UBC Theses and Dissertations

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UBC Theses and Dissertations

Microscale pressure fluctuations measured within the lower atmospheric boundary layer Elliott, James Arthur 1970

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MICROSCALE PRESSURE FLUCTUATIONS MEASURED WITHIN THE LOWER ATMOSPHERIC BOUNDARY LAYER  by JAMES ARTHUR ELLIOTT B . S c , University of Saskatchewan, 1962 M.Sc., University of B r i t i s h Columbia, 1965  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in  the Department of Physics  I n s t i t u t e o f Oceanography  We a c c e p t t h i s  t h e s i s as conforming  t o the  required standard  THE  UNIVERSITY OF BRITISH COLUMBIA September, 19 70  In  presenting  this  an a d v a n c e d d e g r e e the I  Library  further  for  agree  in  at  University  the  make  it  this  for  financial  of  Columbia,  British for  by  the  gain  D e p a r t m e n t o f Physics  Institute of Oceanography, Columbia  shall  not  the  requirements  reference copying of  Head o f  is understood that  written permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  of  extensive  be g r a n t e d  It  fulfilment  available  that permission for  representatives. thesis  partial  freely  s c h o l a r l y p u r p o s e s may  by h i s of  shall  thesis  I  agree  and this  be a l l o w e d  that  study. thesis  my D e p a r t m e n t  copying or  for  or  publication  w i t h o u t my  ii ABSTRACT  An within  i n s t r u m e n t was d e v e l o p e d  t o measure t h e s t a t i c p r e s s u r e  the turbulent flow o f the atmospheric  boundary l a y e r .  w a s u s e d t o m e a s u r e some o f t h e p r o p e r t i e s o f p r e s s u r e  This  data w i t h i n  a t u r b u l e n t boundary  instrument  fluctuations  f l a t b o u n d a r y and o v e r w a t e r waves and h a s p r o v i d e d t h e f i r s t pressure  fluctuations  over a  reliable  layer.  For a l l observations over a f l a t boundary the root-mean-square produced The  b y t h e b o u n d a r y l a y e r t u r b u l e n c e was a b o u t 2.6 t i m e s  pressure  t h e mean  stress.  s p e c t r a h a d a p o w e r l a w b e h a v i o u r w i t h a mean s l o p e o f -1.7 f o r s c a l e s  above t h e peak o f t h e v e r t i c a l v e l o c i t y approximately to the ' l o c a l '  s p h e r i c a l i n shape, and propagated mean w i n d .  downstream a t a r a t e  a t s m a l l s c a l e s t h e r e was a l a r g e p h a s e d i f f e r e n c e  producing  fluctuations  were  equal  i n phase w i t h the downstream v e l o c i t y  phase d i f f e r e n c e s were i n t e r p r e t e d  were  Pressure  Above t h e b o u n d a r y , t h e l a r g e s c a l e p r e s s u r e  f l u c t u a t i o n s were a p p r o x i m a t e l y tions;  spectrum.  t o be t h e r e s u l t  (-135°).  fluctua-  These  of the large pressure  scales interacting with the earth's surface, while the small scales  'free'  of the surface.  P r e s s u r e f o r c e s r e s u l t e d i n an energy  f l u x out i  o f t h e downstream v e l o c i t y source  f o rthe turbulence w i t h i n  term i n the n e t energy ing  fluctuations  o f a b o u t 0.45 o f t h e t o t a l  t h e b a n d o f 0.05 < k z < 2 0 .  b u d g e t was f o u n d  The p r e s s u r e  t o b e a b o u t 1/10 o f t h e e n e r g y  feed-  term. P r e s s u r e measurements n e a r w i n d g e n e r a t e d  hump a t t h e w a v e f r e q u e n c i e s . vertical  The a m p l i t u d e  r a t e o f decay decreased,  waves showed a l a r g e s p e c t r a l o f t h i s hump i n c r e a s e d , a n d i t s  a s t h e mean w i n d s p e e d i n c r e a s e d .  d i f f e r e n c e between p r e s s u r e and waves d u r i n g a c t i v e be  energy  a b o u t 135°, p r e s s u r e  l a g g i n g waves.  The p h a s e  g e n e r a t i o n was f o u n d t o  T h i s d i d n o t change  vertically.  i i i TABLE OF CONTENTS page ABSTRACT TABLE OF CONTENTS  i  L I S T OF TABLES  i  i  i  i v  L I S T OF FIGURES  v i  ACKNOWLEDGEMENTS  x i i  INTRODUCTION  1  BACKGROUND  5  PRESSURE INSTRUMENT  12  Probe  12  T r a n s d u c e r et at  19  A m p l i t u d e and Phase Response  23  IN SITU  C A L I B R A T I O N OF THE PRESSURE INSTRUMENT  24  S u r f a c e P r e s s u r e Measurement  24  Comparison o f Measurements: S u r f a c e and A i r  26  MICROSCALE PRESSURE FLUCTUATIONS OVER A F L A T BOUNDARY  29  Nondimensionalizing of Pressure Spectra  30  Shape and I n t e n s i t y o f t h e S p e c t r u m  32  Some K i n e m a t i c s  37  of thePressure Fluctuations  Pressure-Velocity  Relationship  Energy T r a n s f e r by P r e s s u r e Forces MICROSCALE PRESSURE FLUCTUATIONS OVER WIND GENERATED WAVES  43 48 52  Example S p e c t r a  54  Data  56  A.  Runs 6 0 / 4 , 1 1 9 / 1 , 1 1 9 / 2 , 1 1 9 / 3  56  B.  Runs 1 6 7 / 1 / 1 , 167/1/2, 167/2, 167/3  57  iv page C.  Runs 1 6 4 / 1 , 1 6 4 / 2  59  D.  Runs 8 0 / 3 , 6 0 / 1 , 60/2  59  Discussion  60  SUMMARY OF RESULTS  72  BIBLIOGRAPHY  75  A P P E N D I X A:  EXPERIMENTAL  S I T E S , INSTRUMENTS AND TECHNIQUES  Experimental Sites  78 78  (i)  Spanish  (ii)  Ladner S i t e  79  (iii)  Boundary Bay S i t e  80  Instruments  Banks  Site  and O b s e r v a t i o n a l Techniques Data Recording  78  81  (i)  Analog  (ii)  S o n i c and U-wire  81  (iii)  Cup A n e m o m e t e r s  82  (iv)  Wave P r o b e  83  (v)  Water Height  (vi)  A i r and Water Temperature  and Current  81  84 84  A P P E N D I X B:  A N A L Y S I S OF DATA  86  A P P E N D I X C:  DATA SUMMARY  9A  SYMBOL TABLE  . 192  V  LIST OF TABLES  Table  page  16  I  Data f o r p l o t t i n g d i s k c r o s s - s e c t i o n s  II  P r e s s u r e p r o p a g a t i o n v e l o c i t y , U , as a f r a c t i o n o f u | P p  42  III  V e r t i c a l pressure g r a d i e n t at the s u r f a c e  47  IV  The pw term i n the boundary l a y e r energy budget  49  V  Mean d a t a f o r Runs  96  L  vi L I S T OF  1  2  FIGURES  P r e s s u r e i n s t r u m e n t used t o measure the s t a t i c f l u c t u a t i o n s w i t h i n the turbulent flow (a) assembled (b) w i t h c y l i n d e r removed Probe developed within  f o r measuring  s t a t i c pressure  pressure 102 102 fluctuations  the t u r b u l e n t f l o w  103  3  C r o s s - s e c t i o n s o f the d i s k s o f p r o b e s E,  F,  G  104  4  Dynamic p r e s s u r e n o i s e t e s t speeds  f o r Probe E at d i f f e r e n t  wind  5  Dynamic p r e s s u r e n o i s e t e s t f o r P r o b e F a t d i f f e r e n t  wind  105  speeds  106  6  Schematic  7  Barocel pressure container  8  9  10  11  12  13  of the B a r o c e l t r a n s d u c i n g system t r a n s d u c e r and  107  r e f e r e n c e volume i n  their 108  R e s u l t s of wind t u n n e l t e s t f o r the dynamic p r e s s u r e d i s t r i b u t i o n i n f r o n t of t h e t r a n s d u c e r case Arrangement used f o r c a l i b r a t i n g a m p l i t u d e and p h a s e r e s p o n s e  the p r e s s u r e i n s t r u m e n t  for 110  D e t a i l o f t h e drum u s e d t o c r e a t e a s i n u s o i d a l l y pressure C i r c u i t diagram f o r power a m p l i f i e r used v i b r a t i o n generator  to drive  varying i l l the 112  Sample frequency c a l i b r a t i o n o f the p r e s s u r e ( p r o b e and t r a n s d u c e r ) Arrangement used f o r c a l i b r a t i n g  109  the p r e s s u r e  instrument 113 instrument  in situ 14  15  16  Sample f r e q u e n c y c a l i b r a t i o n of the s y s t e m s u r f a c e p r e s s u r e measurement  114 used f o r the 115  S p e c t r a l comparison of the s t a t i c p r e s s u r e measured i n the a i r a n d a t t h e s u r f a c e ; t h e s e p a r a t i o n was 40 cm v e r t i c a l l y . These measurements were t a k e n at the L a d n e r s i t e  116  S p e c t r a l comparison of the s t a t i c p r e s s u r e measured i n the a i r a n d a t t h e s u r f a c e ; t h e s e p a r a t i o n was 32 cm v e r t i c a l l y . These measurements were t a k e n a t the L a d n e r s i t e  117  vii Figure 17  18  19  20  21  22  23  page Coherence and phase between t h e s t a t i c p r e s s u r e measured i n t h e a i r a n d a t t h e s u r f a c e . T h e s e a r e t h e L a d n e r Runs ....  118  S p e c t r a l comparison of t h e s t a t i c p r e s s u r e measured i n t h e a i r and a t t h e s u r f a c e ; t h e s e p a r a t i o n v e r t i c a l l y , i n c e n t i m e t e r s , i s g i v e n i n b r a c k e t s a f t e r t h e Run number. These measurements were t a k e n a t t h e Boundary Bay s i t e  119  Coherence and phase between t h e s t a t i c p r e s s u r e measured i n t h e a i r and a t t h e s u r f a c e . These a r e t h e B o u n d a r y B a y Runs  120  Comparison o f p r e s s u r e s p e c t r a measured s i m u l t a n e o u s l y a t two d i f f e r e n t h e i g h t s . A z i s t h e d i f f e r e n c e i n h e i g h t , given i n meters  121  Nondimensionalized over water  pressure spectra.  122  Nondimensionalized (a) w a t e r (b) l a n d  pressure spectra.  25 26 27 28 29  30  31  32  Observations  taken  taken  Normalized  over 123 123  Summary o f t h e n o n d i m e n s i o n a l i z e d p r e s s u r e s p e c t r a . plotted  24  Observations  are kll(k) / ( p ^ ) a t a k o f 1 0 2  4  - 2  cm  Values 124  - 1  p r e s s u r e s p e c t r a n o r m a l i z e d by t h e i r  variance  ....  125  Nondimensionalized  u and w s p e c t r a  126  Nondimensionalized  v spectra  127  Nondimensionalized  uw s p e c t r a  128  Comparison of the s p e c t r a l s l o p e of pressure s p e c t r a  129  Comparison between the n o n d i m e n s i o n a l i z e d p r e s s u r e and o f t h e v e l o c i t y components d i f f e r e n t frequency bands  130  variance of the o f Run 1 2 0 / 1 f o r  N o n d i m e n s i o n a l i z e d p r e s s u r e s p e c t r a . The c u r v e i s t h e mean of data g i v e n i n F i g u r e 2 1 ; the dashed l i n e s a r e e x t r a p o l a t e d from the s o l i d curve  131  C o h e r e n c e a n d p h a s e b e t w e e n two p r e s s u r e m e a s u r e m e n t s various v e r t i c a l separations  with 132  C o h e r e n c e a n d p h a s e b e t w e e n two p r e s s u r e m e a s u r e m e n t s various crossstream separations  with 133  viii Figure 33  34  35  36  37  38  39  40  41  42  43  page C o h e r e n c e and phase between a downwind s e p a r a t i o n (a) coherence (b) phase  two p r e s s u r e  measurements  with 134 135  F i x e d c o h e r e n c e s b e t w e e n two p r e s s u r e s i g n a l s f o r v a r i o u s probe separations. The v a l u e s p l o t t e d a r e f o r a c o h e r e n c e o f 0.14  136  Coherence between separations  137  two v e l o c i t y m e a s u r e m e n t s  with  different •  F i x e d c o h e r e n c e s b e t w e e n two v e l o c i t y s i g n a l s f o r v a r i o u s sensor separations. The v a l u e s p l o t t e d a r e f o r a c o h e r e n c e o f 0.14  138  C o h e r e n c e and p h a s e between p and u, u measured w i t h a sonic. Height o f o b s e r v a t i o n s r a n g e d f r o m 1.5 t o 5.5 m e t e r s  139  C o h e r e n c e a n d p h a s e b e t w e e n p a n d w, w m e a s u r e d w i t h sonic. H e i g h t o f o b s e r v a t i o n s r a n g e d f r o m 1.5 t o 5.5 m e t e r s  140  a  C o h e r e n c e and p h a s e b e t w e e n p and u , u measured w i t h a hot-wire. H e i g h t o f o b s e r v a t i o n s r a n g e d f r o m 1.5 t o 3 meters  141  C o h e r e n c e and p h a s e b e t w e e n p a n d u , u m e a s u r e d w i t h hot-wire. H e i g h t o f o b s e r v a t i o n s was 2 m e t e r s  142  a  C o h e r e n c e a n d p h a s e b e t w e e n u a n d w, v e l o c i t y c o m p o n e n t s measured w i t h a s o n i c . H e i g h t o f o b s e r v a t i o n s ranged f r o m 1.5 t o 5.5 m e t e r s Wavelength o f the pressure f l u c t u a t i o n s a s s o c i a t e d w i t h p - u p h a s e t r a n s i t i o n , as a f u n c t i o n o f o b s e r v a t i o n a l height. The b r o k e n l i n e i s t h e m e a s u r e d s c a l e s i z e  143 the 144  C o h e r e n c e b e t w e e n d o w n s t r e a m v e l o c i t y , u , a n d two p r e s s u r e measurements. One p r e s s u r e s e n s o r was b e s i d e t h e u s e n s o r , one was a t t h e s u r f a c e , 30 cm b e l o w  145  44  Spectra  146  45  R a t i o o f t h e pw a n d uwU budget equation  46  o f pw  Spectral distribution from the u v e l o c i t y k z f r o m 0.05 t o 20  terms o f the i n t e g r a t e d n e t energy 146  o f the energy f l u x , by p r e s s u r e f o r c e s , component. The i n t e g r a l g i v e n i s f o r 147  ix Figure 47  page S p e c t r a l d i s t r i b u t i o n o f t h e energy f l u x , by p r e s s u r e f o r c e s , from t h e u v e l o c i t y component. The i n t e g r a l g i v e n i s f o r kz from 0.05 to 20  148  48  Pressure, v e l o c i t y  149  49  Wave s p e c t r a o f Data Group A.  and wave s p e c t r a f o r Run 173/3 The time o f s t a r t and end o f  each Run i s g i v e n i n t h e b r a c k e t s  150  50  Pressure, u v e l o c i t y  and wave s p e c t r a f o r Run 60/4  151  51  Pressure, u v e l o c i t y  and wave s p e c t r a f o r Run 119/1  152  52  Pressure, u v e l o c i t y  and wave s p e c t r a f o r Run 119/2  153  53  Pressure, u v e l o c i t y  and wave s p e c t r a f o r Run 119/3  154  54  Coherence and phase between t h e lower p r e s s u r e s e n s o r and the waves: Data Group A. P ^ * ! phase p o s i t i v e means p ^ leads n -  55  Coherence and phase between t h e two p r e s s u r e Data Group A.  56  U  A  S  E  positive  sensors:  means p ^ l e a d s p ^  Coherence and phase between the u v e l o c i t y Data Group A.  57  PL""P P  N  156  and waves:  u-n phase p o s i t i v e means u l e a d s n  Wave s p e c t r a f o r Data Group B.  155  157  The time o f s t a r t and end o f  each Run i s g i v e n i n b r a c k e t s  158  58  P r e s s u r e and wave s p e c t r a f o r Run  167/1/1  159  59  P r e s s u r e and wave s p e c t r a f o r Run  167/1/2  160  60  P r e s s u r e and wave s p e c t r a f o r Run 167/2  61  P r e s s u r e and wave s p e c t r a f o r Run 167/3  62  Amplitude  o f the F o u r i e r c o e f f i c i e n t s  .  162  f o r p r e s s u r e and  waves o f Run 167/3 63  161  163  Coherence and phase between t h e p r e s s u r e and waves: Data Group B.  p-n phase p o s i t i v e  means p l e a d s r\  164  64  Pressure, u velocity  and wave s p e c t r a f o r Run 164/1  165  65  Pressure, u v e l o c i t y  and wave s p e c t r a f o r Run 164/2  166  66  Coherence and phase between t h e p r e s s u r e and t h e waves: Data Group C.  p-r| phase p o s i t i v e  means p l e a d s n  167  Figure 67  page C o h e r e n c e and phase b e t w e e n t h e u v e l o c i t y D a t a G r o u p C.  u-n p h a s e p o s i t i v e  means u l e a d s n  168  68  Pressure,  69  Coherence and phase between t h e p r e s s u r e and t h e waves: D a t a G r o u p D. p - r i p h a s e p o s i t i v e means p l e a d s n, Coherence and phase between t h e u v e l o c i t y and t h e waves: D a t a G r o u p D. u-r| p h a s e p o s i t i v e means u l e a d s ri  70  71  72  u velocity  and t h e waves:  and wave s p e c t r a f o r D a t a Group D  R a t i o o f measured t o p r e d i c t e d p r e s s u r e p r o p a g a t i n g waves w i t h no w i n d  169  170 171  amplitude f o r 171  p (n) a t v a r i o u s c o n s t a n t f r e q u e n c i e s f o r d i f f e r e n t v a l u e s o f U*| /C. The v a l u e s p l o t t e d a t U ^ / C = 0 a r e f o r the p o t e n t i a l flow s o l u t i o n W  73 74 75  P /p f o r d i f f e r e n t u| /C a t c o n s t a n t k z w o '5 p /p f o r d i f f e r e n t k z a t c o n s t a n t u| /C w o '5 R a t i o o f t h e p m e a s u r e d a t two l e v e l s . The l i n e s d r a w n a r e r  the predicted* r a t i o from equation  173  c  174  17  175  76  Comparison between e q u a t i o n  77  Phase s h i f t between p r e s s u r e  78  u|,-/C. P h a s e p o s i t i v e means p r e s s u r e l e a d s w a v e s Wave a m p l i t u d e a n d c r i t i c a l h e i g h t f o r c o n s t a n t u|,. f o r d i f f e r e n t wave f r e q u e n c i e s  79  172  16 a n d D o b s o n ( 1 9 6 9 )  176  and waves a t v a r i o u s v a l u e s o f 177 plotted 178  S p e c t r a l d i s t r i b u t i o n o f the approximate energy f l u x t o t h e waves, c a l c u l a t e d u s i n g t h e p r e s s u r e measured above the wave c r e s t s  179  Coherence and phase between p r e s s u r e and u v e l o c i t y measured n e a r waves. P h a s e p o s i t i v e means p r e s s u r e l e a d s v e l o c i t y . .  180  C o h e r e n c e and p h a s e between p r e s s u r e and u v e l o c i t y measured n e a r waves. P h a s e p o s i t i v e means p r e s s u r e l e a d s v e l o c i t y . .  181  82  Wavelength a s s o c i a t e d w i t h  182  83  Nondimensional energy f l u x from the u v e l o c i t y measured n e a r waves  component,  Nondimensional energy f l u x from the u v e l o c i t y measured n e a r waves  component,  80  81  84  the p-u phase t r a n s i t i o n  183  184  xi Figure  page  85  Map  o f the S p a n i s h Banks s i t e  86  P l a t f o r m and i n s t r u m e n t masts a t t h e S p a n i s h Banks (a) P l a t f o r m and masts l o o k i n g E a s t (b) I n s t r u m e n t e d mast  87  Map  o f the Ladner  88  Box  in position  89  Instruments  90  Map  91  T y p i c a l wave probe  92  Cj^. e v a l u a t e d f r o m t h e d i r e c t surface stress  185 site 186 186  site  187  f o r s u r f a c e p r e s s u r e measurement ( L a d n e r s i t e )  s e t up  at the Ladner  o f t h e B o u n d a r y Bay  site,  l o o k i n g NNE  188 188  site  189  calibrations  190 and $ ^  estimate of  the 191  ACKNOWLEDGMENTS  T h i s work was done as p a r t o f t h e A i r - S e a I n t e r a c t i o n program a t the Institute has  o f Oceanography, U n i v e r s i t y o f B r i t i s h Columbia.  been supported  The r e s e a r c h  p r i n c i p a l l y by the U n i t e d S t a t e s O f f i c e o f N a v a l Research  under C o n t r a c t N00014-16-C-0047.  A d d t i o n a l support  came from the N a t i o n a l  Research C o u n c i l o f Canada, Defence Research Board, and Department o f Transport  ( M e t e o r o l o g i c a l Branch).  I have been p e r s o n a l l y s u p p o r t e d  a . N a t i o n a l Research C o u n c i l S t u d e n t s h i p  and a M a c M i l l a n  w h i l e on e d u c a t i o n a l l e a v e from the A t l a n t i c Bedford  Institute,  Family  Oceanographic  with  Fellowship,  Laboratory,  Department o f Energy, Mines and R e s o u r c e s .  I w i s h t o thank Dr. R.W. Stewart, Dr. R.W. B u r l i n g , and Dr. M. Miyake f o r t h e i r guidance d u r i n g the course a l l o t h e r s who have a s s i s t e d w i t h particular technicians Finally report.  G.E. E l l i o t t , of this  o f t h i s work.  I a l s o w i s h t o thank  t h i s p r o j e c t : the graduate s t u d e n t s , i n  F.W. Dobson, G.A. McBean and J.R. W i l s o n ,  and t h e  institute.  I thank my w i f e G i l l i a n  f o r h e r p a r t i n the p r e p a r a t i o n o f t h i s  1 INTRODUCTION  T h i s s t u d y was c e n t e r e d around the E u l e r i a n measurement o f t u r b u l e n t s t a t i c pressure  f l u c t u a t i o n s w i t h i n the atmospheric  boundary l a y e r .  The  ' s t a t i c ' p r e s s u r e i s the normal s t r e s s a s s o c i a t e d w i t h motions w i t h i n the fluid  (Hinze, 1959, p.27).  pressure  I n c r e a s e d knowledge o f the r o l e o f s t a t i c  fluctuations within turbulent f l u i d  to many e n g i n e e r i n g and g e o p h y s i c a l s t u d i e s .  flow i s o f g r e a t  interest  There i s a l a c k o f a v a i l a b l e  i n f o r m a t i o n , n o t from a l a c k o f e f f o r t b u t r a t h e r a l a c k o f a b i l i t y t o measure t h i s v a r i a b l e r e l i a b l y w i t h i n the body o f t h e f l u i d . The  importance o f t h i s measurement i s e v i d e n t from the f o l l o w i n g  p o s t u l a t e d p r o p e r t i e s o f the s t a t i c pressure fluctuations  Pressure  a r e c r e d i t e d w i t h b e i n g the ' i s o t r o p y p r o d u c i n g '  they a r e e x p e c t e d Or,  fluctuations.  to t r a n s f e r energy among v e l o c i t y  force; that i s ,  components  (directions).  as has been s t a t e d by B a t c h e l o r (1960, p.88), "... the p r e s s u r e i s  n o n d i r e c t i o n a l and t h e p r o b a b l e velocity  consequence i s t h a t i t b u i l d s up the weaker  component a t t h e expense o f the s t r o n g e r . "  There was l i t t l e  known  of the d e t a i l o f t h i s p r o c e s s whereby a n i s o t r o p i c t u r b u l e n c e , the form initially studied  generated  i n most t u r b u l e n t f l o w s , was t r a n s f o r m e d  toward t h e much  ' i s o t r o p i c t u r b u l e n c e ' f u r t h e r down the energy cascade.  vertical velocity  c o r r e l a t i o n , which e n t e r s as a f l u x d i v e r g e n c e  The p r e s s u r e term i n the  n e t energy budget o f a boundary l a y e r , had n o t been measured e i t h e r .  This  term was u s u a l l y assumed t o be s m a l l (Lumley and Panofsky, 1964, p.121); a recent numerical study, Experimental another  ( D e a r d o r f f , 19 70)  v e r i f i c a t i o n was r e q u i r e d .  agreed w i t h The study  this  assumption.  o f wave g e n e r a t i o n i s  example o f an a c t i v e a r e a o f r e s e a r c h i n which p r e s s u r e  p l a y an important  p a r t i n energy t r a n s f e r .  fluctuations  Knowledge o f t h e s t a t i c  pressure  2 d i s t r i b u t i o n over waves would f u r t h e r our u n d e r s t a n d i n g process.  In a l l these examples, d i r e c t measurement of the s t a t i c  w i t h i n the flow was  required.  Most of the p r e s e n t  the above aspects were i n v e s t i g a t e d .  Some of the important  of the i n t e n s i t y  the s p e c t r a l s l o p e ( B a t c h e l o r ,  He  pressure  w a l l shear  stress.  1960).  c o n t r i b u t i o n to p r e s s u r e  using experimental v e l o c i t y  f l u c t u a t i o n s was  Previous experimental have been mainly  the  data, t h a t the magnitude  o b s e r v a t i o n s o f boundary l a y e r p r e s s u r e  c o n f i n e d t o the measurement of these Two  fluctuations  f l u c t u a t i o n s at Russian  the  the  authors,  (1964) and Gorshkov (1967, 1968) have a n a l y s e d a t m o s p h e r i c s p e c t r a  Golitsyn  and some p r e s s u r e v e l o c i t y  He had  fluctuations  g r e a t e r than, b u t of the o r d e r o f ,  s u r f a c e , e i t h e r o f the e a r t h or of a wind t u n n e l .  Gossard  argument f o r  from i n t e r a c t i o n between the t u r b u l e n c e and  estimated,  of the rms  p r e d i c t i o n s are  and Obukhov's d i m e n s i o n a l  t u r b u l e n t boundary l a y e r flow the p r i m a r y n e a r the s u r f a c e r e s u l t s  fluctuat-  (1956) has shown t h e o r e t i c a l l y t h a t f o r n o n i s o t r o p i c  In c o n t r a s t K r a i c h n a n  mean s h e a r .  static  t h e o r e t i c a l knowledge on t u r b u l e n t p r e s s u r e  i s f o r i s o t r o p i c turbulence.  Batchelor's estimate  pressure  Accordingly, i n this present study,  p r e s s u r e measurements were made and  ions  of the wave g e n e r a t i o n  c r o s s - s p e c t r a from such s u r f a c e o b s e r v a t i o n s .  (1960) showed atmospheric p r e s s u r e s p e c t r a f o r a wide frequency range. a few  'instrument'  examples of m i c r o s c a l e s p e c t r a t h a t were o b t a i n e d l o c a t e d on a tower.  from  an  F o r the m i c r o s c a l e r e g i o n , t h e s e s t u d i e s  2 2 found  a mean s l o p e of about -2  a g a i n s t frequency.  f o r a p l o t of s p e c t r a l d e n s i t y ((dynes/cm )  The p r e s s u r e s p e c t r a shown by Gossard  mid-frequency minimum found  i n v e l o c i t y s p e c t r a as r e p o r t e d by  (see Lumley and Panofsky, 1964, intensity  from the low  d i d not e x h i b i t  frequency  p.43)  b u t g e n e r a l l y decreased  synoptic pressure  Van  /Hz) the  d e r Hoven  continuously i n  fluctuations  t o the  higher  3 frequency  pressure  fluctuations  associated with  This mid-frequency  'filling-in'  i s t h o u g h t t o be due t o m e s o s c a l e  w h i c h do n o t d i r e c t l y for  produce v e l o c i t y  the boundary l a y e r  fluctuations  suggests  that microscale pressure  i n c l u d e some l o w f r e q u e n c y turbulent  energy  observations  that i s not associated with  to evaluate  Because the s t a t i c pressure  fluctuations  requires  Investigations of this  complicated  velocity  and W o o l d r i d g e  from observations  surface pressure  the w a l l s h e a r a b o u t 0.6  eddies  (Hinze,  1959, p.239).  related  each o t h e r , to a field  r e l a t i o n s h i p have so f a rbeen  they of  restricted  p r o p e r t i e s s u c h as t h e rms p r e s s u r e i n  measurements. ( 1 9 6 2 ) g i v e a t h o r o u g h summary o f , as w e l l a s  obtained  fluctuations.  t h e m e a s u r e d rms w a l l p r e s s u r e  is  the l o c a l  turbulence, because a general c o n s i d e r a t i o n of the r e l a t i o n s h i p  Willmarth new, d a t a  may  i n a turbulent flow are, generally  the r e s u l t o f the a i r motions i n t e r a c t i n g w i t h  the consideration of simple  isotropic  aZ,1969).  the p r o p e r t i e s o f the s t a t i c  are n o t an i n d e p e n d e n t q u a n t i t y b u t a r e d i r e c t l y  to  et  near the surface  pressure w i t h i n the f l u i d by r e l a t i n g i t t o the v e l o c i t y  velocity.  surface;  velocities.  There have been attempts  speaking,  phenomena  a t the earth's  example, i n t e r n a l g r a v i t y waves a t h i g h e r e l e v a t i o n s (Herron  This  turbulence.  stress,  t o that date  Conclusions  i n wind  tunnel studies of  d r a w n f r o m t h e i r p a p e r a r e 1) t h a t  i s f a i r l y w e l l e s t a b l i s h e d a t a b o u t 2.5  2) t h a t t h e a d v e c t i o n s p e e d o f t h e p r e s s u r e  t o 0.85 t i m e s  t h e s t r e a m s p e e d , 3) t h a t t h e  o f w a v e l e n g t h X decay a f t e r  travelling  Previous  to this  present  turbulent s t a t i c pressure  study  a d i s t a n c e o f a f e w A, a n d  t h e same  reliable  f l u c t u a t i o n s was  fluctuations  pressure-producing  4) t h a t t h e t r a n s v e r s e s c a l e s a n d l o n g i t u d i n a l s c a l e s o f p r e s s u r e measured a t the w a l l a r e approximately  times  fluctuations  size.  experimental limited  knowledge o f  t o such observations  made  4 at the surface. I t was decided to concentrate on the measurement of pressure fluctuations with scales equal to the v e l o c i t y scales that carry the turbulent momentum flux.  I t i s i n this range that important energy transfers by pressure forces  are expected  (see Background).  Instrumentation that could measure the s t a t i c  pressure fluctuations i n the body of the f l u i d had to be developed and tested (see Pressure Instrument  and In Situ  Calibrations of the Pressure  Instrument).  This instrumentation was then used to obtain data related to the 'description' of the measured pressure fluctuations as w e l l as to obtain estimates o f some of the energy fluxes by the pressure forces (see Microscale Pressure Fluctuations over a Flat Boundary).  Observations taken over wind generated  waves are used to describe some of the properties of the pressure fluctuations associated with wave generation (see Microscale Pressure Fluctuations over Wind Generated Waves). water s i t e s  The data analysed was collected at both land and over-  near the I n s t i t u t e of Oceanography, U.B.C. (I.O.U.B.C.).  In  making observations, other variables, such as, f l u c t u a t i n g wind and wave height, were obtained using instruments developed f o r atmospheric boundary layer research.  In some cases these had been developed at I.0.U.B.C. A  description of the s i t e s and the equipment used, other than the pressure measuring instrument, i s given i n Appendix A. are put i n t o nondimensional  Since most of the data presented  form the actual operating conditions (surface  s t r e s s , mean wind) may not be given e x p l i c i t l y i n the text but are included i n a table i n Appendix C. number (e.g. 120/1).  A l l the data are permanently l a b e l l e d with a 'Run'  The data were analysed d i g i t a l l y ; d e t a i l s on the analysis  methods are given i n Appendix B.  5 BACKGROUND  I t i s the purpose of this section to present f o r l a t e r use some aspects of a turbulent boundary layer, e s p e c i a l l y s t a t i c pressure f l u c t u a t i o n s , that can be predicted from physical arguments. Many of the predictions are based on the Navier-Stokes equation.  In the  usual manner ( c f . Hinze, 1959), equations can be written to represent the momentum balance f o r the mean and f o r the f l u c t u a t i n g part of the flow.  The  equation f o r the fluctuating components i n an incompressible, viscous, constant density f l u i d , written i n Cartesian tensor notation i s  3u. 3U. du 3u. du. — + u. — + U. — + u. — - u. — 3t 3x. 3x. 3 3x. J 3 j 3 2  2  2  2  1  =  1  v  p  X j  where U^ and u^ are the i * " *  2 3 u.  dp +V  3x. 1  —  (1)  3x.3x. 3 3  components of the mean and f l u c t u a t i n g  fluid  v e l o c i t y respectively, p i s the f l u c t u a t i n g pressure, p i s the mean density, and v i s the kinematic v i s c o s i t y .  The bar over a variable indicates an  ensemble average; u^ and p have zero averages.  When analysing observations,  i t i s assumed that the data are measurements of a stationary, random process, and thus that the time averages used are ensemble averages  (Batchelor, 1960,  p.17). The right-handed Cartesian coordinate system to be used has x^ p o s i t i v e i n the d i r e c t i o n of the mean motion i n the boundary layer, and x^ v e r t i c a l l y upward.  The notation x^, x^,  ; u^, u^, u^; U^ i s used interchangeably with  x, y, z; u, v, w; U respectively. The close relationship between the pressure and v e l o c i t y can be seen by taking the divergence of equation (1).  fluctuations  This gives  6  1  8 _p_ ^ 2  p dx x . dx x . K  =  — ~ 9x. x 8 jx  Thus t h e p r e s s u r e i s d e t e r m i n e d b y variable. p.27)  Taking  the i n t e g r a l of  2  r  J  the v e l o c i t y  where x = ' x  "  =  4^F  (  field  dx.'dx.'  1  gradient products  the measurement p o i n t i t s e l f .  )  J  and  i s not  an  independent 1955,  velocity.  1  »,,  t T H 'u.*» - , ,u.'U.') — d Y J J Ixl  1  e x p r e s s e d i n terms  of the  T h i s shows appropriately  the s u r r o u n d i n g f l u i d  T h i s i s sometimes  (3)  T  1  t h e v e l o c i t i e s a t x'.  from  (2)  ( e . g . , Townsend,  t u . ' u . I' - . .u . ' u . ' - TTU J J  - x ; p i s m e a s u r e d a t x and  velocity  of  x i  - u.U.  J  (2) o v e r a l l s p a c e  the p r e s s u r e a t a p o i n t can be  weighted  x i  - U.u.  / • . . » . .  _2  at  x j  - u.u.  J  g i v e s the p r e s s u r e a t a p o i n t i n terms  P  that  i j  ( u.u. J  called  the  and n o t  just  'integral  effect'. The  'isotropy  producing' c h a r a c t e r i s t i c  o f the p r e s s u r e f o r c e s  seen i n the energy budget of the i n d i v i d u a l v e l o c i t y  components.  can  be  These  th equations and  can be  o b t a i n e d by m u l t i p l y i n g  adding t o i t the j  averaging.  A suitable  assuming  energy budgets  by  u^,  and  approximation to these equations which would (Lumley  the f l o w i s s t e a d y s t a t e  mean q u a n t i t i e s  f o r m o f e q u a t i o n (1) by  form o f e q u a t i o n (1) m u l t i p l i e d  an a t m o s p h e r i c b o u n d a r y l a y e r by  the i  i n the x^ d i r e c t i o n  and P a n o f s k y , and  1964,  p.71)  then apply  f o r the i n d i v i d u a l v e l o c i t y  With  these approximations  components  are  to  i s obtained  two-dimensional, with v a r i a t i o n  only.  u^,  the  of  where the f i r s t ~u /2 T  t e r m on  the r i g h t hand  e q u a t i o n , i s the 'energy  feeding'  s i d e , which i s non-zero only  i n the  term r e p r e s e n t i n g e x t r a c t i o n of energy  f r o m t h e mean f l o w a n d p u t t i n g i t i n t o  t h e downwind component o f t h e  turbulence;  the t r a n s f e r of t u r b u l e n t energy  the second term r e p r e s e n t s  the t u r b u l e n t v e l o c i t i e s ,  the t h i r d  the p r e s s u r e g r a d i e n t - v e l o c i t y viscous 'e'. thus  effect  The  on e n e r g y  source or sink.  turbulent  components  (wave n u m b e r s ) . (Batchelor,  This  p.67)  previous to this  t r a n s f e r were o n l y  t r a n s f e r energy between  transfer  the only  terms  Energy  s t u d y and  thus  speculative. the d i f f e r e n t  different  can be seen i n the s p e c t r a l energy  1960, p.87)  effect i s to  t h e u-component ( i n e q u a t i o n  Though t h e p r e s s u r e can t r a n s f e r e n e r g y between i t does n o t  space i s zero,  components a r e t h e p r e s s u r e t e r m s .  of this  dissipation  components and i s n o t a n e t  (Lumley and P a n o f s k y , 1964,  t h e s e terms had n o t been measured  by  total  advection cannot produce a net  the energy b e i n g f e d i n t o  ideas about the p r o p e r t i e s  components,  term the  o f t h e s e p r e s s u r e terms o v e r a l l  t h e o t h e r two v e l o c i t y  t r a n s f e r by  the f i n a l  Since i t i s expected that the net viscous  remaining to t r a n s f e r 4a) i n t o  and  t o t r a n s f e r energy between  d i s s i p a t e e n e r g y and s i n c e of energy between  correlation,  the t r a n s f e r of energy  t r a n s f e r w h i c h i s assumed t o be e n t i r e l y  i n t e g r a l o f t h e sum  the p r e s s u r e acts  term represents  by  Fourier  velocity components  transfer equations  w h e r e t h e p r e s s u r e t e r m d r o p s o u t as a r e s u l t  of  the  8 incompressibility  condition.  Thus any energy  transferred  from a v e l o c i t y  component v i a the p r e s s u r e term must appear i n another v e l o c i t y  component a t  the same wave number. The sum  t o t a l energy budget  f o r the boundary l a y e r can be  of the i n d i v i d u a l e q u a t i o n s  1 1 3 , - u..u - — ( u.u.u 1 3 „ 2 „ i x 3 dx^ dx^  =  Three of these terms ( a l l except  , 1 3 ) - — pu„ + p „ 3 dx^ r  was  ff.).  V  u.V i  u. x  (5)  the p r e s s u r e term) had p r e v i o u s l y been  measured f o r the a t m o s p h e r i c boundary l a y e r (Lumley p.119  and Panofsky,  F o r most cases i t had been found t h a t the energy  1964,  f e e d i n g term  a p p r o x i m a t e l y b a l a n c e d l o c a l l y by the v i s c o u s d i s s i p a t i o n and t h a t  t u r b u l e n t t r a n s f e r term was  small.  Because of the approximate  l o c a l p r o d u c t i o n and d i s s i p a t i o n , s p e c u l a t i o n had been t h a t the d i v e r g e n c e by  the p r e s s u r e f o r c e s was  also small.  the  b a l a n c e between flux  However the i n a c c u r a c y o f  such o b s e r v a t i o n s makes t h i s method o f a p p r o x i m a t i n g  the f l u x d i v e r g e n c e  u n s a t i s f a c t o r y and d i r e c t measurement i s d e s i r a b l e .  The measurements  to e v a l u a t e the r e l a t i v e importance s i m p l i f i e d by  comparing  i n t e g r a t e d from region'  required be  I f e q u a t i o n (5) i s  to z, where z^ i s a lower l e v e l f i x e d n e a r the  viscous e f f e c t s  'transition  p.465) where the t u r b u l e n c e i s i n f l u e n c e d by  the  o f the s u r f a c e , t h i s g i v e s  u u„ 13 n  of the terms i n t h i s e q u a t i o n can  the terms i n m o d i f i e d form.  (see H i n z e , 1959,  the  (4); this gives  9 U  0  r e p r e s e n t e d by  ( U  - U 'z  1  z^.  ) - -T- ( u.u.u 2 i x 3'z  - u.u.uJ ) x x 3'z^  z  - p  (  P lz - P^'z^ u  r  +  3  Z  l  V  2 u V u  ±  dz  =  0  (6)  9 The n o t a t i o n ul  1  z  means the wind a t the l e v e l z.  ' t r a n s i t i o n region' i s thin,  I t i s assumed t h a t the  and t h e r e i s n e g l i g i b l e t u r b u l e n t energy  through i t , the s t r e s s b e i n g c a r r i e d by v i s c o u s f o r c e s .  This  flux  assumption  would only be a p p l i c a b l e t o o b s e r v a t i o n s over a s o l i d s u r f a c e and not over w a t e r when waves are b e i n g g e n e r a t e d .  The approximations are t h a t the terms  e v a l u a t e d a t z^ are s m a l l compared w i t h those e v a l u a t e d at z. tions  These  assump-  give  - u.u.U.I ; - 4 u.u.u I ; - — p n l 1 3 1 z 2 I I 3'z p^3'z 1  as approximations f o r the f i r s t of  three terms which are terms i n the budget  t u r b u l e n t k i n e t i c energy i n the space between the boundary  The f i r s t z by  and h e i g h t z.  term r e p r e s e n t s the n e t r a t e o f w o r k i n g p e r u n i t a r e a on the s u r f a c e  the Reynolds s t r e s s , - ^ -j> u  u  the second the upwards f l u x o f t u r b u l e n t  energy and the t h i r d the r a t e o f w o r k i n g p e r u n i t a r e a by  the p r e s s u r e f o r c e .  A comparison o f these t h r e e terms would i n d i c a t e the r e l a t i v e importance o f each as a n e t energy s o u r c e o f t u r b u l e n t k i n e t i c energy p e r u n i t a r e a f o r the air  below  the l e v e l z.  D i m e n s i o n a l arguments, for  i d e n t i c a l t o those used t o p r e d i c t the -5/3  region  the v e l o c i t y spectrum i n the i n e r t i a l subrange, have been used by Obukhov  to p r e d i c t 1964,  the shape o f the p r e s s u r e spectrum, II(n) (see Lumley  p.84).  and Panofsky,  F o r t h i s r e s t r i c t e d s c a l e range w i t h no p r o d u c t i o n and no  d i s s i p a t i o n , he o b t a i n e d  n(k) where K  =  K  p  p  2  e  4 / 3  k"  (7)  7 / 3  i s some u n i v e r s a l c o n s t a n t .  The p r e d i c t e d power law was  for a  10 condition of ' l o c a l isotropy'. for this  B a t c h e l o r e v a l u a t e d the e x p e c t e d  condition of isotropy.  rms p r e s s u r e  H i s c a l c u l a t i o n , which used measurements o f  the v e l o c i t y a u t o c o r r e l a t i o n (see B a t c h e l o r , 1960, p.182), gave  p  =  2  0.58 p u  (8)  2  S i n c e i t i s n o t c e r t a i n t h a t a c o n d i t i o n o f l o c a l i s o t r o p y occurs a t any l e v e l i n the lower  few meters o f the atmospheric  1969), i t i s d o u b t f u l whether these  results  boundary l a y e r  (Stewart,  can be compared w i t h measured  v a l u e s , even though v e l o c i t y s p e c t r a have a -5/3 r e g i o n . The mean wind p r o f i l e i s assumed, f o r a l l c a l c u l a t i o n s , t o have the ' p r e d i c t e d ' l o g a r i t h m i c form  Ul  -  z  u — — K  In —  (9)  z o  where u. = J - uw , K i s von Karman's c o n s t a n t * h e i g h t where the mean v e l o c i t y  goes t o z e r o .  p r o f i l e assumes n e u t r a l s t a b i l i t y ,  (0.4) and z i s the v i r t u a l o The use o f the l o g a r i t h m i c  a p o i n t t o be d i s c u s s e d l a t e r .  winds a t the e x p e r i m e n t a l s i t e s were 3 t o 10 m s e c ^. this  corresponds  t o a Reynolds number Re = ^  ^^ 5  m  Typical  F o r comparison  purposes,  o f o r d e r 10^.  V When n o n d i m e n s i o n a l i z i n g  the data p r e s e n t e d below, two parameters a r e o f t e n  —  2  used. One, t h e s u r f a c e s t r e s s , x = -puw = p u  A  , i s e v a l u a t e d i n one o f t h r e e  dif-  f e r e n t ways: d i r e c t measurements o f -uw, u s i n g the '^-^ method' o r from the mean wind speed u s i n g a drag c o e f f i c i e n t . Appendix B.  D e t a i l s on these methods a r e c o n t a i n e d i n  The method used f o r a p a r t i c u l a r Run i s g i v e n i n the Data Summary  i n Appendix C.  The o t h e r parameter i s the t u r b u l e n t 'energy f e e d i n g ' term  11 — 9U - uw - r — .  u  I t i s e v a l u a t e d i n the form  dz  a logarithmic p r o f i l e I t was d e c i d e d  Kz  , where t h i s  t o take o b s e r v a t i o n s o f p r e s s u r e  occurs  from a p p r o x i m a t e l y  3  10  r  over  to the t o t a l s h e a r s t r e s s .  f o r the range o f n o n d i m e n s i o n a l -2  0 t o 10 (McBean, 1970).  Another important  frequency  the range of s c a l e s  F o r o b s e r v a t i o n s below  i s t h a t a t the peak o f the w s p e c t r u m .  The  and s h o r t l y  o b s e r v a t i o n a l technique  l e v e l above t h e s u r f a c e . hypothesis  i s assumed.  When  a t about f = 4 x 10  f r e q u e n c i e s above t h i s v a l u e , a l l s p e c t r a o f the v e l o c i t y equal i n t e n s i t y  range  t o 10 Hz.  p l o t t e d i n i n t e g r a b l e l o g a r i t h m i c form, the peak occurs  approximately  nz U  frequencies, f =  Thus t h e frequency _3  r e q u i r e d i n the o b s e r v a t i o n s i s from about 3 x 10  At  l a s t s t e p assumes  ( e q u a t i o n 9) f o r U.  contributing significantly 5 meters, t h i s  *  ^  components have  t h e r e a f t e r a -5/3 s l o p e .  used was t o o b t a i n o b s e r v a t i o n s a t a f i x e d  I n the u s u a l manner, the ' f r o z e n f i e l d '  (Taylor's)  T h i s g i v e s the r e l a t i o n s h i p between f r e q u e n c y n and  wave number k as  k  2  =  ;  where U i s t h e mean a d v e c t i o n wind. corrections  do  n  The same assumption a l l o w s phase  to be made and h o r i z o n t a l g r a d i e n t s t o be c a l c u l a t e d  shift  from the  relation  i r  -  -Fir-  An attempt was made t o take o b s e r v a t i o n s o n l y f o r a steady mean wind speed and d i r e c t i o n , n e u t r a l s t a b i l i t y  and a homogeneous, f l a t  these a r e the assumptions used i n a n a l y s i n g the d a t a .  terrain,  since  12 PRESSURE INSTRUMENT  S i n c e no s u i t a b l e technique  e x i s t e d f o r measuring the s t a t i c  f l u c t u a t i o n s i n a t u r b u l e n t boundary The main d i f f i c u l t y  associated with  l a y e r , i n s t r u m e n t a t i o n was  pressure  developed.  t h i s measurement i s i n e l i m i n a t i n g the  e f f e c t s o f dynamic p r e s s u r e ; dynamic p r e s s u r e i s the normal s t r e s s a s s o c i a t e d with deflecting  flow around a s o l i d body,  i n this  velocity  f l u c t u a t e s , s o does the dynamic p r e s s u r e .  pressure  f l u c t u a t i o n s such  was  specially  designed  acceptable l e v e l .  dynamic p r e s s u r e  As the a i r  When measuring the s t a t i c  fluctuations  are noise.  A probe  t o reduce the dynamic p r e s s u r e v a r i a t i o n t o an  Pressure  f l u c t u a t i o n s sampled by the probe were  i n t o an e l e c t r i c a l s i g n a l by a t r a n s d u c e r . filtering,  case a s e n s o r .  o n l y the frequency  the assembled i n s t r u m e n t  converted  Through t h e use o f pneumatic  range o f i n t e r e s t was r e t a i n e d .  F i g u r e 1 shows  package.  Probe S i n c e i t i s n o t p o s s i b l e to p r e d i c t  the dynamic p r e s s u r e  over a s t r e a m l i n e d body w i t h s u f f i c i e n t a c c u r a c y , developed  empirically.  distribution  the shape o f the probe was  T e s t i n g was done i n a wind t u n n e l .  I t was c o n s i d e r e d d e s i r a b l e to d e s i g n the probe such  that the s i g n a l t o  n o i s e r a t i o was about 10:1. The a n t i c i p a t e d f l u c t u a t i n g s i g n a l l e v e l was taken  to be p u  2 A  ( l a t e r found  t o be a good g u e s s ) .  over water, the s i g n a l would be a p p r o x i m a t e l y -2 maximum n o i s e l e v e l would be 0.03 dynes cm . terms o f a f r a c t i o n o f the s t a g n a t i o n p r e s s u r e  Thus  -1 f o r a 5 m sec  wind  -2 0.3 dynes cm and the d e s i r e d T h i s n o i s e can be g i v e n i n 1 2 pu  where p i s the d e n s i t y  13 of a i r and U i s the mean wind speed. of the s t a g n a t i o n p r e s s u r e .  The d e s i r e d n o i s e  l e v e l i s 0.001 o f the  Thus the task was t o c o n s t r u c t a p r e s s u r e  s a m p l i n g probe which c o u l d operate  at the v a r i o u s  angles  o f i n c i d e n c e o f flow  t h a t would be expected i n the atmospheric boundary l a y e r , and have a maximum dynamic p r e s s u r e  v a r i a t i o n o f only 0.001 o f the s t a g n a t i o n  pressure.  A s u i t a b l e probe would be a shaped s t r e a m l i n e d body, s m a l l w i t h  respect  t o t h e s c a l e s o f i n t e r e s t , which has some p o i n t on i t s s u r f a c e where t h e r e i s sufficiently be  s m a l l v a r i a t i o n i n the dynamic p r e s s u r e ;  located at that p o i n t .  The mean dynamic p r e s s u r e  the s a m p l i n g p o r t would a t some p o s i t i o n away  from the s t a g n a t i o n p o i n t i s m i n i m i z e d when the d i s t o r t i o n o f the n a t u r a l as i t passes a probe i s m i n i m i z e d . R.W.  W.W.  Willmarth  Stewart) s u g g e s t e d t h a t a t h i n s t r e a m l i n e d  flow  ( p e r s o n a l communication t o  disk with  a dipping i n the  c e n t r a l r e g i o n might be a s u i t a b l e method f o r f l a t t e n i n g the s t r e a m l i n e s . A few hundred d i f f e r e n t shapes, v a r i a t i o n s on s t r e a m l i n e d p l a n e t a r y e l l i p s o i d , had t o be t e s t e d b e f o r e The long, two  f i n a l probe was a t h i n ,  t h i n t u b u l a r stem.  sampling ports  probe was designed The  thinness  pressure interest.  c i r c u l a r , streamlined  The d i s k was s l i g h t l y  dipped  t o be used w i t h  the p l a n e  disk attached i n the middle,  a t each o f the two p o r t s i s c l o s e t o z e r o This helped  eliminate pressure fluctuations.  'v', the c r o s s s t r e a m  to a with This  o f the d i s k i n t h e h o r i z o n t a l .  and c e n t r a l d e p r e s s i o n were designed  to eliminate  one was found.  l o c a t e d one on each s i d e a t the c e n t e r , F i g u r e 2.  the downstream v e l o c i t y order  a promising  disks s i m i l a r t o a  such t h a t the dynamic f o r the wind speeds o f  v a r i a t i o n s from a r i s i n g from ' u , 1  C i r c u l a r symmetry was m a i n t a i n e d i n effects.  E l i m i n a t i o n o f dynamic  pressure  changes due t o 'w',  For t h i s  the shape o f the c r o s s - s e c t i o n o f the d i s k was most i m p o r t a n t .  p r o f i l e was such t h a t  the v e r t i c a l wind f l u c t u a t i o n s , was more d i f f i c u l t . The  'w' caused e q u a l changes o f o p p o s i t e s i g n i n the dynamic  14 pressure disk,  a t t h e two p o r t s .  By c o n n e c t i n g  t o a s i n g l e s m a l l n e a r l y r e c t a n g u l a r channel  c a n c e l l i n g was o b t a i n e d  at the mid-point  s i g n a l was s a m p l e d f r o m t h i s m i d - p o i n t . eliminating in  t h e ' u ' a n d 'w' e f f e c t s  o r d e r t o keep  developed,  the s t a l l i n g  the s t a l l i n g  enough f o r t h e e x p e c t e d the s t a l l The  angle,  inches  angle  i n diameter.  tubing.  conflicted,  a c o m p r o m i s e was  as l a r g e as p o s s i b l e .  I n each o f the h a l v e s  end  to provide  of the channel  1  long channel  ports.  a wind  3  t h e c h a n n e l i n g between t h e p o r t s and f o r t h e e x i t t h a t t h e two e n d s o f t h e c h a n n e l n o t i n t e r s e c t , b u t to the ports.  To  t o l e a v e 0.0175 i n c h e s  accomplish between  a n d t h e c e n t e r . . A 0.020 i n c h p o r t w a s d r i l l e d  ( 0 . 0 3 1 i n c h e s w i d e , 0.040 i n c h e s  were glued  a t an  t o i n t e r s e c t w i t h an f o r m e d a 1.50  deep) c o n n e c t i n g  a n d a 3/4 i n c h ( 2 cm) l e n g t h o f s t a i n l e s s  (0.032 i n c h i n t e r n a l d i a m e t e r )  This  than  Initially i t  When t h e two h a l v e s w e r e p u t t o g e t h e r , t h i s  T h e two h a l v e s  i n i t i a l stage  greater  t h i c k and about 1  from the c e n t e r o f t h e o u t e r s u r f a c e o f each h a l f ,  of the channel.  inch  large  a 0 . 0 3 1 i n c h w i d e , 0.020 i n c h d e e p  t h e ends o f t h e c h a n n e l w e r e s t a g g e r e d  angle  F o r t h e shapes  I f t h e w i n d came f r o m a d i r e c t i o n  ( F i g u r e 2) , e a c h 0.050 i n c h e s  I t was n e c e s s a r y  the w a l l  necessary  T h i s a n g l e was c o n s i d e r e d  close t o the center o f the disk f o r connection  this,  The p r e s s u r e  Because the requirements f o r  a n g l e was about 10°. 'w'.  i n the disk,  the channel.  d i s k p a r t o f t h e p r o b e was c o n s t r u c t e d o f b r a s s .  s l o t was m i l l e d  1  along  coiled  t h e measured dynamic p r e s s u r e jumped by an o r d e r o f magnitude.  c o n s i s t e d o f two h a l v e s  be  t h e p o r t s , one o n e a c h s i d e o f t h e  t h e two  steel  stem  t o g e t h e r w i t h epoxy t o form t h e  of the disk.  d i s k u n i t was t h e n s h a p e d on a l a t h e a n d t e s t e d f o r p e r f o r m a n c e i n  tunnel.  standard  Further shaping  engineering units  and t e s t i n g e i t h e r produced a f a i l u r e  or a  15 d i s k which had the d e s i r e d q u a l i t i e s . inability  reason  f o r a f a i l u r e was  t o match the two s i d e s o f the d i s k ; t h i s was n e c e s s a r y  ing w effects.  The shapes (measured w i t h  shown i n F i g u r e 3. these  The p r i n c i p a l  curves.  a micrometer) o f s u i t a b l e d i s k s a r e  T a b l e I , pages 16 and 17, c o n t a i n s  I t appears t h a t i t i s n e c e s s a r y  t h i c k n e s s e s i n the c r o s s - s e c t i o n a c c u r a t e  for eliminat-  the v a l u e s used t o p l o t  t o keep the maximum and minimum  to 0.001 i n c h e s , though the t h i c k -  ness between these p o i n t s may v a r y by a few thousandths o f an i n c h .  T h i s can  be seen by comparing t h e d i s k shapes o f probes E, F, and G, F i g u r e 3. reproducing  these probes each h a l f may be shaped c o m p l e t e l y b e f o r e  In  assembly,  now t h a t the a p p r o p r i a t e shape i s known. The  good d i s k s were s i l v e r s o l d e r e d t o s t a i n l e s s s t e e l t u b i n g ( F i g u r e 1)  o f i n c r e a s i n g o u t e r diameter of approximately i n the next  22 i n c h e s  subsection.  0.069 i n c h e s .  (for rigidity)  t o make an o v e r - a l l stem l e n g t h  (56 cm); t h e reason  The i n t e r n a l diameter  f o r this length i s discussed o f t h i s a d d i t i o n a l stem was  The d i s k and stem t o g e t h e r were t h e 'probe'.  Dynamic n o i s e t e s t i n g o f the probes was done i n a low speed, low turbulence wind tunnel with i s i n the Mechanical  a 90 cm by 70 cm t e s t s e c t i o n .  E n g i n e e r i n g Department o f U.B.C.  The w i n d  I t i s a return type'  t u n n e l i n which the a i r speed can be v a r i e d from 1 t o 15 m s e c \ measured t u r b u l e n c e l e v e l i s a p p r o x i m a t e l y  0.1%.  tunnel  Even i n t h i s  The  low t u r b u l e n c e  wind t u n n e l , o t h e r background n o i s e n e c e s s i t a t e d w o r k i n g on q u i e t , w i n d l e s s nights.  The probe t o be c a l i b r a t e d was mounted n e a r the middle  o f the t e s t  s e c t i o n ; a s p e c i a l clamp was c o n s t r u c t e d t o h o l d the probe at any p r e s e t relative  t o the a i r flow.  the p r e s s u r e observed  angle  The dynamic n o i s e l e v e l was measured by comparing  by the probe t o the p r e s s u r e a t the s t a t i c r i n g o f the  tunnel. The  dynamic p r e s s u r e n o i s e l e v e l s  f o r t h e two probes used f o r most o f  16 TABLE I DATA FOR PLOTTING DISK CROSS-SECTIONS  PROBE E side 1  PROBE F side 2  side 1  side 2  X 0.000 0.069 0.143 0.225 0.295 0.364 0.449 0.519 0.599 0.667 0.722 0.766 0.789 0.855 0.911 0.973 1.029 1.089 1.149 1.202 1.242 1.307 1.374 1.432 1.489 1.528 1.578  0.0000 0.0285 0.0379 0.0421 0.0435 0.0436 0.0429 0.0410 0.0413 0.0403 0.0394 0.0387 0.0388 0.0387 0.0397 0.0402 0.0408 0.0418 0.0432 0.0435 0.0422 0.0424 0.0399 0.0345 0.0285 0.0235 0.0000  Diameter  =  0.000 0.106 0.184 0.263 0.360 0.432 0.507 0.589 0.669 0.719 0.784 0.790 0.857 0.913 0.978 1.038 1.124 1.190 1.235 1.307 1.364 1.415 1.482 1.578  X 0.0000 0.0339 0.0381 0.0422 0.0437 0.0451 0.0422 0.0402 0.0389 0.0373 0.0366 0.0371 0.0368 0.0381 0.0385 0.0390 0.0421 0.0424 0.0422 0.0411 0.0387 0.0345 0.0277 0.0000  1.578 inches  T o t a l Thickness  =  0.087 i n c h e s  0.000 0.086 0.132 0.179 0.240 0.292 0.341 0.388 0.435 0.479 0.533 0.578 0.624 0.686 0.731 0.772 0.789 0.827 0.879 0.930 0.989 1.063 1.108 1.151 1.193 1.240 1.277 1.347 1.383 1.422 1.468 1.580  0.0000 0.0349 0.0404 0.0446 0.0458 0.0446 0.0416 0.0404 0.0395 0.0385 0.0373 0.0370 0.0365 0.0359 0.0358 0.0359 0.0358 0.0359 0.0359 0.0364 0.0372 0.0375 0.0389 0.0397 0.0405 0.0417 0.0435 0.0448 0.0439 0.0407 0.0361 0.0000  Diameter  =  0.000 0.073 0.134 0.189 0.237 0.284 0.331 0.389 0.459 0.504 0.566 0.610 0.657 0.705 0.755 0.790 0.856 0.900 0.951 0.989 1.050 1.086 1.147 1.196 1.242 1.285 1.334 1.390 1.445 1.484 1.535 1.580  0.0000 0.0336 0.0414 0.0453 0.0458 0.0458 0.0458 0.0436 0.0413 0.0408 0.0392 0.0382 0.0371 0.0361 0.0362 0.0362 0.0362 6.0373 0.0380 0.0381 0.0398 0.0408 0.0421 0.0433 0.0455 0.0450 0.0450 0.0445 0.0404 0.0358 0.0247 0.0000  1.580 i n c h e s  T o t a l Thickness  =  0.091 i n c h e s  TABLE I  (continued)  PROBE G side 1  X 0.000 0.115 0.225 0.335 0.415 0.515 0.625 0.715 0.790 0.900 1.015 1.100 1.195 1.295 1.390 1.485 1.581  side 2  X  Z 0.0000 0.0339 0.0426 0.0442 0.0459 0.0436 0.0411 0.0394 0.0379 0.0383 0.0399 0.0426 0.0434 0.0425 0.0374 0.0338 0.0000  Diameter  =  0.000 0.110 0.200 0.325 0.435 0.525 0.615 0.705 0.790 0.900 0.995 1.095 1.185 1.290 1.375 1.470 1.581  Z 0.0000 0.0307 0.0394 0.0430 0.0435 0.0415 0.0399 0.0387 0.0367 0.0383 0.0393 0.0421 0.0434 0.0427 0.0391 0.0300 0.0000  1.581 i n c h e s  T o t a l Thickness  =  0.088 i n c h e s  18 the e x p e r i m e n t a l work can be seen i n F i g u r e s 4 and 5. graphs.  Three of the graphs,  l a b e l l e d as d i f f e r e n t  Each f i g u r e i s f o u r  c o n s t a n t wind speed,  have axes o f p i t c h and yaw which r e p r e s e n t the alignment respect  to the mean wind.  P i t c h i s r o t a t i o n about a h o r i z o n t a l a x i s  p e r p e n d i c u l a r t o the mean f l o w ; t h i s s i m u l a t e d v e r t i c a l axis;  this simulated  of the probe w i t h and  o f the probe w i t h  'v'.  'w'.  Zero angles  Yaw i s r o t a t i o n about a  r e p r e s e n t the i d e a l  r e s p e c t t o the mean wind: the stem p a r a l l e l t o the mean wind  the plane o f the d i s k h o r i z o n t a l .  The f o u r t h graph shows the e f f e c t  change i n mean w i n d speed when the probe had t h e i d e a l alignment; 'u'.  The v a l u e s p l o t t e d a r e the r a t i o s  F i g u r e 4 the v a l u e p l o t t e d a t 0° p i t c h Thus the measured dynamic p r e s s u r e  and 0° yaw when U = 6.1 m s e c ''"is 10.  f o r t h i s alignment  the graphs means t h a t the probe s t a l l e d .  and wind speed was An * p l o t t e d on  I t had been d e c i d e d above t h a t an  r a t i o between the measured dynamic p r e s s u r e  c a l c u l a t e d stagnation pressure i n an atmospheric  simulates  F o r example, i n  10 P / -1000 = -0.01 P where P i s the s t a g n a t i o n p r e s s u r e . s s s  a c c e p t a b l e change i n t h i s  this  of a  o f the measured dynamic p r e s s u r e to  the c a l c u l a t e d s t a g n a t i o n p r e s s u r e m u l t i p l i e d by - 1000.  expected  alignment  fortypical velocity  fluctuations  boundary l a y e r i s about 0.001.  and the  t o be  T h i s i s a change  of 1 between the v a l u e s p l o t t e d on the f i r s t  t h r e e graphs o r a change o f 1  a l o n g the v e r t i c a l a x i s o f the f o u r t h graph.  Superimposed on t h e dynamic  n o i s e p l o t s , by means o f dashed c u r v e s , a r e t h e s t a t i s t i c a l l i m i t s  f o r the  velocity  small  fluctuations  expected  roughness elements, such expected tions,  t o o c c u r over a smooth t e r r a i n w i t h  as over water.  The o u t e r curves  f l u c t u a t i o n s i n the wind, the i n n e r curves  the v e l o c i t y  68%.  c o n t a i n 95% o f the F o r these  f l u c t u a t i o n s were assumed t o have a G a u s s i a n  From the graphs i t can be seen t h a t f o r 95% o f t h e expected stream wind v a r i a t i o n s  calcula-"  distribution.  a n g u l a r o r down-  the dynamic p r e s s u r e n o i s e o f a probe o p e r a t i n g i n  19 a wind between 3.5 pressure  i s about 0.001  (a change of 1 to 2 on the g r a p h s ) .  wind s h i f t s limit  and 9 m s e c  and non-Gaussian, low  curves  shown t o s h i f t  frequency  Transducer The  boundary  et  f o r i n i t i a l studies i n a turbulent  layer.  al  t r a n s d u c e r and pneumatic f i l t e r i n g a p p a r a t u s , which are connected  c o n t a i n e r was  chosen (by c a l c u l a t i o n and  known, the stem l e n g t h of the probe  experimentation)  dynamic p r e s s u r e n o i s e due  t o keep the s a m p l i n g  to b l o c k a g e .  probe-transducer  assembly  c o n d i t i o n i n g and  r e c o r d i n g equipment o f t e n up  The  (see F i g u r e 1) was  (Datametrics  t r a n s m i t t e d by to 100  I n c . , Watertown, Mass., U.S.A.). (Type 511),  supply  (see F i g u r e 6 ) .  (Type 700) 4 x 10  quick disconnect pressure  from  the  c a b l e to  meters away. fluctuations  I t c o n s i s t s of t h r e e  p r e s s u r e s e n s o r was  into  System  a s i g n a l c o n d i t i o n e r (Type 1015), and The  was  p o r t s beyond  e l e c t r i c a l output  the ' B a r o c e l Modular P r e s s u r e T r a n s d u c i n g  a pressure sensor  (0 to 1.3  The  t r a n s d u c e r system used to c o n v e r t the p r e s s u r e  e l e c t r i c a l s i g n a l s was  any  to  o f the probe stem, are e n c l o s e d i n a s t r e a m l i n e d c o n t a i n e r ( F i g u r e 1 ) .  Once the s i z e of t h i s  by  the  5:1.  atmospheric  any  changes c o u l d cause  g i v i n g a minimum s i g n a l to n o i s e  These probes were c o n s i d e r e d s u i t a b l e  the end  velocity  o f the p r o b e , mean  Thus a more r e a l i s t i c n o i s e f i g u r e would  about 0.002 of the s t a g n a t i o n p r e s s u r e  r a t i o of  Misalignment  to an a r e a on the graphs where the dynamic p r e s s u r e  v a r i a t i o n i s l a r g e r than t h a t shown. be  to 0.002 of the s t a g n a t i o n  1  units: a power  a 0 t o 10 mm  Hg  -2 dynes cm fittings.  ) low  i n t e r n a l volume model (0.1 c u b i c i n c h ) w i t h  A diaphragm i n the p r e s s u r e s e n s o r i s d e f l e c t e d  d i f f e r e n c e between two  inputs.  One  i n p u t i s connected  t o the  20 probe, the other Since  t o a r e f e r e n c e volume w h i c h a c t s  as a r e f e r e n c e  t h e d i a p h r a g m i s t h e common p l a t e f o r t w o c a p a c i t o r s w h i c h  excited  a t 10 k H z , i t t a k e s  difference.  This  e l e c t r i c a l signal i s fed to the signal  c o n d i t i o n e r accepts  the amplitude  i n t o a 0 t o ±5 v o l t DC s i g n a l .  corrected  Different full  scale sensitivities are  the ly  5 mv;  In order  closed while  t o make t h e s e  t a k i n g measurements.  and t h e t r a n s i e n t response i s l e s s  Before subjected istic  a r e more t h a n  the pressure  t o the e l e c t r i c a l  s i g n a l i s converted  output.  range could be observed, The h i g h  This  and t h e l e n g t h s  keep the frequency  frequencies frequency slow  than  sensor  adjustments can be  opened.  l e v e l i s approximate-  2 milliseconds.  These  requirements.  i n t o an e l e c t r i c a l s i g n a l ,  filtering  I n order  gives  a band-pass  i t i s  character-  t h a t most o f t h e Reynolds s t r e s s  the frequency  range chosen f o r t h i s  frequencies  a r e damped b y v i s c o s i t y  i n the small  Through e x p e r i m e n t a t i o n  on t h e i n t e r n a l  passages o f t h e d i s k and probe stem. diameter  scale  The q u o t e d a c c u r a c y f o r  adequate f o r the present  t o pneumatic f i l t e r i n g .  0.003 t o 10 H z .  adjust, f u l l  a d j u s t a l l o w the system t o be  ' B a r o c e l ' s y s t e m i s a b o u t 0.5% o f t h e r e a d i n g ; n o i s e  specifications  to  A null  a v a l v e b e t w e e n t h e two i n p u t s o f t h e p r e s s u r e  T h i s v a l v e was  signal  l o a d i n g , ground l o o p s , and c a l i b r a t i o n r e s p e c t i v e l y  c o n n e c t e d i n t h e r e c o r d i n g mode.  easily,  The  cable.  m o d u l a t e d 10 k H z s i g n a l a n d c o n v e r t s i t  a d j u s t , and s e n s i t i v i t y  f o roffsets,  c o n d i t i o n e r by  remote o p e r a t i o n .  o b t a i n e d b y means o f a r e s i s t a n c e v o l t a g e d i v i d e r . adjust, quadrature  are both  on a v o l t a g e p r o p o r t i o n a l t o t h e p r e s s u r e  L o n g c a b l e s , up t o 150 m e t e r s , p e r m i t t e d  while  pressure.  of the connections  response f l a t  study  i s about  t o t h e d i s k , i t was p o s s i b l e  to approximately  20 H z .  The l o w  a r e e l i m i n a t e d by a l l o w i n g the r e f e r e n c e volume t o f o l l o w t h e low  pressure  fluctuations.  This  floating  i s accomplished  by a s m a l l  l e a k between t h e s i g n a l s i d e and t h e r e f e r e n c e s i d e o f t h e t r a n s d u c e r .  21 A 27 gauge, 1/2 i n c h hypodermic n e e d l e was found positions  t o be a s u i t a b l e l e a k .  The  o f the h i g h and low pass c u t o f f s a r e by d e s i g n , n o t d e f a u l t , and a r e  used t o o b t a i n optimum s i g n a l l e v e l s frequency  f o r the frequency  c a l i b r a t i o n i s d e s c r i b e d i n the next  range o f i n t e r e s t .  The  subsection.  S i n c e temperature o r volume changes w i t h i n t h e probe and t r a n s d u c i n g system can a l s o cause a p r e s s u r e especially  on t h e r e f e r e n c e s i d e , t o keep these n o i s e s o u r c e s below the  desired noise l e v e l .  The l i m i t a t i o n s a r e a n e t temperature f l u c t u a t i o n o f  -4 than 10 C° and volume f l u c t u a t i o n s o f l e s s than  less these  restrictions,  r i g i d and adequately a pressure one  change (PV/T = c o n s t a n t ) , care i s n e c e s s a r y ,  the e n t i r e  -5 3 x 10 %.  To meet  t r a n s d u c i n g system and probe package h a s t o be  insulated.  A half  l i t r e vacuum f l a s k  r e f e r e n c e w i t h volume and t h e r m a l s t a b i l i t y .  s i d e o f t h e t r a n s d u c e r by 6 mm diameter,  ( F i g u r e 7) p r o v i d e s  T h i s i s connected t o  i n s u l a t e d , copper t u b i n g . A l l  o t h e r i n t e r c o n n e c t i n g passages a r e formed by d r i l l i n g a s o l i d b l o c k o f a c r y l i c plastic.  The c o n t a i n e r f o r t h e B a r o c e l s e n s o r  c y l i n d r i c a l aluminum p i p e w i t h and  a streamlined  and r e f e r e n c e volume i s a  cone on the upwind, probe s i d e ,  a f l a t p l a t e on the downwind s i d e ( F i g u r e 1 ) .  attached  t o t h e f r o n t cone i s a r a c k on which the t r a n s d u c e r  volume a r e s o l i d l y mounted. position  I n s i d e t h i s p i p e , and  forming  When assembled, the back p l a t e b o l t s  a r i g i d , watertight container.  The e l e c t r i c a l  are through the back of the case and w a t e r t i g h t p l u g s case  can be d i s c o n n e c t e d  from the l o n g i n s t r u m e n t  attachment o f the probe s i m p l e , the f r o n t cone. case  and r e f e r e n c e  To h e l p m a i n t a i n  thermal  and probe a r e k e p t h i g h l y r e f l e c t i v e .  stability,  Once t h e s i z e o f the t r a n s d u c e r  To make the  fitting  i s p r o v i d e d on  the o u t e r s u r f a c e s o f the  These p r e c a u t i o n s  to reduce temperature and m e c h a n i c a l n o i s e s o u r c e s  connections  a r e used s o t h a t the  cable.  a 'quick disconnect'  into  are s u f f i c i e n t  t o the l e v e l r e q u i r e d .  case was known, the l e n g t h o f the stem  22 of the probe had t o chosen j u s t s u f f i c i e n t l y away from the dynamic p r e s s u r e brackets  cylinder.  the d i s k  f i e l d produced by e i t h e r the case o r the  used f o r h o l d i n g the system. P o t e n t i a l flow  c a l c u l a t e the upwind p r e s s u r e  theory was used t o  p e r t u r b a t i o n f o r a sphere and f o r an i n f i n i t e  I t was assumed t h a t most o f the o b j e c t s p r o d u c i n g  be approximated by one o f t h e s e . pressure,  l o n g enough t o keep  F o r a p o s i t i o n x, upwind  blockage could  o f a s p h e r e , the  p, i s g i v e n by  P  where a i s the r a d i u s o f the s p h e r e , U i s the mean a i r v e l o c i t y , density of a i r .  and p i s the  F o r the n o i s e l e v e l r e q u i r e d , the measurements would need t o  be about 8a away.  Thus,  assuming  the l e n g t h o f the stem needed  the case l o o k e d  t o be about 50 cm.  l i k e a sphere t o t h e a i r f l o w , The s i z e o f the dynamic  p r e s s u r e p e r t u r b a t i o n f o r a model o f t h e a c t u a l c o n t a i n e r was checked i n a wind  tunnel.  The r e s u l t s  a r e i l l u s t r a t e d i n F i g u r e 8 and show t h a t the stem  l e n g t h o f about 8a was adequate.  A s i m i l a r c a l c u l a t i o n f o r an i n f i n i t e  c y l i n d e r , o f r a d i u s a, p e r p e n d i c u l a r  P  =  t o the mean flow  gives  P x  For  the same n o i s e l e v e l ,  cylinder.  These  the probe d i s k must be 20a t o 25a ahead o f a  two v a l u e s were used as c r i t e r i a i n e v a l u a t i n g b l o c k a g e by  the case and c y l i n d r i c a l s u p p o r t s d u r i n g measurements.  23 Amplitude  and Phase Response  The p r e s s u r e i n s t r u m e n t amplitude  and phase response.  d a t a can be  1960,  arrangement used  I f the response  i s linear,  f o r c a l i b r a t i n g the i n s t r u m e n t  a l a t e x rubber  as was  assumed, then  produced  i n a c l o s e d 5 g a l l o n drum by  The  diaphragm was  a c i r c u l a r a c r y l i c p l a s t i c p l a t e t h a t was  v i b r a t i o n g e n e r a t o r which was s i g n a l generator.  i s shown i n F i g u r e 9,  diaphragm s t e t c h e d o v e r one end.  shown i n more d e t a i l i n F i g u r e 10. with  calibrated for  p.28).  A s i n u s o i d a l l y v a r y i n g p r e s s u r e was oscillating  t r a n s d u c e r ) was  c o r r e c t e d u s i n g the c a l i b r a t i o n s on the b a s i s o f the c o n v o l u t i o n  theorem ( e . g . , Lee, The  (probe and  A B a r o c e l t r a n s d u c e r (see F i g u r e 9)  drum i s  o s c i l l a t e d by  contact  attached to a Pye-Ling  i n t u r n d r i v e n by  F i g u r e 11 i s the c i r c u i t  The  V45  an a m p l i f i e d v o l t a g e from a  diagram f o r the power a m p l i f i e r .  r e f e r e n c e d t o the atmosphere was  used  d i r e c t l y measure the magnitude and phase o f the p r e s s u r e i n the drum. a strip-chart  r e c o r d e r and an o s c i l l o s c o p e ,  compared w i t h  the p r e s s u r e r e c o r d e d by  was  Using  t h i s measured drum-pressure  was  the p r e s s u r e i n s t r u m e n t when the probe  s e a l e d i n s i d e the drum. A sample c a l i b r a t i o n i s shown i n F i g u r e 12;  6 db/octave  at the h i g h frequency end  and  the measured d r o p o f f i s about  3 db/octave  a t the low  I t i s r e p r e s e n t a t i v e of a l l c a l i b r a t i o n s done f o r t h a t probe and and  to  i s t y p i c a l of those o b t a i n e d f o r the d i f f e r e n t probes.  the c a l i b r a t i o n s To ensure  i s approximately  ±2% i n amplitude  and ±3°  t h a t these c a l i b r a t i o n s were m a i n t a i n e d ,  c a l i b r a t e d b e f o r e and a f t e r each group o f f i e l d  The  frequency  end.  transducer accuracy  of  i n phase.  the i n s t r u m e n t s were  observations.  24  IN SITU  CALIBRATIONS OF THE  PRESSURE INSTRUMENT  Even though the probes had been t e s t e d i n a wind t u n n e l and meet the i n i t i a l  requirements,  were c a l i b r a t e d i n t y p i c a l the t u r b u l e n t p r e s s u r e  atmospheric  fluctuations  tions at a surface port d i r e c t l y  turbulence.  below.  Number o f the p o r t i s s u f f i c i e n t l y  are measured by b o t h w i l l show any  necessary  encountered.  the s u r f a c e and  contaminations  fluctuations with reliably  fluctua-  a i r systems then s u i t a b l e  analysed.  a v e r t i c a l s c a l e much g r e a t e r than  cm.  The  usual  This height  t u r b u l e n c e l e v e l were  a l s o s u f f i c i e n t l y h i g h t o i n c l u d e any range to be  signals  comparisons  the probe.  30 t o 40  diameter  30  important  Thus those to 40  cm  vertical pressure  c o u l d be  compared.  Surface Pressure  Measurement  To o b t a i n a s u r f a c e p r e s s u r e measurement w h i c h does n o t i n c l u d e unwanted dynamic p r e s s u r e be smooth and of  and  p r o v i d e d the Reynolds  I f the same s t a t i c p r e s s u r e  to ensure t h a t a t y p i c a l mean wind and  v e l o c i t y e f f e c t s i n the frequency  probe,  s m a l l (Shaw, 1960); a 0.025 i n c h  requirement.  measuring  A s u r f a c e p r e s s u r e measurement does  dynamic p r e s s u r e n o i s e a s s o c i a t e d w i t h  I t was  done by  measurements o f the p r e s s u r e  d i s t a n c e between a i r and s u r f a c e measurements was was  T h i s was  i n the a i r , w i t h the developed  not have the p r o b l e m o f dynamic p r e s s u r e  used to meet t h i s  to  much more c o n f i d e n c e would be o b t a i n e d i f they  comparing the r e s u l t s w i t h simultaneous  p o r t was  found  level.  the p o r t and  any  f l u c t u a t i o n s , the a r e a s u r r o u n d i n g  There s h o u l d be no s m a l l s c a l e b l o c k a g e  any  the p o r t s h o u l d i n the v i c i n i t y  l o n g , s u r f a c e u n d u l a t i o n s s h o u l d have s c a l e s l a r g e compar-  ed to the s e p a r a t i o n of the a i r and s u r f a c e i n s t r u m e n t s .  The  transducer  and  25 r e f e r e n c e volume used f o r the s u r f a c e measurement were i d e n t i c a l w i t h used w i t h  the probe and were e n c l o s e d  below ground l e v e l , 15  cm  flat  of the box  F i g u r e 13.  aluminum p l a t e . flush with  By  i n a wooden box  t h a t c o u l d be  P a r t of the top of t h i s box was  that  positioned  a 20  cm  c a r e f u l l y p o s i t i o n i n g t h i s p l a t e and  by  the  rest  the l o c a l t e r r a i n , a l l dynamic e f f e c t s were e l i m i n a t e d  over a s u r f a c e p o r t i n the aluminum p l a t e . S i n c e i t was  necessary  p o r t was  not  (2.5  diameter brass plug.  cm)  fitting  drilled  to c a l i b r a t e the s u r f a c e system, the 0.025 i n c h  directly  i n t o the aluminum, but T h i s p l u g c o u l d be  removed from i t s t i g h t l y  p o s i t i o n i n the aluminum p l a t e so t h a t the p o r t and  l o n g s t e e l t u b i n g which l e d from p o r t to t r a n s d u c e r without  modification.  The  i d e n t i c a l t o the one  calibrations  i s shown i n F i g u r e 14.  transducer  for  and  On some o c c a s i o n s  the a i r measurement was The  in situ  Boundary Bay perpendicular  used f o r the a i r system. The  field  connections  At  5 to 10  site,  the t e r r a i n was  transducer with  cm h i g h .  The  c o u l d be  and  runway.  between s u r f a c e p o r t ,  f o r the s u r f a c e p r e s s u r e  considered  used f o r the a i r  and  Upwind the  terrain  was  made 34 meters  F i n e sand made a smooth surface.  At t h i s s i t e  measurement was  At the Boundary the box  conveniently  smooth.  Bay  containing placed  However o n l y an a r e a w i t h i n 2 to 3 meters of the  f l a t and  used  vice versa.  s i t e s : Ladner  s u r f a c e measurement was  the s u r r o u n d i n g  more inhomogeneous.  the sand s u r f a c e .  typical  the Ladner s i t e winds blew from the west  from the l e a d i n g (windward) edge of the runway. t r a n s i t i o n between the box  cm)  phase  the t r a n s d u c i n g system n o r m a l l y  c a l i b r a t i o n s were done a t two  to a 40 meter wide a s p h a l t  mainly t h i c k grass  A  used f o r the s u r f a c e measurement and  (see Appendix A ) .  (10  c o u l d be c a l i b r a t e d  r e f e r e n c e volume were s i m i l a r t o those  measurement.  the 4 i n c h  method of c a l i b r a t i n g f o r amplitude and  response was  pressure  instead i n t o a 1 inch  Patches of g r a s s , w a t e r - f i l l e d  the  flush box  potholes,  26 and  the  o c c a s i o n a l l o g w e r e s o m e t i m e s on  made t o e n s u r e t h a t any was  turbulence  g e n e r a t e d by  o f a s c a l e l a r g e compared t o the  Comparison of Measurements: Surface The  measured by  signals  are  the  A  the probe i n the  p h a s e s and  Ladner s i t e  are  three  d i f f e r e n t p r o b e s and  were c o r r e c t e d f o r amplitude curves  plotted.  denote t y p i c a l  The  each curve  two  and 95%  v e r t i c a l extent  shifting  was  vertical  scale without  becomes p a r a l l e l w i t h are  three i n Figure these  and  confidence  relative  16.  of  the  same  t e n Runs t a k e n  Included  i n these  transducing  systems.  The  limits  dashed l i n e  vertical  A l l the  ( c l . ) f o r each on  the  low  to the  on  frequency  three  m u s t be the  used but 16,  shifted vertically  a b s c i s s a or frequency  the  the  side  until  axis.  the The  the  to the  t h e p r o b e ( p r o b e s E,  F,  32 and  cm.  The  same  in  cm.  The For  only part  G were used).  to  line  curves  systems were i n t e r c h a n g e d .  s e p a r a t i o n was  compari-  vertical  dashed two  of  This  Thus  a v e r t i c a l s e p a r a t i o n o f 40  transducing  the v e r t i c a l  r u n s was  p a i r o f s p e c t r a on  respect  data  estimate  a c t u a l measured v a l u e s .  true p o s i t i o n with  at  comparisons  bars  h i n d e r i n g comparison of p a i r s of curves.  from measurements w i t h  same p r o b e was  in  two  coherence.  d o n e t o a c c o m m o d a t e m o r e t h a n one  the e n t i r e curve  15  I f the  pressure  f o r l a r g e s c a l e s , they have the  different  of the  terrain  sensors.  surface port.  phase response.  r e t u r n a p a i r of s p e c t r a to t h e i r  Figure  a i r and  15  was  i n d i c a t e s t h e amount b y w h i c h e a c h s p e c t r a l p a i r i n a g i v e n  son were s h i f t e d v e r t i c a l l y  axis,  inhomogeneous  phase a r e u s e d t o compare the  have u n i t y  i s shown i n F i g u r e s  Some e f f o r t  Air  c o m p a r i s o n o f p o w e r s p e c t r a , II(n) , f o r f i v e  the  lower  and  same, w h i c h i s e x p e c t e d  power s p e c t r u m and  this  s e p a r a t i o n of the  power s p e c t r a , c o h e r e n c e , and  signals  the upwind s i d e .  the  changed  Each p a i r  of s p e c t r a l e s t i m a t e s 0.010 Run  to 1 Hz. to Run.  agree t o ±20%  Differences i n this  The  values  be  frequency range appeared to be  T h i s was  considered  c o n s i s t e n t l y lower s u r f a c e p r e s s u r e due  i n the  (Z )  U s i n g Panofsky and  an e f f e c t  the p r e s s u r e  the d i f f e r e n c e a t h i g h  as would be  For the  the  -  0.1  q  - 2 cm;  frequency range a n a l y s e d ,  requirement f o r the  phase d i f f e r e n c e be is,  zero  i n F i g u r e 17.  The The  phase and  Q  of  the  7 meters.  When  definite,  t h i s s e t of  observa-  f l u c t u a t i o n s w i t h i n the  two  s i g n a l s to be  the same i s t h a t  flow  the  at which the coherence i s h i g h ;  large with  respect  to the v e r t i c a l  that  separation  coherence f o r the same 5 Ladner Runs are p l o t t e d  coherence i s a p p r o x i m a t e l y 0.95 frequencies.  v e r t i c a l separation.  coherence l e s s than 1 i s an i n d i c a t i o n of the non-  coherent n o i s e between the  two  This  for large scale f l u c t u a t i o n s ,  f a l l i n g o f f a t the h i g h e r The  f a l l o f f i s e x p e c t e d due  systems, i n c l u d i n g dynamic, t h e r m a l ,  f l u c t u a t i o n , and  e l e c t r i c a l noise.  high  i s w i t h i n ±5°, which i s as c l o s e as can be  coherence  A s i m i l a r comparison was In most cases the p r e s s u r e  The  to  with  expected.  made f o r some of the Boundary Bay  Four s p e c t r a from t h i s s i t e  the  volume  phase d i f f e r e n c e f o r the s c a l e s  measurements i n the a i r were 30  s u r f a c e p o r t ; a few were 1 m.  to  ±10%.  f o r frequencies  f o r v e r t i c a l s c a l e lengths  of the p r o b e s .  asphalt, Z  frequency became l e s s  t i o n s showed t h a t the amplitude of the p r e s s u r e  other  thought  probe moved s u c c e s s i v e l y downwind  from the s u r f a c e p o r t ,  c o u l d be measured t o a p p r o x i m a t e l y  often  of the a n a l y s i s .  Townsend (1964), the p r e d i c t e d t h i c k n e s s  measurements were made w i t h  The  random from  range was  i n t e r n a l boundary l a y e r a t the p o i n t of measurement i s o n l y  expected.  from  runway t h a t r e s u l t e d from  (grass, Z  transition  q  to be  1 to 10 Hz  to the i n t e r n a l boundary l a y e r over the  l a r g e s u r f a c e roughness cm).  i n amplitude) f o r f r e q u e n c i e s  a t the l o w e s t frequency p l o t t e d i n the s p e c t r a  d i f f e r e d by more than 20%. The  (±10%  cm  observations.  above  the  are shown i n  28 F i g u r e 18; the v e r t i c a l s e p a r a t i o n i s g i v e n i n b r a c k e t s a f t e r the Run The  number.  curves were s h i f t e d v e r t i c a l l y w i t h r e s p e c t to the v e r t i c a l a x i s i n the  same manner as done i n F i g u r e 15  ( d e s c r i b e d above).  A g a i n each p a i r o f  s p e c t r a l e s t i m a t e s are the same to ±20% i n power, i n c l u d i n g range.  the 1 to 10  No s p e c i f i c i n t e r n a l boundary l a y e r s were e x p e c t e d a t t h i s  however, from some wind d i r e c t i o n s t h a t a t Ladner was  observed.  are a l s o s i m i l a r t o the Ladner  Hz  site,  a h i g h frequency d i f f e r e n c e s i m i l a r t o  The phase and coherence shown i n F i g u r e 19 r e s u l t s ; coherences  are 0.8.to 0.9  and  phases  are the same t o ± 1 0 ° . It i s f e l t air  flow t y p i c a l o f a t m o s p h e r i c boundary l a y e r s w i t h n e u t r a l s t a b i l i t y  has p r o v e n air.  t h a t the i n s t r u m e n t has been t h o r o u g h l y t e s t e d i n a t u r b u l e n t  to be s u i t a b l e  and  f o r making s t a t i c p r e s s u r e measurements i n the  29 MICROSCALE PRESSURE FLUCTUATIONS OVER A FLAT BOUNDARY  Some aspects of the k i n e t i c s  and k i n e m a t i c s  of pressure f l u c t u a t i o n s i n  a t u r b u l e n t boundary l a y e r were measured u s i n g the developed  pressure sensing  probe. The  o b s e r v a t i o n s were made at two  sites:  Spanish Banks and Ladner.  sites  are d e s c r i b e d i n Appendix A.  tidal  f l a t w i t h a t i d a l range of about 4 meters.  The Spanish Banks' s i t e s i s l o c a t e d on a However most o f the  t i o n s used i n t h i s s e c t i o n were taken when the w a t e r was shallow,  l e a v i n g a s u r f a c e of sand  l e s s than h a l f a meter. deeper and  e i t h e r absent  or v e r y  C) taken when the w a t e r  l a r g e r waves were p r e s e n t are a l s o used i n t h i s s e c t i o n .  f o u r Runs were taken at a h e i g h t s u f f i c i e n t l y  was  These  above the waves t h a t the s p e c t r a  d i d not show any i n f l u e n c e from the waves s i m i l a r t o t h a t found  i n the next s e c t i o n .  observa-  o r water w i t h s m a l l waves o f wavelength  Four d a t a Runs (Appendix  t i o n s taken c l o s e r t o the waves.  The  i n observa-  The wave i n f l u e n c e on s p e c t r a i s d e s c r i b e d  A l l o b s e r v a t i o n s were taken below a h e i g h t of 6 meters.  For b o t h s i t e s winds at the 5 meter l e v e l d u r i n g o b s e r v a t i o n s were about 3 t o 10 m s e c \  The wind s t r e s s was  assumed t o be  c o n s t a n t w i t h h e i g h t and f o r  -2 the s u r f a c e roughnesses encountered The method used stability  a t the Spanish Banks s i t e was  of 0 t o -0.1.  g e n e r a l l y between 0.1  t o e v a l u a t e the s t r e s s i s g i v e n i n Appendix B.  s t a b l e during observations  stability  was  1970).  The  local  (see Appendix C ) , w i t h a G r a d i e n t R i c h a r d s o n  The s t a b i l i t y was  however the o b s e r v a t i o n s were taken on cloudy ancy e f f e c t s would be  1 dynes cm  u s u a l l y near n e u t r a l to s l i g h t l y  For t h i s range v e l o c i t y s p e c t r a show l i t t l e  (McBean,  and  at a minimum.  unNumber  dependence on  not measured a t the Ladner s i t e , (but dry) days when l o c a l buoy-  Thus s t a b i l i t y was  f o r most of these p r e s s u r e o b s e r v a t i o n s , except  p r o b a b l y not  f o r those s p e c t r a l  important  estimates  .  30 dependent on any  stability  a t a h i g h e r e l e v a t i o n which, through frequency  values.  the  effect',  c o u l d i n f l u e n c e low  These s i t e s were  suitable  f o r making p r e s s u r e measurements t y p i c a l o f a t u r b u l e n t  boundary  layer.  R e s u l t s o b t a i n e d from o b s e r v a t i o n s a t these s i t e s  'integral  considered atmospheric  are g i v e n i n the  following subsections.  Nondimensionalization  of P r e s s u r e  Spectra  S i n c e the p r e s s u r e i s c l o s e l y t i e d t o the v e l o c i t y , as shown by 2,  the same n o n d i m e n s i o n a l i z a t i o n parameters s h o u l d be v a l i d .  The  of each o f the p o s s i b l e parameters i s c o n s i d e r e d i n terms o f the spectra obtained i n this  equation importance  pressure  study.  The parameters used t o n o n d i m e n s i o n a l i z e  v e l o c i t y s p e c t r a are u s u a l l y a  2 time s c a l e o f z/U  and  an i n t e n s i t y o f u^  .  One  o t h e r parameter t h a t might be  used i s the s t a b i l i t y , which would be more i m p o r t a n t the  'integral effect'  (equation 3).  relatively  s t a b i l i t y was  t o be o f n e a r l y n e u t r a l s t a b i l i t y .  shows t h a t the n o n d i m e n s i o n a l i z i n g  i n s e n s i t i v e to s t a b i l i t y  to  As has been p r e v i o u s l y mentioned a l l d a t a  were c o l l e c t e d under c o n d i t i o n s e s t i m a t e d Recent work (McBean, 1970)  f o r the p r e s s u r e due  under these c o n d i t i o n s .  of v e l o c i t y i s Since  n e a r l y n e u t r a l d u r i n g a l l Runs, i t i s assumed to be  the of  secondary  importance. The  i n f l u e n c e of the  observations f o r 0,  1.8,  ' i n t e g r a l e f f e c t ' on p r e s s u r e s p e c t r a i s s e e n i n  taken s i m u l t a n e o u s l y 3.75,  and 5.5  a t two  levels.  meter v e r t i c a l s e p a r a t i o n s .  18 the dashed l i n e i n d i c a t e s the v e r t i c a l s h i f t on page 26).  F i g u r e 20 shows t h a t t h e r e i s no  s p e c t r a l l e v e l s due  F i g u r e 20 shows s p e c t r a , II, As i n F i g u r e s 15  of each curve  (as d i s c u s s e d  large systematic difference i n  to the v e r t i c a l s e p a r a t i o n of the measurements.  c o n t r a s t , s p e c t r a o f the v e l o c i t y  and  In  components show a d i r e c t dependence on  z  31 ( s e e M c B e a n , 1970) frequency  f =  and .  can be  The  nondimensionalized  'integral effect'  z dependence from the p r e s s u r e tions  is difficult  appears  s p e c t r a at these  with v e r t i c a l separations It  u s i n g the  give s i m i l a r  to define a U  nondimensional  t o h a v e r e m o v e d any  lower  levels.  Other  strong observa-  results.  , or propagation  velocity,  f o r use  in  the  P nondimensionalizing. boundary l a y e r , similar  o b s e r v a t i o n made a t t h e b o t t o m o f  w h e r e t h e mean v e l o c i t y  t o , i f not  velocity  F o r e x a m p l e , an  identical with,  i s z e r o , has  that a t , say,  the p r e s s u r e  sionalized =0)/ U The 2 p u  4 A  .  1 m e t e r , w h e r e t h e mean  s p e c t r a w i l l h a v e some d i r e c t  w i n d b u t h a v e b e e n shown a b o v e t o h a v e l i t t l e  p  power s p e c t r u m  i s non-zero.  Since  k  a pressure  the  i n the c  analysis but  , where U _>  intensity Since  different  i s changed i n t o  i s t h e mean w i n d a t 5  j  on  of the p r e s s u r e  z,  dependence on  frequency  the  i s not  mean  nondimen-  a wave number d e f i n e d  by  meters,  fluctuations  was  nondimensionalized  by  t h e same k i n d s  o f d a t a w e r e n o t a v a i l a b l e f o r e a c h Run, three 2 methods o f e v a l u a t i n g u were u s e d : d i r e c t measurement u s i n g a A  s o n i c anemometer ( t h e most r e l i a b l e method) ; c a l c u l a t i o n  using  the $ ^  method;  -3 and  use  of a drag  coefficient  methods i s c o n t a i n e d  i n Appendix  Examples o f p r e s s u r e a r e shown i n F i g u r e s  -3  of  21  =  1.2  x 10  .  F u r t h e r d i s c u s s i o n on  B.  s p e c t r a which are nondimensionalized  and  22.  the  For values  o f wave number k  i n this greater  way than  -1  3 x 10 cm , t h e s p e c t r a h a v e a p p r o x i m a t e l y t h e same s l o p e , - 0 . 7 . At lower wave numbers t h e s l o p e i s l e s s s t e e p and t h e r e i s more s c a t t e r , s i m i l a r t o t h a t 4 which occurs 1 x 10^ given k ^ by  i n low  t o 50 now  a factor  x  10^.  frequency After  d i f f e r by  o f a b o u t 50.  velocity  spectra.  The  range o f u^  n o n d i m e n s i o n a l i z i n g , extreme values  a factor The  of 2 whereas  the  dimensional  involved i s of kll(k),  spectra  v a r i a n c e b e t w e e n s p e c t r a c o u l d n o t be  at  a  differed  improved  32 with the present data since that of ±40%.  2  2 4 i s about ±20% and of p u^ about  The levels of the nondimensionalized pressure spectra s c a t t e r w i t h i n 2  this value; therefore the scatter might be due e n t i r e l y to the error i n u^ rather than to dependence on some other v a r i a b l e . A l l spectra which were nondimensionalized i n this manner are summarized i n Figure 23. of z.  The value of  The mean i s 3.5 ± 1.  kll(k) 2 4 P u*  at k  —7;—r  Pp  =10  -2  cm  -1  i s p l o t t e d as a function  As noted e a r l i e r there i s no n o t i c a b l e dependence  on z. The data given by Gorshkov (1967) do not seem to agree with these present 4 r e s u l t s ; they do not exhibit the U  dependence shown here.  As the wind speed  increased the i n t e n s i t y of his pressure spectra did not necessarily increase. It i s not known however whether a l l of h i s measurements were taken with a nearly constant surface roughness. From the present study, i t appears that the pressure s p e c t r a below 5 meters i n an atmospheric boundary layer of nearly n e u t r a l s t a b i l i t y are 2 adequately nondimensionalized i n terms of the s t r e s s , pu^ and a wave number k = to/ U L . p '5 t  Shape and Intensity of the Spectrum  - _  As with any turbulent variable, the shape and i n t e n s i t y of the power spectrum  for pressure fluctuations gives some clue of the r o l e of pressure  at d i f f e r e n t frequencies. Normalized pressure spectra, II(n)/a  2  - l " ), are p l o t t e d i n Figure 24. v>  (Hz  2 They are normalized by t h e i r i n t e g r a l s , which equal t h e i r variances a -2 between 2.7 x 10  ,  0 and 7.4 x 10  Hz, the frequency range p l o t t e d .  These  33 s p e c t r a , p r e v i o u s l y shown i n n o n d i m e n s i o n a l f o r m i n F i g u r e because a s s o c i a t e d v e l o c i t y  s p e c t r a are  r e p r e s e n t a t i v e of a l l those  obtained  were taken 0.8  at heights  d y n e s cm  .  The  of  available.  They a r e  over a f l a t boundary.  Vertical lines  The  i n d i c a t e the  95%  confidence  limits  to  be  observations approximately  s p e c t r a show a r e g u l a r p o w e r l a w b e h a v i o u r at  chosen  considered  3 t o 5 m e t e r s ; s u r f a c e w i n d s t r e s s was  most of the v a r i a t i o n s between d i f f e r e n t s p e c t r a o c c u r i n g end.  21, were  a b o v e 0.3  the  low  ( c l . ) of  Hz,  frequency  individual  es t i m a t e s . The  velocity  spectra associated with  a r e shown i n F i g u r e s  25  f o r the i*"*  component.  1  velocity  ' u n i v e r s a l curves' The  slopes  and  obtained  26.  by  ^  and  and  -7/3  fit  to the  and  26;  respectively.  data  the s t r a i g h t l i n e has  range, the p r e s s u r e significantly the peak of of  the w  frequency $  .  spectra i n isotropic  (Stewart,  24,  has  1969).  spectra i s a  t o any  s i g n i f i c a n t values  27  reasonable  spectrum, Figures  25  frequency  a mean s l o p e  of about  -1.7,  the  The  arrow.  suggestion such  approximate p o s i t i o n of Despite turbulence  may  not  slope be  pressure  anisotropy.  i s a plot of  n e a r f = 0.6;  t h e -5/3  i s t h a t the  i n d i c a t i o n s that complete i s o t r o p y i s not Figure  be  t h e same  range, the  The  to  For  predicted.  frequency  a l s o found.  the  turbulence  ( s e e B a c k g r o u n d p.9)  f o r the v e l o c i t y  f r o m t h e -2.3  24  spectral density  s p e c t r a conform w i t h  this predicted slope.  spectra i n this  range are  T h i s has  frequency  above the peak o f the w  more s e n s i t i v e t h a n t h e v e l o c i t y Three other  i e  spectra i n Figure  (1970).  s p e c t r u m i s i n d i c a t e d by  isotropic  *  arguments  -5/3  spectra, Figure  different  the v e l o c i t y  completely is  The  for frequencies  t  pressure  have been p r e d i c t e d from dimensional -5/3  s  These v e l o c i t y McBean  of the v e l o c i t y  the p r e s s u r e  present  the u and  that i s , at  the  in w  this cospectrum,  lower  34 frequencies of the  o f the -5/3  flow cannot be  t h i s s e c t i o n , see  slope  r e g i o n of the v e l o c i t y s p e c t r a .  d e s c r i b e d as i s o t r o p i c .  F i g u r e 46)  significant  energy f l u x out of the u  the p r e s s u r e  1 to 10 Hz.  I t i s a l s o shown l a t e r t h a t throughout the h i g h e r  turbulence  velocity  d e s c r i b e d as  through most of the  completely  plotted.  than 10)  pressure-  highest  Thus f o r these n o n d i m e n s i o n a l f r e q u e n c i e s  studied  the d a t a seem t o i n d i c a t e a l a c k o f complete i s o t r o p y .  behaviour f o r pressure  spectra in isotropic  the K o l m o g o r o f f c o n s t a n t  for velocity,  of the u n i v e r s a l c o n s t a n t ,  a c r i t i c a l t e s t of  the  turbulence.  cu/u|^ > 10  Even though the wave number range  estimate  range  frequencies,  i s o t r o p i c s i n c e the  Because of the l a c k o f i s o t r o p y these d a t a are not -7/3  velocity  frequency  coherences do not become i n s i g n i f i c a n t u n t i l n e a r the  frequencies (less  cannot be  part  ( t o be shown l a t e r i n  component by  the  f o r c e s occurs  Also  Thus t h i s  has  been used t o o b t a i n  i t i s q u e s t i o n a b l e whether a rough  K , i n Obukhov's f o r m u l a t i o n  (p.9)  can  P be made s i n c e the p r e s s u r e difficulty  s p e c t r a do not have a -7/3  i n t r y i n g to e v a l u a t e  z dependence i n the p r e s s u r e d i s s i p a t i o n , £, i s g i v e n by  K  p  Thus f o r the  -  k  !? 2  P  ( k ) A  U  *  4  data obtained  A different  the p r e s e n t  A further  d a t a i s the l a c k of  s p e c t r a , kll(k) (see F i g u r e 21). u  / K Z (the r a t e of energy  A  ( Kkz  K  with  slope.  P  )  4  /  3  I f the r a t e o f  production),  .  would v a r y  as  z  4/3  and  not be  a  constant.  t h e o r e t i c a l argument p r e d i c t i n g the s l o p e o f the  spectrum has been g i v e n by H. Based on s i m i l a r i t y  any  pressure  Charnock ( p e r s o n a l communication to R.W.  asssumptions, he p r e d i c t e d a -1 s l o p e .  Stewart).  T h i s i s a l s o not  35 p r e s e n t i n the d a t a f o r any s i g n i f i c a n t  range of f r e q u e n c i e s .  The mean shape of the p r e s s u r e s p e c t r a i n F i g u r e 24 i s used f o r comparison w i t h p r e v i o u s l y p u b l i s h e d p r e s s u r e s p e c t r a , F i g u r e 28. were s h i f t e d v e r t i c a l l y  to l i e near  the mean curve  The  from F i g u r e 24.  latter  A l l of  these s p e c t r a were o b t a i n e d i n the atmospheric boundary l a y e r a t comparable wind speeds.  The  o b s e r v a t i o n s by  the two  Russian  authors, G o l i t s y n  Gorshkov (1967), a r e of s u r f a c e p r e s s u r e measurements; those by were taken i n the a i r .  The  same o r d e r of magnitude as Gossard's  than the boundary l a y e r t u r b u l e n c e ; such  probe,  Nevertheless  while  the mean  have been due  to sources  At  other  as, i n t e r n a l g r a v i t y waves a t h i g h e r  (Herron e t a l , 1969).  Variations l y observed  (1960)  are s i m i l a r t o t h a t o b t a i n e d i n the p r e s e n t s t u d y .  f r e q u e n c i e s some o f the d i f f e r e n c e s may  elevations  Gossard  o b s e r v a t i o n s i s o f the  t h a t o b t a i n e d u s i n g the developed  r e s u l t s are an o r d e r of magnitude l a r g e r .  s l o p e s of these curves low  i n t e n s i t y o f the R u s s i a n  (1964) and  from the w e l l d e f i n e d s l o p e shown i n F i g u r e 24 were o c c a s i o n a l -  i n t h i s s t u d y ; they were s i m i l a r t o those found by Gorshkov  They c o u l d be  a t t r i b u t e d to a lack of s t a t i o n a r i t y  and n o n - u n i f o r m i t y  (1967).  of  the  terrain. A more d e t a i l e d comparison between the p r e s s u r e and shown i n F i g u r e 29.  P l o t t e d a g a i n s t frequency  are two  the v e l o c i t y i s  curves r e p r e s e n t i n g  the v a r i a n c e w i t h i n narrow frequency bands of the n o n d i m e n s i o n a l of the n o n d i m e n s i o n a l The v a l u e s p l o t t e d are  sum  / II(n) An  where An i s the bandwidth. measured w i t h The  o f the t h r e e v e l o c i t y  The  /( pu^ ) 2  velocity  and  pressure  components from Run ( §^  + $  components and  2 2  + $  3 3  form  to show how  120/1. ) An  / u^  the s t r e s s were  a s o n i c anemometer a t the same l e v e l as the p r e s s u r e  v a l u e s have been p l o t t e d i n t h i s  and  probe.  the r e l a t i o n s h i p between  the p r e s s u r e v a r i a n c e and v e l o c i t y v a r i a n c e changes f o r d i f f e r e n t s c a l e  ranges.  36 As  can be  seen both  pressure  curves  the p r e s s u r e curve  curves  i s roughly  curve  e x h i b i t a s i m i l a r shape.  At h i g h  twice  at low  i s more t h a n  i s a f u n c t i o n o f z and  s h i p has  the v e l o c i t y  twice the v e l o c i t y  the pressure  some z d e p e n d e n c e w h i c h w o u l d be  c i e s , n e a r and maxima and  Runs i n t h i s  group  properties.  Batchelor evaluated,  amplitude  r e s u l t was c a n be  / p  of the p r e s s u r e = 0.58  2  compared w i t h  Since  pu  (p.10).  2  the present  (p.30) t h i s  lower  f r e q u e n c i e s , f > 1,  from B a t c h e l o r s  a c t i o n between the He  turbulence  and  s c a l e s of the  cm,  sufficiently  turbulence  correlation,  the  not  completely  isotropic.  At  v  other general  a value  I t i s questionable whether this  the  for His  result the  higher  F i g u r e 2 9 , w h e r e some s e m b l a n c e o f i s o t r o p y i s about ten times  This higher pressure t h e mean s h e a r  might be  as s u g g e s t e d of the  form  at frequencies near f = 1 are  l a r g e t h a t an  The  a n d h a v e t h e same  p r e d i c t e d t h a t the m a j o r t e r m w o u l d be  The  frequen-  f r o m u and  the o b s e r v a t i o n h e i g h t .  root-mean-square pressure  relationship.  1  relation-  frequencies arise  1,  velocity  m e a s u r e m e n t s s i n c e , as s h o w n a b o v e , i n  t u r b u l e n c e was  have e x i s t e d , the  the  fluctuations i n isotropic turbulence.  nondimensional  (1956).  At  the  frequencies, f <  most n o t i c e a b l e a t t h e h i g h  from the v e l o c i t y  the  ed  i s not  (p.33) were at s i m i l a r h e i g h t s  range a n a l y s e d  may  curve.  minima w o u l d not have a z dependence s i n c e they o f s c a l e s much l a r g e r t h a n  rms  curve  above the peak o f the w s p e c t r u m .  fluctuations  the  curve;  frequencies  interaction with  by  that  due  to  expectinter-  Kraichnan  p(3U/3z)(3w/3x).  of the  order of  t h e mean s h e a r w o u l d  50  be  expected. The data,  s p e c t r a p l o t t e d i n F i g u r e 2 1 show t h a t , a t l e a s t  t h e r e i s no  s t r o n g i n f l u e n c e f r o m the low  which were found i n p r e s s u r e to drop o f f a t t h e s e spectra. variance  lower  s p e c t r a by  frequencies  Gossard  frequency (1960).  the  group  of  m e s o s c a l e phenomena These s p e c t r a  i n a manner s i m i l a r  These d a t a are used t o e v a l u a t e and  for this  to the  appear  velocity  r e l a t i o n s h i p between the  the s u r f a c e s t r e s s assuming t h a t the p r e s s u r e f l u c t u a t i o n s  pressure  37 arise entirely  from boundary l a y e r  turbulence.  A l i n e a r p l o t showing the average of the n o n d i m e n s i o n a l i z e d F i g u r e 21 as a f u n c t i o n of wave number i s g i v e n i n F i g u r e 30. c o n s i d e r e d to be  r e p r e s e n t a t i v e of a l l the d a t a c o l l e c t e d .  a l i z e d p r e s s u r e , kll(k) / ( p u ^ * ) , i n F i g u r e 30 was 2  In k from a wave number, k lines  1  a)/u| ,  =  p  'b  c  o f 10  —5  pressure  The  The  -2  cm  —1  .  curve i s  nondimension-  integrated with  to 2 x 10  of  r e s p e c t to The  i n d i c a t e the curve used near the l i m i t s o f the i n t e g r a t i o n .  dashed This  integ-  r a t i o n g i v e s the root-mean-square p r e s s u r e i n terms o f the s u r f a c e s t r e s s , p u  =  2.6  p u  (12).  2 A  T h i s r e l a t i o n s h i p i s almost measurements i n wind t u n n e l s w i l l be shown l a t e r ,  i d e n t i c a l t o t h a t o b t a i n e d from s u r f a c e  ( W i l l m a r t h and W o o l d r i d g e , 1962).  the n o n d i m e n s i o n a l i z e d  S i n c e , as  curve i n t e g r a t e d to get the r o o t -  mean-square p r e s s u r e i s not a f u n c t i o n of h e i g h t , the r e l a t i o n s h i p would expected  t o h o l d a t the s u r f a c e .  The magnitude g i v e n by e q u a t i o n  the range p r e d i c t e d t h e o r e t i c a l l y by K r a i c h n a n  Some K i n e m a t i c s  a v a r i a n c e of about 6.5  (12)  velocity  p ^ *. 2  1  measurement o f s t a t i c p r e s s u r e  fluctuations  p o i n t s i t i s p o s s i b l e to deduce some p r o p e r t i e s of the s t r u c t u r e of  directions.  is in  o f the P r e s s u r e F l u c t u a t i o n s  From the simultaneous  fluctuations.  be  (1956).  In summary, the p r e s s u r e spectrum i s s i m i l a r i n shape to the spectrum and has  A  Observations Phase and  s i z e and p r o p a g a t i o n  were spaced  i n each o f the three  at  two  these  principal  coherence a r e used to e v a l u a t e the o r i e n t a t i o n , s c a l e  velocity  o f the  fluctuations.  Coherence and phase between d i f f e r e n t p a i r s o f p o i n t s w i t h p u r e l y  :  38 vertical  (Az)  and  The  32.  and  purely  transverse  phases p l o t t e d are  g r e a t e r t h a n 0.2.  The  shifts  present  t h a t may  of i n t e r e s t .  be  for  separations  f o r frequencies  separations  i n the p r e s s u r e  transverse separations From a comparison o f  o f up  range.  As  Ideally,  expected,  c o h e r e n c e and  c o h e r e n c e s h o u l d be  to conform w i t h  a phase d i f f e r e n c e s h o u l d s e p a r a t i o n of Figure  33,  result,  the p r e s s u r e  A  energy had b e e n l o s t by to three wavelengths  expected  to y i e l d  From t h e scale  a l a r g e r and  two  a high  can be  will  a  'scale'comparable  a down-  pressure the  downstream  f o r phase  Willmarth  travelled  and  shifts  Wooldridge  that  significant  a d i s t a n c e of  Time l a g c o v a r i a n c e s of  and  coherence,  incoherent  would  about be  'decay r a t e ' .  s i g n a l s at a given s e p a r a t i o n ,  determined.  When m e a s u r i n g  l a r g e compared t o  simultaneously  fluctuations with  t o t h e p r o b e s e p a r a t i o n can  i n the  two  a 'scale' size  compared t o the s e p a r a t i o n cannot o c c u r s i m u l t a n e o u s l y . with  the  the  lag covariances  a 'scale' size  often occur  coherence, w h i l e  with  at a fixed separation perpendicular  fluctuations with  s e p a r a t i o n of the sensors  time  correct estimate  sensors  sensors  'decay r a t e ' of  wavelength.  pressure  phase  a t a l l downstream s e p a r a t i o n s  t h e i r F i g u r e 10).  fluctuations  pressure  mean f l o w , p r e s s u r e  producing  the  for  non-zero.  p a t t e r n t h a t had  c o h e r e n c e b e t w e e n two  f o r the p r e s s u r e  pressure with  (see  range  average r e l a t i v e  c o m p a r i s o n o f p h a s e and  a f t e r one  a pressure  frequency  o f w h i c h d e p e n d s on  (1962) found from w i n d t u n n e l s t u d i e s u s i n g  two  the  shows t h a t the s i g n a l s become e s s e n t i a l l y  o f a b o u t 360° o r a p p r o x i m a t e l y  i n the  was  phase  'frozen f i e l d hypothesis',  and  the s i z e  sensors.  t o o b s e r v e any  p h a s e f o r two  the  1 at a l l frequencies  coherence  preferred vertical orientation  stream separation i t i s p o s s i b l e to estimate fluctuations.  the  31  to 5 meters, the average phase  i s not s i g n i f i c a n t l y the  at which  fluctuations  Thus t h e r e i s no  fluctuation i n this  a r e shown i n F i g u r e s  used are s u i t a b l e  For v e r t i c a l separations  difference i s near zero. a pressure  (Ay)  Those  a  the to  the  the  signals  small  fluctuations  o c c a s i o n a l l y produce  39 some c o h e r e n t frequency through  s i g n a l a t t h e two p r o b e s .  scale length at  n , L ^ ( n ) , i s d e f i n e d as t h a t s e p a r a t i o n a t w h i c h  some l o w b u t m e a s u r a b l e v a l u e .  w h e r e IT^^ r e p r e s e n t s and  Thus t h e p r e s s u r e  the coherent  I I , a n d e = 2.72.  falls  chosen i s t h a t a t which  e n e r g y b e t w e e n two s i g n a l s o f e n e r g y II  I n o t h e r words, where the  0  coherence  The f r e q u e n c y  the coherence  =  =  0.14 .  ( F o r s e p a r a t i o n s p e r p e n d i c u l a r t o t h e mean f l o w , a s c a l e b a s e d o n t h e c o h e r e n c e i s e q u i v a l e n t t o a s c a l e b a s e d on t h e c o r r e l a t i o n The  c o h e r e n c e o f 0.14 r e p r e s e n t s  two  pressure  coherences  given i n Figures  coherence f a l l s into  a d e f i n i t e b u t l o w common e n e r g y  between  signals.  Representative are  coefficient).  f o r the three d i f f e r e n t separation d i r e c t i o n s  3 1 , 32, and 33.  Since  the frequency  t o 0.14 d e p e n d s on t h e p r o p a g a t i o n  n^ a t which the  velocity,  a w a v e l e n g t h , A , w h i c h i s i n d e p e n d e n t o f t h e mean w i n d  i t i s converted using  P  (13).  I t w i l l b e s h o w n l a t e r t h a t u|^  i s a close approximation  propagation  velocity  manner.  i s t o be compared t o L .  1  This  A  can a r i s e  o f the pressure  f r o m wow  to the actual  fluctuations  f o r data analysed  i n this  I f coherent  noise''' i s p r e s e n t  before  and f l u t t e r i n t h e a n a l o g  tape  recorder.  40 the  coherence f a l l s  Probe separations  t o 0.14  the  o f 0.14  on  d r a w n among t h e p o i n t s h a s  cm.  Therefore 1/2  the  P  and  A  P  .  Figure  The 34  a first An  P  The  be  represented  by  of  constant  as  32,  corresponding  t h o u g h t t o be  34.  a b o u t ±100%. due  The  coherences  constant  coherence p l o t t e d  can be  32,  .  seen i n Figures  o f f roughly  to  between  As  The  34.  of  P (L^) i s  limit.  of constant  31,  and  l i n e a r l y when p l o t t e d  t h e same i n a l l c a s e s  T h i s s l o p e was  as  and  used to p l o t  coherence at a given  a p l a t e a u which decreases Figure  to a A  the  the  can lines  separation, separation  This plateau i s not w e l l defined  probe s e p a r a t i o n values  These r e s u l t s expected  ( l n n)  a l s o has  i n d i c a t e d on  o c c u r s , v a r y by is  coherence  a  These are used t o e v a l u a t e  i s approximately  coherence i n Figure  31 a n d  increases,  falloff  of d i f f e r e n t  be  .  at a given s e p a r a t i o n , coherence f a l l s This  the  data.  observations  t h e mean s h a p e o f  the p r o p o r t i o n a l i t y  P  A . P  h o r i z o n t a l scales to  i s c l o s e to the p r a c t i c a l  i n f l u e n c e o f p r o b e s e p a r a t i o n on  Figures  choice  a l s o shows a f a m i l y o f c u r v e s  a g a i n s t I n n.  Wind t u n n e l  L  .  changes o n l y  o f 0.14  two  as  downstream  o f 100 cm c o r r e s p o n d s P of the p r e s s u r e f l u c t u a t i o n s  of a wavelength, A  value  (including  approximation,  f r o m t h e same Runs u s e d i n e v a l u a t i n g L  33,  line.  varies directly  P  cycle).  a l s o found the  actual size  determine the s c a l e s i z e  that i s , L  i s a b o u t one  fluctuation is spherical.  approximately  L  time  T h u s , as  o f 1;  f o r a g i v e n A^  a n d W o o l d r i d g e , 1962)  comparable i n s i z e .  210  the  a slope  s e p a r a t i o n , s i n c e the decay  pressure  a straight  f o r n = n ) a r e p l o t t e d as p o i n t s a g a i n s t P L l o g - l o g p l o t i n F i g u r e 34. The s o l i d l i n e  directions yielded similar  (Willmarth  i s e x t r a p o l a t e d by  (equivalent to L  f o r coherences  All  curve  shown, f o r w h i c h a g i v e n  drop i n coherence a t the l o w e r  and  plateau  frequencies  to n o i s e .  of s c a l e s i z e  and'decay r a t e can be  magnitude of the p r e s s u r e  1  fluctuations.  used to estimate  Assuming t h a t the  the  pressure  41 fluctuations result velocity 3  from the complete a c c e l e r a t i o n o r d e c e l e r a t i o n o f a  fluctuation,  the o r d e r o f magnitude 6  of — p  of  Au./At, where A i n d i c a t e s the rms f l u c t u a t i o n s l  Run  120/1  ( F i g u r e s 24 and 25) at 0.7 Hz  -1 -2 10 cm s e c ; Ap - 1 dyne cm . of about Lp/2.  Az  =  Thus  —  w i l l be of the o r d e r  from the mean.  (bandwidth = 0.21  For  Hz), w - u - v -  The g r a d i e n t of p w i l l a c t o v e r a d i s t a n c e  f o r the example,  U  L 2  Az  U  —1  =  4 n  ~  250  cm.  These v a l u e s give A t = p Au_^ Az/Ap - 3 s e c .  T h i s i s comparable t o the  c a l c u l a t e d 'decay time' o f about 4 seconds assuming the d i s t a n c e r e q u i r e d f o r a p p r e c i a b l e decay of a p r e s s u r e f l u c t u a t i o n i s about 3 wavelengths The p r o p a g a t i o n v e l o c i t y i s e v a l u a t e d from the phase d i f f e r e n c e two s i m u l t a n e o u s p r e s s u r e measurements w i t h a downwind s e p a r a t i o n . 33(b) shows the phase d i f f e r e n c e , 0, f o r downwind s e p a r a t i o n 0, 1, 2, and 4 meters. t h a t downwind was  The'measurement upwind was  i n the a i r ( a t 32 cm) .  (see p.38) between Figure  (D) o f about  o f s u r f a c e p r e s s u r e and  The p r o p a g a t i o n v e l o c i t y i s  c a l c u l a t e d from  U  where  P  =  ~lFDne  >  (14)  i s the frequency a t which the phase d i f f e r e n c e i s G.  U , i s then compared w i t h the mean wind, u|  , a t the l e v e l L  L  P  P  The  velocity,  appropriate  P  t o the frequency UQ, s i n c e t h i s h e i g h t i s more r e p r e s e n t a t i v e o f the mean wind at which the p r e s s u r e f l u c t u a t i o n s o f frequency TIQ o r i g i n a t e d . at l e v e l L  P  i s i n t e r p o l a t e d from o b s e r v e d cup p r o f i l e s .  c a l c u l a t e d by t a k i n g  u|^/n'g =  L ' as a f i r s t  The mean wind  The h e i g h t L  P  is  a p p r o x i m a t i o n and then l e t t i n g  42 L  =  p  gives  i/n„ . The s e c o n d s t e p adds l e s s than a 10% c o r r e c t i o n . T a b l e I I L W P t h e r e s u l t s of the v e l o c i t y comparison. Four d i f f e r e n t phase d i f f e r e n c e s U  w e r e u s e d : 9 0 ° , 180°, 270° a n d 360°.  Since  the s c a l e s i z e L  i s different for P  each phase d i f f e r e n c e ,  t h e U"|  used  f o r c o m p a r i s o n w i t h U- i s e v a l u a t e d f o r  P  each phase s h i f t .  P  The L a d n e r o b s e r v a t i o n s , c o n s i d e r e d  because o f low instrument  n o i s e and steady  t o be t h e most  accurate  s t a t e mean f l o w , g i v e v a l u e s o f  TABLE I I Pressure Site Run  Propagation  Velocity,  U , as a F r a c t i o n o f u|  L  L  L  L  B.B.  B.B.  S.B.  S.B.  S.B.  320/2  425/1  425/2  426/1  137/2  142/1  196/1  196/2  7.7  6.1  5.2  6.1  4.1  4.3  3.7  3.4  3.7  0.96  2.0  3.1  4.1  0.56  0.56  4.3  2.7  1.5  0.90 0.91 0.96 1.00 0.94  0.97 0.93 0.91 0.86 0.92  1.49 1.17 1.04 0.98 1.17  1.08 1.04 0.99 0.93 1.01  0.96 0.99 1.10 1.30 1.07  0.95 0.99 1.05 1.20 1.05  1.20 1.30 1.10 1.05 1.16  1.15 1.15 1.14 1.10 1.14  1.10 1.00 1.05  196/3  m/sec D  (m)  U  *t 1 Av.  p  1.0 ± 0.1 ( f r o m 4 R u n s ) f o r U / u L P  give  1.1 ±0.15 ( f r o m  Thus t h e p r e s s u r e frequencies  L  .  Similar observations  a t Spanish  3 R u n s ) a n d a t B o u n d a r y B a y , 1.05 ±0.1 ( f r o m 2 R u n s ) .  field  travels  a t a b o u t t h e l o c a l mean w i n d s p e e d , t h e h i g h e r than  the lower  C a l c u l a t i o n s by o t h e r i n v e s t i g a t o r s working  1962) g i v e an a s y m p t o t i c v a l u e  for  This  velocity.  difference i s considered  c h o i c e o f t h e mean w i n d u s e d f o r t h e c o m p a r i s o n . atmospheric  f o r the difference.  tunnels  o f a b o u t 0.8 u| t o b e due t o t h e  The v a l u e o f u|  b o u n d a r y l a y e r c o u l d e a s i l y b e 15 t o 2 0 % h i g h e r  h e i g h t L , which would account  frequencies or  i n wind  (see W i l l m a r t h and W o o l d r i d g e , the propagation  Banks  P  or smaller scales t r a v e l l i n g slower  larger scales.  1.05  than  f o r the the wind at  The d i f f e r e n c e i n  43 propagation v e l o c i t i e s as a function of frequency has also been observed i n wind tunnels. To compare the pressure fluctuations with the v e l o c i t y s i m i l a r analysis was  done on some v e l o c i t y data.  fluctuations,  The data comes p a r t l y  from  observations taken by others at the i n s t i t u t e , using sonic and hot-wire anemometers, and partly from the hot-wire anemometer observations at Ladner. Figure 35 shows examples of coherences 36 a composite  of a l l such graphs.  f o r two v e l o c i t y sensors, and Figure  Though the data are more scattered i t i s  assumed that the v e l o c i t y and pressure behave s i m i l a r l y and the best f i t l i n e i s drawn f o r separations proportional to A^. X  v  = U/n  L  = 100 cm i s about 30 cm, where L  v  frequencies at which the coherence i s 0.14. v e l o c i t y fluctuations i s approximately 1/3  The scale L^ corresponding to i s defined as before from the Therefore the s i z e of the  of that given by X^.  The  coherences  —0 8 f a l l o f f approximately as (In n)  * , about the same as f o r the pressure f i e l d .  V e l o c i t i e s are also i n phase at points separated v e r t i c a l l y and across the stream, and the propagation v e l o c i t y i s about U, as expected.  These results  indicate that the pressure and v e l o c i t y fluctuations are s i m i l a r i n geometry and are advected at the same rate.  Pressure-Velocity Relationships In this subsection a number of pressure measurements taken i n conjunction with v e l o c i t y measurements are used to e s t a b l i s h some of the relationships between the two.  The results apply to the pressure-velocity relationship f o r most  of the scale range f o r which there i s an active Reynolds s t r e s s . A priori, i s no s p e c i f i c relationship expected.  there  I f the pressure were passive, the phase  2 might be B e r n o u l l i type (p varying as -u /2). I f active, and responsible f o r  44 the t r a n s f e r of energy  between components, such  to i s o t r o p y , a q u a d r a t u r e turbulent shear p l a n e , then  flow (see e q u a t i o n s  the v e l o c i t y  towards the f l u i d pressure.  component i n the pu  velocities  d i r e c t e d up  p-w,  reversed f o r a gain of  the s o n i c , w i t h  upwind o f the c e n t e r of the s o n i c p a t h s ; i n a w i n d t u n n e l t o ensure  would be p r e s e n t .  marked by  I n a l l the f i g u r e s  energy.  40.  P o s i t i v e phases Figures cm  was  dynamic p r e s s u r e n o i s e  c o r r e c t e d f o r i t s r e s u l t i n g phase a plot  of u-w  phase  and  Data o b t a i n e d from the p r e s s u r e probe and the probe,  are p l o t t e d i n F i g u r e s  the approximate peak of the w spectrum i s  an arrow f o r ease o f comparison w i t h s t a n d a r d v e l o c i t y s p e c t r a .  These p l o t s show t h a t the p r e s s u r e i s ' i n phase' w i t h u at low (the o p p o s i t e o f B e r n o u l l i frequencies energy  the  etc., respectively.  t h a t no s i g n i f i c a n t  h o t - w i r e , 4 cm t o the s i d e and 5 cm b e h i n d 39 and 40.  component, the  t h i s p o s i t i o n i n g o f the probe  For comparison,  i s shown i n F i g u r e 41.  the  the p r e s s u r e probe p l a c e d about 25  The p r e s s u r e s i g n a l was  lead using Taylor's hypothesis. coherence  i n phase w i t h  and phase r e l a t i o n s h i p s between p and  e t c . , means t h a t p l e a d s u, w,  38 use d a t a from  direction  the f l u c t u a t i n g p r e s s u r e g r a d i e n t ,  u and w a r e p l o t t e d i n F i g u r e s 37, 38, 39 and  l a b e l l e d p-u,  required i n  i n the  I f the energy were b e i n g e x t r a c t e d from a v e l o c i t y  T y p i c a l measured coherence  tendency  I f p r e s s u r e i s d o i n g work a c r o s s a  r e c e i v i n g energy would on the average be  o r d e c e l e r a t i n g ; the s i g n would be  checked  p r o d u c t would be  component normal to the p l a n e and  v e l o c i t y would on the average be  37 and  4).  as i s r e q u i r e d f o r a  type) w i t h  coherences  up  the phase d i f f e r e n c e becomes about 135°  t r a n s f e r was  t a k i n g p l a c e ) w i t h coherences  t o 0.8,  ' i n phase' and  w h i l e at h i g h  ( i n d i c a t i n g t h a t some  of about 0.1  phase t r a n s i t i o n i s a s s o c i a t e d w i t h a l o s s of coherence between the  frequencies  i n pu.  t o 0.2. The  division  ' l a r g e phase d i f f e r e n c e ' i s a t a frequency  what h i g h e r than at the peak o f the w spectrum.  The  coherence  The  i n the  somepw  a  45 r e l a t i o n s h i p shows a g r a d u a l decrease n e a r zero a t h i g h about 180°  The  to near 0 ° .  be due  to probe s e p a r a t i o n .  above the s u r f a c e ) .  (L  previous s u b s e c t i o n , p.37).  as e v a l u a t e d i n a  z. p  from those w i t h s c a l e s i z e l e s s  than  p o s i t i v e pressure i s here  on the average i s n e g a t i v e  s c a l e s s m a l l e r than  z.  -  between p and  the measurement h e i g h t , a d i f f e r e n t  This A  (downward)  ( F i g u r e 41),  a s s o c i a t e d w i t h a p o s i t i v e u.  z e r o phase r e l a t i o n s h i p a t l a r g e s c a l e s  z.  ' f e e l i n g ' the bottom.  p o s i t i v e pressure at l a r g e s c a l e s i s a s s o c i a t e d w i t h a n e g a t i v e S i n c e uw  =  a s c a l e s i z e l a r g e r than z have a  to the l a r g e r s c a l e f l u c t u a t i o n s  (see F i g u r e 38).  Also  pressure  A l l p o i n t s f a l l near o r below the l i n e  That i s , a l l p r e s s u r e f l u c t u a t i o n s w i t h d i f f e r e n t phase r e l a t i o n s h i p  , of the  - -y A p  w  range.  The wavelength i s c a l c u l a t e d  d a t a p o i n t a f t e r the phase t r a n s i t i o n to near 135°.  f o r the t r a n s i t i o n frequency  attributed  As would be  t r a n s i t i o n , as a f u n c t i o n of z  shown i s a dashed l i n e i n d i c a t i n g the s c a l e s i z e ,  is  relationship  coherence i s n e a r z e r o f o r the same frequency  of wavelength, A , a t t h i s  ( h e i g h t of o b s e r v a t i o n s  fluctuations  to  f o r the w e l l d e f i n e d change i n the p-u phase can be s e e n from  a p l o t , F i g u r e 42,  u s i n g the f i r s t  frequencies  Some o f t h i s l o s s o f coherence i n the pw  the measured pv reason  at low  f r e q u e n c i e s ; the c o r r e s p o n d i n g phase change i s g r a d u a l from  a t the h i g h e s t f r e q u e n c i e s may expected  from about 0.5  the  Thus t h e r e i s a u.  For  turbulence  relationship  results  from t h e i r independence from the bottom. Even though the major s o u r c e of the low is  attributed  to a i r motions i n t e r a c t i n g w i t h  t i o n s produce c o r r e s p o n d i n g p r e s s u r e pressure Figures  and w i s lower 37 and  38).  pressure  the s u r f a c e , n o t  fluctuations.  than between p r e s s u r e  Since i t i s f e l t  frequency  and  The  fluctuations a l lw  fluctua-  coherence between the  u a t these s c a l e s  t h a t t h i s i s r e a l and not due  (see to the  i n s t r u m e n t a t i o n , the flow must c o n t a i n s i g n i f i c a n t w f l u c t u a t i o n s w h i c h do  not  46 produce c o r r e s p o n d i n g u o r p f l u c t u a t i o n s . F i g u r e s 41 and  38,  the u-w  and p-w  As  coherences  can be seen by are b o t h  comparing  about 0.5  at  these  scales. Further evidence  t h a t most of the p r e s s u r e a t low  frequencies i s  a s s o c i a t e d with d e c e l e r a t i o n of v e r t i c a l v e l o c i t i e s near seen  from the coherence  between v e l o c i t y  and  the s u r f a c e can  be  two p r e s s u r e measurements  0  n e a r the s u r f a c e , F i g u r e 43.  One  p r e s s u r e s e n s o r was  a t the s u r f a c e and  h o t - w i r e anemometer and a p r e s s u r e probe were t o g e t h e r a t 30 p r e s s u r e s i g n a l has  cm.  a h i g h e r coherence w i t h downstream v e l o c i t y  The  a  surface  fluctuations  than does the p r e s s u r e s i g n a l from the p r e s s u r e measurement i n the a i r . mean d i f f e r e n c e i n coherence  i s about 0.1 w i t h  the 30  p r e s s u r e s are i n phase f o r f r e q u e n c i e s l e s s than 5 Hz,  cm s e p a r a t i o n .  The  The  F i g u r e 33(b).  two  Since  the two p r e s s u r e s i g n a l s have the same s p e c t r a l l e v e l and 0° phase w i t h r e s p e c t t o the v e l o c i t y ,  the d i f f e r e n c e i n coherence  p r e s s u r e a t the s u r f a c e b e i n g on the average at the l e v e l o f the v e l o c i t y s e n s o r . is  on the average  this  f o r Run  d i r e c t e d upward.  319/1.  coherences  significantly i n F i g u r e s 37, effect'  l a r g e r than the in-phase  pressure  T h i s means t h a t the p r e s s u r e g r a d i e n t A c a l c u l a t i o n , T a b l e I I I , page 47, shows  the t u r b u l e n c e i n t e r a c t i n g w i t h  between u and p, a t t h i s  s m a l l e r than those 39,  in-phase  Thus a t l a r g e s c a l e s the m a j o r i t y o f the p r e s s u r e  t u a t i o n s were a s s o c i a t e d w i t h The  i s the r e s u l t of the  and 40.  low  level,  F i g u r e 43,  t o be  are  an example of the  (p.6) where the a i r motions c o n t r i b u t i n g to uw may  the boundary w i t h o u t  the s u r f a c e .  t y p i c a l l y measured a t h i g h e r l e v e l s  T h i s i s thought  the a s s o c i a t e d v e l o c i t i e s  be  fluc-  as shown 'integral  d e c e l e r a t e d by  a r r i v i n g s i m u l t a n e o u s l y a t the  boundary. Data c o l l e c t e d , measuring t e c h n i q u e  using a hot-wire  f o r measuring u and  the s u r f a c e p r e s s u r e  t o o b t a i n p, were compared t o the r e s u l t s o f Gorshkov  47  TABLE I I I  V e r t i c a l Pressure  D a t a f r o m Run 3 1 9 / 1  frequency  at the Surface  ( s e e F i g u r e 43)  —1 = 10 m s e c  u|  Gradient  2  u,  -0.4m  2 • sec  B.W.  AP  cm s e c<  Hz  Hz  Hz "1/2  Ap/Az  >  ( 2  , dynes  cm  -2  dynes  3  cm  0.026  3.1x10"  2  -6.3x10  3  4.6xl0  2  2.4  -7.7xlO~  2  0.059  3.1xl0~  2  -4.2xl0  3  3.6xl0  2  2.1  -6.8xl0"  2  0.090  3.IxlO  -2.2x10  3  3.0xl0  2  1.3  -4.2xl0"  2  0.12  3.IxlO"  -1.2xl0  3  2.4xl0  2  0.87  -2.9xl0~  2  0.17  6.1x10"  2  -6.0xl0  2  1.8xl0  2  0.81  -2.7xlO"  2  0.23  6.IxlO"  2  -5.8xl0  2  1. 7 x 1 0  0.83  -2.8xl0"  2  0.41  1.2xlO  - 1  -2.5xl0  2  l.lxlO  2  0.79  -2.6xlO~  2  0.54  1.5xlO  _ 1  -2.0xl0  2  l.lxlO  2  0.73  -2.4xl0~  2  0.72  2.1xl0  - 1  -1.5xl0  2  9.5x10  1  0.73  -2.4xl0~  2  0.97  2.7xlO  _ 1  -9.5x10  7.2x10  1  0.62  -2.IxlO"  2  (1)  - 2  2  T h i s v a l u e was o b t a i n e d b y v e c t o r i a l l y values between the v e l o c i t y are  (2)  1  (dynes  Ap = ( A p u  cm  -2 $  within  subtracting  the cross  a n d t h e two p r e s s u r e s i g n a l s .  spectral  The u n i t s <  -1 -1 ) (cm s e c ) ( H z ) . -1/2  u  pressure difference r  2  „ -1/2 B.W. T 7  ) i s a magnitude f o r t h a t p a r t o f the  (p . - p . ) which Aground air r  the appropriate bandwidth.  i s c o h e r e n t w i t h u and l i e s  48 (1968). as  When s i m i l a r s p a c i n g s  a r e used, 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 ( d e f i n e d  the cospectrum d i v i d e d by the square  r o o t o f the p r o d u c t  o f the two  s p e c t r a l d e n s i t i e s ) i s s i m i l a r i n magnitude t o t h e v a l u e s he o b t a i n e d , b u t o f the o p p o s i t e s i g n .  The o n l y s u g g e s t i o n  t h a t can be p u t forward  f o r the  d i f f e r e n c e i n the r e s u l t s i s t h e d i f f e r e n t method used t o o b t a i n a s u r f a c e pressure  f r e e o f dynamic n o i s e .  can n o t be reproduced,  they a r e n o t compared f u r t h e r w i t h  Energy T r a n s f e r by P r e s s u r e Two a s p e c t s first  i s the  Because the g e n e r a l f e a t u r e s o f h i s the p r e s e n t  o f energy t r a n s f e r by p r e s s u r e  forces are evaluated.  3pw/3z term, r e p r e s e n t i n g the n e t e f f e c t o f p r e s s u r e  u3p/3x term by which p r e s s u r e  velocity  data.  Forces  i n t h e t o t a l t u r b u l e n c e energy budget o f the boundary l a y e r . the  results  The  forces  The second i s  f o r c e s t r a n s f e r energy t o o r from t h e u  component.  For t h e e v a l u a t i o n o f the r e l a t i v e s i z e o f the 3pw/3z term , t h e equation p.8),  f o r the boundary l a y e r energy budget was i n t e g r a t e d (see Background,  the term  -uw 3U/3z becoming -uw u|  These two terms r e p r e s e n t  z  and - —  pw  becoming - — p w | »  the r a t e o f w o r k i n g by Reynolds s t r e s s  f e e d i n g term) and t h e p r e s s u r e  (the energy  f o r c e s on a column o f h e i g h t z and u n i t  These terms a r e compared f o r f i v e Runs, each o f a p p r o x i m a t e l y duration.  z  area.  1/2 h o u r  The s p e c t r a o f p, u, w, v, uw, and pw a r e p l o t t e d i n F i g u r e s 28, 22,  22, 23, 24, and 44 r e s p e c t i v e l y .  The i n t e g r a l o f pw i s n e g a t i v e ; t h a t i s ,  t r a n s f e r o f energy i s downwards.  The c a l c u l a t e d  T a b l e IV, page 49.  The r a t i o  terms a r e summarized i n  the  49 1 — - — pw R  - uw U  i s plotted i n Figure 45 as a function of z.  As can be seen, the r a t i o R i s  approximately equal to 0 , 1 for z between 2 and 6 meters.  The Run at 1.5 meters  has some wave generation present, therefore the assumption of no energy flux through the bottom boundary i s not completely v a l i d .  TABLE IV  The pw Term i n the Boundary Layer Energy Budget Run  u|  z  -uw  m sec  m  cm sec  O  /u^  -pw/p  -  cm sec  —  qw  cm sec  -uw  U  R =  cm sec 50.5xl0  4  0.125  4  52.5xl0  4  0.105  -2.4xl0  4  39.5xl0  4  0.095  4  -3.9xl0  4  29.0xl0  4  0.094  4  -6.5xl0  4  27.0xl0  4  0.084  110/1  7.1  5.5  698  1.32  6.3x10  4  110/2  7.4  4.0  729  1.25  5.5xl0  4  120/1  6.5  3.4  580  1.40  3.7xl0  4  120/2  6.2  4.8  443  1.47  2.7x10  121/1  6.4  1.5  463  1.40  2.3x10  -6.5x10  4  -5.5xl0  Another term i n the boundary layer turbulent energy budget i s - ^ — ^ — 2 dz 2 2 2 2 where q = u + v + w . When integrated between the surface and height z this i s approximated by - ^ q^w| , which (when p o s i t i v e ) represents v e r t i c a l ^ z energy flux i n t o the unit column by the turbulence. to  The r a t i o of this flux  - uwU i s about - 0 . 1 (roughly balancing the -pw term). The energy transferred by the - u 3 p / 3 x term i n the energy budget of the  50 u velocity u and p. of  component was  calculated  from the simultaneous measurements o f  A h o t - w i r e p o s i t i o n e d about 7 cm t o the s i d e and 4 cm t o the back  the p r e s s u r e probe was  used t o measure u.  were a p p l i e d u s i n g T a y l o r ' s h y p o t h e s i s . the  The energy  q u a d r a t u r e spectrum between u and p.  calculated  T h i s t e c h n i q u e was  checked by  47  show the r e s u l t s  The two  c a l u c l a t i o n agree w i t h i n ±10%.  i n n o n d i m e n s i o n a l form.  between v a l u e s o f kz from 0.05  using  = - 7 ; 7 ^ - and c a l c u l a t i n g i t s U dt  dx  r  cospectrum w i t h u.  corrections  f l u x was  d i f f e r e n t i a t i n g the p r e s s u r e term t o o b t a i n 0  Necessary phase  F i g u r e s 46  and  As can be seen when i n t e g r a t e d  t o 20, the r a t e o f energy l o s s  (per u n i t  3 volume) from the u f l u c t u a t i o n s i s about 0.3  t o 0.7  pu^ / ( K Z ) , where K i s  von Karman's c o n s t a n t . As shown i n the Background  s e c t i o n , i t would be e x p e c t e d t h a t i f d a t a  were a v a i l a b l e f o r the e n t i r e range of t u r b u l e n t s c a l e s , the i n t e g r a l would have a maximum v a l u e o f about 0.67, becomes i s o t r o p i c .  p r o v i d e d t h a t the t u r b u l e n c e e v e n t u a l l y  Both w and v f l u c t u a t i o n s are p o s s i b l e s i n k s  energy, however f o r the s c a l e range observed the w f l u c t u a t i o n s  for this are e x p e c t e d  to be the major s i n k , s i n c e the w gains energy i n t h i s s c a l e range, and v has a l r e a d y a c q u i r e d s i g n i f i c a n t energy a t s c a l e s S i n c e the t u r b u l e n c e has n o t become f u l l y  l a r g e r than those observed.  i s o t r o p i c w i t h i n the s c a l e  range  observed, f u r t h e r energy f l u x i s expected at kz l a r g e r than t h a t o b s e r v e d . For at  t h e s e reasons the i n t e g r a l a maximum be l e s s  than 0.67.  (the energy l o s s  The r e l a t i v e l y l a r g e v a r i a t i o n i n the measure-  ed i n t e g r a l i n c l u d i n g two l a r g e r than 0.67 of  complete s t a t i o n a r i t y  tical reliability.  from the u component) s h o u l d  c o u l d have r e s u l t e d from the l a c k  and the l e n g t h of the runs b e i n g too s h o r t  The observed energy l o s s from the u v e l o c i t y 3  a mean v a l u e o f about 0.45  pu  A  for statis-  component has  / K Z ; t h i s i s s u f f i c i e n t t o account f o r t h a t  a c q u i r e d by w f l u c t u a t i o n s i n t h i s same frequency range. The energy t r a n s f e r by -udp/9x can be d i s c u s s e d i n terms  of two  scale  51 ranges.  The  first  i n which energy i s l o s t i s a t low v a l u e s o f kz where the w  s p e c t r a f i r s t have a p p r e c i a b l e energy. 46 and 47 f o r comparison.  The r a t i o $ / $ w  The second range which  i s shown i n F i g u r e s  u  c o n t a i n s most o f the energy  l o s s measured o c c u r s j u s t a f t e r the peak of the w spectrum; t h a t i s , where the  t u r b u l e n c e becomes f r e e o f the s u r f a c e  (p.45).  The energy t r a n s f e r i n  most cases drops o f f toward z e r o at the h i g h f r e q u e n c i e s T h i s i s c o n s i d e r e d t o be r e a l r a t h e r than due v a l u e s were n o t p l o t t e d beyond becoming  (that i s , high k z ) .  t o probe s e p a r a t i o n a l t h o u g h  those shown s i n c e probe s e p a r a t i o n may  i m p o r t a n t i n the c a l c u l a t i o n s by  e v a l u a t i n g the a p p r o p r i a t e s c a l e s i z e  this point.  be  T h i s can be seen by  f o r the f l u c t u a t i o n s  (see F i g u r e 34).  From t h e s e energy f l u x measurements i t appears t h a t , i n the t o t a l  energy  budget below 5 meters, under n e u t r a l c o n d i t i o n s , the assumption of s m a l l c o n t r i b u t i o n by  the p r e s s u r e term i s r e a s o n a b l e .  Not o n l y i s the term s m a l l  but  i t i s a l s o p a r t i a l l y b a b l a n c e d by the t u r b u l e n t f l u x term.  the  energy budget o f the i n d i v i d u a l v e l o c i t y  However f o r  components n e a r the f r e q u e n c y  range where the t u r b u l e n c e i s c a r r y i n g the s t r e s s ,  the p r e s s u r e terms a r e  v e r y i m p o r t a n t as e x p e c t e d and as has been shown f o r t h e u component.  52 MICROSCALE PRESSURE FLUCTUATIONS OVER WIND GENERATED WATER WAVES  When a w i n d b l o w s  o v e r w a t e r , waves c a n b e g e n e r a t e d t h r o u g h t h e a c t i o n  of the surface pressure f l u c t u a t i o n s . some p r o p e r t i e s is  Measurements were taken t o e v a l u a t e  of thes t a t i c pressure i n this  the a i r layer  close  t o a pressure f i e l d which  of this (Dobson,  transfer,  waves.  theboundary  fraction  layer stress,  i s g e n e r a t i n g the waves.  Recent measurements  o f t h e momentum t r a n s f e r r e d  Dobson measured t h e t r a n s f e r d i r e c t l y  the water s u r f a c e . a short distance  velocity transfers  The e x a c t m e c h a n i s m  t h e s t u d y o f wave g e n e r a t i o n i s an a r e a o f a c t i v e r e s e a r c h  1969; M a n t o n , 1970).  that a large  The r e g i o n o f i n t e r e s t  t o t h e w a t e r s u r f a c e where t h e t u r b u l e n t  c o r r e l a t i o n uw, w h i c h n o r m a l l y c a r r i e s energy  role.  (Dobson,  1969) i n d i c a t e d  t o t h e w a t e r was v i a t h e  from p r e s s u r e measurements on  I n c o n t r a s t , t h e p r e s e n t measurements were E u l e r i a n ,  taken  above t h e c r e s t o f t h e waves and a r e c o n c e r n e d w i t h t h e  n a t u r e o f t h e a i r flow over the waves. The d a t a w e r e c o l l e c t e d a t t h e S p a n i s h B a n k s s i t e o f t h e o b s e r v a t i o n s w e r e t a k e n when t h e w i n d b l e w The s t a t i s t i c s  o f t h e wave f i e l d  at this  have been t h o r o u g h l y s t u d i e d by G a r r e t t  site  that t h enon-uniform fetch which produced  from an e a s t e r l y  f o r winds  (1970).  (see Appendix A ) .  Most  direction.  from t h i s  direction  H i s measurements  indicated  an asymmetry t o t h e d i r e c t i o n a l  s p e c t r a d i d n o t p r e v e n t t h e wave f r e q u e n c y s p e c t r u m f r o m a t t a i n i n g t h e ' e q u i l i b r i u m form'  (see P h i l l i p s ,  1966, p . l 0 9 f f . ) .  from b o t h e a s t and west were checked range; that i s , conditions  In this  s t u d y t h e waves  f o r t h e e x i s t e n c e o f an e q u i l i b r i u m  where the h i g h f r e q u e n c y spectrum i s o f t h e form n  at this  site  are considered suitable  f o r obtaining  .  The  measurements  t y p i c a l o f t h e wave g e n e r a t i o n mechanism. D u r i n g m o s t o f t h e o b s e r v a t i o n s t h e w a t e r d e p t h w a s 3 t o 3.5 m e t e r s a n d  the t i d a l c u r r e n t s m a l l .  The i n f l u e n c e of w a t e r depth and t i d a l c u r r e n t on  wave f r e q u e n c y and a m p l i t u d e was than 10%.  c o n s i d e r e d ; the c o r r e c t i o n was  usually  less  F o r example, waves of 3 second p e r i o d were t y p i c a l f o r the peak  o f the wave s p e c t r u m a t t h i s s i t e . o f about 4.9 x 10 assuming i n f i n i t e  -3  cm  -1  These waves have a wave number k  2lT /X  =  i n 3 meters of w a t e r as compared t o 4.5 x 10  -3  cm  -1  depth.  A wave p r o b e , p r e s s u r e probe and v e l o c i t y s e n s o r were mounted on one o f the i n s t r u m e n t masts n e a r the p l a t f o r m (see Appendix A f o r d e t a i l ) .  The  v e l o c i t y measurements r e f e r r e d t o i n t h i s s e c t i o n were made w i t h a s i n g l e ' u - w i r e ' probe w h i c h measured the downstream f l u c t u a t i o n s .  These t h r e e s e n s o r s  were p l a c e d as n e a r l y as p r a c t i c a l i n a l i n e p e r p e n d i c u l a r t o the mean w i n d d i r e c t i o n ; t h a t i s , a l o n g wave c r e s t s .  Phase d i f f e r e n c e s due t o n o n - a l i g n m e n t  were c o r r e c t e d u s i n g the ' f r o z e n f i e l d ' h y p o t h e s i s . The s p a c i n g c r o s s w i n d between s e n s o r s was  o f the o r d e r o f 5 t o 10 cm w i t h t h e wave probe n o r m a l l y  o p e r a t i n g a t the m i d - p o i n t .  A minimum h e i g h t of the a i r s e n s o r s was  30 t o 50 cm above mean w a t e r l e v e l . g e n e r a t i o n by e a s t winds t o 20 cm.  ' v i s u a l ' wave a m p l i t u d e d u r i n g a c t i v e  ( i n w h i c h t h e waves a r e f e t c h l i m i t e d ) was  about 15  On one o c c a s i o n t h e s e n s o r s were w i t h i n 10 t o 15 cm from t h e tops  of the h i g h e r waves. was  The  typically  I n t h i s p o s i t i o n the case f o r t h e p r e s s u r e t r a n s d u c e r  o c c a s i o n a l l y h i t by the waves. More t h a n twenty Runs were made under a v a r i e t y o f w i n d c o n d i t i o n s  Data Summary, Appendix C ) .  (see  Most o f the u s e f u l i n f o r m a t i o n comes from f o u r  groups o f Runs; the Runs w i t h i n each group were t a k e n s e q u e n t i a l l y .  These  f o u r groups l a b e l l e d A, B, C and D a r e used as r e p r e s e n t a t i v e o f the r e s u l t s . S i n c e a l l the d a t a have some common p r o p e r t i e s , a s i n g l e Run i s used as an example f o r d e t a i l e d d e s c r i p t i o n .  The s p e c t r a , coherences and phase  relation-  s h i p s f o r the f o u r groups o f d a t a a r e t h e n d e s c r i b e d , f o l l o w e d by a d i s c u s s i o n  ,  54 which summarizes the information and presents conclusions.  Example Spectra A p l o t i l l u s t r a t i n g the t y p i c a l c h a r a c t e r i s t i c s of spectra over waves, Figure 48, i s for data obtained from two pressure sensors, a hot-wire measuring u and a wave probe. vertically.  The two pressure probes were separated  The lower pressure sensor and the hot-wire anemometer were at a  height of 90 cm above mean water l e v e l ; the upper pressure sensor was 50 cm higher.  The wind was from the west at 3.6 m/sec, s l i g h t l y slower than the  phase speed, C, of the waves at the peak of the wave spectrum. The pressure spectra, Figure 48, always contain a 'hump' superimposed on a spectrum which i s s i m i l a r to that found over a f l a t boundary.  The  extent i n bandwidth of the pressure hump i s denoted by a double arrow l a b e l l e d 'H'.  This hump corresponds closely with the wave spectrum, though not  exactly proportionally.  For example, the slope on the high frequency side of  the hump i s not always -4.5 to -5 as i t i s f o r the waves. of for  The humped portion  the spectrum f o r the higher l e v e l pressure sensor, p^, i s s i m i l a r to that the lower sensor, p , but i s smaller i n amplitude, p a r t i c u l a r l y at high Li  frequencies, as would be expected.  At higher frequencies than at the 'humped'  p o r t i o n , the two pressure spectra do not a l i g n , as they do at the frequencies below the hump, the lower l e v e l having a higher i n t e n s i t y .  Observations at  s i m i l a r l e v e l s over land and at higher elevations over water do not show this high frequency difference, as may be seen from Figures 18 and 20.  The s p e c t r a l  slopes at higher frequencies than at the hump are the same as those observed at s i m i l a r heights over a f l a t boundary. To compare the wave induced pressure, p , observed i n d i f f e r e n t Runs and  55 at  different  required. in  frequencies  The q u e s t i o n  a n d h e i g h t s , some m e a s u r e o f t h i s p r e s s u r e i s a r i s e s as t o what f r a c t i o n  of the pressure  t h e hump i s a s s o c i a t e d d i r e c t l y w i t h w a v e s , a n d w h a t i s a s s o c i a t e d w i t h  random t u r b u l e n c e . pressure zero,  S i n c e , as w i l l  and t h e waves a t h i g h e r  this  b e shown l a t e r ,  frequencies  than  r e g i o n o f the spectrum can be s a i d  the coherence between t h e a t t h e hump i s e s s e n t i a l l y  to result  It  i s assumed t h a t t h e s p e c t r a l s l o p e a s s o c i a t e d w i t h  in  the frequency  of i t .  r a n g e o f t h e hump w i l l b e s i m i l a r  Thus as a f i r s t  approximation  hump, a s s o c i a t e d d i r e c t l y w i t h  the pressure  high  frequency The  tail  (see dashed l i n e s  similar  to t h a t observed at thehigher  form a t a l l f r e q u e n c i e s .  t o be the d i f f e r e n c e  l i n e p r o j e c t i o n s from the  i n the pressure  a t the s i t e  Generally,  t h e - 4 . 5 t o -5 s l o p e , h o w e v e r t h i s  e q u i l i b r i u m w a v e s p e c t r u m was c o n s i d e r e d  to  p , i n the w  48, does  spectra.  At  spectrum  frequencies.  very near t o t h e peak o f t h e spectrum.  way.  outside  i n t h e absence o f waves; f o r example, t h e -5/3  wave s p e c t r a f r o m o b s e r v a t i o n s  equilibrium  All  amplitude,  o n e i t h e r s i d e o f t h e r a n g e m a r k e d b y 'H', t h e v e l o c i t y  region exists  labelled  turbulence  spectrum f o r t h e u - v e l o c i t y measured near t h e waves, F i g u r e  frequencies  exhibited  t h e random  turbulence.  i n Figure 48).  n o t h a v e a s d o m i n a n t a hump a s t h a t o b s e r v e d  The  f r o m random  t o t h a t observed  t h e w a v e s may b e t a k e n  between t h e i n t e n s i t y measured and t h e s t r a i g h t  is  amplitude  d i d n o t always have the  the high  frequencies  slope often did n o t continue to  The l o w e s t  frequency  t o which the  t o e x i s t i s marked b y an arrow  'eq. p e a k , s e e F i g u r e 48. 1  data  a s s o c i a t e d w i t h w a v e g e n e r a t i o n h a v e b e e n t r e a t e d i n t h e same  As a c h e c k on t h e a n a l y s i s m e t h o d s , t h e d a t a w e r e o c c a s i o n a l l y r e a n a l y s e d include hanning.  H a n n i n g does n o t a l t e r  the results  significantly.  56 Data  A.  Runs 60/4, 119/1, 119/2, 119/3 This group of data consists of four sequential Runs recorded during an  east wind.  The instruments used were the wave probe, two pressure sensors  spaced v e r t i c a l l y 50 cm apart, and a hot-wire measuring downstream f l u c t u a tions.  The lower pressure sensor and the v e l o c i t y sensor were about 30 cm  above mean water l e v e l . each of the Runs. number.  Figure 49 shows the wave spectra recorded during  The time of the Run i s given i n brackets a f t e r the Run  V i s u a l l y the highest wave was about 10 cm i n amplitude; the root-  mean-square amplitude i s about 3 cm.  The spectra have a secondary peak at  a frequency near 0.25 Hz, thought to be due to waves generated elsewhere and propagating into the region (Garrett, 1970).  The sequence 60/4 to 119/3  show that the wave f i e l d was growing i n time under almost steady but slowly increasing winds (see Table V, Appendix C ) . 4.5 m sec \  The mean wind,  was  about  giving a value f o r ( u | ^ - C ) , where C i s the phase speed of the  waves, of about 2 m sec  at the main peak ('eq. peak') of the wave spectrum.  Figures 50 to 53 show spectra f o r the four Runs.  A l l exhibited properties  s i m i l a r to those described f o r the example shown i n Figure 48.  The phase and  coherence between the lower pressure ( p ) and the wave amplitude (r) ), and L a between the two pressures (p and p ) are p l o t t e d i n Figures 54 and 55 i-i u T  respectively.  A phase s h i f t i n the p-r) relationship occurred at the wave  peak and continued out over the equilibrium wave spectrum.  As w i l l be shown  l a t e r , this s h i f t of about 30 to 50° from 180° i s associated with the wave generation.  The corresponding coherences are about 0.3 to 0.4.  At lower  frequencies than at the 'eq. peak' coherences are higher and phase differences are near 180°.  This i s associated with the r e s i d u a l longer waves.  The phase  information indicates generated.  that these low  frequency waves were n o t b e i n g  F i g u r e 55, a p l o t of the coherence  actively  and phase of the two p r e s s u r e  s i g n a l s shows t h a t they are i n phase to ±5°.throughout the e x t e n t of the hump. Data n o t a s s o c i a t e d w i t h waves a t n < 0.1  are n o t p l o t t e d .  Thus most of the  phase s h i f t between p and T) occurs below the lower p r e s s u r e s e n s o r , w i t h almost no s h i f t i n g o c c u r i n g i n the next 50 the observed u-r| coherence The non-zero  coherence  and phase.  cm v e r t i c a l l y .  Coherences  are low a t a l l f r e q u e n c i e s .  a t f r e q u e n c i e s o u t s i d e the range marked 'H' would be  e x p e c t e d s i m p l y from random coherence because The h i g h e s t coherence,  F i g u r e 56 shows  about 0.3,  o f the f i n i t e l e n g t h o f sample.  o c c u r s f o r waves o f f r e q u e n c i e s lower  the frequency a t the e q u i l i b r i u m peak. g e n e r a t i o n i s o c c u r i n g , coherences  than  W i t h i n the f r e q u e n c y range where  are s m a l l , l e s s  than 0.1.  The  active  cross  2 c o r r e l a t i o n between u  and r| g i v e s r e s u l t s s i m i l a r t o t h a t shown f o r u and n.  The phase shows no d e f i n i t e p a t t e r n , w i t h g r o u p i n g n e a r b o t h 140° T h i s group  B.  40°.  of Runs (A) r e p r e s e n t s the most d e t a i l e d o b s e r v a t i o n s taken.  Runs 167/1/1, 167/1/2, 167/2, T h i s group  167/3  o f f o u r d a t a Runs was  also recorded during east winds.  wave s p e c t r a f o r a l l f o u r are shown i n F i g u r e 57. s p e c t r a are almost i d e n t i c a l , The  and  o f the wave spectrum the wave probe was water l e v e l .  can be seen,  i m p l y i n g steady s t a t e , f e t c h - l i m i t e d  root-mean-square wave amplitude  5 meter mean w i n d was  As  f o r these Runs i s about 6 cm.  The  the wave conditions. The  7 t o 8 m s e c ^ g i v i n g a v a l u e of (u|,_ - C) a t the peak o f about 4.5  m sec \  The o n l y i n s t r u m e n t used b e s i d e s  a s i n g l e p r e s s u r e probe, p o s i t i o n e d about  40 cm above mean  F i g u r e s 58 t o 61 show the s p e c t r a f o r t h e s e Runs.  s i m i l a r to the p r e v i o u s group  o f Runs ( A ) , e x c e p t t h a t  They a r e  the peak o f the  p r e s s u r e hump i s a t a lower frequency than the peak o f the wave  spectrum.  58 This i s thought to be due to waves t r a v e l l i n g against the mean wind, which had been refracted to the s i t e from the other side of Point Grey, see Figure 85. Such waves, t r a v e l l i n g from the west during a SE wind have been measured (Garrett, 1970) by means of a d i r e c t i o n a l wave array.  In order to  substantiate the above reason for this abnormal p-r] r e l a t i o n s h i p , the amplitude of the Fourier c o e f f i c i e n t s f o r the pressure and wave signals of Run 167/3 was plotted, Figure 62.  This shows that the energy i n the pressure  s i g n a l at frequencies lower than the peak of the wave spectrum i s d i r e c t l y associated with wave energy. sequence.  This i s true f o r a l l the other Runs i n this  To show that these pressure magnitudes are i n accord with this  hypothesis the pressure amplitude was  calculated assuming that the a i r  responds i n a p o t e n t i a l flow manner to the measured wave amplitude.  For  example, f o r Run 167/1/2, at 0.27 _2  Hz, bandwidth An = 0.077 Hz, / 211 (n)An  = 5.3 dynes cm  =1.3  and  / 2$^(n)An  cm.  From a p o t e n t i a l flow c a l c u l a t i o n  using the mean wind at the pressure observation l e v e l / 211 (n)An  =  p  =  -2 4.9 dynes cm  (U +  |c|)  k  with the usual d e f i n i t i o n s (Lamb, 1932,  • 2* (n)An  section 231).  e"  k z  The calculated  measured values agree to within the accuracy of the assumptions.  and  Thus i n this  group of data the pressure s i g n a l at frequencies lower than the frequency at peak of the wave spectrum i s not that normally encountered i n wave generation. The phase and coherence between pressure and waves f o r these Runs are shown i n Figure 63.  As before, the phase s h i f t at the wave generation frequencies i s  about 30 to 50°, with coherences  of 0.5  to 0.6.  For the frequency range where  the waves were propagating against the wind, the coherence i s higher and phase differences are about 180°, as would be expected f o r a p o t e n t i a l type of flow.  59 This group of Runs have the highest values of (U|^ - C) f o r the data obtained.  C.  Runs 164/1, 164/2 This group consists of two examples i n l i g h t WNW  4 m sec \  or NNW  winds of 2.5 and  The waves at the peak of the wave spectrum were t r a v e l l i n g about  2 m sec ^ faster than the wind.  They had been generated by strong winds i n  Howe Sound and had then fanned out from the mouth, part t r a v e l l i n g i n t o the English Bay region.  The root-mean-square wave amplitude i s about 9 cm.  The  waves t r a v e l l e d at a small angle to the wind, a r r i v i n g from a d i r e c t i o n of about NW.  The instruments used were the wave probe, a single pressure sensor  and a 'u-wire'. level.  The l a t t e r two were located about 50 cm above the mean water  The spectra f o r these Runs are shown i n Figures 64 and 65.  The p-n.  phase and coherence are given i n Figure 66; coherences are high; phase d i f f e r ences are near 180°.  Figure 67 shows phase and coherence f o r u-n.  At this  low wind speed, the coherence i s higher than for a l l other Runs and the phase differences are about 180°.  D.  Runs 80/3, 60/1,  60/2  This group of three Runs i s t y p i c a l of the data obtained when the value of (u|^  - C) at the peak of the wave spectrum i s near zero.  used here, the wind was from the west. spectra are shown i n Figure 68.  In the examples  The wave, pressure and u-velocity  The high frequency end of the wave spectrum,  p a r t i a l l y cut o f f i n the graph, follows the -5 slope, and therefore can be considered as part of the equilibrium spectrum. amplitude f o r these Runs i s about 6 cm.  The root-mean-square wave  The mean wind was 4 to 4.5 m sec ^.  Observations were taken at about 50 cm above mean water l e v e l .  The phase and  coherence f o r p-n and u-n, Figures 69 and 70 are s i m i l a r to previous examples.  60 p-H phase s h i f t s are near 180° when ( u | ^ - C) i s small and negative, increasing  as ( u | ^ - C) increases.  For waves near the peak of the wave spectrum,  where u | ^ / C < 1, the u-r| phase difference i s near 180°.  This f i n a l group are  representative of the eight Runs f o r which ( u | ^ - C) i s near zero at the.peak of  the wave spectrum.  Pis cussion Compared to the pressure spectrum over a f l a t boundary, that measured close to a wavy water surface i s greatly modified.  The most prominent change  i s the 'hump' i n the pressure spectrum that i s associated with the wave spectrum.  The i n t e n s i t y i n this hump i s up to 10 times larger than the  s p e c t r a l i n t e n s i t y expected f o r a f l a t boundary under s i m i l a r wind conditions. Remnants of the hump are observed during normal wave conditions up to heights z between X /2 and X w w w  where X  i s the wavelength of the waves.  This can be  estimated from the plots of the pressure spectra by using the highest frequency at which the hump i s definable. occurs f o r p  u  at a frequency n - 0.9 Hz.  For Run 173/3  i n Figure 48, this  Waves of this frequency have a  wavelength X - 200 cm; the measurement height was w  140 cm.  For Run 167/1/1,  Figure 60, corresponding" figures a r e % = 1.5 Hz, X - 70 cm and z = 30 w ;,  cm.  A hump, s i m i l a r to that observed, would be expected even i f no mean wind or turbulence was present, and the wave f i e l d was simply propagating past the pressure sensor. s o l u t i o n (Lamb, 1932,  This could be described by a p o t e n t i a l flow  section 231).  The pressure (phase and magnitude (Pp))  predicted by the p o t e n t i a l flow s o l u t i o n were checked i n the f i e l d .  Figure  71 shows the results obtained on s t i l l , windless days when a swell was propagating past the instrument mast.  The pressure and wave height were  61 recorded on a s t r i p - c h a r t recorder instead of the usual method on magnetic tape.  The values plotted each came from the average of about 100 estimates  of i n d i v i d u a l amplitudes. about 10%. method.  The measured and predicted values agree w i t h i n  Phase differences for p-n were 180°, within the accuracy of the  Thus p o t e n t i a l flow theory adequately predicts the pressure f i e l d  (and hence supposedly  the v e l o c i t y f i e l d ) for propagating waves i n the absence  of wind. When there was  a wind, i t might have been expected that the pressure  could have been approximated  by using a v e l o c i t y of (U|,- - C) i n the p o t e n t i a l  flow s o l u t i o n ; that i s ,  P  where n  W  *  - p n  k (u|  a  i s wave amplitude.  5  - c)  2  e"  k z  ,  This behaviour was not found f o r the present data.  For example, f o r the ( u | ^ - C) = 0 between 0.3 and 0.4 Hz i n Run 164/2, Figure 65, and near the peak of the wave spectrum i n Runs 80/3 and 60/2,  Figure 68,  there i s no i n d i c a t i o n of a drop i n the measured p . w Two  cases have already shown that the measured pressure was  approximated  closely  by p o t e n t i a l flow c a l c u l a t i o n s ; one for u|^/C = 0 and the other  for u|^/C negative.  However when u|^/C > 0 the data does not have such a  simple i n t e r p r e t a t i o n . The non-dimensional  variables which might cause variations i n the pressure  (p ) associated with the waves are: kz, representative of the f r a c t i o n a l height of the observations i n terms of wavelength; kn  representative of the  wave slope; and u|^/C, the r a t i o of the mean wind at 5 meters to the phase speed of the waves.  r ) can be approximated a  by  / 2<J>^(n)An  where  $ ( ) n  n  I  s  the wave s p e c t r a l density and An i s the -^-octave bandwidth f o r a narrow band of  62  frequencies. kn  a  When the wave spectrum has the equilibrium form, the product  =; k/(0 (n)An) can be taken as a constant. f)  For s i m p l i c i t y , pressure data  from one 'fixed height' above mean water l e v e l and only f o r the frequency range where the waves have the equilibrium form are i n i t i a l l y considered. p r a c t i c e this kz and kn P (n) w  'fixed height' ranged from 3 0 to 5 0 cm.  as a parameter.  - / 2IT (n)An o  ^ (n) ^  s t  n  Q  e  Thus, f o r this data,  In Figure 7 2 ,  are constant at any fixed frequency.  = (/ 2H(n)An  In  ) i s p l o t t e d against u| /C 5  with  frequency  background pressure spectrum i l l u s t r a t e d by the  dashed lines i n Figure 4 8 . The points on the ordinate i n Figure 7 2 are derived from the l i m i t i n g cases of u|^/C = 0 which are assumed to be given at each frequency by the p o t e n t i a l flow s o l u t i o n  p (n) = w  p / 2 $ (n)An r)  k C  e  -kz  (15)  These calculations use the mean values from the measured wave spectra and the 'fixed height' z of 4 0 cm.  The values of k and C at a given frequency were  obtained from the s o l u t i o n for small amplitude C  2  = ^ tanh kh and n = k 2TT  As can be seen, Figure 7 2 , the data tends to ' ' 6  group along l i n e s which could be approximately flow c a l c u l a t i o n s .  g r a v i t a t i o n a l waves:  extrapolated to the p o t e n t i a l  As U|,./C increases, the pressure i n t e n s i t y at a l l  frequencies also increases.  There i s no i n d i c a t i o n of a d i s t i n c t l y  different  behaviour near u | ^ = C. With this p l o t (Figure 7 2 ) as background, data from a l l heights were considered i n terms of the nondimensional and p /p *w *o  where  p = pk/20 (n)An C *o n K  .  variables kz, ll|^/C, k/2$^(n)An ,  .  The product k / 2 $ (n)An was chosen  ^  n  to be constant although i t i s not exactly so f o r this data, varying by about 20%.  This i s not important provided the role of k r i  a  iri p  w  i s the same as i n  p  o  .  Two p l o t s  are used,  F i g u r e s 73 and 74, i n which p /p ° *w *o  f u n c t i o n o f u|,_/C a t c o n s t a n t kz and v i c e v e r s a .  The r e s u l t s  are s i m i l a r t o those a l r e a d y shown i n F i g u r e 72, w i t h resulting  from" t h e a d d i t i o n a l d a t a a v a i l a b l e  i s shown as a  little  change  f o r h e i g h t s o t h e r than 40 cm.  F i g u r e 74 shows a l e s s d e f i n i t e dependence o f n o n d i m e n s i o n a l than on u|^/C as shown i n F i g u r e 73.  i n F i g u r e 73  Straight lines  p r e s s u r e on kz  representing constant  v a l u e s o f kz have been drawn by hand among the d a t a p l o t t e d i n F i g u r e , 7 3 . It  is felt  t h a t t h e r e i s i n s u f f i c i e n t d a t a t o warrant  a closer f i t t i n g of  ' c u r v e s ' and there a r e no t h e o r e t i c a l p r e d i c t i o n s t o a c t as g u i d e l i n e s . A c t i n g as a f i r s t a p p r o x i m a t i o n , by  the d a t a i n F i g u r e 73, as r e p r e s e n t e d  the l i n e s shown a r e summarized by the f o r m u l a  p (n) = w  p k • 2* (n)An  n  C  2  exp(0.27 uL/C - k z ( l - 0.08 u L / C ) )  ->  ->  (16) The  l i n e s shown i n F i g u r e 74 r e p r e s e n t i n g c o n s t a n t v a l u e s o f u|,- /C a r e  c a l c u l a t e d from t h i s independently is  formula,  and agree v e r y c l o s e l y w i t h those drawn  on the b a s i s o f t h e d a t a a l o n e . The l i m i t i n g case o f u|^/C  the p o t e n t i a l flow s o l u t i o n as g i v e n by e q u a t i o n 15.  accuracy  to show t h a t ' a s  number i s i n c r e a s i n g l y E q u a t i o n 16, used  There i s s u f f i c i e n t  ( u | ^ / C) i n c r e a s e s , t h e s l o p e o f the l i n e s  Thus as the w i n d i n c r e a s e s , the p r e s s u r e decay v e r t i c a l l y less  decreases.  a t a g i v e n wave  than the e x p o n e n t i a l decay i n p o t e n t i a l  flow.  t o r e l a t e t h e o b s e r v a t i o n s t o an e m p i r i c a l f o r m u l a t i o n ,  becomes p h y s i c a l l y  u n r e a l i s t i c i f extended  the d a t a p l o t t e d .  I f Tj|,./C = 12.5 i s s u b s t i t u t e d i n t o e q u a t i o n 16 a l l z  dependence d i s a p p e a r s increasing v e r t i c a l l y ; T h i s 12.5  = 0  and a t U|^/C  t o l a r g e v a l u e s o f u|^/C, beyond  > 12.5 e q u a t i o n 16 has the p r e s s u r e  t h e o p p o s i t e o f t h a t which would be expected  t o occur.  value, f o r u | c / C c o u l d r e p r e s e n t a wavelength o f 10 cm and a u|  of  5 m sec  .  Therefore the formula given should not be extrapolated to regions  outside that covered by the data, approximately 0 < u| /C 5  < 7 and 0.5  < kz <  without caution, p a r t i c u l a r l y at larger values of u|^/C. I t i s noticed that calculated pressures at frequencies where the equilibrium wave spectrum did not e x i s t have magnitudes s i m i l a r to those predicted by equation 16. I t i s possible to check the v e r t i c a l dependence shown i n equation 16 using the simultaneous measurements at two levels described i n Data Group A (p.56).  By taking the r a t i o of the pressure, p (n), at the two l e v e l s , a w Az dependence would be l e f t . In terms of equation 16  =  f o r z^ > z^.  exp( - kAz  +  0.08  U kAz )  (17)  Measured values of this r a t i o and those calculated from  equation 17 are plotted i n Figure 75 against kAz.  The f i t i s reasonable.  In summary, the pressure hump has a magnitude which i s s i m i l a r to the p o t e n t i a l flow s o l u t i o n i n very low winds; i t increases monotonically as U increases and decays v e r t i c a l l y at a rate less than exponential, the higher the mean wind, the slower the decay. The surface pressure spectra obtained by Dobson (1969) have a s i m i l a r type of pressure hump, but i n general i t i s not as w e l l defined as those obtained i n the present study (his low frequency i n t e n s i t i e s were i n general an order of magnitude l a r g e r ) .  There was some question as to how  to compare  Dobson's data with the present results since h i s instrument followed the water surface, and hence h i s measurements were not Eulerian.  Nevertheless i t  seems reasonable to compare Dobson's spectra with values predicted by  65 equation 16, s e t t i n g z = 0.  n(n)  =  p  2  k  2  C  4  Thus  * (n) exp(0.54 u| /C) 5  A comparison f o r three cases i s shown i n Figure 76 for which the values of $^(n) were taken from data i n Dobson's thesis.  One of high wind speed runs  and two low wind speed runs (2a and 2 b ) were chosen.  (4b)  Since no extrapolation  of the pressure spectra, s i m i l a r to that represented by the dashed l i n e s i n Figure 48 was  obvious, no attempt was made to remove the energy associated with  random turbulence.  At frequencies near the peak of the wave spectrum, see  Figure 76, this should not give any large e r r o r since the hump pressure i s expected to be about an order of magnitude larger than the pressure associated with random turbulence.  For each run three curves of pressure i n t e n s i t y are  compared: Dobson's t o t a l s p e c t r a l estimate, Dobson's s p e c t r a l estimate with pgn  removed, and the s p e c t r a l estimate predicted by equation 16.  As can be  3.  seen the data collected by Dobson appear to agree reasonably w e l l (within a factor of about 2) with the values predicted by the formula. equation 16 may  Therefore  predict the hump pressure, P ( ) » down to the wave surface. n  w  The pressure which generates the waves i s the component of the pressure, P ( n ) , which i s i n quadrature with the wave. w  Even though the pressure  fluctuations associated with the waves are up to one order larger than that expected from the random turbulence, the coherence with the waves i s only about 0.4  to 0.6.  This suggests that the process of wave generation i s intermittent  and hence that the phase difference between pressure and waves fluctuates significantly. I t was  shown i n e a r l i e r diagrams that the average phase difference  observed at about 50 cm above the waves during active wave generation i s such  66 that pressure lags the waves about 140 to 120°. generation the phase i s near 180°.  In the absence of active  Figure 77 i s a composite  phase differences plotted against u|^/C.  of average p-n.  This p l o t includes a l l of the data  from Data Groups A to D (page 56 to 60) f o r frequencies w i t h i n the extent of the equilibrium wave spectrum  ($^(n) « n  .  d i f f e r e n t symbol to indicate the data group. associated with wave generation  The data are l a b e l l e d with a Most of the large angles  occur f o r u|,-/C > 2 and do not show any  further s h i f t from 180° f o r increasing u|^/C; i n f a c t , i f anything, the opposite appears  to be true.  For a l l other data e i t h e r those outside the  range of the equilibrium wave spectrum f o r which 0 < u|,-/C < 2 or those t r a v e l l i n g against the wind f o r which u|^/C < 0 the phases were 180° ± 10° with no d e f i n i t e trend. The fact that the large p-n phase difference occurs at values of u|,./C greater than about 2 i s thought to be due to the r e l a t i v e height of the c r i t i c a l l e v e l and wave amplitude n  f o r these p a r t i c u l a r groups o f data.  The  3.  ' c r i t i c a l height', z^, i s the height at which U = C ( P h i l l i p s , 1966, p.91). For the data p l o t t e d i n Figure 77 the c r i t i c a l height i s w e l l above the waves for u|^/C near 1.  Values of U"|^/C - 2 are necessary before the c r i t i c a l  height approaches a value equal to the wave amplitude. the use of Figure 78.  This can be seen  from  In deriving the curves i n this figure a logarithmic  wind p r o f i l e and a roughness length of 0.01 cm"'" are assumed.  The p l o t i s to  show which wave frequency has an amplitude equal to the c r i t i c a l height, given a fixed mean wind at 5 meters.  Plotted are a family of curves representing  the c r i t i c a l height for d i f f e r e n t 5 meter winds at various wave frequencies. The curve of r|  1  = / 2$ (n)An against frequency i s f o r the measured equilibrium  This value of roughness length i s approximately equivalent to a drag c o e f f i c i e n t C„ = 1.2 x 10 .  wave spectrum described above i n Data Groups A, B, C and D.  Once a value of  u|,. i s known, there w i l l be a d i f f e r e n t z^ f o r every wave frequency, but only one which has a z 5 m sec  -l  = X] . C  .  For example, i n Data Group A, page 56, u|  3.  In Figure 78, Z  frequency of 0.62  c  = n  a  i - l Hz when U _ = 5 m sec . 5  at 0.62  Hz i s near the frequency at which the large p ^  s h i f t s occur as shown i n Figure 54.  - n  i s about 3  This phase  For waves of this frequency u|^/C - 2.  Therefore when r e p l o t t i n g the e n t i r e set of phase differences from Figure 54 into Figure 77, the large phase s h i f t from 180° occurs at about u|,-/C = 2. This can also be shown f o r a l l the other data groups.  Thus the large p-r\  phase s h i f t from 180° occurs only f o r those waves which have a z  < n .. G  Dobson's (1969) r e s u l t s , before pgr)  was  cl  removed, gave a comparable  SL  phase d i s t r i b u t i o n when p l o t t e d against u|^/C  (M.J. Manton, personal communica-  t i o n ) , although the s c a t t e r i s larger than f o r the present data and the s h i f t from 180° appeared to increase continuously with i n c r e a s i n g U j / C . j was  When pgn a  removed from h i s s i g n a l , the phases between surface pressure and waves  were larger by 20 to 50°. The energy f l u x to the waves by the action of surface pressure, noting that wl = -r- , can be represented by 'ri dt r  En  =  pw(n)|  =  • Z — Tj Z(to. Quad(pn)|  J  n  )An.|  z  =  ^  (18)  Values of En were approximated using the pressure measured above the waves. Since active wave generation was present f o r group A and group B (page 56) one example was  taken from each.  The results are shown i n Figure 79.  Using  the pressure measurement above the waves shows maximum energy f l u x at the peak of the wave spectrum l a b e l l e d 'peak' i n the figure.  The  integrals  shown on the graphs are approximately one f i f t h of the values obtained  68 by  Dobson (1969)  at a comparable wind speed.  Cases i n  •  which the  waves were moving faster than the wind, or the waves were i n the opposite d i r e c t i o n to the wind; that i s , there was no z^; did not have the phase s h i f t s necessary for such energy  transfer, see Figures 54, 63, 66 and  I t i s s u r p r i s i n g that there i s not an obvious  69.  'hump' of energy i n the  v e l o c i t y spectra through the frequencies near the peak of the wave spectra i n view of the large increase i n energy observed i n the pressure spectra.  It is  d i f f i c u l t to make an estimation of the expected amplitude of the v e l o c i t y fluctuations associated with the waves or with the observed pressure since the relationships between them are not known.  A rough estimation of the  amplitude of the expected v e l o c i t y fluctuations can be made using data from group A, page 56.  The two v e r t i c a l l y spaced pressure measurements can be  used to evaluate a v e r t i c a l pressure gradient.  Assuming that this gradient  i s accelerating or decelerating the a i r v e r t i c a l l y , an approximate v e l o c i t y may be i n f e r r e d from at n = 0.55  ~ f^" ~ T T •  Hz (bandwidth = 0.15  For example, i n Run 119/2, Figure 52,  Hz) the Ap v e r t i c a l l y i s approximately  -2 2.5 dynes cm  over a distance of Az = 50 cm; this can be e a s i l y obtained  from Figure 52 since at this frequency the coherence between the two pressure signals i s 1 and the phase difference i s 0° (see Figure 55).  Since a t y p i c a l  Aw  must be accelerated (or decelerated) during one quarter of a cycle, -1 -3 -3 At - 0.45 sec. This gives Aw - 18 cm sec , assuming p - 1.2 x 10 gm cm The corresponding observed value of / 2$ (n)An u  17 cm sec  -1  ( $^(0.55 Hz) = 10  calculated f o r Aw.  3  2-2 cm sec  Hz  -1  i n this frequency band i s  ) which i s comparable with that  However this i s only a rough agreement, since the  relationship between u and w i s not known near waves, and the u was  measured  next to the lower pressure sensor rather than at a p o s i t i o n midway between the pressure sensors where the prediction would be most v a l i d .  Nevertheless  the v e l o c i t i e s observed may be s u f f i c i e n t l y high to account for the observed  69 v e r t i c a l pressure gradients which are required to produce them.  I t i s also  possible that some of the observed pressure i n the frequency range referred to as the 'hump' may  result from the ' i n t e g r a l e f f e c t ' (p.6) with motions  near and below the wave crests requiring the pressure observed at the higher l e v e l above the wave crests. The p o t e n t i a l flow s o l u t i o n (p.62)  predicts a phase difference between  u and n of 180° f o r either no wind, or a mean wind constant with height and slower than the phase speed of the waves.  This u-r| phase difference of 180°  and the r e s t r i c t i o n on the wind speed are approximately those shown f o r the coherent part of the observed u-r) s i g n a l s . wave height n  p l o t t e d i n Figures 56, 67 and 70 f o r the Data Groups A, C and D  respectively are generally near 180°. are  The phases between v e l o c i t y u and  The few points near 40° i n Figure 56  for waves t r a v e l l i n g from an unknown d i r e c t i o n .  When the wind speed i s  f a s t e r than the phase speed of the waves, the coherence i s low, <0.1, phases are random.  and  The 180° phase difference occurs only for those frequencies  when most or a l l of the a i r below 5 meters has a speed less than the wave speed, as required by the p o t e n t i a l flow c a l c u l a t i o n s .  A comparison of Figures  55 and 56, 66 and 67, and 69 and 70 shows that the u-r) 180°  phase difference  occurs only when the p-T| phase differences are also near 180°.  I t i s shown  above (p.66) that this range of p-r) phases near 180° corresponds to a c r i t i c a l height z  w e l l above the wave amplitude (r) ); that i s , when the wind C  3.  at the observation levels i s less than, the phase speed of the waves (z_ »  n).  An example of the strong influence the wave f i e l d has on the turbulence i n the a i r above i s seen i n the p-u cross c o r r e l a t i o n . i t was the  Over a f l a t boundary  found that the p and u were i n phase f o r those scales (L ) l a r g e r than  l o c a l height of the observations, s h i f t i n g to the neighbourhood of 135° at  smaller scales.  The coherence and phase of p and u over waves are shown i n  70 Figures 80 and 81.  The broad features appear to be the same as those obtained  from observations over a f l a t boundary, Figures 39 and 40, except f o r the lower coherence through the region of the 'hump'.  However the frequency of  the phase ' t r a n s i t i o n ' i s e n t i r e l y d i f f e r e n t , being much lower than over land. Figure 82 shows the wavelength A^ of the pressure at the phase t r a n s i t i o n compared to those obtained over a f l a t boundary.  The scales, L P  = A /2, at P  the t r a n s i t i o n are several times larger than those expected over a f l a t boundary at a s i m i l a r height.  In every case i t was  found that this phase  t r a n s i t i o n over waves occurred at the frequency of the peak o f the pressure hump when the pressure spectra were p l o t t e d as nll(n).  In most cases this also  corresponded to the peak of the n$^(n) wave spectrum.  The behaviour of the  p-u coherence and phase at frequencies above the phase t r a n s i t i o n i s s i m i l a r to that found over a f l a t boundary, except the t r a n s i t i o n occurred at a lower frequency.  The wavelength  pressure f i e l d a new  of the waves appears to introduce through the  length scale with which the turbulence i n t e r a c t s .  In p a r a l l e l with the observations over a f l a t boundary there was a large energy loss from the u-velocity component at frequencies above the phase transition.  Using the same method as was  used e a r l i e d , the nondimensional  energy flux from the u-component,  »  was  calculated f o r the observations over waves.  against kz i n Figures 83 and 84.  The d i s t r i b u t i o n of energy f l u x i s s i m i l a r  to that found over a f l a t boundary. immediately above the t r a n s i t i o n . peak of the wave spectrum,  The results are p l o t t e d  Most of the flux occurred at scales For those values of kz associated with the  the sign of the flux i s often p o s i t i v e and the  magnitude i s highly variable.  The integrals under the curves are s i m i l a r t  those found f o r the data collected over a f l a t boundary being t y p i c a l l y between 0.3 and 0.4.  Thus the energy loss from the u-component to the othe  v e l o c i t y components i s s i m i l a r i n magnitude to that found over the f l a t boundary layer but occurs at a nondimensional height kz which i s lower by an order of magnitude than over land.  72 SUMMARY OF RESULTS  An instrument was developed to measure the s t a t i c pressure fluctuations within the turbulent flow of the atmospheric boundary.  From an in s i t u  c a l i b r a t i o n , which compared the pressure measured by the developed  instrument  with that measured by a r e l i a b l e surface measuring technique, the accuracy of the new instrument was found to be about ±10% i n amplitude and ±5° i n phase.  This instrument was used to measure some of the properties of the  s t a t i c pressure fluctuations found over a f l a t boundary and over water waves. The data included the mean square pressure, s p e c t r a l i n t e n s i t y and shape, coherence  and phase between two pressure measurements separated i n each of  the three coordinate directions, pressure-velocity relationship f o r a l l three v e l o c i t y components, h o r i z o n t a l pressure gradient-velocity r e l a t i o n s h i p s , and pressure, wave, downstream-velocity  relationships.  For a l l observations over a f l a t boundary the root-mean-square pressure r e s u l t i n g from the boundary layer turbulence i s about 2.6 times the mean s t r e s s ; thus the pressure can be nondimensionalized by the s t r e s s .  The  s p e c t r a l d i s t r i b u t i o n was found to be only weakly dependent on height, i n contrast to the v e l o c i t y which i s d i r e c t l y dependent.  At frequencies above  the peak i n the v e r t i c a l v e l o c i t y spectrum, the pressure spectra have a mean slope of about -1.7; the slope i s less steep at lower frequencies.  A scale  was defined for the pressure fluctuations based on the coherence between two simultaneous pressure measurements.  This scale was found to be the same i n .  a l l three coordinate d i r e c t i o n s ; thus, to a f i r s t approximation, pressure fluctuations are s p h e r i c a l . interpretation.  the i n d i v i d u a l  The phase measurements agree with this  From near-surface, simultaneous measurements with a down-  stream separation, the propagation v e l o c i t y of a pressure f l u c t u a t i o n was  73 estimated.  When this rate was  compared to the mean wind at a l e v e l  corresponding to the size of the pressure fluctuations they were found to be about equal. " In this same measurement, consistent phase differences i n the cross-spectrum could not be traced further than about 360° before the signals became incoherent. The simultaneous measurement of pressure and v e l o c i t y showed that the downstream v e l o c i t y fluctuations are approximately i n phase with pressure at low frequencies, while at higher frequencies there i s large phase difference of about 135°.  This phase difference i s a function of the height of observa-  tions, the in-phase portion occuring f o r pressure scales larger than the measurement height.  At these larger scales the pressure appears  to be i n t e r -  acting d i r e c t l y with the surface; smaller scales are e f f e c t i v e l y free of the surface.  Measurements at the surface support this i n t e r p r e t a t i o n .  Pressure measurements were used to calculate the energy f l u x by pressure forces i n two cases. In the f i r s t , the energy f l u x out of the downstream v e l o c i t y fluctuations was the downstream component.  found to be about 0.35  of the net energy source to  A possible sink for this energy i s i n t o the v e r t i c a l  and crossstream v e l o c i t y f l u c t u a t i o n s ; the v e r t i c a l v e l o c i t y fluctuations are developing i n this same frequency range. divergence term was  In the second case, the pressure  found to be a small f r a c t i o n , about 1/10,  feeding term i n the net energy budget of a boundary layer.  of the energy  The terms were  compared i n integrated form. Pressure measurements near wind generated water waves showed a large hump i n the spectrum at the wave frequencies.  The amplitude of this hump  increased, and the rate of i t s decay v e r t i c a l l y decreased, as the mean wind speed increased.  The phase difference between pressure and waves during  active wave generation i s about 135°, pressure lagging waves, and does not  change v e r t i c a l l y for measurements at heights greater than the wave crests. In non-generating  conditions the phase difference i s near 180°.  The active  generation occurs only when the c r i t i c a l height i s low enough to be near crest heights or lower.  Wave generation, i n f e r r e d from these  observations  above the surface, occurs most a c t i v e l y at the peak of the wave spectrum. The pressure-downstream v e l o c i t y relationship over waves i s d i f f e r e n t from that found for s i m i l a r observations over a f l a t boundary. the phase t r a n s i t i o n occuring at a frequency  Instead of  dependent on the s i z e of the  pressure producing scales which are d i r e c t l y proportional to the height, i t occurs at the frequency  of the peak of the wave spectrum.  Energy transfer  out of the downstream v e l o c i t y component measured near the waves i s s i m i l a r to that found f o r observations over a f l a t boundary, only i t i s s h i f t e d to l a r g e r scales at a given height.  The measurements suggest some strong i n t e r -  action between the normal boundary layer turbulence and the more organized flow over the waves. These measurements made with the developed  instrument have provided  the f i r s t r e l i a b l e pressure data w i t h i n a turbulent boundary l a y e r .  75 BIBLIOGRAPHY  Ampex Co. (1966) U.S.A.  Instruction Manual, FR-1300 Recorder/Reproducer.  Batchelor, G.K. (1960) The Theory of Homogeneous Turbulence. University Press, 197pp.  Calif.,  Cambridge  Blackman, R.B. and J.W. Tukey (1959) The Measurement of Power Spectra. Dover Publications, Inc., New York, 190pp. C.F. Casella and Co. Ltd., Instruction L e a f l e t - //3034/RA, Sensitive Anemometer. London, England. Deardorff,  J.W. (19 70) A three-dimensional numerical i n v e s t i g a t i o n of the i d e a l i z e d planetary boundary layer. J. F l u i d Mech. hX pt.2: 453-480.  DISA Elecktronik A/S (1967) Instruction and Service Manual, Type 55D05 Battery Operated C.T.A. Herlev, Denmark. Dobson, F.W. (1969) Observations of normal pressure on wind-generated sea waves. Ph.D. d i s s e r t a t i o n , University of B.C., 240pp. Garrett, J.F. (1970) F i e l d observations of frequency domain s t a t i s t i c s and nonlinear effects i n wind-generated ocean waves. Ph.D. d i s s e r t a t i o n , University of B.C., 176pp. Golitsyn, G.S. (1964) On the time spectrum of micropulsations i n atmospheric pressure. Izvestiya, Geophysical Series, No.8:1253-1258. (Am. Geophys. Union translation:761-763) Gorshkov, N.F. (1967) Measurements of the spectrum of pressure micropulsations i n the near-earth layer of the atmosphere. Izvestiya, Atmospheric and Oceanic Physics, 3^ (4):447-451. (Am. Geophys. Union translation:255-257) Gorshkov, N.F. (1968) On micropressure-fluctuations i n the near-earth layer. Izvestiya, Atmospheric and Oceanic Physics, 4^ (4):460-462. (Am. Geophys. Union translation:259-261) Gossard, E.E. (1960) Spectra of atmospheric scalars. 65(10) .-3339-3351.  J . of Geophys. Res.,  Herron, T.J., I. Tolstoy and D.W. Kraft (1969) Atmospheric pressure background fluctuations i n the microscale range. J . of Geophys. Res., 74(6):1321-1329. Hinze, J.O. (1959) Turbulence, An Introduction to Its Mechanism and Theory. McGraw-Hill Book Co., Inc. Toronto. 586pp.  76 Hume, D. ( 1 9 6 7 ) I n s t r u c t i o n Manual, Wind P r o f i l e System. O c e a n o g r a p h y , U n i v e r s i t y o f B.C., V a n c o u v e r .  Institute of  Hume, D. ( 1 9 6 9 ) I n s t r u c t i o n M a n u a l , C a p a c i t i v e Wave P r o b e . O c e a n o g r a p h y , U n i v e r s i t y o f B.C., V a n c o u v e r .  Institute of  I.E.E.E. T r a n s a c t i o n s on A u d i o and E l e c t r o a c o u s t i c s . S p e c i a l I s s u e on F a s t F o u r i e r T r a n s f o r m and i t s A p p l i c a t i o n t o D i g i t a l F i l t e r i n g and S p e c t r a l A n a l y s i s . June 1967, AU15(2). K a i j o D e n k i Co. L t d . ( 1 9 6 7 ) I n s t r u c t i o n Manual, Model PAT-311 Anemometer thermometer. Tokyo, Japan. Kraichnan,  Ultrasonic  R.H. ( 1 9 5 6 ) P r e s s u r e f l u c t u a t i o n s i n t u r b u l e n t f l o w o v e r a plate. J . o f t h e A c o u s t i c a l Soc. o f America, 28(3):378-390.  flat  Lamb, S i r H. ( 1 9 3 2 ) H y d r o d y n a m i c s ( 6 t h e d . ) . C a m b r i d g e U n i v e r s i t y P r e s s ( r e p r i n t e d b y D o v e r P u b l i c a t i o n s , I n c . , New Y o r k , 1 9 4 5 ) , 7 3 8 p p . Lee,  Y.W.  (1967) S t a t i s t i c a l Theory o f Communication. I n c . , New Y o r k , 5 0 9 p p .  L u m l e y , J . L . a n d H.A. P a n o f s k y ( 1 9 6 4 ) The S t r u c t u r e I n t e r s c i e n c e P u b l i s h e r s , New Y o r k , 2 3 9 p p .  John W i l e y  and Sons,  of Atmospheric Turbulence.  M a k i n o Co., L t d . , I n s t r u c t i o n M a n u a l , M a k i n o ' s P h o t o e l e c t r i c Tokyo, Japan.  Anemometers.  M a n t o n , M . J . (19 70) T h e o r e t i c a l s t u d i e s o f t h e g e n e r a t i o n o f s u r f a c e waves a n d t h e p r o p a g a t i o n o f i n t e r n a l w a v e s i n t h e s e a . P h . D. d i s s e r t a t i o n , U n i v e r s i t y o f B.C., 1 7 5 p p . M c B e a n , G.A. (19 70) S i m i l a r i t y of turbulent transfers near the surface. Ph.D. d i s s e r t a t i o n , U n i v e r s i t y o f B.C., 1 5 0 p p . P a n o f s k y , H.A. a n d A.A. T o w n s e n d ( 1 9 6 4 ) Change o f t e r r a i n r o u g h n e s s a n d t h e wind p r o f i l e . Q u a r t . J . Roy. M e t e o r o l . S o c . 90:147-155. Phillips,  O.M. ( 1 9 6 6 ) T h e D y n a m i c s P r e s s , L o n d o n , 261pp.  o f the Upper Ocean.  Cambridge  Shaw, R. ( 1 9 6 0 ) I n f l u e n c e o f h o l e d i m e n s i o n s on s t a t i c p r e s s u r e J . F l u i d M e c h . , _7 = 5 5 0 - 5 6 4 . S t e w a r t , R.W. ( 1 9 6 9 ) T u r b u l e n c e a n d w a v e s i n a s t r a t i f i e d Radio Science, 4(12):1269-1278. T o w n s e n d , A.A. ( 1 9 5 5 ) The S t r u c t u r e U n i v e r s i t y P r e s s , London.  University  measurements.  atmosphere.  o f Turbulent Shear Flow.  Cambridge  77 Weiler, H.S. and R.W. Burling (1967) Direct measurements of stress and spectra of turbulence i n the boundary layer over the sea. J . Atmos. S c i . , 24(6):653-664. Willmarth, W.W. and C E . Wooldridge (1962) Measurements of the f l u c t u a t i n g pressure at the w a l l beneath a thick turbulent boundary layer. J . F l u i d Mech., 14:187-210.  APPENDIX A EXPERIMENTAL SITES, INSTRUMENTS, AND TECHNIQUES  The primary objective when c o l l e c t i n g data i n the f i e l d was recorded data i n raw form f o r l a t e r analysis.  to obtain  Data were c o l l e c t e d at one  of three d i f f e r e n t s i t e s ; over water or sand at the SPANISH BANKS SITE, over asphalt and cut grass at the LADNER SITE, or over sand at the BOUNDARY BAY SITE.  Even though a t y p i c a l length of recorded data, or a 'Run', was  about  30 minutes each expedition providing several Runs lasted from one day to a few weeks, c h i e f l y dependent on the weather.  Analog signals from instruments  responding to s t a t i c pressure, wind v e l o c i t y and wave height were recorded on magnetic tape.  A u x i l i a r y data were logged manually; t y p i c a l l y these included  the mean wind p r o f i l e and d i r e c t i o n at both land and sea s i t e s , with wet dry bulb temperatures, water temperature,  and  currents and mean water l e v e l added  at the Spanish Banks s i t e . The method and instruments used to obtain these measurements, along with a description of the s i t e s , i s given i n the following paragraphs.  Experimental Sites  (i)  Spanish Banks S i t e A l l over-water observations i n this thesis are from the Spanish Banks  site.  I t i s located on a t i d a l f l a t on the south side of English  Bay,  Figure 85, 1/2 km from shore. The s i t e has two common wind d i r e c t i o n s , easterly or westerly, both s u i t a b l e f o r recording data.  Wind speeds up to 10 m/sec are not uncommon,  79 5 m/sec i s more t y p i c a l . 7 km;  this asymmetry was  An easterly wind has an asymmetric  considered when choosing recording conditions.  Winds from the west usually occurred when the wind was i n the S t r a i t of Georgia. 50 km,  fetch of about  from the north-west  Thus even though the fetch to the west i s about  the wave and wind f i e l d would not necessarily be uniform over this  dis tance. A hut on p i l i n g s , c a l l e d the platform, provided, l i v i n g and working space, Figure 86 (a) and (b). tides, by boat at higher tides.  I t was  accessible by walking at mean low  The maximum t i d a l range i s approximately  4 m. V e r t i c a l aluminum masts located about 50 m to the seaward side of the platform were used as mounts f o r instrument sensors.  These masts, about  7 m high and 15 cm i n diameter, rested on the sand and were held r i g i d by a tripod bracing arrangement.  A carriage on the masts could be raised or  lowered h y d r a u l i c a l l y and turned e l e c t r i c a l l y by controls at the platform to accommodate changes i n tide and wind.  Sensors mounted on brackets were  placed such that there was n e g l i g i b l e interference from the masts.  Cables,  weighted to the bottom, connected the sensors to the hut where signals were conditioned and then recorded.  The AC e l e c t r i c a l power f o r operating the  equipment was supplied by a 3 kw ONAN generator, fed through a S0RENS0N AC power regulator.  The voltage and cycles of the AC power were monitored to  ensure that they remained within instrument requirements.  (ii)  Ladner S i t e The Ladner s i t e i s located on an asphalt runway at an abandoned a i r p o r t ,  Figure 87, an area now part of the Canadian Forces S t a t i o n , Ladner. F a c i l i t i e s at the s i t e were arranged by a fellow graduate student, G.A. McBean. Grass growing between the runways was normally cut, providing a reasonably  80 uniform t e r r a i n f o r about 1 km i n a l l d i r e c t i o n s .  Typical roughness elements  were about 10 to 30 cm high i n the grassed area and less than .5 cm on the runways.  The s t a t i o n i s surrounded by farmland and t i d a l f l a t s ; the nearest  buildings or other large obstructions upwind (west) were always more than 2 km away. The instrument sensors were mounted at fixed levels on a 5 m mast which was  aligned with the wind by rotating i t manually.  Some surface pressure  measurements were made at this s i t e i n winds up to 10 m/sec.  A hole was dug  i n the asphalt runway to contain the box used for the surface measurements, Figure 88. Cables l e d downwind to the s i g n a l conditioners and tape recorder that were i n the back of an I.0.U.B.C. truck, Figure 89. B.C. Hydro e l e c t r i c a l power, 115 VAC, was available from a nearby outlet.  (iii)  Boundary Bay S i t e The Boundary Bay s i t e i s located approximately  l i n e on the mud f l a t s of Boundary Bay, Figure 90.  75 m from the high tide The f l a t s to the south of  the s i t e were free of obstruction except f o r the occassional log or patches of grass.  Changes i n surface elevation were about 10 cm; the potholes which  occurred were f i l l e d with water.  The area to the north i s farmland.  the high tide l i n e i s a 2 m high dike.  Along  Since this s i t e was used f o r  instrument c a l i b r a t i o n only, uniform t e r r a i n was not c r i t i c a l . The instrument box used f o r surface pressure measurements was placed flush with the surrounding surface i n an area which was uniform and f l a t f o r a few meters.  Mean wind p r o f i l e measurements were made on a 4 m aluminum mast.  Other instruments were attached to a 2 m aluminum stand.  As at the Ladner  s i t e , the electronics were kept i n an I.0.U.B.C. truck and e l e c t r i c a l power was  obtained from a nearby outlet.  81 Instruments and Observational Techniques  (i)  Analog Data Recording The analog data were recorded on 14-track 1" magnetic tapes using an  AMPEX Model FR-1300 Recorder/Reproducer recorder.  (Ampex Co., 1966) portable tape  Signals were recorded FM using the IRIG scheme.  An input l e v e l of  ± 1 v o l t rms produces ± 40% deviation from the center frequency. were recorded at 7 —  ips.  Most data  At this speed, the frequency response was  flat  2  (within 1.0 db) from 0 to 2.5 kHz, and the rms s i g n a l to noise r a t i o was 44 db; adequate  f o r the purpose.  One feature of this tape recorder which i s  very useful i s the two sets of tape heads; one set for recording and the other f o r simultaneous monitoring.  A separate switching box permitted any  two of the signals being recorded to be viewed on the dual beam o s c i l l o s c o p e .  (ii)  Sonic and U-Wire The turbulent v e l o c i t y components were measured with a KAIJO-DENKI  three dimensional u l t r a s o n i c anemometer-thermometer (Kaijo-Denki Co. Ltd., 1967) referred to as the 'sonic' and the downstream component using a DISA Type 55D05 battery operated constant temperature hot-wire anemometer (Disa Elecktronik A/S, 1967)  referred to as a 'u-wire' or 'hot wire'.  used has a probe with a path length of 20 cm.  The sonic  Thus f o r t y p i c a l mean wind  speeds, less than 10 m/sec, v e l o c i t y fluctuations from DC to greater than 10 Hz could be measured before the e f f e c t of averaging over the 20 cm path became important.  The junction box and probe were mounted at a w e l l exposed  p o s i t i o n on the mast, usually more than 1 m from the main mast .  A 100 m  cable connected the junction box to the remaining e l e c t r o n i c s , , i n the hut or  82 truck.  The analog output of the sonic i s ± 1 v peak to peak with offsets to  adjust f o r the mean wind.  Accuracies are about ± 3% of the f u l l scale ranges  of 1 m/sec, 3 m/sec and 10 m/sec. The u-wires were mounted e i t h e r separately from, or attached to, the pressure measuring instrument. led  Coaxial s i g n a l cable and compensating  cable  to the Disa u-wire electronics which give an analog s i g n a l output.  The  s i g n a l had the DC l e v e l and gain adjusted before recording; this a d d i t i o n a l equipment was b u i l t by E. Jerome, a fellow graduate student. of  The accuracy  the instrument i s l i m i t e d by the c a l i b r a t i o n of the probes.  used were c a l i b r a t e d i n a wind tunnel i n i t i a l l y , anemometers or the sonic -in the f i e l d .  Most probes  then checked against cup  The c a l i b r a t i o n was  probably known  to ± 15%.  (iii)  Cup Anemometers The mean wind speed p r o f i l e was measured with cup anemometers, normally  positioned with a logarithmic spacing at levels between .5 and 5 m. cups were mounted on arms up to 50 cm from the main mast. more than one cup was  i n working order.  The  For most Runs  A d i f f e r e n t set was  used at each of  the s i t e s : I.0.U.B.C. Wind P r o f i l e System at the Spanish Banks s i t e (Hume, 1967), MAKINO system at the Ladner s i t e (Makino Co. L t d . ) , and CASELLA system at  the Boundary Bay s i t e ( C F . Casella and Co. Ltd.).  A l l these systems are  of  the counter type, where e i t h e r a p h o t o c e l l or a reed switch i s pulsed by  the turning cups; the pulses are then modified to drive a counter which counted the t o t a l number of pulses.  The I.0.U.B.C. and Makino systems  include an rms meter f o r instantaneous v i s u a l monitoring.  The t o t a l counts  from each cup were obtained at timed i n t e r v a l s , usually spanning the period of analog data recording; the mean wind at fixed l e v e l s was  read from the  c a l i b r a t i o n curves. tunnel.  The c a l i b r a t i o n  of the cups was  The mean wind for any other l e v e l was  checked i n a wind  obtained graphically using  a best line f i t to the cup readings p l o t t e d on a l o g - l i n e a r p l o t .  For  observations over water, the winds have been referenced to a coordinate system moving with the mean current.  Results are accurate to .1 m/sec.  Observations were analysed only when the mean wind speed and d i r e c t i o n were l a t e r found to be reasonably steady; i f a 5 minute average wind speed changed by more than 20 to 30% from the previous 5 minute average, conditions were considered to be non-stationary and the Run was  (iv)  not used.  Wave Probe Two  d i f f e r e n t systems were used f o r wave height measurements, both  employed a capacitive type of wave probe. rod 150 cm long and .635  The probe consisted of a brass  cm (1/4 inch) i n diameter covered with a sleeve of  t e f l o n .0254 cm (1/100 inch) thick which was  sealed at one end and attached  by a water tight connection to a coaxial cable at the other.  The brass rod  formed one plate of a capacitor, the t e f l o n the d i e l e c t r i c and sea water the other p l a t e ; as the water height changed so did the capacitance.  This rod  was held i n a bracket arranged so that i t could be mounted v e r t i c a l l y on the masts.  The two systems used d i f f e r e n t methods of measuring the capacitance.  One system i s the equipment as modified by a fellow graduate student 1969)  i n which the wave probe capacity i s part of the frequency  network of a blocking o s c i l l a t o r ;  the FM s i g n a l was  (Dobson,  controlling  returned to the platform,  demodulated with a VETTER Model 3 FM Recording Adaptor and then recorded on magnetic tape.  The other system (Hume, 1969)  used a constant current source  to charge the capacity of the probe and measured the time taken to charge to -4 a given voltage l e v e l ; the r a t i o of this time to the c y c l i n g time of 10  sec  84 was converted to an analog s i g n a l . s e n s i t i v i t y adjustment  The resolution i s 1/1000 of the range; a  allowed use of d i f f e r e n t wave height ranges.  The  system has very l i t t l e d r i f t . The probes were calibrated before and a f t e r each f i e l d t r i p by holding the probe at d i f f e r e n t depths i n a tank of s a l t y water.  The probe was  frequently wiped with an o i l y cloth to keep the wetting  characteristics  constant; this improved the r e p r o d u c i b i l i t y of the c a l i b r a t i o n s . shows t y p i c a l calibrations  f o r the two systems.  Figure 91  Both systems should give  wave height to ±10%.  (v)  Water Height and Current Mean water height was measured by reference to bands of r e f l e c t i n g ( f o r  working at night) tape on one of the masts.  The tape i n t e r v a l was 1/2 meter;  the mean could be estimated to ±10 cm. The surface current was obtained by measuring with a stop watch the time taken f o r a piece of tissue paper to t r a v e l 7.5 m between two of the supporting members of the platform. features.  Direction was by reference to topographic  The t i d a l current normally flows i n an east-west  speeds up to 30 cm/sec.  d i r e c t i o n with  The measuring technique gave results to ±1 cm/sec.  Some current speeds at various depths were measured with a calibrated Savonius rotor current meter.  The speed did not vary with depth w i t h i n the  top meter.  (vi)  A i r and Water Temperature Wet and dry bulb temperatures were obtained to ±0.1 C° from mercury i n  glass thermometers.  These thermometers were mounted i n a sun screen that  could be moved to a w e l l exposed location on the platform.  Water temperature  was obtained by immersing a s i m i l a r thermometer i n the upper few cm of water below the platform. standard.  A l l thermometers were calibrated against a laboratory  86 APPENDIX B ANALYSIS OF DATA The data analysis can be considered i n two parts; that concerned with the s t a t i s t i c a l description of variables such as turbulence or waves and that concerned with the general description of the flow by mean values such as stress or s t a b i l i t y .  The s t a t i s t i c a l analysis was  done d i g i t a l l y , using an IBM 7044 or 360  computor at the U.B.C. Computing Center. Since the data was was necessary.  This was  b i t s ) designed and b u i l t  i n i t i a l l y recorded analog, conversion to d i g i t a l form done using an analog to d i g i t a l converter (10 binary at I.0.U.B.C.  Up to ten channels of information  could be sampled sequentially i n a cross-channel sweep, with a delay of approximately 45 micro-seconds between channels.  The time between cross-2  channel sweeps could be varied from about 3 x 10  -4 to 2 x 10  sec.  Provided that data i s band l i m i t e d to frequencies less than n the data i s d i g i t i z e d  , and max , Blackman and Tukey (1959,  at a minimum rate of 2n max  J  p.117) show that a l l such data can be represented i n frequency space with no aliasing.  To reduce a l i a s i n g the signals were f i l t e r e d with matched l i n e a r  phase s h i f t f i l t e r s before d i g i t i z i n g .  Since most of the data were recorded  at tape speeds of 7— ips and reproduced f o r d i g i t i z i n g  at 60 ips (which  2  increased a l l frequencies by a factor of 8), the cutoffs of the f i l t e r s were designed accordingly. In r e a l time the f i l t e r cutoff (3 db down) was  at about  20 Hz and the folding frequency, n^, f o r most of the data was set at 31 Hz ( i . e . , data were d i g i t i z e d  at 500 Hz).  The output of the analog to d i g i t a l converter was w r i t t e n on an IBM compatible magnetic tape using a Control Data Corporation 8092 Teleprogrammer  at the U.B.C. Computing Center. The method used to obtain s t a t i s t i c a l information from the data on the d i g i t a l tape requires two steps.  The f i r s t step uses a main program, 'FTOR',  which takes the time s e r i e s d i g i t a l data and creates a second magnetic tape containing the corresponding  complex Fourier c o e f f i c i e n t s of the data.  step makes use of the 'Fast Fourier Transform' algorithm, 'FFT'  This  (I.E.E.E.  Transactions, S p e c i a l issue on Fast Fourier Transform, June 1967).  The second  step takes these Fourier c o e f f i c i e n t s and produces spectra, etc., from programs b u i l t around a main program c a l l e d 'SCOR'. w r i t t e n by J.R. Wilson  These b a s i c programs were  and J.F. Garrett of this i n s t i t u t e (see J.F. Garrett,  1970). In 'FTOR', the maximum number of data points per block that can be handled i s 10,240.  The actual number of points used i n each block i s the  number of channels times the number, N, of data points from each where the l a t t e r has  to be a power of 2.  The FFT technique  channel,  then produces  complex Fourier c o e f f i c i e n t s f o r each channel for harmonic frequencies from the fundamental frequency  of 1 cycle per block to n^, the f o l d i n g  This i s done sequentially f o r a l l blocks i n the e n t i r e Run.  frequency.  For a h a l f hour  Run, with 4 to 6 channels of data, the t o t a l number of data blocks, M,  was  t y p i c a l l y 30 to 50. When analysing a time series of length NAt, where At i s the number of seconds between data points, the Fourier c o e f f i c i e n t s are calculated f o r 2frr s p e c i f i c angular frequencies, to^ = ^ ^ J T J where r i s an integer.  I f the time  function to be analysed contains a frequency, to^, not equal to an to^, this produces a set of Fourier c o e f f i c i e n t s that peak near the frequency f a l l o f f asymptotically as l/(to - to ) (Blackman and Tukey, 1959,  tu^ and  p. 33) or as  2 l/(u) - tu^)  for the s p e c t r a l estimates.  This i s e s s e n t i a l l y the s p e c t r a l  88 window for the i n i t i a l part of the analysis.  To improve the window, the  Fourier c o e f f i c i e n t s could be 'hanned' using the formulation  — A' + k r - l  — A' r  r+1  tt  2  (19) and  f r - l  1 B' 2 r  „ r+1 B  where A^ and B^ are the cosine and sine c o e f f i c i e n t s , r e s p e c t i v e l y . The window f o r the hanned c o e f f i c i e n t s gives a s p e c t r a l f a l l o f f rate of l/(w - W ) * Q  Hanning was used only i n a few s p e c i a l cases. The program 'SCOR* uses the c o e f f i c i e n t s from FTOR' to obtain the 1  desired s t a t i s t i c s C  til  rm  ttl  , f o r the r  C  rm  harmonic i n the m  =  where i = / -1,.  (see J.F. Garrett, 1970).  A + rm  block, can be w r i t t e n as  i B , rm  (20)  The s p e c t r a l energy density, S, i s then obtained for the  frequency, n^ = r/NAt, by multiplying d i v i d i n g by 2.  The complex Fourier c o e f f i c i e n t ,  by i t s complex conjugate and  The values of S are then grouped i n t o bands.  h a l f octave bands are used f o r the frequency 5 s p e c t r a l estimates  For this work,  range where there are more than  (5 harmonics) per h a l f octave.  However, since the  i n d i v i d u a l s p e c t r a l estimates at the lower frequencies are more than h a l f an octave apart, the f i r s t 9 bands are preset to a larger bandwidth so that at least one c o e f f i c i e n t i s included i n each band.  When averaged over a l l blocks  the s p e c t r a l energy density for a band, S, , can be w r i t t e n as  89  C  /  N At  N  W  \  1 + r - r  '  2  "  A  M  2  1 \  2  + B  rm  2  rm  2  x  r=r^  •  (  2  1  )  m=l  -  w h e r e  i s the geometric mean of the end frequencies and the 1 + r - r bandwidth, B . W . = N~At " T y p i c a l l y , the number of bands i n each W  °b  N At  2  ±  _2 analysis i s 23, with a minimum frequency of 2.7 x 10  Hz and a maximum of  3.0 x 1 0 Hz. 1  The cospectrum between, say, data channels 1 and 2 was estimated from  r  s  n C  \  °12 b ( n  )  =  1  +  N At r - r  2  \  M \ _____ m=l  1 M  2  r=r^  A,lrm A„ 2rm + B,lrmB 2rm  ,„„,.  r  2  (  2  2  )5  the quadrature spectrum from  r  n  Q U  f  \  12 V (  =  N At  1+ r  2  2  M  \  -r  1  \  i  M _____  r=r^  m=l  A2rm „ B, lrm  A, lrmB, 2rm  2~  / 0 0  ,  ( 2 3 5 )  the coherence from  / 12 (n ) = - — C o  Coh  2 ( n  b  )  Q 12  +  u  2(n  / b l V b2<V S  (  S  b>'  •  (24);  90  and the phase from  ©-^(i^) = tan  -1  (25). 12 b ( n  )  Confidence l i m i t s were calculated d i r e c t l y by assuming each block to be an independent  sample of the data.  I f the difference between the s p e c t r a l  estimate f o r each block and the mean over a l l blocks i s assumed to have a Gaussian d i s t r i b u t i o n , then these differences can be used to find the 95% confidence l i m i t s .  The assumption  i s reasonable only i f M, the number of  data blocks, i s quite large, which i s true f o r most of the Runs. Information on the s p e c t r a l shape at lower frequencies was obtained from an a d d i t i o n a l program (G.A. McBean, 1970) which uses the same techniques as already discussed but with the block averages as data points or by d i g i t i z i n g data at a lower frequency. The data had to be corrected f o r instrument and f i l t e r response.  A  program w r i t t e n by Dobson (1969) was used f o r phase correction; i t also appropriately adjusted the Co- and Quad-spectra.  Amplitude  corrections were  done by hand. Since some wave data were c o l l e c t e d when there was a s i g n i f i c a n t mean water current, the frequency had to be corrected.  In order to do this the  influence of the water current on the wave frequency,  (rad/sec), was  removed by means of the equation  n  (26) w  w  w  91 where U i s the mean current and co i s the measured wave w m  In addition to the s p e c t r a l description, the flow was described of mean conditions  i n terms  including the surface stress and s t a b i l i t y .  The surface stress was estimated by three d i f f e r e n t methods: d i r e c t measurement, the ' m e t h o d ' , or using a drag c o e f f i c i e n t . The  direct measurement method involved estimating  variance of uw  the stress from the  ( T = -puw ); the v e l o c i t y components were measured with a  sonic anemometer.  Coordinate rotation was used to correct f o r non-alignment  with the mean wind by appropriately be used i n the SCOR program.  adjusting the c a l i b r a t i o n c o e f f i c i e n t s to  This method f o r f i n d i n g the stress i s considered  the most accurate. The  '®2_i  m e t  h ° d ' estimates the stress from a knowledge of the magnitude  of downstream v e l o c i t y fluctuations i n the i n e r t i a l subrange (Weiler and Burling, 1967).  For this range, the s p e c t r a l density of the downstream  v e l o c i t y fluctuations ($,,)  *„(k)  =  K' £  at wave number k i s approximately  2/3 -5/3  (27)  k  where e i s the rate of energy d i s s i p a t i o n and K' i s the Kolmogoroff constant, taken to be 0.5.  Assuming that the rate of production of turbulent energy i s  equal to the rate of d i s s i p a t i o n and that the wind p r o f i l e i s logarithmic, and  using  equation  2  The value of  =  1  (27), the s t r e s s  ( T = pu^  ) can be w r i t t e n :  z .2/3 5/3 3.86 p ( £ )  ( n ) at the frequency n was taken from a p l o t of log $  (28).  11  92 against log n for which a best f i t -5/3 l i n e was drawn. For observations over water a drag c o e f f i c i e n t ,  , was occasionally  used to relate the 5 meter mean wind, i n cm/sec, to the surface stress by the formula  T  =  P  u  *  =  2  C  D5  P  l  U  2  (  2  9  )  5  -3 where  = 1.2 x 10  . A plot of the drag c o e f f i c i e n t as a function of wind  speed, Figure 92, uses and the $  method.  values of stress estimated from d i r e c t measurement  As can be seen, a l l the methods are compatible and each  suitable for estimating a value f o r the surface s t r e s s . The s t a b i l i t y of the a i r over water was estimated i n terms of the gradient Richardson Number, Ri,-,. Ri  for 9 = T  r  =  rf-  I t can be w r i t t e n as  ^Z3|  (1 - 0.61 h  (30)  ), where g i s the g r a v i t a t i o n a l acceleration,  T^ i s the a i r temperature, U i s a i r v e l o c i t y , z i s height, and h humidity.  i s specific  6 i s a v i r t u a l temperature, which includes the e f f e c t of both a i r  temperature  and humidity on the buoyancy.  R i was calculated i n a difference  form: the difference between the value at some height z and at z = .01 cm. I t i s assumed that at this lower height ul  rt1  •U I  temperature).  Ri  G  = 0 and T  = T .UI  (surface water W  Then  =  980 -f^mean  z " ^Ol* —z-. ~ ^ l ^  ( 9  z  where the 6's were calculated from  AOTz  ( l n z + 4.61)  (31)  93  6  z  =  T ( 1 + 5 . 0 x 10 A  4  A  h  re  e l ) s a' z (32)  and  e.01  =  T (1 + 5.0 x 10 w  The r e l a t i v e humidity, h  -2  , and the saturation vapour pressure, e  , were  S 3.  X*6  obtained from handbook tables using the mean wet and dry bulb and surface water temperatures  observed during a Run.  I t i s intended that t h i s method  of estimating the s t a b i l i t y should give at least an order of magnitude value for comparison w i t h i n this study and with other studies.  94 APPENDIX C DATA SUMMARY  TABLE V (see below) l i s t s  the  'mean' c o n d i t i o n s under which each o f  Runs mentioned i n t h i s r e p o r t were taken. used i n the more g e n e r a l summary p l o t s . s i m i l a r to those data for  shown.  The  Banks, Spanish  sections: part A  The  Runs are i n n u m e r i c a l  s i t e a b b r e v i a t i o n s used were: 'S.B.' f o r  'L' f o r Ladner, and  shallow  wave g e n e r a t i o n was d i g i t i z e d data.  'B.B.' f o r Boundary Bay.  o r absent  present.  data  order Spanish  Measurements at  The  and when the w a t e r was  the  s a t u r a t i o n or d r i f t  s h o r t e r p i e c e s o f data f o r a n a l y s i s . -3 x 10  The  i n minutes, o f  about h a l f an hour i n often necessitated using  v a l u e f o r the  stress,  2 u  *  » i s f o l l o w e d by a number, 1,  2, o r 3, i n b r a c k e t s .  number i n d i c a t e s the method used to e v a l u a t e the s t r e s s : measurement, (2) f o r the $ instruments  both  deeper and a c t i v e  ' d u r a t i o n ' i s the t o t a l time,  Most of the Runs were o r i g i n a l l y  d u r a t i o n , however instrument  at d i f f e r e n t  method, and  Banks s i t e g e n e r a l l y flowed  This  (1) f o r d i r e c t  (3) f o r the drag c o e f f i c i e n t .  l e v e l s were used, the h e i g h t s  mean w a t e r l e v e l ) a r e g i v e n i n s u c c e e d i n g Spanish  gives  Banks s i t e are used i n both p a r t s s i n c e o b s e r v a t i o n s were taken  when the w a t e r was  T = 1.25  i n two  a f l a t boundary, and p a r t B g i v e s  measurements a s s o c i a t e d w i t h waves. The  from u n l i s t e d Runs were  They were taken under c o n d i t i o n s  table i s presented  f o r measurements a s s o c i a t e d w i t h  w i t h i n each s e c t i o n .  Some data  the  lines.  The  If  above the s u r f a c e  water c u r r e n t at  i n an east-west d i r e c t i o n .  two  (or  the  Listed  after  the magnitude of the c u r r e n t i s the d i r e c t i o n s g i v e n as E f o r a c u r r e n t f l o w i n g from the e a s t , and W f o r flow from the west. A,  for observations  system moving w i t h  As mentioned i n Appendix  over water, the winds have been r e f e r e n c e d t o a the mean c u r r e n t .  coordinate  F o r Runs i n s e c t i o n B o f the t a b l e , the  95 difference between the 5 meter wind and phase speed of the waves at the peak of the wave spectrum, ( u|  - C ), i s given;  the frequency of the peak i s  given i n brackets a f t e r this v e l o c i t y difference.  TABLE V MEAN DATA FOR RUNS A.  FLAT BOUNDARY  RUN  DATE  SITE  tt  U  l  5  (1)  (2)  WIND DIR  (3)  T  z  U  h  (4)  (5)  (6)  (7)  U w (8)  72/1  Mar 21/69  S.B.  18  6.8  270°  -0.01  0.650(2)  2.0  6.5  1.0  0  72/2  Mar 21/69  S.B.  19  6.2  270°  -0.02  0.511(2)  2.0  6.0  1.0  0  73/1  Apr 3/69  S.B.  16  8.2  100°  0.974(2)  2.0  7.8  1.0  0  73/2  Apr 6/69  S.B.  10  3.9  260°  -  0.287(2)  3.5  3.9  0  73/3  Apr 6/69  S.B.  11  5.5  260°  -  0.221(2)  1.00  4.5  0  110/1  Aug 8/68  S.B.  27  7.2  285°  0.870(1)  5.5  7.1  0  110/2  Aug 8/68  S.B.  26  7.2  285°  0.910(1)  4.0  7.4  0  120/1  Aug 8/68  S.B.  22  6.8  270°  0.724(1)  3.4  6.5  0.75  0.40W  120/2  Aug 8/68  S.B.  30  6.5  280°  -  -  0.553(1)  4.8  6.2  1.2  0.40W  121/1  Aug 8/68  S.B.  27  5.8  275°  -  0.479(1)  1.5  5.4  2.2  0.63W  132/2/1  Sept 4/68  B.B.  9  3.7  280°  0.30  3.4  133/3/1  Sept 17/68  B.B.  26  6.1  270°  1.00  5.1  133/3/2  Sept 17/68  B.B.'  17  7.0  270°  1.00  5.9  137/1  Sept 17/68  B.B.  18  5.8  270°  0.30  5.0  -  -  -  -  TABLE V (continued) A.  (continued) RUN  DATE  SITE  tt  "Is.  WIND DIR  ^G  137/2  Sept 27/68  B.B.  25  4.1  295°  -  141/2/1  Apr 3/69  S.B.  18  7.8  120°  141/2/2  Apr 3/69  S.B.  9  7.8  141/3  Apr 3/69  S.B.  19  142/1  Sept 27/68  B.B.  165/2  Mar 12/69  172/1  T  z  U  h  U w  -  0.30  3.4  -  -  -0.01  0.900(2)  2.0  7.5  1.0  0  120°  -0.01  0.900(2)  2.0  7.5  1.0  0  7.6  130°  -0.01  0.900(2)  2.2  7.3  1.0  0  16  4.3  280°  -  -  0.30  3.5  -  -  S.B.  13  4.4  280°  -0.02  0.277(2)  2.5  4.3  2.0  0  Mar 20/69  S.B.  12  5.3  270°  -0.04  0.367(2)  1.5  5.0  1.5  0  172/2  Mar 20/69  S.B.  20  5.9  270°  -0.04  0.518(2)  3.0  5.7  1.0  0  173/1  Mar 20/69  S.B.  19  6.8  280°  -0.03  0.611(2)  2.5 4.6  6.5 6.8  0.7  0  173/2  Mar 20/69  S.B.  22  7.4  280°  -0.02  0.941(2)  2.0 2.5  7.0 7.1  1.0  186/3  Apr 7/69  S.B.  15  3.6  280°  -0.02  0.156(2)  2.5  3.6  0.5  0  186/4  Apr 7/69  S.B.  9  3.7  270°  -  0.196(2)  3.0 5.1  3.6 3.7  0  -  186/5  Apr 7/69  S.B.  8  2.7  270°  -  0.136(2)  1.25 6.75  2.6 2.7  0  -  0.2;  TABLE V (continued) A.  (continued) RUN  DATE  SITE  tt  "Is  WIND DIR  T  z  U  196/1  J u l 15/69  S.B.  13  3.7  270°  -0.12  0.189(3)  0.46 1.05  -  196/2  J u l 15/69  S.B.  20  3.4  270°  -0.29  0.160(3)  0.46 1.05  -  196/3  J u l 15/69  S.B.  8  3.7  270°  -0.13  0.189(3)  0.20 0.76  200/2  J u l 17/69  S.B.  23  4.7  260°  -0.01  0.302(3)  205/1  J u l 19/69  S.B.  30  3.8  260°  -0.04  205/2  J u l 19/69  S.B.  23  3.8  260°  318/1  Aug 23/69  L  30  4.8  318/2  Aug 23/69  L  31  319/1  Jan 27/70  L  319/2  Jan 27/70  320/1  h  U w  0.20  0  0.20  0  -  0.30  0  4.0 4.5  4.6 4.6  2.0  0.64W  0.197(3)  5.0  3.8  1.0  0.30W  -0.03  0.197(3)  5.0  3.8  1.0  0.46W  270°  -  1.23 (1)  0.40  3.5  -  -  4.8  270°  -  1.17 (1)  0.40  3.3  -  -  24  9.9  270°  -  3.84 (2)  0.32  6.7  -  -  L  22  9.8  270°  -  3.84 (2)  0.32  6.7  -  -  Jan 27/70  L  32  8.8  270°  -  1.84 (2)  0.32  6.0  -  -  320/2  Jan 27/70  L  29  7.7  270°  -  1.16 (2)  0.32  5.3  -  -  425/1  Jan 27/70  L  24  6.1  270°  —  0.862(2)  0.32  4.1  '  •  —  —  TABLE V (continued) A.  (continued) RUN  DATE  SITE  tt  UL 5  WIND DIR  Ri  T  z  U  425/2  Jan 27/70  L  23  5.2  260°  -  0.756(2)  0.32  3.5  426/1  Jan 27/70  L  32  6.1  270°  -  0.862(2)  0.32  4.1  h  U  vo  TABLE V (continueB.  NEAR WAVES RUN  60/1  60/2  60/4  80/3  119/1  119/2  119/3  DATE  Mar 27/69  Mar 27/69  SITE'  tt  -Is  WIND DIR  S.B.  16  4.3  250°  S.B.  S.B.  Apr 2/69  S.B.  Mar 27/69  S.B.  Apr 2/69  S.B.  Apr 2/69  Apr 2/69  S.B.  12  22  17  15  19  17  4.7  4.1  3.9  4.1  4.7  4.8  250°  130°  260°  90°  120°  120°  -0.01  0.001  -0.05  -0.01  -0.05  -0.04  -0.04  0.274(3)  0.331(3)  0.252(3)  0.228(3)  0.252(3)  0.331(3)  0.344(3)  1  z  U  h  0.40 0.90  3.5 3.8  2.5  0.50 1.00  3.9 4.1  2.5  0.30 0.80  2.9 3.3  3.0  0.30 0.80  3.3 3.5  2.5  0.40 0.90  3.5 3.7  3.0  0.30 0.80  4.1 4.3  3.0  0.30 0.80  3.8 4.2  3.0  U w  UL - C '5 (9)  0.22E  0.2(0.32)  0.22E  0.6(0.32)  0  1.7(0.65)  0.22E  -0.2(0.32)  0  1.8(0.70)  0  2.3(0.65)  0  2.2(0.60)  164/1  Dec 18/68  S.B.  14  2.6  290°  -0.19  0.101(3)  0.50  2.2  3.5  0  -2.3(0.25)  164/2  Dec 18/68  S.B.  16  4.1  340°  -0.09  0.252(3)  0.60  3.5  3.5  0  -1.5(0.18)  167/1/1  Dec 14/68  S.B.  19  8.1  115°  0.02  0.985(3)  0.50  6.3  3.5  0.24E  5.0(0.50)  167/1/2  Dec 14/68  S.B.  18  7.2  120°  0.02  0.776(3)  0.50  5.7  3.5  0.24E  4.1(0.50)  167/2  Dec 14/68  S.B.  14  7.9  100°  0.03  0.935(3)  0.30  5.8  3.5  0.24E  4.8(0.50)  TABLE V (continued) B.  (continued)  RUN  DATE  SITE  tt  uL 5  WIND  Ri  DIR  T  z  U  h  U  G  W  u|  -C  5  167/3  Dec 14/68  S.B.  6  6.4  125°  0.05  0.615(3)  0.30  4.8  3.5  0.24E  3.3(0.50)  173/3  Mar 20/69  S.B.  14  3.6  240°  0.02  0.194(3)  0.90 1.40  3.1 3.2  2.5  0.30W  -0.5(0.30)  (1)  Duration  (minutes)  (2)  Mean wind at 5 meters (m sec ^)  (3)  Gradient Richardson Number -2  (4)  Surface Stress (dynes cm  )  (5)  Instrument height (m)  (6)  Mean wind at the instrument height (m sec ^)  (7)  Water depth (th)  (8)  Current (m sec ^)  (9)  u| _ - C  at the peak of the wave spectrum  (m sec  102  Figure 1.  Instrument used to measure the s t a t i c pressure fluctuations w i t h i n the turbulent flow  Pressure  (a)  assembled  (b)  '•.'iti  c y l i n d e r removed  Figure 2.  Probe developed f o r measuring s t a t i c pressure fluctuations within the turbulent flow  o OJ  104  PROBE 'E' .04 to a> .c o c  •x  *  x  x  PORTS  .02  /  M  .2  .6  .8 X (inches)  1.0  1.2  4~  1.4  1.6  PROBE 'F' .04  /  •X \  t  JZ  PORTS  a c .021  .4  6  .8 X (i n c h e s )  1.0  1.2  1.4  i.6  1.0  1.2  1.4  1.6  PROBE 'G' .04  *  OJ  .02  i  *  PORTS  /  /  rsi .2  .6  .8 X (inches)  x SIDE 2 • SIOE I  Figure 3.  Cross-sections of the disks of probes E, F, G  IO°r  15 l<0 i£  U=3.6 m-sec"' 25"  lie  -95%  68%^-  10°  28  * U=8.9m-sec-  5°  /a  K o°| CL -5<>\  -I0°  L  \  to  '8  it-  16  18  16 21  23 •10°  _5f 0°  YAW  Figure 4.  /-  I—o° h7 CL  IB  10°  -5° -IO  o L  -95%  68%^  u  u  3 4  5  > 4  5"  7 9 9 -10°  8  -*  0°  YAW  Dynamic pressure noise test f o r Probe E at different wind speeds  c  *•  10°  IO f #  15 14 IS  14  U=3.7m-sec'' /4  10°  zo  68%-v ^ Jl^f • ~  95%  lS~  3  5°  19  is-  N  IS  <*  \ )  y /  -IO  o L  16-  IS  ZD 23  19  IS ll  -5«  -10°  I  -10"  I0«  IS io  ii/  '•  /5-  18 19  -5°  17  YAW U=6.2m-sec-'  /  IS  8  o°  / ^ V  U  CL  /3  9 5 %  -I0°  L  8  -10-  0°  YAW IS~ 12  0°  10  s  II  O N \ \  Q /2  O,o  o  12  H  II  I'  lb>-95%  !I-' l ^ > 6 8 % I' II It II 4 -  —i  i  to  II  20  isll  YAW  io-  6  8  VELOCITY (m-sec") P  Figure 5.  8 «-  i _  ll 68%-v  5°'  I r  h- 0 °  28  -io«  10°-  u  zo  95%  68%  12  U  U=8.9 m-sec'i  R  O  B  E  io  F  Dynamic pressure noise test f o r Probe F at d i f f e r e n t wind speeds  o  ON  to probe  POWER SUPPLY (in recording hut) lOKhz  Reference  ^ Ipressure | f" Inputs  £  to reference Diaphragm PRESSURE SENSOR (mounted with probe)  ±5VDC  SIGNAL CONDITIONER (in recording hut ) 1—i  Figure 6.  Schematic of the Barocel transducing system  o  Figure 7.  Barocel pressure transducer and reference volume i n t h e i r container  r-» o CO  X  I  0  I  I  20  I  I  40  1  1  60  Distance from Transducer Case (cm) Figure 6.  Results of wind tunnel t e s t f o r the dynamic pressure d i s t r i b u t i o n i n front of the transducer case  g  Drum  Reference Barocel  >  T r a n s d u c e r et a l  V i brat ion Generator  Power Amplifier  Probe  -cables Strip-chart Recorder  w o  Oscilloscope  CD o o o  Barocel  Figure 9.  Signal Generator  o o  System  Arrangement  used f o r c a l i b r a t i n g the pressure instrument f o r amplitude and phase response  Al  plate-  5gallon  rubber  drum  diaphragm  reference barocel^  probe  vibration generator  i  •'r t n  J n  n  / n  J) ) / ) ) ) ) ) )  I 0 cm  Figure 10.  D e t a i l of the drum used to create a sinusoidally varying pressure  n  112  I2VDC  IW  25& IOW  I20& 2W  2N3054 5$, IW A6C2  2N4574 2NI53I  o/p  i/p  A6C2 off  5 &  on 2N36IS  -I2V0C  I20& 2W  Figure 1 1 . C i r c u i t diagram f o r power amplifier used to drive the v i b r a t i o n generator  Figure 12.  Sample frequency c a l i b r a t i o n of the pressure instrument (probe and transducer)  Figure 13.  Arrangement used for c a l i b r a t i n g the pressure instrument in s i t u  1.0 A M P L I T U D E  R E S P O N S E  o  .8  20'  /  u CO  o  UJ CO  o  co .6 UJ or  Q. CO UJ  0° P H A S E  R E S P O N S E  rr UJ co <  UJ Q  L _J •  4  20°  Q.  o a>  j—i  i  1111  -i—t—i  <  i  i  i  111  J — i  »  1111  n(Hz) Figure 14.  Sample frequency c a l i b r a t i o n of the system used f o r the surface pressure measurement  J  116  ure 15.  Spectral comparison of the s t a t i c pressure measured i n the a i r and at the surface; the separation was 40 cm v e r t i c a l l y . These measurements were taken at the Ladner s i t e .  IO  117  3  * AIR •SURFACE I 95 % c l .  102  N  X  'e i o '  u  CM* c >» "O  \  10°  *  •1  x  A \  \.  \ \  x  "  io-»  v  -I  L  IMI  j—•  .01  n(Hz) Figure  16.  •  i  •  •i  j — i — i — i  \. i 11  iii  io  S p e c t r a l c o m p a r i s o n o f t h e s t a t i c p r e s s u r e measured i n t h e a i r and a t t h e s u r f a c e ; t h e s e p a r a t i o n was 32 cm v e r t i c a l l y . These measurements were taken a t the Ladner s i t e .  118  + A  $  ** *  +  +  +  P-P  OA  +  o o X  .8 o  X  LU O -Z LU  or  LU X  A  "319/1 -319/2 --320/I •318/1 + 318/2  0.4 CJ  ,i i  J — I  I I I  n(Hz)  11  i  o X  i ii io  i  1  •20°r LU  I  ?  *  .  °2  0  -  *  *  • ;  °  io  n(Hz) o l  F i g u r e 17.  Coherence and phase between the s t a t i c p r e s s u r e at the s u r f a c e . These are the Ladner Runs.  measured i n the a i r and  .*  137/1  119  (30cm)  "AIR • SURFACE I 9 5 % c. I.  n(Hz) ure 18.  Spectral comparison of the s t a t i c pressure measured l n the a i r and at the surface; the separation v e r t i c a l l y , i n meters, i s given i n brackets a f t e r the Run number. These measurements were taken at the Boundary Bay s i t e .  120 I.Or  p-p e  AK  X O  6-4  OX  *  X  0  .8  UJ  o UJ or UJ  X  4  i  o  132/2/1 * 133/3/1 133/3/2  0  x  o  A  A  o  X  -I—I—' •  J_I_L  11 1  .01  X  I I  I  10  n(Hz)  -20° UJ CO <0°  X  *  20  ° a  JA  10  n(Hz)  a. o L  Figure 19.  Coherence and phase between the s t a t i c pressure measured i n the a i r and at the surface. These are the Boundary Bay Runs.  121  / \ 165/2  °UPPER x LOWER A Z =0  AZ=l.8m  n(Hz) Figure 20.  Comparison of pressure spectra measured simultaneously at two d i f f e r e n t heights. Az i s the difference i n height, given i n meters.  X  IO  OA  o  0A  X  1  +  10° * * + *  110/1 110/2 120/1 120/2 121/1  1  95%c.l.  0  io-  J  10"  I  '  •  '  io-  IO"  IO"  3  kp =  Figure 21.  ' •' I  JLii.  M i l  tu/Ul  5  2  (cm" )  Nondimensional pressure spectra. Observations taken over water.  1  10"  123  10  IO"  10 kp = cu/UI  3  10-I  2  (cm-')  (a)  + +  10'  * 319/1 * 319/2  10°  * 320/1 * 320/2 * 425/1 *  425/2  I  95%c.I.  _i  10"  i  i  I i i  • • • '  IO'  3  k =oj/UJ p  5  J  IO' (cm- )  L  2  1  (b) ure 22.  Nondimensionalized pressure spectra. (a) water (b) land  Observations taken over  I I  10°  5-  CM  ^4  O II  •  <X  •  X  XX  X  9  t=  9  2  x using S o n i c s t r e s s » using Cp or </>n method 01 0  i I  , i 2  • 3  Z Figure 23.  •  i  4  5  IO"  cm" . 1  i 7  (m)  Summary of the nondimensionalized pressure spectra. 2  i 6  Values plotted are k I T ( k ) / ( p u . ) at a k of 2  1 1  M  125  ure 24.  Normalized pressure spectra normalized by t h e i r variance.  2  z CM  * 10°  e  s  3'Z  4 4  A  S  3  *  5 12  •6F  i*  2  • » - !  +-  3  X.  4  3  o  o  2i l*  * 5  4  4  o  x  ^  5 x  %  +  34 * § 4  lo-+  X  * ,.4  3 X  ICH  u-w x  °  o  HO/1  >-<»  110/2  a--  120/1  4-*  120/2  *-+  121/1  s  io10  -l  -3  i_  •I  I  ,-2 10  -I  ,-l  10  l_  • *• i  io  (  11  10'  f=nz/U Figure 25.  N o n d i m e n s i o n a l i z e d u and w s p e c t r a i--  ON  127  A  °  X  X  °  °  +  * X  10°  a  AX  'OH  CM *  x  +  o  o  to  10 -Il  " 110/1 «110/2 •120/1 AI20/2 +121/1  10-21 I0"  • 3  1  •—•—i i i i I IO"  1 2  1  1—i—i i i i I 10"'  f=nz/U Figure 27.  Nondimensionalized uw spectra  i  i  i i i i iiI 10°  i  i_ i i  re 28.  Comparison of the s p e c t r a l slope of pressure spectra  f = nz/U Figure 29.  Comparison between the nondimensionalized variance of the pressure and of the v e l o c i t y for Run 120/1 f o r d i f f e r e n t frequency bands  components  M  U>  O  k = CL>/ UL ure 30.  (cm- ) 1  Nondimensionalized pressure spectra. The curve i s the mean of data given i n Figure 21; the dashed l i n e s are extrapolated from the s o l i d curve.  132 I.Or  * * + *  173/2 200/2 173/1 186/4  <-186/5  UJ  o z  UJ  or ui  o o  AZ = .5m  AZ=.56m  k  ui co  = cu/UI  6  (cm- ) 1  20° o  0n o  <  p  CL  -20°  Figure 31.  1  t  M  t  +  -  IO"  A  A.  t'  0  • ' '° "  _1_  I  3  I I  I 1  IO' kp = o j / U I  5  1  (cm"'}  Coherence and phase between two pressure measurements with various v e r t i c a l separations Phase p o s i t i v e means p upper leads p lower.  20« Ixl  to < 0°'  X Q_  -20  Figure 32.  OL  » x  10-3  10-2 k =o>/UI5 (cm"')  10- i  Coherence and phase between two pressure measurements with various crossstream separations  135  20°r 70 120 170' 140'  " 319/1 • 319/2 * 320/1 320/2 • 425/1 * 426/1 +  all have A Z = . 3 m  -90« -40* LU co  <  D = 2m  10°  X  °- 6 0 D=4m  110' 160° 150° I00  o1  -50° D=0m  0°r  &! & *> * t  .1  A 4 4, $ [  r]  (Hz)  JL  io  (b) Figure 33(b).  Phase between two pressure measurements with a dowEnwind separation  136  I0 r 4  IO 3  £ o \  c in  "?I0  2  CL  Data  plotted  for  C 0 H E R E N C E = .I4  Xp(x) Xp(y) Xp (Z)  10'  _L  IQ° 10'  10'  •  i  •  •  10*  PROBE SEPARATION  Figure 34.  •  • •  I0  (cm)  Fixed coherences between two pressure signals f o r various probe separations. The values plotted are f o r a coherence of 0.14.  ;  u-u A  A  A  A  A  A  w-w  *  * 146/1  °  • 139/1 AY = Im  °  • 130/1  AZ=.9m AY=2.4m  .8  o  .6  UJ  rr  UJ  8  .41  •  a  o  „  01—i—i  i i i 11  J  1  1  1  a  I  °  •  I I I  •  o °  •  i I  D D OB  o e>S ~  •* • D  o  r  •  I  f n i l  .1  10  n(Hz) Figure 35.  Coherence between two v e l o c i t y measurements with different separations  I0 r  138  I  4  I  COHERENCE  .8  /  IO  3  E o  3 II  > I0 r2  Data plotted for COHERENCE^.14  U-U w-w  10'  O  A  Mx)  My)  X»(z)  io ' I0  -i  0  Figure 36.  V  io SENSOR 1  i  i i_  •  io SEPARATION  •  1 1 1 1 1  10*  2  (cm)  Fixed coherences between two v e l o c i t y signals f o r various sensor separations. The values plotted are f o r a coherence of 0.14.  .9  X  139  p-u  A X  * • * + •  t o  .8 A  +  120/2 121/1 110/2 110/1 120/!  .7 LU .6 O LU .5  or  LU X .4  o  o  .3 xo  W peak  .2  ©  .1  X  0  0  J  I  L  J  io-  •120°  l_  k=u)/U  I  +  I  10  •  A  J  AX  Ay  1**  X  I  I  I i l l  10 •I  -2  (cm- ) 1  •160° 160° I20  e  80  e  LU C/)40«  <  X CL  0°  4+  •40*  1  I  *  _l  I I  I  I  I I I I I  -2  k=w/U Figure 37.  4*  (cm- ) 1  Coherence and.phase between p and u, u measured w i t h a s o n i c . H e i g h t o f o b s e r v a t i o n s ranged from 1.5 t o 5 . 5 m e t e r s . Phase p o s i t i v e means p l e a d s u.  10'  0-  4g  I  140  p-w  .8  * 120/2 o 121/I + 110/1 * 110/2 120/1  r  *  A  + •o  LU O  A*  LU OC  o  LU 4 -  o  +  +  J  X  o  A  +  .  ?  S ' O  A  AX  +  *  O  • „  X + A  , A  •  +  A  +  +  e f  *  *  AX  0  X  .2 -  o . +  ^ J  v.  A X  X A  <  *  +  T  V  x A •  +  W peak  I  J—i  i i iiI  IO"  i  i  I  %  i**  +  IO"  3  A*  '  i i i iiI  i  «  •  i  i  i  i * iiii  10"'  2  k=w/U (cm* ) 1  0° A*.  +  +  -40°  °  LU  t  *X  A  O  °  *0  £-80* X CL  * Ajf.  i°  -120°  H»X  X  +X  +  4*  •  A.  +  ^  A  *  A O  -160° 160°  Figure 38.  J  I  -I • • • 'J _  I I L_l_  I0"  3  k=aj/U  I0"  •  •  •  2  (cm- ) 1  Coherence and phase between p and w, w measured with, a sonic. Height of observations ranged, from 1.5 to 5.5 meters. Phase p o s i t i v e means p leads w.  10"  #  ,  p-u .8-  x o + •  o*  o  UJ  141  c  X  172/1 172/2 173/1 173/2  .6 +  o  e  UJ  or ui X  .4  O  o  o  T  o  «  x ©  0«X  W peak  0  io"  l  , /,. k = cu/U  3  I  I I J  " (cm- ) I 0  2  +  O e  +  •  •  i  i.. I  I iiii  X o»  10"  1  -160°  160°  + •  X  120°  + o  c  x  .x .  f  f  *©  UJ80°  to  <  X40° Q. 0°  -40  A  Figure 39.  +  + +  +  • O  J  l_  • •• 1 10  °  *  o  +  X  „+  +  °  •x  * X W  J  I  k = a>/U  I  '  '  ' •  10-2  (cm- ) 1  -I  I  I  I  I I I  10  Coherence and phase between p and u, u measured with a hot-wire. Height of observations ranged from 1.5 to 3 meters. Phase p o s i t i v e means p leads u.  -i  p-u  .8 0 X  LU .6  +• 0  x°  Ho  o  * 141/2/1 ° 141/2/2 •141/3 + 73/1  x  •  o  •  +  X  4.  LU  X  f  +  0  •  or LU X  O o  *  .4  X  o  X  'W p e a k ' 4&  ••i • • >  J  i . f  I I I I  10"  10"  k=CL)/U  10' (cm"')  -160° 160°  + •  120° LU if) 80° < X CL  40°  +8 £  *S > g -*—«?-»-r T— •nr +  0°  x  +  x  +  x  x  o  10" -40  o  L  T — I I I I  10  k=CU/U  -2  10"  (cm-')  Figure 40. Coherence and phase between p and u, u measured with a hot-wire. Height of observations was 2 meters. Phase p o s i t i v e means p leads u.  .8  u-w +  o  X  L  *  X  +  +  4  UJ O  * 120/2 121/1 * 110/2 110/1 • 120/1  +  A  _°  •  >A  •  4  o •  rr .41  I  o o  143  +  +  A  »  «  *  a o  a  x  •  * X  *» A  .2  X A  o * A  O  X  o  4-  W peak  '  i i i  111  1  IO"  1  i  3  k=a>/U  x x  i i i i 11 IO (cm' )  A  • +  .  f  .. i  4  10"'  - 2  1  160* UJ  <!80 X Q. -I60°h e  •I40  Figure 41.  J  +• x  o  A I I lAt  • • a f ml  I I,  A  A +  X  A  • £ X  A  • 1 x  *  *  A  .  °  * •  O  o  o  -I  IIII  10"'  °.  k=«/U  (cml  O L  Coherence and phase between u and w, v e l o c i t y components measured with a sonic. Height of observations ranged from 1.5 to 5.5 meters. Phase p o s i t i v e means u leads w.  144  Z  Figure 42.  (m)  Wavelength of the pressure fluctuations associated with the p-u phase t r a n s i t i o n , as a function of observational height. The broken l i n e i s the measured scale s i z e .  145  320/1  *30cm A  Surface  n(Hz)  319/1  o 30cm •  Surface  n(Hz)  Figure 43.  Coherence between downstream v e l o c i t y , u, and two pressure measurements. One pressure sensor was beside the u sensor, one was at the surface, 30 cm below.  .01  T—i—r A  „-\  I  146  n(Hz) IIII  \  ok-,. £ o  i E u  to •10 a> c >»  T3  c-20 CL  x  ° •  -30  110/1 110/2 120/1  * 120/2 +121/1 •40  L  Figure 44.  ,  5  Spectra of pw  R = pw//)uwU  .10  .05h  Z Figure 45.  Ratio of the pw and uwU equation.  (ml  terms of the integrated net energy budget  1A7 10  *  51  -I  1  -r-l .1  I T ~ l  •  -i  i i  •  •  •  io  kz  kz IIII  T  1  1  IIIII  •  i—i—i—IIIII  io  = --il c  -.21  * 73/3 * 72/1 o 141/3 * 73/1 + 141/2/2 -.4  Figure 46.  Spectral d i s t r i b u t i o n of the energy flux, by pressure forces, from the u v e l o c i t y component. The i n t e g r a l given i s f o r kz from 0.05 to 20.  148 i.Or •0V to  -i—i ' • • ' I  •T-'TI  -i  1 — i  i  '  i  i  i  10  kz  kz T  1  I I I I  1  1 — I I I I  i  T  1  1 — I I I I  10  ^° x \ \ V - f t  -  udp/dx/pul/KZ  -.2  -.3  Figure 47.  * 165/2 ° 172/2 4 172/1 + 173/2 • 141/2/1  Spectral d i s t r i b u t i o n of the energy flux, by pressure forces, from the u v e l o c i t y component. The i n t e g r a l given i s f o r kz from 0.05 to 20.  Figure 48.  Pressure, v e l o c i t y , and wave spectra for Run 173/3.  eq.peok  150  J  10  x 10° CM  £  10  60/4 "119/1 "119/2 * 119/3  10 -2  10'  .0)  (1650-1712) (1745-1800) (1820-1840) (1850-1908)  •  •  •  •  n(Hz) ure 49.  Wave spectra of Data Group A. i s given i n brackets.  io  The time of s t a r t and end of each Run  Figure 50.  Pressure, u v e l o c i t y and wave spectra f o r Run  60/4.  Figure 52.  Pressure, u v e l o c i t y and wave spectra f o r Run  119/2  Figure 53.  Pressure and wave spectra f o r Run  119/3  1.0  .8  155  * * o *  60/4 119/1 119/2 119/3  o  A  x  o  o  A  o  LU O LU  or LU x .4  O  o A 0  o  e o  •  eq. peak  A  o 0  01  J  1  1 L  J  J  '  '  '  n(Hz)  160V 180°  1—I  IIII  J—I—t  •x •  -160°  1  a  * x  •  ll 1  'xa *  I I  -l  n(Hz)  w  ©  X 0  — L  X  LU  co <-l40° CL  a  O  m  o  -120* -I00°L  re 54.  Coherence and phase between the lower pressure sensor and the waves: Data Group A. P - H phase p o s i t i v e means p leads n. L  L  156  P-P  IO, x  *60/4 * 119/1 ° 119/2 * 119/3  o  .8  O e  LU  X  LU  o  ce  X  LU X  o °  o  .4  X  o  .2  o  eq. peak  o  H  o J  .1  I  L  i i iif.  10  n(Hz)  20° LU  £  c  X CL  X  -20°  J  I  -I—*  L  n  Figure 55.  X  o  x  IIII  •  AO  « » 10  (Hz)  Coherence and phase between the two pressure sensors: Data Group A. P P.. phase p o s i t i v e means p leads p . u L u -  T  T  r  157  u- V  .4 LU O LU  or .2h LU X  o o  o _2_U J  x c  o  0  X  o  X  J  l_  .1  L J_L  io  n(Hz)  20*  • 60/4 x 119/1 ° 119/2  X  o  100*  eq.peak  LU CO < X Q_  H •  J  180*  i • • • •  J  1  i  i  J  1  I  I L  10  n(Hz)  •ioo  Figure 56.  e L  Coherence and phase between the u v e l o c i t y and waves: Data Group A. u-f| phase p o s i t i v e means u leads r\.  158  eq. peak  * 167/1/1 (1209-1228) • 167/1/2 (1228-1246) (1252-1306) 167/2 167/3 {1312 - 1318 )  X  a  o A  X  \  O  .01  I  I I  '  I i l l  n(Hz)  ure 57.  Wave spectra for Data Group B. i s given i n the brackets.  I I I I II I  \  I I I I  10  The time of s t a r t and end of each Run  Figure 58.  Pressure and wave spectra for Run 167/1/1  Figure 59.  Pressure and wave spectra f o r Run 167/1/2  Figure 60.  Pressure and wave spectra for Run  167/2  167/3  Figure 61.  Pressure and wave spectra f o r Run  167/3  162  163  Fourier i  i  0  i  0.2  i  Coefficient i  0.4  i  i  0.6  J  i 0.8  _  n(Hz)  Figure 62.  Amplitude of the Fourier c o e f f i c i e n t s f o r pressure and waves o f Run 167/3  J  p-77  I.Or  .8  A 167/l/l •167/1/2 ° 167/2 "167/3  o  • LU O •  o  LU  0  A  A  or  LU X  4  A  o  o o  X  A  .2  •  o  o  »  A  0  «  •  o 1—'  e  o  •  eq.peak X  A  A  -I  x  1  o  -H  A  I  •  S  • •  n  p 1  o I  a  i  10  (Hz)  160° x A  LU CO  1  8  -1 L  0  —"A-  1— l #  1—'  '  • »  -1  10  i  <  X-I60° Q_  1 ' • ' •  o  m  n(Hz)  A?  -140° -I20°  Figure 63.  X  A  X  L  Coherence and phase between the pressure and p-H phase p o s i t i v e means p leads T).  Data Group B.  Figure 64.  Pressure, u v e l o c i t y and wave spectra for Run  164/1  Figure 65.  Pressure, u v e l o c i t y and wave spectra for Run  164/2  167  P-7? *I64/I (1408-1422) ° l 6 4 / 2 (1612-1625) .8  xo  o Ul  x o  o  rr  UJ  x o o  x o  H  o  .2  X  eq. peak  0'  -i-iJ  1  o  o  I  1—  io  n(Hz)  160* -i—i—IIII  w 180° <  -lS  'X  ' n  • • •• I O X  CL-I60°f  •I40°  Figure 66.  x x o o  -  I  1  1  l  l  n(Hz)  l  i  io  l  L  Coherence and phase between the pressure and the waves: Data Group C. p-n phase p o s i t i v e means p leads n  ,  U-77  1.0  168  * 164/1 o 164/2  .8  .6  UJ  o UJ cc UJ X  .4  o o  .2  o  H  «  eq. peal^  :oi  -I  OJ  1  I *  -I  1 1 1  1  1  I  I  L.  x  1  —i  n(Hz)  10  160° UJ  co 180° <  X CL  -160°  -I40  Figure 67.  j—1  1  -sr o  • •  o X  6 • 'iiii o x  n(Hz)  10  O L  Coherence and phase between the u v e l o c i t y and the waves: Data Group C. u-n phase p o s i t i v e means u leads n. .  169 * 80/3  (MI2-II29)  ° 60/1  (1140-1156)  + 60/2  (1214-1226)  n(Hz) Figure 68. Pressure, u v e l o c i t y and wave spectra for Data Group D  p-7/  I.Or  A 173/3-p  170  L  * 80/3 .8  o 60/1 + 60/2  LU  o  o .6  A  LU CC LU X  o  +  O .4  O  +  X  0  X  .2  o ° * o  X  X  A X JL.  + o  X  'H o X  eq.peok  O _I_L  1  • • I•I I.+ I 10  n(Hz)  160'  x  o +  LU  co 180° <  X  °- - 1 6 0 °  -i  1  i_  -oA  + X  JL j_i£i_iaL A  x + o  A  O A+  n(Hz)  10  o x O O  -140°  +  -120° Figure 69.  Coherence and phase between the pressure and the waves: Data Group D. p-r) phase p o s i t i v e means p leads n  171  u-77  * 60/1 * 60/2 * 80/3 ^ 173/3  X  A  LU O LU  X  rr  LU X  o o  .2  o  A X  +  o t  A  A  X  o H  * t  eq. peak  ' • • ••I  .01  +  X  t  i  X  I I I I  * x  X o  n(hz)  140° LU CO  < 180°  1  L  1 .1  Q_  -I40° Figure 70.  A  +  i •  1  *  +  1  &  1  A  *  L  1  •  i> ' ' ' O  X  1  1 1  ' '  1  I  1  B  1  9  n(hz)  Coherence and phase between the u v e l o c i t y and the waves: Data Group D, u-n phase positive means u leads n.  1.0  xx  ex  CL  ,5  CL  2  3 Z  Figure 71.  (m)  Ratio of measured to predicted pressure amplitude f o r propagating waves with no wind. : &  5  CM I  e o  t/J Q> C  -A0.4IHZ  0.55 Hz  E o  6 II  N  0 . 7 3 Hz X  Q?  X  0.98 Hz  • .41 Hz + . 5 5 Hz * .73Hz  ° . 9 8 Hz x 1.30 Hz 1.30 Hz  J  I  UL/C Figure  72.  I  4  p (n) a t v a r i o u s constant f r e q u e n c i e s f o r d i f f e r e n t values u|^/C = 0 a r e f o r t h e p o t e n t i a l f l o w s o l u t i o n . w  L  o f u],-/C.  The v a l u e s  plotted at  177  x  I20  e  Data Group A B C D  o • *  o  A  x  O  O  x  X  x  -140°  A  X  OO  x  OO  o  LU CO < X -160°} Q_  ox  A • A  A  180*  160'  0  J  i_  1  -J  Ul /C  1  L.  I  4  ~5~  5  F i g u r e 77. Phase s h i f t between p r e s s u r e and waves a t v a r i o u s v a l u e s o f u| /C Phase p o s i t i v e means p r e s s u r e l e a d s waves.  III! 1  M l 1  1  \  |  3 \  \  I  rrvsec"'  \  .6  .8  Wave F r e q u e n c y (  Wave amplitude and c r i t i c a l height for constant u|  5  1.0 Hz)  plotted for d i f f e r e n t wave frequencies  179  Figure 79.  Spectral d i s t r i b u t i o n of the approximate energy flux to the waves, calculated using the pressure measured above the wave crests.  p-u  .8  180  o  * 119/1 o 119/2 • 60/4 * 164/1  LU O  X  •  164/2  o  173/3  •»-  LU CC .4 LU X  A  H  a  o o  A  o  CJ X  o X  l_  X  •  +  0  o  X*  A  A  J  o  A  o  J  s  I  O O X  0  X  L  io  n(Hz)  -160°  x  160'  a 120°  o  X  X  o 80°  o  X o  X  o  LU  co 4 0 ° X Q_  A  A  0°  40* -80  ure 80,  _I3_  Axb  L  1-2.  _l—1,1 I I I •f  n(Hz)  io  o L  Coherence and phase between p r e s s u r e and u v e l o c i t y measured n e a r waves Phase p o s i t i v e means p r e s s u r e l e a d s v e l o c i t y .  181  p-u  .8  A  *  80/3  *  60/1  *  60/2  *  80/2  +  60/3  +  LU O 2 LU cc LU X  X  A  .  .4  H  X A  •  o o  A o  X  i  + o  +  X  4 ?  A  o X  ct X A  A A  o  O  X  X  I I hi  i i i  A  t  X  J  1  X  OA  L  t  a?  10  n(Hz) -120°  -160° A  160°  A  o LU 1 2 0 ° CO  4 X  < X  A X  o A O  X  o  A  A  +  80  X  0- one* X  40°  0°  +  + x A  *  I*I  1 1 *l  A  +  X  -e-A-ia.—  I I I  J  L,  ' ' • •  10 -40<>L  Figure 81.  n(Hz)  Coherence and phase between p r e s s u r e and u v e l o c i t y measured n e a r w a v e s . Phase p o s i t i v e means p r e s s u r e l e a d s v e l o c i t y .  182  I4r • Over w a v e s * Over a flat surface 12  10  E  8  /  /  /x /  /  /  x X X  '0  •J  1  Z=L  1  X  1_  4  z(m)  Figure 82.  Wavelength associated with the p-u phase t r a n s i t i o n  —i 8  .  Nondimensional energy flux from the u v e l o c i t y component, measured near waves.  184  x  80/3 ° 60/1 * 60/2  INTEGRAL .22 .34 .37  -udp/dx/pu$/KZ  Figure 84.  Nondimensional energy flux from the u v e l o c i t y component, measured near waves.  POINT ATKINSON  ENGLISH BAY STANLEY^ PARK  SPANISH  BANKS  SITE  Y"low tide line  POINT GREY -cliffs  Figure 85.  Map  of the Spanish Banks s i t e  2KM  oo  Figure  86.  P l a t f o r m and i n s t r u m e n t masts at the Spanish Banks (a) p l a t f o r m and masts l o o k i n g e a s t (b) i n s t r u m e n t e d mast  site  Figure 87.  Map of the Ladner s i t e  r—  co  188  Figure  89.  instruments  s e t up  at  the  Ladner s i t e ,  looking  NNE  Figure 90.  Map of the Boundary Bay s i t e  190  120  eiool u  UJ m  HUME SYSTEM  L I  o  rr o_ 8 0 | LU  > <  o 601 hX  <£ LU X  40|  20 J  1  •  L  L  . 0 . . 2. VOLTS  Figure 91.  Typical wave probe calibrations  (DC)  , 4  4rXI0"  3  * SONIC  V  ^  OU-WIREJ^"^ * 0  *  * O  OX  X  o  *  °  x  o xx  X X  *°  3  xx  o  x*  x  y ~* o  "  "  °•  :  x x  4 MEAN  e>  x  X  °  Figure 92.  SONIC-Direct  WIND  5  6  (msec"')  evaluated from the d i r e c t and $ ^ estimate of the surface s t r e s s .  7  8  192  SYMBOL TABLE  A  rm  a  r e a l p a r t o f the complex F o u r i e r c o e f f i c i e n t C radius  B  rm  i m a g i n a r y p a r t o f the complex F o u r i e r c o e f f i c i e n t C rm r  B.W.  bandwidth  b  as a s u b s c r i p t denotes  C  phase speed o f the waves  C  drag  Q  Co  a particular  f r e q u e n c y band  coefficient  drag c o e f f i c i e n t  C  related  t o wind a t 5 meters  cospectrum  °12  cospectrum  f o r d a t a channels 1 and 2  Coh^  coherence  C  complex F o u r i e r c o e f f i c i e n t  rm  f o r d a t a channels 1 and 2 tti tii f o r the r harmonic i n the m block  D  downwind s e p a r a t i o n o f i n s t r u m e n t s  E  east  En  energy  e  e = 2.72  e  f l u x i n t o t h e waves  s a t u r a t i o n vapour p r e s s u r e S  SL  f  nondimensional  g  gravitational  H  denotes  h  water  h  r e l a t i v e humidity  h  s p e c i f i c humidity  K'  Kolmogoroff  K  Obukhov's u n i v e r s a l p r e s s u r e c o n s t a n t  k  rm  P  frequency constant  '  '" -  the hump, a s s o c i a t e d w i t h waves, i n the p r e s s u r e  depth  wave number  constant  spectrum  193  kp  a pressure wave number, k  L  scale s i z e of pressure fluctuations  L  P  scale s i z e of v e l o c i t y  v  1  = oo/U|^  fluctuations  M  number of data blocks per Run  m  block number  N  number of data points per channel per block  n  frequency i n cycles per second  An  bandwidth  n^  geometric mean of the end frequencies i n a bandwidth  n^  folding  P  t o t a l pressure  P  stagnation pressure  g  p P  frequency  f l u c t u a t i n g pressure f l u c t u a t i n g pressure associated with the waves  w  p^  f l u c t u a t i n g pressure predicted by the p o t e n t i a l flow s o l u t i o n  Qu  quadrature  Qu^2  quadrature spectrum f o r data channels 1 and 2  spectrum  2 2 , 2 , 2 q = u + v + w  q R  r a t i o of work done by the pressure force to work done by the Reynolds stress  Re  Reynolds number  Ri  gradient Richardson number Cr  Rp  r a t i o of measured dynamic pressure to calculated stagnation pressure  r  denotes the  r^,  the harmonics at the ends of a frequency band  S  s p e c t r a l energy density  T T  temperature a i r temperature  harmonic  194 T|  a i r temperature  at height z  T w  water  t  time  U  mean velocity i n the downwind d i r e c t i o n  temperature ^  U"|  mean v e l o c i t y i n the downwind d i r e c t i o n at height z  U.  mean v e l o c i t y i n the i ^  U  pressure propagation v e l o c i t y  U w  mean water v e l o c i t y  u  v e l o c i t y fluctuations  i n the downwind d i r e c t i o n  v e l o c iJt y fluctuations  th i n the i direction  z  J  1  u. u  *  direction  1  u  *  =-™  2  V  volume  v  crossstream v e l o c i t y fluctuations  W  west  w  v e r t i c a l velocity  x  downstream coordinate  x. x  • l  y  crossstream coordinate  z  height above the surface  T  H  i n the horizontal  fluctuations  A+ coordxnate  Z  £  c r i t i c a l height  Z  Q  surface roughness  z^  lower l e v e l where turbulent energy transfer goes to zero  Y  dy incremental volume  E  rate of viscous energy  n  f l u c t u a t i n g water elevation  X] 3L  0  dissipation r e s u l t i n g from waves  wave amplitude phase between two data channels  v i r t u a l temperature v i r t u a l temperature at height z von Karman's constant wavelength wavelength of pressure fluctuations wavelength of v e l o c i t y  fluctuations  wavelength of the waves kinematic v i s c o s i t y pressure spectrum cospectrum between two pressure signals 1 and 2 fr = 3.14.. . density of a i r variance of pressure s i g n a l surface stress cospectrum between i and j v e l o c i t y components cospectrum between p and w u spectrum w spectrum wave spectrum X = x' - x frequency i n radians/sec measured wave frequency i n radians/sec nonharmonic frequency i n radians/sec harmonic frequency i n radians/sec wave frequency i n radians/sec  

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