  the  e r r o r i n bulk  e g u a t i o n 2.9,  i s about  2%  from  0Z, perhaps 10% from CTN  and o n l y 5% from Z/I, because the  bulk  stability  always  considerable  estimate  e r r o r i s introduced  be i n e r r o r by 0.5°C. 10%,  making  the  u n c e r t a i n than possible  those  error  and  through AT,  sensible of  the  heat  momentum  In  which may of 5°C,  flux  addition sometimes  the e r r o r i s  c a l c u l a t i o n s more  flux.  With  a  d i s s i p a t i o n e s t i m a t e s i n the  estimates  (pluses),  e x c e l l e n t agreement between t h e two sensible  large  problems w i t h the d a t a , i t i s d i f f i c u l t t o time  series.  Reynolds f l u x c a l c u l a t i o n s (sguares) l e n d c r e d i b i l i t y  dissipation  the  available.  Even w i t h a l a r g e AT  bulk  compare the b u l k and The  is  because methods.  of  the  Figure  heat f l u x time s e r i e s from run D38B and  momentum f l u x of f i g u r e 34)  the b u l k , eddy c o r r e l a t i o n  to  the  generally 39  shows  (like  the  and  the  164  2Z . - M l .  E*~ I  ifi±  COo  12.  i — r  i — r  24  CM  ++++ +++  o O  A +  + ++ ++  ++  + +  +  i — i — i — r  24  CO  2ZoJ  +++  +  ZD  ~ i — i — i — i — i — i — i — i — i — i — r 12  18  24  30  36  42  TIME (HOURS) FIGOEE 39  S e n s i b l e heat f l u x time s e r i e s from r u n D38B ( f i g u r e 3 4 ) . Time i s from 16:00 GMT March 12, 1977 and symbols a r e t h e same as i n f i g u r e 36.  165  dissipation  estimates  of  the  sensible  agree f o r a c o n s i d e r a b l e l e n g t h sensible  heat  flux  of  combination capable  time.  parameterization  r e s u l t s of F r i e h e and S c h m i t t ,  heat f l u x c o n t i n u e On  is  1 9 7 6 , and  the  whole  compatible Smith,  the  with  1979,  to  so  the a  of a l l a v a i l a b l e data s h o u l d g i v e a C T N f o r m u l a t i o n days  or  more) of s e n s i b l e heat f l u x v a l u e s , depending on the a c c u r a c y  of  AT.  of p r o v i d i n g r e a s o n a b l e  However,  lived  as  situations,  parameterization, s t r i c t l y apply. causing  the  calculations  with as  the  averages (over  few  momentum f l u x , t h e r e may  possibly  valid  a  for  seen long  in  term  D33C,  averages,  be  short  where does  I t i s a l s o p o s s i b l e t h a t erronous A T values  difference between  between  hours  2  and  the 10  bulk of  has been d i s c u s s e d , between hours 1 2 and  D33C,  24.  and figure  a not are  dissipation 36  and,  as  166 CHAPTER 7  SUMMARY AND CONCLUSIONS  The  experimental  program  described  in  this  thesis  s u c c e s s f u l l y measured t h e momentum and s e n s i b l e heat f l u x e s over the  sea  a t winds between 4 and 26 m/s.  As hoped, a g r e a t many  hours o f momentum f l u x data were s u i t a b l e f o r a n a l y s i s , b u t much l e s s s e n s i b l e heat f l u x and no m o i s t u r e f l u x data were found be r e l i a b l e . sensors  Success depended c h i e f l y on t h e performance  to  of t h e  and on t h e e s t a b l i s h m e n t of t h e d i s s i p a t i o n method as a  v i a b l e means of measuring  the fluxes of  momentum  and  sensible  heat. The  velocity  problems w i t h sensor  was  sensor worked very w e l l , t u t t h e r e were some  the  temperature  found  to  s a l t - a i r environment. operated  be  measurements  suitable  The G i l l t w i n  and  no  humidity  f o r remote o p e r a t i o n i n a propeller-vane  anemometer  f o r p e r i o d s o f more than a month i n adverse c o n d i t i o n s  without s e r v i c i n g .  I t provided the f l u c t u a t i n g  horizontal  and  v e r t i c a l v e l o c i t i e s t o t h e Reynolds f l u x system and responded t o t h e lower f r e q u e n c i e s of t h e downstream v e l o c i t y spectrum's -5/3 region  sufficiently  f o r the  i n f e r r e d , although the determined.  The  propeller  distance  molecular  dissipation  responses  first  had  The  microbeads  was r e c o g n i z e d by t h e l a c k o f low freguency  t h e temperature  sensitivity  spectrum,  but only  of  salt  the angle  attack.  in  t o be  c o n s t a n t was found t o depend on t h e  type and weight of p r o p e l l e r , t h e wind speed and humidity  t o be  of  contaminated variance  sometimes were o t h e r  c h a r a c t e r i s t i c s , such as t h e absence o f a -5/3 r e g i o n , observed.  167 T h i s b e h a v i o r r e m a i n s a major problem w i t h t h e remote of to  this  type of sensor.  operation  The response of t h e microbeads seemed  be l i m i t e d by i t s p r o t e c t i v e e n c l o s u r e and was d e s c r i b e d by a  d i s t a n c e c o n s t a n t o f about 0.90m, which i s adequate f o r b o t h t h e Reynolds f l u x and d i s s i p a t i o n methods. Reynolds f l u x measurements  from  the Bedford  tower  were  shown t o be r e a l i s t i c by comparisons with s p e c t r a , c o s p e c t r a and turbulence  statistics  from p r e v i o u s s t u d i e s .  I n a d d i t i o n , the  drag c o e f f i c i e n t s and S t a n t o n numbers were g e n e r a l l y  comparable  to  the r e s u l t s of S m i t h , 1979, however t h e r e i s p r o b a b l y a b i a s  to  s m a l l drag c o e f f i c i e n t s a t low wind speeds as a r e s u l t of t h e  Reynolds f l u x spectra  and  sampling. cospectra  Universal  shapes  f o r the  velocity  i n both t h e s t a b l e and u n s t a b l e c a s e s ,  were found from averages over the 196 momentum f l u x r u n s . only  60  temperature  runs  available,  uncertainty i n the normalized cospectrum.  there  temperature  was c o n s i d e r a b l e spectrum  and  w,t  The i n t e g r a t i o n of a l l c o s p e c t r a began a t n=0.004,  then t h e u n s t a b l e and s t a b l e 0uw (f) and t h e u n s t a b l e and •wt (f)  With  stable  i n t e g r a l s were m u l t i p l i e d by 1.06, 1.005, 1.10 and 1.04,  r e s p e c t i v e l y , i n o r d e r t o account  f o r t h e lower  freguencies.  T h i s method was found t o p r e s e r v e c o v a r i a n c e , on average, and t o reduce the  the scatter  i n eddy c o r r e l a t i o n measurements caused by  u n c e r t a i n low f r e q u e n c y c o n t r i b u t i o n s t o t h e f l u x e s .  168  R e l i a b l e Reynolds f l u x e s t i m a t e s were needed f o r comparison w i t h s i m u l t a n e o u s d i s s i p a t i o n c a l c u l a t i o n s and  the  method  same r e s u l t s * on  was  average.  shown  to  give  the  The agreement between t h e two methods was found t o  b e s t when t h e magnitude most  essentially  dissipation  stable  of the f l u x e s was l a r g e .  stratification  (Z/L>0.05),  be  In a l l but t h e  U*DISS1  ,  the n e u t r a l  d i s s i p a t i o n method, which does not r e q u i r e an e x p l i c i t s t a b i l i t y parameter, was found t o be i n q u i t e good about  with  2055)  agreement  eddy c o r r e l a t i o n v a l u e s o f u*.  (to  The agreement  between the two t e c h n i q u e s improved, p a r t i c u l a r l y the heat  flux  profiles  incorporated  into  and  the  the  buoyant  dissipation  production  method  (u*DISS2  These c o r r e c t i o n s i n v o l v e d the s t a b i l i t y  <wt>DISS2).  which a b u l k e s t i m a t e Z/L(AT) was shown t o be  a p p r o x i m a t i o n , on average.  u*DISS  where  the  sensible  c a l c u l a t i o n s , when t h e s t a b i l i t y m o d i f i c a t i o n of the  logarithmic  for  within  =  0.96  A l i n e a r regression  u*FL0X  +  0.025  m/s  a  were and  parameter, reasonable  gave  ,  p o s i t i v e o f f s e t r e s u l t s from a tendency f o r <uw>DISS  t o be g r e a t e r t h a n <uw>FL0X by more than 3 0 % , i n the most s t a b l e runs at  (Z/L>0. 1 0 ) .  a l l wind  In near n e u t r a l c o n d i t i o n s  speeds  w i t h i n 4 % , on average.  the  (-0.45  =  The agreement between t h e s e n s i b l e  1.04  0.05)  momentum f l u x c a l c u l a t i o n s agreed t o  f l u x c a l c u l a t i o n s was v e r y good, w i t h a r e g r e s s i o n  <wt>DISS  <Z/L<  <wt>FL0X.  giving  heat  169 The  Bedford  tower  experiment  established  d i s s i p a t i o n e s t i m a t e s o f both the momentum fluxes CCGS  and  that r e l i a b l e sensible  heat  and t h e bulk e s t i m a t e s o f Z/L c o u l d be o b t a i n e d from the Quadra.  dissipation  A  favourable  drag  comparison  coefficients  showed  of  ship  and  tower  t h e B e d f o r d tower t o be  e s s e n t i a l l y an open ocean s i t e , which a l l o w e d t h e combined hours  of  momentum  flux  and  260  1591  hours of s e n s i b l e heat f l u x  measurements t o be c o n s i d e r e d as a s i n g l e open ocean d a t a s e t . The d i s s i p a t i o n d a t a showed t h e n e u t r a l drag c o e f f i c i e n t t o depend on wind speed, as approximated by  103CDN  =1.14  103CDN  =  4 < 010 <  0.49 + 0.065 010  10 < 010 <  10 m/s 26 m/s.  Below 10 m/s t h e v a r i a b i l i t y o f CDN w i t h wind speed, f e t c h , stability  was  minimal,  <  5%  on  average.  Time  series  c a l c u l a t e d CDN's d i s p l a y e d about a 10% random f l u c t u a t i o n . e s t i m a t e s o f t h e momentum f l u x formulation  by:  were  obtained  f i r s t , s h i f t i n g t h e measured  w i t h an i t e r a t i v e t e c h n i q u e i n v o l v i n g CDN; CDN;  third,  shifting  CDN  from  applying  the  of Bulk  above  wind speed t o 10m  second,  calculating  t o CD (the drag c o e f f i c i e n t a t t h e  measurement h e i g h t , Z, wind speed, OZ, and s t a b i l i t y fourth,  and  Z/L(AT) ) ;  t h e b u l k aerodynamic f o r m u l a -<uw> = CD 0 Z . 2  I t was shown t h a t t h e n e g l e c t o f Z/L would produce a minor e r r o r i n the c a l c u l a t e d 010 and CDN, but t h a t t h e CD found i n s t e p could  be  affected  by  as much a s 20%.  However t h i s e r r o r was  reduced t o 5% by u s i n g t h e bulk s t a b i l i t y e s t i m a t e . the  3  Errors i n  CDN f o r m u l a t i o n , OZ and Z/L c o u l d add up t o 15% i n t h e b u l k  170  e s t i m a t e s , which were  seen  to  give  a  good  measure  o f the  momentum f l u x averaged over a few days o r more and a good average the  when t h e wind was s t e a d y .  Over p e r i o d s of up t o a day,  b u l k and d i s s i p a t i o n c a l c u l a t i o n s  differ  by as much a s 30%.  were seen t o  consistently  These d i s c r e p a n c i e s were found t o be  a s s o c i a t e d w i t h v a r y i n g winds, being  hourly  with  the  dissipation  estimate  s m a l l e r on t h e r i s i n g wind and l a r g e r on t h e f a l l i n g wind  or a f t e r a change i n wind d i r e c t i o n . that  The c o n c l u s i o n  drawn  was  t h e s u r f a c e roughness and hence drag c o e f f i c i e n t depend on  s u r f a c e parameters which are a p r o d u c t o f b o t h p a s t and  present  winds. A  c o n s t a n t n e u t r a l 10m drag c o e f f i c i e n t was found t o be an  adequate d e s c r i p t i o n  of almost a l l r e c e n t measurements o v e r deep  water, throughout t h e wind speed r a n g e , 4 t o 10 m/s. of  the constant  v a r i e d from about 1.1x10~  3  The  t o 1.3x10~ . 3  value This  b e h a v i o r has been found by the eddy c o r r e l a t i o n , d i s s i p a t i o n and p r o f i l e methods, but measurements from onshore o r s h a l l o w  water  sites  wind  speed  ocean  would  often  dependency. be  a  distinctly  different  A r e a s o n a b l e compromise over t h e open  t o use 10 CDN = 1.2 i n t h e b u l k aerodynamic method f o r winds 3  up t o 11 m/s. of  displayed  this  At 010 = 11 m/s, t h e h i g h wind  study,  10 CDN 3  speed  regression  = 0.49 + 0.065 010 = 1.2 .  Since t h i s  r e g r e s s i o n f i t s t h e o n l y o t h e r l a r g e s e t of open sea speed the  data  high  wind  (Smith, 1979), i t s h o u l d g i v e s a t i s f a c t o r y CDN's at  h i g h e r wind speeds  (to a t l e a s t 26 m/s).  171 I t was n e c e s s a r y  t o parameterize  the  sensible  d i f f e r e n t l y i n s t a b l e and u n s t a b l e s t r a t i f i c a t i o n . of  heat  flux  The m a j o r i t y  t h e data were i n t h e ranges -40 <U10 A T < 60°Cm/s, -0.3 <Z/L<  0.1 and 6 <D10< 18 m/s, f o r which e i t h e r  or  103<wt> = 1.00 D10 A T + 2.9 °Cm/s  stable  103<wt> = 0.75 010 A T + 2.0 °Cm/s  unstable  103CTN  =  1.08  103CTN  =  0.68 ,  unstable stable  described the r e s u l t s .  More measurements of CTN were needed  order  deny  to  confirm  or  suggested by some o f t h e d a t a .  in  a wind speed dependency, which was Bulk estimates of  the  sensible  heat f l u x were o b t a i n e d w i t h <wt> = CT OZ AT, where CT was found from  Z/L,  CDN, CD and t h e s t a b i l i t y dependent CTN.  were comparable t o those o f t h e b u l k except  f o r the  uncertainty  i n AT,  c o n s i d e r a b l e e r r o r depending on i t s  momentum  flux  estimates,  which  could  have added  magnitude.  t h a t a l l a v a i l a b l e d a t a are r e a s o n a b l y  The e r r o r s  It  was  noted  c o n s i s t e n t , making a good  p a r a m e t e r i z a t i o n of t h e s e n s i b l e heat f l u x  feasible.  172 REFERENCES Antonia, R. A., A. J . Chambers, S. R a j a g o p a l a n , K. R. S r e e n i v a s a n and C. A. F r i e h e , 1978: Measurement of t u r b u l e n t f l u x e s i n Bass S t r a i t . J . Phys- Oc., 8: 28-37. Banke, E. G. and S. D. 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THE INTERCOMPARISON RESULTS  |  1  RUN  TIME GMT  1  —r T1 17:00 17/ 9 6. 4 T2 18: 00 17/ 9 6. 4 T3 19:00 17/ 9 6. 1 T4 20: 00 17/ 9 6. 3 T5 21:00 17/ 9 6. 3 T6 3:00 18/ 9 6. 8 T7 4:00 18/ 9 7. 7 T8 5: 00 18/ 9 7. 3 T9 0 :00 19/ 9 5,.8 T 10 1: 00 19/ 9 6. 1 T1 1 2:00 19/ 9 6. 2 T12 3: CO 19/ 9 6. 8 T13 14:00 19/ 9 6. 8 T14 18: 00 19/ 9 6. 0 T15 19:00 19/ 9 6. 7 T16 20: 00 19/ 9 8. 4 T17 21:00 19/ 9 9. 5 T18 22:00 19/ 9 10. 4 T19 23:00 19/ 9 9. 0 T20 0: 00 20/ 9 8. 5 T21 1:00 20/ 9 9. 2 T22 2: 00 20/ 9 8. 6 T23 3:00 20/ 9 7. 3 T24 4: CO 20/ 9 6. 8 T25 5:00 20/ 9 6. 6 T26 6: 00 20/ 9 7. 0 T27 7:00 20/ 9 7. 4 T28 8: 00 20/ 9 7. 6 T2 9 9:00 20/ 9 7. 7 T30 14: 00 20/ 9 7. 3 T31 15:00 20/ 9 6. 9 T32 16: 00 20/ 9 8. 0 T33 17:00 20/ 9 7. 5 T34 18: 00 20/ 9 5. 9 T35 5:00 21/ 9 7. 2 T36 6: 00 2 1 / 9 6. 8 T37 7:00 21/ 9 7. 5 T38 8: 00 21/ 9 8. 7 T39 9:00 21/ 9 8. 3 T40 10: 00 2 1 / 9 8. 2 T41 11:00 21/ 9 8. 4 T42 12: 00 21/ 9 9. 1 T43 13:00 21/ 9 8. 6 uzj 14: 00 21/ 9 8. 6 T45 15 :00 21/ 9 9. 0 T46 16: 00 21/ 9 9. 5 T47 19:02 23/ 9 9. 9 T48 20: 00 23/ 9 10. 1 T4 9 23:00 23/ 9 11. 7  1 ••  -1•  T  L  R  1i  1—  DATE UZ (M/S) TZ TSFC 1976 °True °C • —i  232 240 243 236 235 238 232 243 233 233 228 236 167 199 214 209 213 212 217 226 230 234 231 236 238 233 238 250 244 220 220 221 220 220 201 204 198 197 193 190 182 178 182 180 183 183 231 230 224  1  1  1  Z/L  u* (m/s)  FLUX DISS ... . ir r 16.8 17. •5 -. 12 0. 197 0. 193 16.6 17. 5 -.13 0. 173 0. 171 16.6 17. 5 -. 16 0. 158 0. 166 16.3 17. 5 -.17 0. 197 0. 167 16.3 17. 5 -.18 0. 195 0. 177 17.1 17. 5 -.09 0. 176 0. 224 17. 2 17. 5 -.05 0. 229 0. 244 16. 9 17. 5 -.08 0.225 0. 240 17. 1 16. 7 0.00 0.185 0. 215 17.2 16. 7 0.01 0. 179 0. 211 17. 1 16. 7 -.01 0. 192 0. 207 17.0 16. 7 -.01 0. 187 0. 217 16.7 16. 3 -.01 0.227 0.250 17.4 16. 0 0.09 0. 164 0. 170 17.3 16. 0 0.07 0. 190 0. 192 16.9 16. 0 0.02 0. 207 0. 235 16.9 16. 1 0.02 0.296 0.291 17.0 16. 2 0.01 0.349 0. 326 16.9 16. 6 -.01 0. 324 0.286 16.8 16. 8 -.03 0.287 0. 270 16.6 16. 8 -.04 0.326 0. 285 16.3 16. 9 -.06 0. 266 0. 272 16. 2 16. 8 -.09 0. 242 0. 2 34 16.2 16. 8 -.10 0. 220 0. 229 16. 2 16. 8 -. 10 0. 200 0.247 16.2 16. 7 -.08 0.220 0.238 15.7 16. 4 -.08 0.240 0. 229 15.3 16. 3 -.11 0.221 0. 228 14. 8 16. 3 -.14 0. 202 0. 213 16.7 16. 3 0.00 0.219 0. 204 16.8 16. 4 -.00 0. 187 0. 191 16.3 16. 4 -.03 0.244 0. 239 16. 8 16. 6 -.02 0.240 0. 235 17.3 16. 7 0.01 0. 168 0. 180 17. 1 16. 8 -.01 0. 246 0.267 17.3 16. 9 -.00 0.222 0. 242 17. 4 16. 9 0.01 0.242 0. 264 17.5 17. 0 0.00 0.267 0. 290 17.6 17. 1 0.00 0. 258 0.270 17.9 17. 2 0.01 0. 290 0. 267 18.0 17. 2 0.02 0.259 0.273 18.3 17. 2 0.04 0.238 0. 253 18. 4 17. 2 0.04 0. 263 0. 277 18.4 17. 3 0.03 0. 278 0. 285 18. 6 17. 4 0.04 0.295 0. 302 19.0 17. 4 0.05 0.302 0. 317 16. 4 16. 9 -.04 0.362 0. 298 16.6 16. 9 -.03 0.335 0. 318 16. 1 17. 0 -.04 0.359 0. 359  +  10<tit> °Cm/s FLUX DISS +  T  0. 038 0. 042 0. 051 0. 042  0 22 • 022 - . 003 "™ a011 """* • 014 0. 010 0.021 0. 058 0.063 0.056 0. 040 0. 024 0. 032 0. 054 0.048 0. 054 •  0. 043 0. 036 0. 031 0.030  034 028 • 017 015 — . 019 030 "~ • 043 0.062 0. 081 0. 075 0. 063 0.060 0.058 0. 058 0. 058 0. 057 —  .  •  —  i  178 1  I  EUN I  T50 T51 T52 T53 T54 T55 T56 T57 T58 T59 T60 T61 T62 T63 T64 T65 T66 T67 T68 T69 T7C T71 T72 T73 T74 T75 T76 T77 T78 T79 T80 T81 T82 T83 T84 T85 T86 T87 T88 T89 T90 T91 T92 T93 T94 T95 T96 T97 T98  1  TIME GMT 1  1  1  DATE UZ °TEUE 1976 1  2:00 5:00 11:00 13:16 14:32 20:12 11:00 12:11 13:38 15:42 16: 36 20: 14 23:00 11:00 12:48 23:00 5:00 17:00 18:06 19:48 23:00 2:00 5:00 11 :30 2:23 5:23 8:23 11:23 12:53 14:01 17:23 20:23 22:23 23:23 2:23 5:23 16:01 17:17 18: 35 20: 17 8:23 11:23 12:29 14:23 17:23 19:00 2:10 2:10 0:00  1  24/ 9 24/ 9 24/ 9 24/ 9 24/ 9 24/ 9 27/ 9 27/ 9 27/ 9 27/ 9 27/ 9 27/ 9 27/ 9 28/ 9 28/ 9 28/ 9 29/ 9 29/ 9 29/ 9 29/ 9 29/ 9 30/ 9 30/ 9 30/ 9 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 11/10 11/10 14/10 14/10 14/10 14/10 15/10 15/10 15/10 15/10 15/10 15/10 27/11 28/11 3/12  T  TZ 1  TSFC 1  1  T  Z/L  U*  FLUX 1  :  10<Wt>  (m/s)  DISS  FLUX 1  DISS  11.9 228 15.5 17.0 -.06 0.396 0.367 10. 2 229 15.6 16. 5 -.06 0.356 0.326 9.6 215 16.1 16.3 -.03 0.321 0.298 9.8 211 16.4 16.4 -.02 0.340 0.302 10.3 208 16.7 16.6 -.01 0.303 0.311 7.2 210 16.2 15.9 -.01 0.231 0.247 11.4 162 14.7 16.0 -*06 0.394 0.349 12.1 162 15.0 15.9 -.04 0.458 0.365 13.5 166 15.8 15.8 -.01 0.442 0.438 11. 9 167 16.8 15. 2 0.03 0.448 0.368 11. 1 194 16.6 14.5 0.05 0.338 0.360 -. 146 -. 160 15. 2 210 16.7 14.2 0.04 0.585 0.529 -.302 -.257 10^7 228 15.8 14.1 0.04 0.331 0.352 -.121 -.144 9.8 11 10.9 14.7 -.19 0.300 0.308 0.236 0.250 8.5 10 10.4 15.1 -.29 0.253 0.264 0.233 0.260 12.0 311 10.8 14.0 -. 12 0.379 0.413 0.284 0.352 8.9 333 8.5 14.7 -.35 0.339 0.298 0.388 0.413 10.0 230 12.4 16.0 -.16 0.341 0.321 0.324 0.294 11.0 232 12.8 15.5 -.11 0.370 0.352 10.2 226 13.3 14.3 -.06 0.356 0.321 11.8 222 13.9 13.7 -.01 0.392 0.410 13.6 236 14. 1 13.2 0.01 0.420 0.437 10.1 243 13.4 12.8 0.01 0.352 0.329 8. 3 239 12. 4 13. 1 -.07 0.270 0.256 0.059 0.075 13.9 194 18.8 16.2 0.04 0.523 0.496 -.276 -.246 17.1 191 19.4 16.3 0.04 0.638 0.670 -.368 -.374 12.7 224 16.5 16.2 -.00 0.476 0.470 -.055 -.064 15.8 223 17.1 16.2 0.01 0.660 0.580 -.043 -.067 17.5 232 16.6 16.1 0.00 0.714 0.682 17.8 234 15. 6 16.0 -.01 0.762 0.676 19.2 238 13.8 15.1 -.02 0.786 0.755 16.6 254 12.2 14.2 -.04 0.641 0.624 14.0 268 11.5 13.6 -.05 0.523 0.504 13.6 271 11.1 13.3 -.06 0.442 0.495 12.3 265 10.1 12.4 -.07 0.396 0.417 10.5 269 9.2 12.5 -.14 0.401 0.373 7.7 177 13.3 7.7 0.30 0.173 0.203 -.027 -.052 10. 2 174 13.6 8. 3 0.18 0.318 0.297 -.112 -.105 11.4 179 13.2 1.0-2 0.08 0.355 0.376 -.162 -. 158 6. 3 242 12. 1 10.7 0.09 0.224 0.237 16.1 259 7.6 10.5 -.05 0.625 15.7 263 7.9 10.1 -.04 0.692 14.4 263 7.7 9.7 -.05 0.515 14.6 259 8.2 9.3 -.03 0.559 13.7 259 10.5 9.0 0.02 0.546 0.491 13.2 260 11.4 8.8 0.04 0.535 0.496 -.186 -.187 12.4 199 7.9 5.7 0.04 0.496 0.441 -.181 -.168 11.3 215 8.1 5.4 0.07 0.377 0.416 -.173 -.229 11.7 123 5.4 4.6 0.02 0.393 0.411 -.052 -.059  179 \  1  RON  1  T  T99 T100 T101 T102 T103 T104 T105 T106 T107 T108 T109 T 110 T11 1 T112 T113 T11 4 T115 T116 T117 T118 T119 T120 T121 T122 T123 T124 T125 T126 T127 T128 T129 T130 T131 T132 T133 T134 T135 T136 T137 T138 T139 T140 T141 T142 T143 T144 T145 T146 T147 I  T  TIME GMT  1  1  6 :00 3/1 2 9: 00 3/12 12:00 3/12 15:00 3/12 18:00 3/12 2-1:00 3/12 0 :00 4/12 3:00 4/12 6:00 4/12 9: 00 4/12 12:00 4/12 15:00 4/12 15:00 7/12 18: 00 7/12 21:00 7/12 0: 00 8/12 3:00 8/12 6: 00 8/12 18:00 9/12 21: 00 9/12 0:00 10/12 3: 00 10/12 6:00 10/12 9: 00 10/12 2:00 11/12 8: 00 11/12 11:00 11/12 14:00 11/12 17:00 11/12 20: 00 11/12 23 :00 11/12 14:00 12/12 5:00 14/12 8:00 14/12 23 :00 14/12 2: 00 15/12 5:00 15/12 8: 00 15/12 11 :00 15/12 1977 0:48 1 3 / 3 9: 48 17/ 3 12:48 1 7 / 3 15: 48 1 7 / 3 18:48 1 7 / 3 21: 48 1 7 / 3 0:48 1 8 / 3 3: 48 1 8 / 3 6:48 1 8 / 3 9: 48 18/ 3 1  1  DATE OZ °TROE 1976 1  '  12i 4 216 17.9 250 18.6 264 18.5 274 16. 9 278 15. 0 270 16. 8 267 19.3 269 15. 9 266 16. 0 261 14. 4 264 10.7 261 11. 7 169 14. 6 139 17. 1 143 18.6 153 18. 9 159 13.3 170 14. 6 300 18.3 302 17. 1 302 15.6 292 16. 9 289 13.5 278 10. 5 211 12. 4 220 15. 3 230 16. 0 231 17. 2 291 16. 0 290 11. 9 308 12.6 201 14. 2 317 14.6 312 13. 2 218 18.2 220 17. 5 219 15. 9 213 15.6 231  1  10. 6 10. 4 11. 2 11.0 12. 6 12.8 12. 6 10.5 11. 3 11. 7  233 236 240 234 259 270 278 280 271 270  1  I  TZ  1  TSFC '  6^9 3.1 -2. 5 -9.7 -11. -12. -11. -9.6 -10. -8.9 -7.8 -5.8 2.5 4.1 5. 8 7.6 7.8 7.9 -11. -14. -17. -17. -15. -14. 5.2 5.9 6.3 6.5 1.8 -1.0 -2. 6 1.6 -14. -16. -7.0 2.2 3.9 -4.8 5. 4  4. 6 4. 6 4. 6 4. 6 4. 6 4. 5 4. 5 4. 5 4. 4 4.3 4. 3 4. 2 3. 5 3. 5 3. 6 3. 5 3. 6 3. 6 3. 6 3. 5 3. 4 3. 4 3. 3 3. 3 3. 3 3. 4 3. 5 3. 5 3. 5 3. 5 3. 5 3. 4 3. 2 3. 2 3. 0 3. 0 2. 9 2..9 2. 9  1.9 1.8 1.6 1.5 1.0 -0.3 -1.3 -1.9 -2. 4 -2.2  0. 0 0. 2 0. 3 0. 2 0. 3 0. 3 0. 2 0. 2 0. 2 0. 2  1  I  1  Z/L  1  I  u* (m/s) FLOX DISS  1 1  +  10<wt> FLOX DISS  0.05 0. 424 0.447 180 — .185 -.02 0.826 0.752 -.09 0^733 0.737 -.19 0.746 0.724 -.26 0. 672 0.690 -.33 0. 552 0.588 -.25 0. 735 0.690 -.17 0. 817 0.806 -.27 0. 633 0.599 -.22 0.551 0.559 -.26 0.500 0.495 -.34 0. 352 0.414 -.04 0.418 0.380 0. 179 0 .200 0. 01 0.478 0.519 0.03 0.660 0.651 • 131 .125 — .352 0. 04 0.746 0.736 385 0.04 0. 728 0.729 • 435 .516 0.08 0.518 0.506 372 - .452 -.31 0.601 0.598 -.27 0.640 0.739 -.33 0. 675 0.695 -.38 0.656 0.607 -.31 0. 487 0.592 -.45 0.463 0.485 0.06 0.362 0.3 48 • 069 .089 0.06 0.483 0.462 • 159 — . 152 0. 04 0.661 0.578 • 228 — .176 0.04 0.606 0.613 251 — . 186 -.03 0.645 0.673 -. 08 0.565 0.591 -.21 0.378 0.433 -.06 0.446 0.4 05 0. 265 0 . 296 -.35 0.531 0.541 -.43 0.534 0.543 -.27 0.493 0.456 -.01 0.769 0.735 0.01 0. 693 0.681 023 .047 0.03 0.663 0.602 o 132 —- .082 0.04 0.613 0.592  +  -  •>  0.06 0.05 0.03 0.04 0.01 -.02 -.04 -.09 -.09 -.07  0. 221 0.264 097 — .146 0.363 0.355 142 — . 104 0.395 0.387 071 .097 0.356 0.359 079 —- .061 0.456 0.456 0.440 0.464 0.442 0.457 0.360 0.387 0. 214 0 .253 0.389 0.371 0. 2 68 0.237 0.380 0.410 0. 227 0.279 m  m  m  1  1  +  180 1 1  T  T  RUN  TIME GMT T  T148 T149 T150 T151 T152 T153 T154 T155 T156 T157 T158 T159 T160 T161 T162 T163 T164 T165 T166 T167 T168 T169 T170 T171 T172 T173 T174 T175 T176 T177 T178 T17S T180 T181 T182 T183 T184 T185 T186 T187 T188 T189 T190 T191 T192 T193 T194 T19 5 T196  T  1  12:48 18/ 15: 48 18/ 6:48 19/ 9: 48 19/ 12:48 19/ 15: 48 19/ 18:48 19/ 0: 48 20/ 21:48 24/ 0: 48 25/ 3 :48 25/ 9: 48 25/ 12:48 25/ 15: 48 25/ 18:48 25/ 21: 48 25/ 3:48 26/ 6: 48 26/ 9:48 26/ 12: 48 26/ 15:48 26/ 18: 48 26/ 21:48 26/ 3: 48 27/ 12:48 27/ 15: 48 27/ 18:48 27/ 21: 48 27/ 21: 48 29/ 18: 48 31/ 21:48 3 1 / 12: 48 3/ 15:48 3/ 18: 48 3/ 3:48 4/ 6: 48 V 9: 48 V 12: 48 4/ 15:48 18: 48 4/ 21:48 V . 3: 48 6/ 6:48 6/ 9: 48 6/ 12:48 6/ 15: 48 6/ 18:48 6/ 21: 48 6/ 0:48 7/  y—i  1  DATE UZ °TRUE 1977  1  3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 T  1  11. 5 282 12.7 254 17. 3 61 12.8 16 16. 4 347 17.6 325 14. 1 323 10.7 296 12.3 358 12.2 356 11. 3 357 10.7 353 10. 3 3 10.6 359 10. 5 358 10.4 356 10. 7 353 10. 5 350 10. 3 353 11.4 352 10.6 351 12. 2 17 12. 3 14 10.8 10 11. 3 4 10. 4 17 10. 9 3 8. 0 1 8.6 172 11. 5 168 7.8 204 12. 6 147 14. 2 125 11. 4 170 19. 1 288 18. 0 300 16. 2 313 15. 2 311 13. 5 315 10.8 321 10. 9 311 15. 1 189 13. 0 209 10.7 223 12. 4 224 12. 4 220 Mi. 5 223 13.2 223 11. 6 217  1  1  TZ  -1. 7 0.4 -1. 0 -1. 7 -2. 8 -2. 9 -2. 8 -1. 9 -0. 7 -1. 1 -0. 9 -0. 5 0. 3 1. 5 2. 2 0.9 0. 1 0. 1 0. 5 1.3 0. 9 1. 4 1. 0 1. 4 1. 6 2.4 3. 5 2.7 2. 2 3. 0 3. 1 0.6 1. 2 3. 1 1. 8 -0. 3 -1. 4 -0.7 0. 4 1.7 1. 8 6. 0 4. 7 1.3 1.3 1.2 1. 9 1. 5 0. 9  1  TSFC 0. 2 0.3 0. 3 0. 2 0. 2 0. 3 0. 3 0. 2 0. 1 -0. 1 -0. 2 -0. 2 -0. 2 -0. 2 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0,.0 0. 0 0. 0  1  Z/L  1  1  06 •00 02 • 05 05 05 • 08 08 03 • 03 03 • 02 0. 01 0. 05 0. 07 0. 03 00 0. 00 0. 01 0. 04 0. 02 0. 03 0. 02 0. 04 0.04 0. 07 0. 10 0. 13 0. 10 0. 08 0. 16 0. 01 0.02 0. 09 0. 02 • 01 03 01 0. 01 0. 05 o: 05 0. 09 0. 11 0. 04 0. 03 0.02 0. 03 0. 03 0. 02  -.  T  1  u* (m/s) FLOX DISS  1  1  ;  0. 405 0. 421 0. 398 0. 444 0. 694 0. 685 0. 458 0. 488 0. 646 0. 645 0. 685 0. 708 0. 469 0.530 0.347 0. 405 0. 369 0. 425 0. 359 0. 415 0. 321 0.369 0.321 o. 360 0. 290 0.329 0. 310 0. 342 0. 276 0.341 0. 312 0.368 0. 303 0. 352 0. 259 0. 333 0. 267 0.333 0. 328 0. 369 0. 323 0. 365 0. 388 0. 424 0. 395 0. 421 0. 341 0. 371 0. 315 0.370 0. 313 0. 350 0. 266 0. 335 0. 235 0. 287 0. 232 0. 298 0. 367 0. 413 0. 200 0.242 0. 451 0. 428 0. 562 0. 531 0. 407 0. 445 0. 626 0. 762 0. 684 0. 723 0. 610 0. 628 0. 511 0. 566 0. 462 0. 519 0. 311 0. 388 0. 316 0. 374 0. 566 0. 573 0. 482 0. 471 0. 346 0.399 0. 466 0. 460 0. 460 0. 448 0. 5.45 0.540 0. 461 0. 494 0. 406 0. 427 ;  —r-  10<wt> FLUX DISS  +  h  [  

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