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Direct measurements of stress and spectra of turbulence in the boundary layer over the sea Weiler, Henry Sven 1966

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DIRECT  MEASUREMENTS IN  THE  OF  STRESS  BOUNDARY  AND  LAYER  SPECTRA OVER  OF  THE  TURBULENCE  SEA  by  HENRY  B.Sc.  A.THESIS  University  SUBMITTED  THE  SVEN  IN  REQUIREMENTS DOCTOR  accept  required  THE  this  of  Toronto  FULFILMENT  FOR  DEGREE  THE  PHILOSOPHY  in  the of  thesis  (962  PARTIAL  OF  Department  We  WEILER  OF  Physics  as  conforming  to  standard  UNIVERSITY  OF  JULY  BRITISH ,  OF  1966  COLUMBIA  the  In  presenting  requirements British freely that  for  an  Columbia, available  permission  this  thesis  advanced  I  agree  for for  or  representatives.  his  publication allowed  without  Department  The  of  University  Vancouver  Date  of  8,  jL lA  that  extensive  purposes  may  be  this  thesis  my  written  the  granted If for  British  Canada.  ll J$U  at  is  the  study.  I  by  further  this  thesis  the  Head  of  understood gain  that  my  the  of  make  of  permission.  of  University should  financial  Columbia  fulfilment  library  copying  2L of  partial  degree  reference'and  scholarly by  in  it agree for  Department  copying  shall  not  be  or  THE UNIVERSITY OF BRITISH COLUMBIA . FACULTY OF GRADUATE STUDIES  PROGRAMME OF THE FINAL  ORAL EXAMINATION  FOR THE  DEGREE OF  DOCTOR OF PHILOSOPHY  of  HENRY SVEN WEILER  B.Sc.j  University  MONDAY  s  of T o x o n t o  s  1962  JULY 11, 1966, a t 3;30 P.M.  IN ROOM 301, RUNNINGS BUILDING  COMMITTEE IN CHARGE Chairman;  J. R,„ Adams  R. W. B u r l i n g G. V. P a r k i n s o n G. L . P i c k a r d External  •R. D. R u s s e l l Rc W„ Stewart. N. H. Thyer  Examiners  S„ C b r r s i n  Department, of Mechanics The Johns Hopkins U n i v e r s i t y Baltimore;, Maryland Supervisor;  R. W. B u r l i n g  DIRECT MEASUREMENTS OF STRESS AND SPECTRA OF TURBULENCE IN THE BOUNDARY LAYER OVER. THE SEA ABSTRACT Fluctuations nents  i n the v e r t i c a l and h o r i z o n t a l  of wind v e l o c i t y i n the boundary l a y e r  sea were measured w i t h an X - a r r a y  compo-  over the  of hot w i r e s .  Special  T  techniques were developed  t o mount arid c a l i b r a t e the  w i r e s , and t o measure d i r e c t l y t h e i r responses two v e l o c i t y f l u c t u a t i o n s . Analog  t e c h n i q u e s were deve-  loped, t o a n a l y z e the hot w i r e s i g n a l s , spectra  t o the  t o g i v e the  of the two v e l o c i t y f l u c t u a t i o n s , and t h e i r  cospectrum, over a range of mean wind speeds from to 1000 cm/sec, and at f r e q u e n c i e s between 0.016 Hz.  Three runs w i t h U-wire probes  checks  The measurements  showed that X-wire techniques can be used to measure v e l o c i t y f l u c t u a t i o n s g i v e s p e c t r a l and c o s p e c t r a l or b e t t e r , Spectral  i n two d i r e c t i o n s t o  estimates w i t h i n ~t 30 and  estimates were obtained,  anisotropy existed  much s m a l l e r s c a l e s The observed  between about  successfully  respectively.  and c o s p e c t r a l  which showed that  cated.  on the s i m i -  theory of t u r b u l e n c e .  Ten X-wire runs were a n a l y z e d .  1" 50%  t o 60  mounted v e r t i c a l l y  were a n a l y z e d t o p r o v i d e a d d i t i o n a l larity  140  i n turbulence to  than t h e o r e t i c a l p r e d i c t i o n s s t r e s s had maximum  indi-  contributions  .01 t o 10 Hz,, and f o r most runs  analyzed,  the l a r g e s t p r o p o r t i o n of the s t r e s s was p r e s e n t a t f r e q u e n c i e s lower dominant waves.  than t h e estimated f r e q u e n c i e s of the Ten d i r e c t estimates  of s t r e s s were  obtained, which gave drag c o e f f i c i e n t s ( c o r r e c t e d  to  the 5 m. h e i g h t ) which were a p p a r e n t l y i n v a r i a n t w i t h -3 mean wind speed. The average v a l u e was 1.5x10  Indirect  estimates of s t r e s s , u s i n g the mean wind  method g e n e r a l l y underestimated i t . of the s t r e s s u s i n g the wavenumber inertial  Indirect  profile  estimates  spectrum i n the  subrange o v e r e s t i m a t e d the s t r e s s by about 407 . o  Of the two i n d i r e c t more c o n s i s t e n t  e s t i m a t e s , the s p e c t r a l method  gave  results.  Measurements  by the t h r e e U-wires spaced v e r t i c a l l y  p r o v i d e d c o n f i r m a t i o n of the v a l i d i t y Obukhov s i m i l a r i t y  of the Monin-  theory at h e i g h t s below about 5 m.  GRADUATE STUDIES  Field  of Study;  Hydrodynamics  I n t r o d u c t i o n to Synoptic Oceanography  • G. L.  Pickard  I n t r o d u c t i o n t o Dynamical Oceanography  R. W.  Burling  Advanced Dynamical Oceanography  R. W.-Burling  Oceanographic Methods  G* L . P i c k a r d  I n t r o d u c t i o n t o Chemical Oceanography Introduction to B i o l o g i c a l Oceanography Fluid  Dynamics  P. M.  Williams  R. F. Scagel R. W. Stewart  Turbulence  R. W. Stewart  Waves and T i d e s  R. W.  Burling  Waves  J . A.  Advanced Geophysics  J . A. Jacobs  E l e c t r o m a g n e t i c Theory  G. M.  Savage  Volkoff  3  PRIZES 1958-59 - U n i v e r s i t y C o l l e g e Alumni  Scholarship  1960-62 - U n i v e r s i t y C o l l e g e Alumni  Scholarship  1962-66 - 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 s  PUBLICATION We:i,ler  s  H. S.  3  Convergence  P r e d i c t i o n s Using T r i l i n e a r  G r a d i e n t Approximation, August 1962,, Defence Research Board Lab.  Note No. 62-14.  ii  ABSTRACT  The  work  carried  air-sea  interaction  I96l  the  at  British  in  an  and liiO  order  special  -  to  and  to  made  by  digital  were  used the  use  on  hot  to  forms  been of  measure  the  the  part  under  the  of  way  the since  University  which  comparison  of  the  are the  wires  n  t  h  e  to  of  theory  of  horizontal  of  properly  in  and  hot  of  layer  the  mean  to  the  wire  the  to  were probes  fluctuations  provide  sea.  two  developed  hot  the  field,  the  calculations  wind  over  calibrate  were  velocity  to  additional  turbulence.  techniques  fluctuations  responses  only  range  responses  X-wire  velocity  accurate  a  mount  to  using  spectra  (U-wire)  and  and  boundary  final  horizontal  X-wires,  made  the  techniques  Single  have  were  probe  and  that  vertical  over  their  Analog  showed  field.Hot  the  study  developed  signals,  measure  i  X-wire  similarity  to  to  directly  of  in  velocity  cm./sec.  computer.  behaviour  successfully  levels  has  co-spectrum  were  wire  Measurements  the  1000  air order  fluctuations. the  in  in  measure  analyze  checks  which  Oceanography  of  their  techniques  velocity  check  thesis  fluctuations  X-array,  from  In  of  components  fluctuations,  wires,  of  this  Columb i a .  horizontal  speeds  for  program,  Institute  Measurements  wires  out  within  velocity  can  in  two  be  used directions  which  give  spectral  about  3 5% >  but  spectrum  measured  ill  simultaneously spectral  with  shapes  the  were  X-  and  similar,  U-wire giving  probes  showed  confidence  in  that the  their X-wire  measurements.  In two  the  high  velocity  fluctuations  predictions.  The to  the  frequency  The  did  observed  cospectrum  Reynolds*  range,  gives  stress  by  the  not  observed  conform  behaviour  a  direct  is  to  spectra  the  of  the  theoretical  believed  estimate  of  to  be  real.  contributions  small  ranges  of  frequency.  The to  10  stress  Hz  had  frequency  experimental  largest  which  Estimates  Significant  between  significant  decade,  extremes. the  observed  of  site  stress  proportion  was of  the  contributions  apparently the  fell  over  lies  between in  about this  observed  of  about  within  to  was  these  waves  0.5  interval,  stress  one  dominant  0.2  O.Ol6  limits  entirely  frequencies  present the  frequency  at  Hz.  but  the  present  at  lower  frequenc i es.  Ten X-wire. tended the  direct  estimates  of  Values  estimated  indirectly  to  give  direct  low  estimates  estimates.  subrange  appeared  directly  estimated  stress,  coefficients  and  Values  inertial  Drag  stress  corrected  to but to  were from  were  the  poorly  determined be  obtained wind  consistently  5  m  height  the  profiles  correlated  indirectly  overestimated the  with  using  related  it  by  were  with  to  about near  the the lx.0%.  iv  1.5  x  I0~5  for  wind  Measurements provided  speeds  by  confirmation  similarity  theory  at  three of  between  I .li  U-wires  spaced  the  v a l i d i t y  h e i g h t s - b e Iow  and  of  about  10  m.sec '. -  v e r t i c a l l y , the 5  m  Monin-Obukhov «  V  TABLE  OF  CONTENTS  ABSTRACT TABLE L 1ST  OF OF  ii CONTENTS  v  TABLES  .'  x  ACKNOWLEDGEMENTS  xi  I  I  II  INTRODUCTION THEORETICAL A.  DISCUSSION  k  Velocity  Fluctuations  .1  Spectral  Representation  .2  T a y l o r ' s  Hypothesis  •3  The  Shear  Flow  Anisotropy The  Inertial  .6  The  Two-DimensionaI  The  Mon i n - O b u k h o v  .1  The  Theory  .2  D e f i n i t i o n s  .3  The  Behaviour  The  Mean  C.  Data  k-  and  Assumptions  8  Isotropy  .5  B.  of  7  Model  and  1+  10  Subrange  II  Reynold's  S i m i l a r i t y  Stress  Tensor  Theory  13 13  of  u-«- a n d of  L  VeIocity  L  with  13 S t a b i l i t y  ProfiIe  and  1J4.  Drag  C o e f f i c i e n t  15  .1  The  Mean  Velocity  .2  The  Drag  C o e f f i c i e n t  The  Indirect  D.  12  .1  Using  0||(k)  .2  Using  the  P r o f i l e C  2  D  Determination in  Mean  the  15  of  Inertial  Velocity  u-*  _  =-U\UT  Subrange  P r o f i l e  >  17  ..  17  . . . .  17 l 8  V I  E.  The  Results  of  Other  .1  The  Shear  Flow  Model  .2  The  Inertial  .'3  The  Mean  Workers  1.8 • l8  Subrange  21  Pr of i I e  Velocity  Over  a  Wa t e r  Surface .ii  The  22  Drag  Coefficient  23  III  EXPERIMENTAL  METHODS  25  IV  EXPERIMENTAL  RESULTS  28  A.  General Information on"Each Run, and'Wi Direction and Cup Anemometer D a t a  B.  X-  and  U-Wi r e  C.  Data  D.  Summary  from  Three  35  V e r t i c a l l y  of'Prof i i e  and  Spaced  D i a g o n a I i z a t i on  The  V  Stress  The  Mon i n - O b u k h o v  G.  The  Effect  H.  The  Ratio  AND  A.  Wind  B.  X-  o  H o t W i r e N u m e r i c a l ; «•«» ' l i l  Aiig I e ' 9  of ' the ' i|-3  Length  ILU.  0  k5  ^35/^1  of  j  for  All  X-Wire  Runs  .  CONCLUSIONS Direction  and  U-Wi r e  ,1  Performance  .2  Spectra  .3  Spectrum  of  .J4.  Evidence  for  Sma II C.  f  39  Tensor  F.  DISCUSSION  U-Wires--  i  Reynolds'  28  Data  Resul ts E.  h d •  Direct  of  I4.8  and  Cup  Anemometer  Data  X-  ii8 1+9  and  Kinetic  U-Wi r e s  Energy  Momentum  (f$||  Transfer  Non-Ex i s fence  I4.9  of  and  f0^^)  (fj#|j) Isotropy  Scales and  . . .  Data  of  I16  •'  52 5^1-  at 58  I nd i r e q t  Kinematjc Stress Coefficient CQ  E s t i rna t e s . o f . t h e  u-«* ,  and  the  Drag  03  V  •I  Direct  and  Kinematic The  .2 D.  Data  Drag  Indirect Stress  Estimates  the  u-"  ..  Coefficient C  from'Three  of  63 65  D  V e r t i c a l Iy  Spaced  U-Wires VI  ii  68  SUMMARY  73  REFERENCES  78  FIGURE CAPTIONS  8ii  FIGURES  . ... ___  APPENDIX  I:-  APPENDICES  The  Cons t r u e t i o n and  Hot  Wire  A.  The  Wind  B..  The  Single,  88  Calibration  Probes  Tunnel or  and  AI Manometer  U-Wire  The  X-Wi r e  Probe  .1  C o n s t r u c t i on  .2  The  .3  C a l i b r a t i o n of  APPENDIX  II;  M l :  •  A3  •  Alj.  .  A5 A5  Theory  . the  X-Wire  .L(. E m p i r i c a l De t e r m i na t i o n ' o f C o n s t a n t b' D. E f f e c t of D e v i a t i o n i n t h e V e l o c i t y f r o m the P l a n e of APPENDIX  The E l e c t r o n i c s System Auxiliary  Al A3  .2 Cal i b r a t i on C.  System  Probe  Construction  .1  of  of  Measuring  . the  < AI0 Wire  D i r e c t i o n of the X-Wires  the Hot  A6  ... A I 2 Mean . . . . . Alii  Wire A 17  Equipment  ...........  AI9  Vi i i  A.  The  Cup  Anemometer  . I  The  System  .2  Calibration  System  A I 9 of  the  Cup  Anemometers  B.  Wind  C.  Temperature .Measurements  D.  Tide  APPENDIX  IV:  Analysis  of  B.  Selection  C.  Single,  D.  X-Wire  or  Treatment  of  .3 C a l c u l a t i o n s Changes  in  Sample  A.  Glossary  B.  Data  of  Data  of  X-Wire APPENDIX  VI:  The  Hot  Wire  Data  Rerecording  of  Data  A29 A35 A35  Rerecorded from  Data  X-Wire  A38  AJ4O  Analysis  Level  f ory(9/  0  ...........  Calculations Terms  Used  for  Calculations'  1550-1629/29/6/1965:  . . . .  AI4.7  : Aij.8  555-I 629/29/6/1 965:  Calculations E r r o r s ' t o  be  . . .  Ai^9  Expected'ih  Numerical  Results Wi n d  Ai|2 Al±7  Calculations I  A23 A25  Ana I ys i s  Spectral  of  A22 A23  Analysis  .2  U-Wire  . . . .  U-Wi r e  I ntroduct ion  C.  A2I  •  and  . I  V:  A2I  Measurements  Introduction  APPENDIX  A20  Direction. Indicators  A.  E.  A 19  A5I4.  A.  Mean  Data  B.  CaIibration Tunnel  of  ^5k the  FIow  Corporation  Wind A55  C.  U-Wire  Data  A56  D.  X-Wire  Data  A58  iX  E. F.  Maximum  Errors  in D e t e r m i n a t i o n  Maximum  Errors'ih"Determihing  of  the  2  u»  Drag  Coefficient  A6IL  FIGURE CAPTIONS FOR APPENDICES •FIGURES FOR APPENDICES  A62  A65 . . . . i . . . . . . .  A67  LIST  OF  TABLES  Table  IV  A.I  Wind  Direction  Table  IV  A .2  Mean  Wind  Table  IV  B.I  X-  Table  IV  C.I  Data f o r U-Wires  Table  IV  D.I:  V a l u e s of u * Hot W i r e Runs  Table  IV  D,2:  Values  T a b Ie  IV  G.I:  Table  IV  H.I:  Table  A  V I . I :  and  Data  Profile  U-Wire  of  CD  Hot  Wire  The  Effect  Data  Spectral  Three  2  »•  VerticaI  • Data Iy  Spaced  Determinedfor Determined  for  All All  Runs of/3^ 0  T h e R a t i o 033 ( f )/0l Runs Maximum P e r c e n t a g e Values  I (f)  for  Errors  in  X-Wire Spectral  xi ACKNOWLEDGEMENTS  This  investigation  Oceanography  of  the  orogram  which  is  Canada,  Grant  No.  supported  Research  and  from  Canada  by  the  Grant Office  of  Council  the  Institute  of  British  Columbia  research  the Defence  Research  Board  of  Department  Naval  of  Support  5920-0.  No.  of  by  9550-09*  National  Branch,  part  University  the  the  formed  also  Canada,  on  obtained  Grant  Transport,  Further  Research  was  support  (U.S.A.),  No.  of  from  BT-IOO,  '  Meteorological  was  also  Grant  provided  No.  N000 I IJ.-66-COOI4.7. I  wouI6\Iike't0  Department us  to  use  In  I R.  a l l  help Mr.  wish W.  of  and F.  Mr.  H,  to  the  M,  this  Council  for  course  of  In  of  staff  I  debt  given  of  to  work.. and  went  gave  Lastly,  Columbia  of  my  permitting  support  by  the  Canada.  Dr.  R.  My  I  W.  and  his  to  my h e a r t f e l t  help  and  due  also  for  their  thank  way  thisis,  invaluable  are  students  wish  of  Burling,  guidance  thanks  graduate  out  for  f a c i l i t i e s .  was  particular  preparation who  tunnel  Engineering  encouragement  this  In  British  Canada  my  who o f t e n  Inostroza, diagrams.  of  work  their  Institute  Dobson,  along,  original  of  Mechanical  wind  acknowledge  Stewart the  speed  cooperation.  W.  project  course  the  University  low  Research  throughout to  the  their  the  National  Dr.  of  thank  my in  thanks  to  help  thanks  my go  preparing go  to  my  to the  wife, and  who  who  often  has  helped  rendered  me  during  invaluable  instrument aid  in  calibrations  preparing  my  thesis.  I .  I N T R O D U C T I ON  I96I,  Since been  in  progress  University  of  the  sea  Past  program  at  the  British  concerned.with above  a  fluctuations  the  wind  temperature  in  the  the  d i r e c t i o n ,  some  fluctuations,  program  in  the  water  with  wind  the  has  the  been  of  air  just  i t s e l f .  the  mean  velocity  with  of  has  layer  preliminary  and  interaction  Oceanography  This  concerned  of  air-sea  of  occurring  and  been  p r o f i l e , mean  Columbia.  surface,  has  study  Institute  processes  work  to  wind  velocity  component  along  measurements  two  of  the  dimensional  wave-  showed  hot  spectrum.  The wire  measurements  techniques  velocity  to  used  boundary  demonstrate to  measure  mean  v e l o c i t y .  techniques wires  responses to  analyze  the  to  on  both  the  fluctuations  measure  in  order  to  wide the  ocean. of  horizontal entailed  wires  to  frequency  measure range  hot  wires  can  in  two  directions,  the  direction  developing  directly  the  dependence  components.  to  Another  representing spectra  of  be one  the  special  probes,  the  the  two"  the  extract  in  objective  in  data  horizontal  f i r s t  on  analog  that  My  fluctuations  velocity  recorded  a  X-array  This the  19^5)  successfully  over  an  other  mount  and  over  velocity  and  wind  used  that  (19^3,  Pond  layer  v e r t i c a l ,  these  be  fluctuations  turbulent was  can  of  of  calibrate of  their  objective  is  wind both  velocity  . 2  components  and  0.0l6  from  methods  collection for  and  the  horizontal  the  These  objectives  developed  analysis  of  s t a t i s t i c a l  spectra and  will  a  were aid  s u f f i c i e n t  frequency met,  the  of  and  range  the  future  amounts  examination  measured,  vertical  important.  turbulent this  Hz.  throughout  of  their  X-wire  data  re I ation  to  phenomena.  Of  most  cospectrum  techniques  adequate  other  60  to  and  their  spectrum stress  important  also  close  in  parameter  the  the in  of  furnishing  a  of  velocity  is  the  insight  into  the  integral  of  numericaI  estimate  of  boundary;  theories  between  greater  layer,  direct  air-sea  wind  a  boundary  provides  to  cospectrum  components  Besides  structure  the  this  is  wind-driven  an  ocean  c i r c u I at i ons •  Unti I surface stress  were  indirect  velocity  inertial  iubrange.  determine  measured  the  mean  over  winds  the  other  with  are  on  velocity  stress  on  over  own  a  water  direct  two  independently  One  is  based  nature  on  the  of"the  fluctuations  in  also  the  allowed  me  CQ.  frequently  regions  the  My  measurements  c o e f f i c i e n t  extensive  stress  methods.  comparison  wind  These  drag  surface  determinations.  and  horizontal  of  indirect  allow  p r o f i l e  of  Since  by  stress  spectrum  to  estimates  obtained  measurements  measured mean  r e c e n t Iy,  and  the  f a i r l y  oceans,  easily and  since  C  N  5  multiplied speed  by  provides  evaluation parameter easily  is,  the  wind  be  to  used  rigorous  energy their  in  quite  the  over  of  provide  behaviour  introduction  of  a  the  measurements  an  attempt  theoretical  To are  made  the  to  the  to  measured  r e l a t i v e l y  d i f f i c u l t y  to  the  is  of  a  range  0  to  vertical of  The  transverse the  the  plane  the  effect  the of  the  observed  of  wind  wind  of  Thus  it  oceans, even  more  kinetic  predictions  mean  mean  level  parameter  horizontal  theoretica I  frequencies.  of  wide  and  the  stress. over  C  of  This  stress  the  for  Another  estimate  ocean.  from  useful.  the,  wind  proper  subrange.  the  deviation  the  mean  covariances,  related  Monin-Obukhov  three  vertical  line  at  The  frequency  velocity  on  the  of  the  component,  direction X-wires,  deviations  in  is  used  from  predictions.  test  components  with  or  test  account  with  high  be  inertial  horizontal  from  in  a  at-high  resulting f i e l d  the  of  most  also  closely  measurements  spectra  stress,  evaluation  conditions  The  the  compared  extensively  extend  of  profiles  spectrum  physically,  could and  wind  square  perhaps  oceans,  on  the  potentially  could  the  and  estimate is  which  over  density  an  of  observations of  air  is  different  used  (u-»-)'at  single  end to  the  of  hot  s i m i l a r i t y wire  heights the  three  probes from  spectra  indirectly  of  to  see  measurements  mounted  the  estimate  heights  theory,  sea  the the if  in  a  surface.  velocity f r i c t i o n a l the  values  3a  remain  invariant  The  by  the  Unfortunately,  is  not  thesis,  in  to  which  observations  and  for  AI.A,  analysis  written  as  that  in  a  some  turbulence  hot  adequate no  general  continuity  are  appendices.  the  and data  also  structure.  of  measurements  s t a b i l i t y  effects  sense.  of  the  theory  discussed,  c a l i b r a t i o n  AI.D) wire  of  strongly  temperature  discussion  aspects  and  are  temperature  very  results  AI.C, of  so  maintain  theory,manipuI ation (Section  of  s u f f i c i e n t l y  except  order  height.  prevailing  available,  possible  In  the  characteristics  influenced  are  with  my  of  hot  my  work  (Appendix  IV),  f i r s t of  of  the  turbulence,  work  on  wires on  part  in  the  have  the an  X-array  techniques been  k I I .  THEORETICAL  A.  VeIoc i ty  A.I.  axes, from where  x^,  X|, a  V.  =  I  I  x^  U.  +  I  of  u.  is  in  wind  Spectral velocity  contribution number  f  is  d e f i n i t i o n ,  stationary  a  time  t h e X|  to  Spectral  -  frequency  U,  so  radian  represents state,  a  =  x . .  U., so  that  densities  cycles  is  taken _V =  a r e used  and a r e so  in  V  of  upwards  ( V | , V\p,  I  U.  is the  I  the f l u c t u a t i n g  axis  the covariance  interval  is  system  positive  is_V = of  a  that  velocity  u~~  0,  =  average.  representations  one-dimensional  UjUj  u^  f i e l d ,  x^ is  the direction  velocity  f i e l d .  that  velocity  velocity;  this  Data  velocity  such  The wind  convenience  t h e mean  where  chosen  the bar denotes  For  wave  is  mean By  of  the turbulent  boundary.  component. where  Representation  describe  component  of  F I uctuat i ons  Spectral  To  DISCUSSION  uju .  (U +  to  0jj in a  time  average  a n d 0.. ( k ) ' r e p r e s e n t s  u^) .  the the  frequency  or  (II  A  that  ( Grant  at  direction  Uj,  describe  unit  per second  number  the  represent  defined  wave  in  (Hz) and k et  a I,  one point  I.I  is the  1962;Pond,196  f o r a  the contributions  to  5  the  covar.iance  The  equality  is  possible  to  achieve  space The of  of by  hypothesis in S e c t i o n  the  physical  integrals  scale in  numbers  length  order  to  k  Taylor's  centered eqn.  II  in  such  a way  of  on  the  validity  limitations  on  it;  these  the of  k.  I.I  A  k represent  hypothesis  interpretations  at  in  have  depends  ergodic  hypothesis  assumptions  the  variables  e.g.  more  same  of  values  if  variable  x which in  general  as a  must  hold.  k spectra  and  Taylor's  matters  F(x) has  time  in  is the  implies  average  from  environment)  coordinates  that  in  ensemble  moments,  example,  stationary,  the  average  otherwise  or  two s p e c t r a l  wave  are  discussed  A.2,  probability  one  of  turbulence,  thus  and  range  However,  the  of  scales  certain  the  defining  of  validity  The  a unit  this..  scale  the  jh  (e.g.  different  of  any  or  by  time.  a function  of  probability  under  the  places  function  estimated  space  that  of  but  random  an a v e r a g e This  over  means,  a continuous  density  in  for  random  f(x)  which  is  are  averages  then  F ( x) f ( x) d x  F ( t) dt  T  "o  -oo  u  where  over to  F(t)  is  the  In  geophysics,  one  unique  generalize  value  time  time  from  of  F at  time  t.  averages  such  as  interval  such  at  a single  one  UJ Uj  point  record,  in  one  space. always  In must  order  6  assume  that  From  log k  The  It  2 .  is  S  hypothesis  I.I,  the re I ationship  poo  fJZJ.j(f)d(-|nf)  practice is  of  origin  shifted  log  k  =  log  10,  . the  fjZijj(f)  The s c a l e is  Ink)  (II  A  1.2)  ci-eo  for presenting  =  kjZJ,j(k)d(  =1  -oo  the base  kjZfj'j(k)  holds.  ao  common  (where  reasons  1.  A  e q n , II  follows. or  the ergodic  plot  f0jj(f)  so  that  Inx  = 2.303  in  this  fashion  data  against  log f  log x ) . are:  everywhere,  log k  2TT  to  is  t h e same  as  (from  eqn. I I  +  f,  log  for  log  f  but the  A 2 . 2 )  U 3.  The area  f0jj(f) the wave  li,  under (or  number  A wide  range  .frequency  correlation  segment  k0|j(k))  covariance  represented  A  a  in  of  a  curve  represents  representing  the c o n t r i b u t i o n  the corresponding  frequency  to  or  i n t e r v a l ,  of  frequencies  without  and  a n d wave  crowding  low wave  coefficient  the data  number  R.j(f)  numbers in  c a n be  t h e low  regions.  is  also  defined,  such  that  0; ij-  :  &  u  ( f ) - &  n  ( f W  '  ( l l  A  1.3)  7  The  repeated  This  coefficient  The  —2 and  and not  j  are  not  represent  interpretation  represent  energy  directions  the  vertical  (Lumley A.2.  and  space  the  the  unit  of  of  summed  in  this  the  coherence.  the  covariances  formula.  is  that  mass  of  p  a  in  covariance  u ju^  momentum  63;  Hinze,  by  number"  using  U  of  between  the time  "ox  per  the the  unit  1959,  turbulent and  X|  represents mass.  19-21).  pp  a  only  shear as  flow,  long  is  related  number to  the  hypothesis.  carried  past  a  k  This  as  states  given  Hinze,  I959»  space  scales  is  point  PP U-0 -1+.2) .  then  (II  i i _ U dt  this  was  physical  (see  flow and  wave  2jTTf U"  k  in  is  Taylor's  structure  velocity  relationship  one-dimensional  "wave  number  approximation  to  fluctuations  The  196I4.,  A.I,  This  However,  contributions  Hypothes i s  turbulence  mean  the  horizontal  Panofsky,  Section  wave  twice  respectively. flux  introduced.  that  per  TayI o r ' s  In  The  does  physical  u^  kinetic  at  i  —2  Uj  x^  indices  ( M A  hypothesis  is  a  good  A  2.1)  2.2)  8  1953)»  (Lin, or  F  o  turbulence  functions  of  r  is  k.  Thus k  are  it  over  one by  a  take  linear  hypothesis  •3 •  boundary  Shear  the  tenable,  in  the to  is  shear give  terms  k),  flow  a  spatial  in  longer  no  of  this  since  near  physical the  the  physical  structure  large  boundary.  interpretation  to  interest.  d i f f i c u l t i e s  attitude  that  in  which  assumed  to  f i t ,  shear  flow  is  k a  is  interpretation,  defined  frequency  II  and  the  physical  discussion  Section  Model  of  a  from  Further  Flow  model  approximated  is  of  found  the  (small  transformation  is  The  In  the  k),  scales  possible  these  (large  large  parameter.  -  A  k  scales  avoid  length '  well  of  not  all  can  quite  distorted  is  To  scales  For  interpretation eddies  small  of  by  eqn.  II  A  parameter  to  a  2.2,  Taylor's  E.I.  Assumptions  actual the  shear  flow  following  above  the  assumptions  are  made:  I ,  The  homogeneity  in  2,  The  mean  3»  The  direction  with  It.  A  wind  two-dimensional  the  -  Xj  velocity  of  the  x  p  is  mean  height,  stationary  state  exists,  and  has  horizontal  plane,  in  the  wind  Xj  d i r e c t i o n ,  velocity  is  invariant  9  5.  N  local  o  6,  The  7*  Transport  by  wi t h  transports  Use  of  only  these  conservation  and  Panofsky,  budget  energy  per  working the  mean  of  mean  forces  flow  feed  along  scales  dissipate of  remaining  It  reasonable  this  case,  and  that  part  contained stress  production or  energy is  in  of by  term  out  all  necessary  of  reasonably  not  in  yet  some  of  good  Analysis  the the  is the  Lumley  the  energy  of  Energy  is  turbulent  p  kinetic  is  the  x^-component this  due  .  components. the  Buoyancy  energy  along energy  forces The  existence  turbulence.  approximation  on  of  redistribute viscous  to  density)  -pu~j~u^ ^ U / d x ^ )  and  fed  xj-component,  forces  sustain  (see  over  This  boundaries  space.  certain  approximation spatial  compared  equations  energy  redistribute  three to  simplified  (-pu~7u\,  gradients  same  negligible  facts.  component,  the  to  following  into  is  thermal  of  fixed  simultaneous  leads  the  Reynolds  plane)  .  inertial  a  is  action  eqn..2.38)..  into  e x i s t >( x | , x^,  gravity,  components;  the  gives  divergences  72,  volume  (the  anisotropy  model  p.  pressure  velocity  is  mechanical  energy  turbulence; all  of  flow  the  force  molecular  shows  unit  or  assumptions  I9&1+,  equation the  body  eddy  for  from  convergences  and the  whether  over  a  water  temporal  above  the  model surface  variations  assumptions  gives which in  appear  a has  shape.  In  questionable,  10  even  in  the  The  v a l i d i t y  discussed  absence  in  of  detail  Anisotropy  the than two  that  for  heat  some in  and  Measurements showed  of  in  Section  a  wind  the  direction  those  in  the  lateral  transverse distance  and  from  The  nature  determine  the  the  the  structure  (19^-1)  the  anisotropic  eddies  is  anisotropy less is  and  of less  "handed  become  in  redistributed  fluctuations.  more  These the at  and  by a  the  Favre  model  et  will  be  mean  order.  wind  (1957)  al  horizontal  vertical  shear  were  The  asymmetry with  flow,  much  directions.  decreased  more  the  an  flow  larger  The of  latter  the  increasing  fend  to  velocity decrease  isotropic  the  which  are  postulates  smaller  in  at  components  by  the by  anisotropy.  wave  thus  The  Since tends  number  same pressure  influences  scales.  of  these  scales  and  structure as  convection  present  process  smaller  turbulent  the  cascade",  feeding and  to  to  of  eddies  energy  down  "energy  among  and  largest  According  passed  energy  the  shear  turbulent  smaller  down",  and  of  Kolmogoroff  is  of  mean  anisotropic.  time  this  boundary.  of  transfer  in  scales  necessarily  inertial  tunnel  same  vertical the  of  E.I.  "eddies"  in  of  sinks.  Isotropy  large  were  or  assumptions  scales  scales  sources  the  energy  the  energy  to  increases.  11  A  lower  kx >li,5 5  A«5*  limit  for  (Pond  isotropy  et  a l ,  The I n e r t i a l  The Hinze  estimated  to  be  at  1963),  subrange"  181 - 2 0 0 )  pp  been  Subrange  " i n e r t i a l  (1959,  has  region  and Lumley  is  discussed  fully  in  U96I1,  and Panofsky  pp 7 9 - 8 5 a n d 1 6 2 - 3 ) , (19I+I)  Kolmogoroff Reynolds of  number  scales,  properties  called of  dissipation form  to  were  made  large  the hypothesis enough,  the " i n e r t i a l  turbulence  rate.  the 0||(k)  then  Dimensional  analysis  spectrum  this  in  2/  K'  is  the universal  measured  value  the  rate  of  In  this  dissipation From  appropriate the  energy  dissipation  region, takes  analysis  of to  (Pond  gives  isotropic  form  of  region  which  a  range  the  by t h e  the  following  (II A 3 - D  5/5  constant, et  having  1963),  a l . ,  a  and £  is  mass.  energy  The t u r b u l e n c e  the s p e c i a l  the  exists  entirely  per unit  no s i g n i f i c a n t  place.  the  relationship  Kolmogoroff  O.I4.8 + 0 , 0 5 5  of  in  if  region:  0, , Ck) = K ' £ V where  there  subrange",  are determined  that  is  production here  the energy (Hinze,  1959,  or  isotropic. equations PP  165—T)>  12 0  5 5  = ij. 0, , ( k )  (k)  (II  A  5,2)  3 is  derived.  A.6,  The The  is  Two-Dimensional (negative)  ujuj.  As  seen  u  ,  elements  f  Reynolds  in  u ^  and  turbulence,  tensor  u 6: j,  j  considered, wavenumber condition  where  2  However,  if  the  but of  for  II  A.I,  in  the  must  8 . .  ij  entire  only  a  u,u^ it  the  be  is  "Tensor"  tensor the x  x^  to  of  spectrum,  a  units  the In  express  this •  delta,  component  contribution  has  plane.  Kronecker  velocity  kinematic  tensor  -  (  in  possible  the  one-dimensional  isotropy  Stress  stress  Section  isotropic as  Reynolds  is  not  single then  a  necessary  is  =o  % Thus  where  isotropic  In  J ^ u ^ k ^ at  order  anisotropy introduce  of the  the  to  =4(^11 " k ^ l l ) 0^  wavenumber  express  the  (I4./3 )0 j  =  the  ,  if  ( M A 6.1a) the  field  k.  degree  turbulence  "pseudo-tensor"  at  the  and  nature  wavenumber  of k,  the we  is  12a In  isotropic  The  orientation  tensor", can  be  turbulence  which  9,  estimated  this  of  the  gives  would  be  given  by  principal  axes  of  the ' W i r e e t i o n "  using  the  of  the  the  "pseudo-  anisotropy,  relationship  A 6.1  (II  This  process  is  analogous  to  that  (1956, pp  377-9)•  It  at  constant,  then  is  probable  is  while  real;  probability are  scales  to are  if  the  uncertain  respect  it  varies  9  measured  enough  that  anisotropy. isotropic,  indeterminate.  small  The  indication  as  to  anisotropy  at  small  the  that  Corrsin,  9 remains  the  the  value  of  values  values  existence  or  other  9  anisotropy  then  in  (especially can  be  hand,  9 should of  approximately  observed  conclusion  pn  scales.  by  significantly,  no  measured  the  scales,  spectral  If,  used  thus  drawn the  a l l 0\j) with  small  become give  non-existence  of  a  good  )  13  B,  The  B.I.  Monin-Obukhov  The  In  this  scaling  universal. the  "viscous  (the  is  universal  B.2.  factors. Then  ature  boundary  assumed by  the  are  with  validity  the  in  quantities  d e f i n e d a s f o l l o w s :  the  flow  itself  as  When  can  boundary  except  (and  a  length  L  T-* w h i c h  be  of  is  outside  are  v e l o c i t i e s ,  fractions  the  grouping  boundary u-«-,  of  lengths  these  formed  which  are  layer.  L  work  and  structure  temperature  equations  will  K - w i l l  u#  a  height.  u-»- a n d  present  the  velocity  and  non-dimensional  of  a  expressed  the  dimensionless  near  layer")  invariant  that  turbulent  any  exist  length),  distributions,  The  is  Hence,  there  Definitions  Since  it  determined  temperatures  quantities, of  theory,  Mon i n - O b u k h o v  essentially and  Theory  Theory  turbulence for  Similarity  not  L  not be  be  dealing  with  temper-  discussed,.  describing  the  turbulence  are  where  K =  is  a c c e l e r a t i o n , temperature  The  the  T  von Karman  t h e mean  flux,  where  scale  is  B„3.  The Behaviour  temperature, is  0  non-dimensional  constant,  g  the  a n d Wu^T  the p o t e n t i a l  grouping  g r a v i t a t i onaI the  temperature.  usually  used  for  the  length  x^/L.  The  flux  of  with  L  Richardson  (I96I1,  Panofsky  eqn.  Stability  number  2.39,  R^  7 2 ) .  P  is  defined  It  has  by  the  Lumley  f  T  o(u u )(dU/dXj) (  For  large  density  (MB3.I)  =-2___2  R  positive  R^,  gradients,  and  form  9U"  stable  average  5  characteristic  of  extremely  no  turbulence  exists,  of  Rf  heat  L  is  i n d e t e r m i na t e .  For and  the  above  case  The c h a r a c t e r i s t i c  =oO,  L  neutral  a  boundary.  For  negative  Rf,  L  increases  and c o n v e c t i o n  become  the  In  of  the  turbulence  order  extreme is  characteristic  not  of  is  0,  length  f i n i t e  grows.  no is  then  flux x^,  and decreases The value  of  is  present  the  as  height  instability  X J / Lcan  then  unity.  cases  of  present.  length  =  is  x^,  pure Here  convection, L  =  0,  so  mechanical  that  the  15  Physical flows,  conditions  except  f or  near-neutral  or  to  use  a  is  known  C.  The  C.I.  x^  as and  The  The neutral  s ome v e r y s f a b l e  unstable  very  much  Velocity  Mean  mean  z  Q  is  a A  Lumley  Panofsky  and  For  derivation  near  small  since  small  when  -neutral,  thus  not  the  shear  correct  value  of  L  x^.  Coefficient  over  a  =  u * l n ( x  of  It  5  / z  length  this  solid  0  has  boundary the  under  form  )  (I,  K«0.1L  and  expression  is  is  von  found  I.I)  C  Karman's  on  p.  103,  (I96IL)»  neutral  the  is  unless  Drag  logarithmic.  characteristic  constant.  It  than  and  profile  U  where  larger  areusually  .  Profile  velocity is  c o n d i t i ons  length  Profile  Velocity  conditions  in atrriospheric  conditions.  characteristic  is  Mean  encountered  rate  compared  conditions, of  to  production the  rate  of  L  is of  f i n i t e  but  convective  production  of  x^/L  is  energy  is  mechanical  energy.  For the  mean  partly  this  condition,  velocity  linear*  p r o f i l e  The  form  under  the  becomes of  the  Monin-Obukhov partly  p r o f i l e  assumption,  logarithmic is  and  " l o g - l i n e a r "  |6  U  (pp  106-107  Xj/z  0  must  be  o< i s  one.  In  of  a  the  is  then  Lumley much  3  commonly  than  which  L  is  I96I+).  be  used,  In  this  x^/L much  empirically  appears.  rarely  (  M  C  «  !  5  one and  must  1.2,  which  +o<(x /L)]  o  Panofsky,  larger  constant  flux  ln(x /z 0  and  e q n . II C  temperature L'  = f l  This  A  )  case,  less  than  determined.  contains  available.  2  the  modified  where  L'  u*(dU/dx J T , • Kg(dT/dx )  5.  =  (II C  I.3)  5  This  gives  the modified  = ^ i [  U  The  value  from  ii to  The  of 7,  log-linear  ,  n  (  3 /  x  the c o n s t a n t © ^ (See  Lumley  relationships  z  o  profile  +  )  has  f  been  1  estimated  and Panofsky,  between  L  11=  ( II C I .ii)  « < (xjA -)]  196^,  and L ' ,  to  pp  be  anywhere  IO7-IO8.)  and © ^ a n d t *  1  are  ti ,  K~  m  o< ' where The  value  dispute;  is of in  the eddy this  h  = R- <*  a i r  ( II  m  conductivity  ratio  neutral  K  of  eddy  it  is  and K  m  the eddy  coefficients  considered  to  near  • I  viscosity.  remains be  C  in unity.  .5)  17  C.2.  The  At stress mean  Drag  a  Coefficient  uniform  is  found  wind  def i n e d ,  solid  to  speed. such  C  D  surface  increase This  allows  a  always  P r i e s t I ey D,  The  D,l,  be  referred  discussion  A  of  square  c o e f f i c i e n t "  the  eqn,  in  A  dissipation.  If  it  p r o f i l e  (neutral  holds  production  of  to  a  fixed  be  C 2.1)  height.  c o e f f i c i e n t  is  then  of  u-»  Inertial  =  is  found  in  now  assumed  from  II  C  the that  conditions), energy  -U|U^  Subrange  c o n t a i n s £ ,  5«')  turbulent  u-"- dU dx  3  and  equals I . I,  rate the  and  I I  energy  logarithmic  that  the  of  the  rate  dissipation A  wind  of rate  5.1.  - I  (II D I.I)  * =[^rH (kx ) M (k)  u  2/5  2  3  the  to  the  U  drag  the  (II  where  of  (II  = ~  Determination  ,0||(k)  Using  i .e. e _  "drag  the  the  ( 1959'., p p 2 1 - 2 2 . )  Indirect  The  with  conditions,  tha t  D  must  neutral  linearly  C  Cjj  in  value  of  the. c o n s t a n t  u  bracketed  term  is  around  I,I3«  18  Use  of  the  measurements  of  fluctuations, conditions  D .2.  the an  mean  wind  simply  log  Xj.  E.  The  The  allows  the  one  0||(k),  spectrum inertial  Mean  Wind  II  I.I  C  profile  of be  u-«  to  estimate  of  u-«-  from  horizontal  subrange,  can  of  Shear  model  under be  provided  the  above  Profile  contain  1.2  neutral  or  obtained. from  Other  Flow  and  Velocity  and  estimated  Results  The  I I  the  estimate  EiI•  in  eqns.  can  the  eqn.  hold.  Using  Both  above  the  u-«-«  By  measuring  near-neutraI  I t ' l l  slope  of  C  I.I  a  graph  conditions,  holds, of  U  this versus  Workers  Model  its  assumptions  are  discussed  in  Section  A.3. Although  the  widely  used  recent  studies  Kraus  (1966)  to  two-dimensional  describe  shear  boundary  by  Fleagle  et  al  have  brought  some  layer  flow flows  (1958), of  its  model in  F a l l e r  has  the  atmosphere,  (196 3 ) ,  assumptions  been  and  into  question.  Faller generated  in  (1963) an  studied  Ekman  flow  boundary  layer  produced  in  a  i n s t a b i l i t i e s rotating  tank.  He  19  found a  that  c r i t i c a l  had  a  angle  boundary  laminar  Reynolds  banded  small  of  the  form to  number, with  the  layer  the  basic  layer  and  band  phenomenon,  that at  flow.  became  a  the  i n i t i a l  and  i n s t a b i l i t i e s  persisted  even  above  i n s t a b i l i t y  characteristic  These  and  unstable  quite  were  after  a  the  onset  turbulence.  Since layers  to  Ekman-type heights  of  i n s t a b i l i t i e s  are  drawn  since  too  exhibit  far  thermal  elongated to  the  be  present  of  the  in  unless  boundary  of  downwind, in  large might  .  would one  averages  since  change  localized  by  give are  of  measurements erroneous  taken  over  layer.  may  can  any  extend  could  distribution thus  be  momentum.  structures, time,  so  change  average  estimates  be  advections  with  would  The would  transfer  of  not  and  convergences  c e l l u l a r  the  must  structure  vertical  area  such  non-homogenous  the  slowly  boundary  turbulent  transfer  also  large  is  and  then  analogy  such  boundary  momentum  Estimation  area, then  with  meters,  layer If  atmospheric  the  occurs,  convergences  associated  of  divergences  turbulent rate  the  although  structure that  the  non+stationary  only,  so  with  distribution  very  the  in  hundreds  non-homogeneous,  associated  almost  many  occur  i n s t a b i l i t i e s .  downwards  phenomena  flows  possible,  c e l l u l a r  surface  spatially  a  boundary  kind of  s u f f i c i e n t l y  at  the long  elongated  that  slowly  stress  Also,  the and  acting one  over  point  momentum time  be  flux,  periods.  20  Measurements  (1958)  pointed  ordered  roll  that  a  occurred.  a v e r a g i ng  The scale are  profiles  axes  (I966)  not  observations  out  off  over  to  the  al  mean  Aruba  showed  the  velocity  in  be  et  large-scale  to  variation  appeared  Fleagle  of  perpendicular  variations average  by  existence  three-dimensional The  did  wind  possible  with  Kraus'  systematic  and  the  vortices  d i r e c t i o n .  nature,  vertical  toward  wind  f i e l d  of  of  reasonably  a  c e l l u l a r  short  t imes.  above  results  horizontal  suspect.  question,  that  homogeneity  Until  the  show  further  assumptions  in  the a  fieId  can  be  assumptions  of  two-dimensional measurements accepted  large  shear  resolve  only  flow, this  with  reservat i ons.  The can  be  assumption  imposed  only  those  (see  Appendix  In velocity with  hundred of  has  are  as  an  the  time  f i e l d  reasonably  layer of  the a  over  height  upper  on  of  limit.  phenomena,  effects  the  order  conservation,for  similar  negligible  on  in  is  one  data  exhibit  which  by  analyzing  this  condition  B.),  scales(at  and or  which  boundary  meters  motion  vortices  IV  scales  length  stationarity  approximately  sections  the  of  the  sea  of  a  a  the  few  few  horizontal  meters  meters)  Analysis  of  per of  the  second,  a  few  equations  situations  not  involving  shows  the  Coriolis  that  variation  of  stress  in  roll force  the  21  lowest the  few meters  only  in  body  direction  boundary  E,2.  force,  and allows  of^the  mean  Inertial  Wind  tunnel  been  made  wind  turbulence  The data  Grant  (I9&2)  in  Pond's  (I9&3,  et  al  agreement. boundary  layer  over  He a l s o  constant  measured  K'  0,055  agreement of  The  of  to  over  among flow  universally  £  in  in  a  quite  well  by  A 5''«  I I  channel  I9&5)  gravity  the  this  as  variation bottom  an  demonstrates  in  that  with  also  of  show  K'  very  in  the  the  by  good  turbulent  k"5/3  Kolmogoroff  value  Reynolds  195,  the  Measurements  the  different  scales  Nature,  an a i r j e t , water  average of  small  I9&2;  confirm  values  range  found  very  measurements  the ocean,  wide  tunnel,  of  number.  media  and  This different  is  indeed  approximately  clearly  allows  the  constant.  value  inferred  the one-dimensional  subrange.  tidal  obtaining  values  measured be  described a  to  (see Gibson,  summarizes  the atmosphere,  rate  height  the sea further  behaviour.  types  leaves  neglect  measurements  agree  spectrum  O.I18 +  one to  with  workers  Kolmogoroff  and  This  Subrange  by many  1281-1283).  pp  the surface.  layer,  The  have  from  of  (from  K' II  energy  A 5 » 0 from spectrum  in  the the  dissipation  measurements inertial  22  E.3.  The  The  mean  measured Deacon  Mean  by  et  the  log  has  water were  surface  observed at  the  Takeda,  have  large  been  found  by  been  scatter  measured  mean  wind  profile  was  1963;  in  (19^5) He  wind  speed  measured,  been  and  water  Brocks  and  for  Surface  surface  and  about  The in  the  Fitzgerald's  Negative  which  p r o f i l e  the  p r o f i l e  increasing  vice  versa  exists  for  when  related  higher  just  over  a  curvatures  that be  f i t  data  be  to  versus  best  not  tended  majority  U  could  found  been  19^ 3 5  Hasse,  1965.) linear  has  I955>  Charnock,  Hamblin,  slope  also  speed,  had  Water  approximately  tunnel.  Hamblin  a  I9&3;  in  wind  a  (Including  except  a  over  over  observed,  phenomenon.  same  profile  Sheppard,  1963;  but  Profile  workers.  al,  profiles  x^,  line  velocity  many  Fitzgerald, of  Velocity  following  any  slopes,  when  before  to  the  the a  decrease.  No  proven  averaging periods found  is  used  that  between that  time  shorter  s t i l l  for  have  10  the  c r i t e r i o n mean thus  minute  slope  and  periods  unresoIved.  velocity depended  averages average gave  determining  p r o f i l e s . on  gave  the  worker,  significant  speed,  smaller  The  at  a  fixed  correlations.  the  best  averaging Hamblin  (19^5)  correlation height, The  and  matter  23  The  E,l±,  The has of  m,  used 5  drag  been 10  in  Drag  in  CQ  practice  although  5  arid  m  following  m height,  is  c o e f f i c i e n t  common  the  The  Coef f i c i ent  since  my  behaviour  dispute.  is  to  defined  refer  lesser  of  C  wind  with  D  it  to  heights  discussion mean  have  data  eqn. winds  have  all  does  not  C  at  a  height Values  adjusted  mean  to  any  speed  value  of  -I  -3 for  ;|.5xl0  all  but  his  are  disputed  mean  increase at  by  with  Fitzgerald tank  and  height  it  results  in  cm)  own  p r o f i l e  sonic  anemometer).  a  height  a  value.of  I.I  X  values  of  10"' a t of  wind  by  their  cm  0.6  x  the  stress  to  They  at  "3 2.xl0, a l t h o u g h  a  below  from  using over  about  increasing  which  stress  wind  water  with 3  wind  were  the  drag  jncreasing m.sec"'to  Hamblin  (196 ?)  scatter  was  1  a  ina  10"^  included compared  wave  at  a  above The stress with  (using  a  c o e f f i c i e n t  at  wind  from  value  obtained  very  l . x l O ^  p r o f i l e s .  speed.  measurements  that  =  ij. m . s e c " ' ,  (I965)  ),  linear  c o e f f i c i e n t (2,2l|. x  found  5 m.sec"'.  p r o f i l e  workers  increased 10"^  the  again  m.sec  20  determinations  m.sec"',  |8  Timanovskii  direct  about  (I963) o b t a i n e d  m.sec"',  with  and  for  about  speeds  other  and  200  used  drag  increased  made  to  8  constant at  (up  observed  Zubkovskii  measurements  up  |.8xld"^at  a  measured  Sheppard  wind  I9&3  slowly of  profiles  mean to  2  speeds  some.  found  of  which  wind  wind  m.sec"'  2  a  higher.  wind  constant  It  2*1.  used.  extend  the  a  II  been  been  i n c r e a s e in  (1963) o b t a i n e d  Brocks  by  large,  speed, of average e.g.  near  2k  one  wind  speed  Hamblin scatter method  be  stress  (1958),  Fal ler  II  would  E.I)  pointed  out  stationary length  in  also  due  to  (1963), seem  parameter  to  over  space  in  from  about  or  1 ,xlO  suggested inherent  measurement.  that  be.important  varied  (I9&5)  could of  it  and  an  boundary  determined determining  besides by  of of  amount the  wave  Also,  the  in  Stewart  which  is  height,  et  the  p r o f i l e al  Section (I96I)  not another  characteristics  turbulence  of  wind  Fleagle  (I966)(described  this.  time,  large  results  indicate ocean  a  weaknesses  The  Kraus  that  t o 4- . * 10  may  c h a r a c t e r i s t i c s .  also  25  •I 11  EXPERIMENTAL  The north  data  of  raised  recording  The so  and  c a b Ies  collected  Banks 20  f t .  instruments, liO  N.N.W.  m  sensors that  were  Spanish  platform  high  METHODS  were  they  site  located  Beach  (see  Fig.  III.I),  above  the  and  rotatable  be  a  the  attached  could  carried  a  of  sandy  platform  to  moved  signals  at  a up  from  bottom  about A  supported  the  frame  or  together.  sensors  to  on  the  km  on  a  the  mast  movable  the  hut  housed  aluminum  down  0.5  6  m  sensors.  the  mast,  Electrical  recording  equipment.  The  sensing  instruments  anemometers,  and  indicators.  These  Measurements  were  anemometer, these  bead  form  It  should  is  an  on  the  was  of  be  noted  part to  that  the  attempt-to  and  arm  the  and  a  is  apparent not  observed  reguIar  University obtain  of  the  air-sea of  lean  real. at  the  I  with  a  thrust  wave  the  in  III.  to  probe;  air-sea  this  thesis.  experimental  s i t e .  of  the  main  Also,  the  equipment  left  of  the  interaction  Washington,  simultaneous  cup  direction  within  discussed  photograph the  wind  capacitance  not  a  probes,  simultaneously  and  are  wire  Appendices  projects  effect  of  in  various  shows  horizontal  belonged joint  III.2  made  hot  absolute  discussed  also  program  optical  not  are  and  thermistors,  parts  interaction  Fig.  relative  were  and  and  main  mast  mast  program.  was  used  independent  in  It a  26  measurements  All  of  various  outputs  from  quantities  and  signals  an Ampex  on  Digital direction  ensure the as  the  cup  film  anemometers  instruments,  was at  on  a single,  used the  to  top  cross-wind lowered rode the  Cup wind  regular  wind  an  on  recorder.  wind  recorded  automatic  speed  recorded  tape  the  were  analog  data, the  on  timer.  pulses  To  from  magnetic  tape  to  and  cup  inch  instrument  pointer  to  boxes  the  cups  diameter mast.  indicate  in  was to  the  caused  on  the  called a situ.  aluminum  It  attached  flows  mounted  anemometer  calibrate I  to wind  This mast  raised  the  "Rover"  10 m  and  Rover  reI a t i v e  was  mast  height  of  anemometer.  anemometer  direction  relevant  with  cables  well-exposed  a fixed  meter  interference  supports,  the  magnetic  as  signals.  a separate  from  mean  fluctuating  recorded  anemometers,  hy-drau I i c a I I y ; a s c a l e  past cup  of  cup  also  possible  attempt  measuring  lli-channel  a camera  were  turbulence.  were  a current  using  multiplexed F.M,  mast,  the  a v a i l a b i l i t y of  To c h e c k by  CP-100  and  of  equipment  information  from  indicator  photographic  the  spoken  data  statistics  data  readings,  information intervals  from and  were  and a l s o  the tidal  entered read  electro-mechanical current in  into  readings  data  log  the  voice  sheets  counters, and at  channel.  other  27  The  descriptions  electronics  The tape in  are.found  data  were  Times written  on  Logarithms  these  in  Appendix  collected  analyzed  Appendix  of  on  later  instruments III,  photographic  using  analysis  and  Section  film  of  their  A.  and  magnetic  techniques  discussed  IV.  are a  2ij.  are  quoted  in  hour  basis  as  the  base  all  to  Pacific  Day I i g h t  Saving  Time  hour/day/month/year. 10.  ,  28  IV,  EXPERIMENTAL  A,  General Cup  ...  a n d mean  speed  (see Section  summarized  during they  spaced  U-wires  quoted  are those  mounted the  above  speed  probe.  only  The  time  Numerical  with  at which  near  are  water  wind,  to almost were  zero  speed.  slightly  U-wire  runs,  hot wire  results  are  .The f e t c h  r u n 1555-1620 /20/9/1965  was t h e  had the lowest swung  from  The t i d e  unstable,  and a i r temperature  surface,  1  p r o b e was  the central  and also  the r u n , the wind  Conditions I7.7*C  speeds  the X-wire  in numerical  listed  vertically  wind  For the three  measured  Multiple  three  Mean  results  arranged  speed.  interval  the end.  log  VI.  an e a s t e r l y  dropped  temperature mean  wind  Runs  surface.  t o be e x p e c t e d  At t h e end of  maximum.  the  long  the height  that  IV),  wind  data  and A.2, and are  recorded. at  from  r u n 2 0 1 0 - 2 0 3 l t /2 l / 6 / l 965 ( F i g . I V . A . I )  east,and a  at  in Appendix  run with  speed.  obtained  increasing  a single  t h e mean  Errors  The  of  were  is  were  IV A . I  are grouped  quoted  discussed  data  in Tables  runs  the order  D i r e c t i o n and  r u n 1555-I629 /20/9/1965,  M l , and Appendix  in order  recorded  R u n , and Wind  Data  approximately  in  on Each  t h e e x c e p t i on of  direction  are  Information  Anemometer  With  sheets  RESULTS  17.7 °C  was a b o u t  wind  NE t o d u e was r i s i n g  with about  water 36O cm a b o v e  7 km.  ( F i g . IV A.2)  was  to  recorded  29  in. a westerly unstable, li4-.5°C  run.  A  then  end  of  were  of  temperature  Fetch  was a b o u t  For  of  sections, with 0  was  ana I y s i s . turned  last  about  IV  this  A.5  water, the  and^after  southward.-::of  2I4.O cm a b o v e  four  After  three  ebbing  ending  runs  tide;  t h e end of  the mast,  (Figs.  During  temperature  runs  were  the f i r s t  turned -sIightIy 'to point  At  for  and runs,  the  Conditions 1 6 . 6 C and  t h e mean  surface.  4-0 k m .  mast  a slowly  were  degree  • slack  dropped,  veered  water  t h e day /22/7/1965,  and the  during  wind  A.6, A.7 and A . 8 ) .  during  one p i e c e  the westerly  |8.1|. C  temperature  24-0 k m .  as  A.5,  wind,  one-half  for analysis.  stable,  were  Temperatures  two s e c t i o n s  the recorded  strongly  and a i r  a n d 2122-2206 /29/6/1965  recorded  speed  Conditions  15.0°C  the nearest  was a b o u t  into  water..  the s u r f a c e .  to about  2059-2122  divided mean  air  only  slack  temperature  l+O c m a b o v e  were  the  during  water  The f e t c h  Runs and  with  about  estimated  wind  were  it  the f i n a l  run, the  better  recorded  this, piece  analyzed  into as  instrument the  one  was d i v i d e d  r u n , t h e waves  the recording  for-the  (Figs.  day.  westerly  piece for suddenly Conditions  Later analysis us i ng o n e - m i n u t e a v e r a g e s s h o w e d t h a t f o r t h e l a s t 5 m i n u t e s o f t h e r u n ' 2 1 2 2 - 2 2 0 6 , t h e ' mean' w i n d drooped f r o m n e a r t h e mean s p e e d q u o t e d t o a b o u t h a l f the v a l u e .  $0  during  the four  and  the a i r a t  The  fetch  of  were  of  building  dropped  the  up s p e e d ,  slack  during  t h e end of  and  A . 12)  during  turned  15.7°C  The f e t c h  been  midnight.  constant,  about  runs.  r u n were  unstable  was a b o u t  with 15.2  during  stable,  about  were  recorded  a slowly  Three  as  rising  with l6.0°C,  the second  the water  C  tide  Conditions  slightly  Midway  at  The  60°.  From  and  and the a i r temperature  the surface.  slightly  before  evening  was t e r m i n a t e d  t h e mast  the analyzed  the  had  A,9  IV wind  run,  temperature  330 cm  about  70 k m .  1550-1605 a n d I607-I6I15 /2I1/7/1965 ( F i g s .  Runs  C  surface.  (Figs.  useful  wind  almost  Recording  and the a i r temperature  surface.  1  gradient  remained  the f i r s t  temperature  3^4-0 cm a b o v e  15 • 7 ° C  t h e mean  During  t h e maximum  thereafter.  almost  conditions-were  the  the speed  waves  wafer  10 m . s e c " ' .  reaching  heavy  about  cm a b o v e  the highest  a north-westerly  rapidly  during  350  during  about  when  0010, was  recorded  2220-2235*  about  about  I9»0  liO k m .  t h e summer,  26/6/1965,  at  ;  2230-2258 a n d 2305-2336 /26/6/1965  A.10)  speeds  - w e r e , u n s t a b I e , • w. i t h , t h e w a t e r  |8.0°C  was a b o u t  Runs and  runs  one p i e c e  in a westerly  IV  A. I I  wind  tide.  U-w i re., p r o b e s  at  different  The  mean  wind  remained  approximately  but  decreased  slightly  f o r the second  heights in  were  t h e same  r u n , and  used.  direction,  continued  31  bIowing  with  Conditions  for  temperature 300  decreasing the  at  cm a b o v e  wind. s p e e d  two r u n s  •I9.3°C,-  t h e mean  were  and a i r  after  the  stable,  with  temperature  surface.  last  The F e t c h  recording.  water  at  2I.O°C,  was  about  about km.  *f0  T h e r u n I 5 O I - 1 5 2 5 / 2 5 / 7 / 1 9 6 5 ( F i g . IV A . 1 3 ) w a s t h e f i r s t. s e c t i o n  of  westerly  during  section speed  couId  rapidly  wind  water  above  piece  in  below  the  speed  remained  the  Profiles  surface.  for '  the  IV  A .9). a r e  bottom  i t . Rover  No  operated  Wind  are  in  has  Table  in  15  the  f i r s t  was  about  a  the  the  first  wind  and  then  section.  constant  The  throughout.  neutral,  I9..7°C,  at  i t ,  minutes,  effectively  included  data IV  described  with  320  about  cm  liO km.  IV A . 5 ) ,  (Fig.  the speeds  those  determined since  the  periods  for  a l l  below.  Appendix  measured  s  the  A.I in  that  exceed  been  during  direction  summarized methods  not  properly  of  a i r  anomalous  expI ana t i on were  next  Only  in  ( F i g . IV A . 8 ) a n d 2 2 3 0 - 2 2 5 8 / 2 6 / 6 / I 9 6 5  cup anemometer  data  after  almost  Fetch  U-wires  since  I'1|JI8-I525 / 2 2 / 7 / I 9 6 5  I65O-I715 /22/7/I965 (Fig.  the  3  tide.  the  r u n were  and  u s i ng  rising  used,  15$  19.6°C  t h e mean  rapidly  about  during at  a  recorded  usefuI Iy  dIrection  Conditions the  be  increased  dropped mean  wind  a  of  of  the  for  this  the  above  condltion.  instrument  the above  was  not  measurements.  runs  Direction III.  cup just  by  are  recording  The a v e r a g e s  0^" a r e  32  given  for  N readings  for  the r u n by  9' 'c  with  the s t a n d a r d  error  Z / 9'  M  subscripts  probe a t  the  relative  to P t .  at Pt. of  the  "r"  instrument Atkinson  platform.  Atkinson  The  for  direction relative  mast  and " a "  . , (9  vane was • = 0 ) ,  a  zero d i r e c t i o n  coefficient  for  i n d i c a t e d by  latter  lighthouse  the a b s o l u t e  correlation  stand  A.I)  (IV  A.I)  o § , where  s  The  (IV  i^i  N  p'is  the  the  the C a s e l l a  wind  lined  the  9j-  = r u e  X-wire  direction  up on  True north  i.e.  to  lies  e' a  o 19  vane  east The  19".  d e f i n e d by  (0' -9p(9' -0' ) r  a  a  (IV °> where  the  similar  overbars  in  form to e q n .  this  case  x  A.2)  °"a  denote  the a v e r a g e s  of  MA,I.  -tt In o r d e r to make these are p r o v i d e d below:  angles  clearer,  explanatory  diagrams  0. 'a .0  90* ^  Probe  To  Point A tk i nson  arm Ins trument hut  33 ^able  IV A , l : W/i ndJ .Di r e c t Ion D a t a .  I965  Time  Date  of Run  r  N  *T  ( Angles  *r  a  N  i n degrees  ^  ):  °a  21/6 20/9 29/6 29/6 22/7 22/7 22/7 22/7 26/6 26/6  2010-2034 1555-1629 2059-2122 2122-2206 11418-1525 1553-1625 1620-1652 1650-1715 2230-2258 2305-2336  7 9.6 J-i-1 - -2.7 ?7 3.5. 49 .-3.5 36 6.8 33 3.5 30 9.9 21 11.3 17 1.7 25 -2.8  6.9 k.4 4.7 5.1 4.7 3,k 3.5 7.1 7,9  3 4l ?6 J4.9 36 33 30 21 17 25  5 264 26k 258 273 270 276 27I+ 30U305  7.3 0 . 8 3 5.3 0.2k 7.2 o.5k 5.7 0.51 5.2 0.60 2.7 0.11 s.k 0.38 k.i 0.38 k.8 0.35  24/7 2I4./7 25/7  1550-1605 1607-1645 1501-1525  16 3s 24  5.0 4.2 4.4  16 35 24  260 250 273  3.9  For  2010-2034 /2I/6/1965,  the r u n  computed  since  absolute  d i r e c t i o n was j u d g e d  coefficient absolute nearest  there  8.2 7.3 1.8  i s an i n s u f f i c i e n t  was c a l c u l a t e d .  d i r e c t i o n data 5°,  s  coefficients  that  o  would  were  have  distribution observed and  values  p'>0.5  values  ofp'is  two s e p a r a t e d f I u c tua t i ons .  instruments  on 24/7/I9&5,  part  read  t o the  significance.  (1946,  Nevertheless,  observe  No c o r r e l a t i o n  55°'  significance  It  The a v e r a g e  of p i s w e l l  by Cramer  a l l of one s i g n ,  were  and c o r r e l a t i o n  statistica I  have r e a s o n a b l e  (approximately).  of p ' a r e  f o r the most  of e s t i m a t e s  discussed  number.  F o r the two runs  little  The u n r e l i a b i l i t y  no v a r i a n c e s  to be about  computed v a r i a n c e s  0.83  p  known.  397) 5  only,  since  when  N E  I O 2 0  observed  c a n be a s s e r t e d  dominantly  *"  The  t h a t the  the same  3k  Wind Table a  IV  p r o f i l e A,2  below.  reasonable  points  for  Section  II  column.  N  data  for'  u  C.)  is  runs  Linearity  straight  the  all  line  versus  log  denoted  denotes  can  that  a  are  of  the  be  f i t t e d  plots  by  summarized  the  curve  p r o f i l e ,  letter with  implying  through  (Fig.  IV.A  L  in  the and  the  negative  in that  measured see  appropriate  curvature  ,  gives  2 the  best  f i t ;  These  o b s e r v e d , p r o f i Ies and-Appendix local the  slope  X-wire  during S  -  between  runs  is  stable.  temperature  When  unstable.  If  Section  IV  F,  the  second  the  by: air  just  the  CI,I  U  and  (see  -  third  cups-  minus  surface),,  was  N'-  w  a  is  used,  neutraI the  because  and  water  positive,  s  negative,  zero,  or  a  few  tenths  of  neutral. A.2  are  D  S t a b i l i t y  if  Table  II  c a s e s , t h e  and  considered  the  Section  there.  unstable,  stable,  also  from  curvature  temperature  of  computed  positioned  under  two.columns  are  negative  di f f e r e n c e were  u-»-  11  the  considered  c o n d i t i 6ns last  eqn.  normally  (measured were  The  is  of  For  denoted  conditions  degree  using  III).  probe  values  described  in  a  35  Table  IV  A.2:  I965  Mean  Time  Wind.Prof Me  (and  Line-  S t a b i l -  arity  ity  Temperature)  U-«-  Data:  L<  2  -2 Date  of  Run  21/6 20/9 29/6 29/6 22/7  2OIO-2034 1555-1629 2039-2122 2122-2206 1448-1525  N L L L N  U U . s S' U  22/7 22/7 26/6 26/6  I62O-I.652 I65O-I715 ,2230-2258 2305-2336  L L  U U  N  S  24/7  1550-1605  24/7 25/7  22/7  B.  hot  L  S  428  1607-1645  N  S  122  1501-1525  L  N  U-Wi r e  wire  The  and  measurements  are  described  system  are  (see.Appendix Wire  remained  rigid  measured  wire  Appendix  I,  as  calibration  of  turbulence  fully  in  described  construction  successful.  -200  -0.7  300 • (200) -600  0.6 (I. ) -0.3  -900  -0.2  -1x10? - 8 0 0 1.  -0.1 -0*2 0.03 -0.05  IxlOk  -6x10? S4:700 (S^:500) S4:700 (S^:500) , S4:lxl0^ (S3:6xl03)  126  7  L'  0.2 (0.5) 0.2 (0.5) 0.01 (0.03)  Data  construction  fieId  probes  128  U  X-and  probes  U  N  cm.  1.7 M2 356 151 2.8 109 47.1 1320 645  The for  L  I553-I625  —  cm.sec  Section  during B.2  and  I.  X-  developed and'U-wire  Electronics'of  mounting  the  B.I  and  proved  C.l)  negligible, the  repeated  wires  and  constancy  of  example,  for  onto  to  the  calibrations  For  the  II.  for  by  C«3).  the  Appendix  were  demonstrated  angles  in  Section  breakages  by  Appendix  developed I,  techniques  be  wires  the (see the  X-wire  36  probes 1°  used,  or  forward  and  did  in  same  velocity  usual  for  about  level  20$, are  in  at  the  two  wires  changed  to  the  any  less  Repeated  the  constant  was  straight-  d i f f i c u l t i e s .  B.2.  that  the  U-wires  of  the  most.between  to  King's  Law  eqn.  calibrations  with  considered  measurements,However,  the  absolute  constant  A  of  c a l i b r a t i o n s .  determinations  of  This  the  i l l u s t r a t i n g  the  not  instruments  re I i a b I e  eqn.  common  A  would  mean  up  cause  velocity  opinion for  changed  1.12)  of  relative  was  (the  t h a n L|-.$.  is  calibrations  s e n s i t i v i t y  B  It  This  between  10$  (the  being  for  Section  showed  i+.L^  f i e l d  differences  probes  by  change  calibration  about  probe  of  c a l i b r a t i o n s .  rise  I,  fluctuations  adequate  to  give  Appendix  changed  1.12)  angles  procedure  not  U-wire  wire  repeated  c a l i b r a t i o n  described  the  measured  lessbetwe'en The  the  the  that  U  only  hot  measuring  of  wire  absolute  winds. Section procedure the  A  usual  1.12  between  for  X-wire of  the  (the  of  I  describes  probes.  Repeated  constants less  maximum  calibrations  i n  than  change  the  were  Law,  the  gave  constant  l\.,2%). again  c a l i b r a t i o n  calibrations  Ki ng's in  was  new  Changes less  than  for  a  B  of  in  A,  10$.  ca I i bra t i ons •  The (which  Appendix  change  repeated  between  '  ..  .  empiricaj  determines  ve I oc i ty the  used  in  determination  similar eqn.  C .3  the  component,  X-wire  probes  \.  determination wire's  eqns.  used  for  A  of  the  s e n s i t i v i t y 1.10  data  and coI  A  wire to  constant the  I . lli)  Iection  in  f or  b'  vertical each  1965  is  wind  wire  of  A  37  described  in  d e t e r m i n a t i o n " of-  I965  for  I,  Appendix  each  b'  was  wire  worked • s u c c e s s f u l  of  is  that  very  of  conditions  measure  the  wire  X-wire  The  technique best  accomplished  the  I y-. it  is  only  very it  angle,  the  two  an  probe.  of  The hot  X-wire  procedures  wire  analog  The  used  data  analysis  straightforward,  to  are  the  is  during  used, 10  best  the  discussed  and  for  discussed  part  b'  of  for  method  under  the  a  to  day and  each  and  Appendix  of  the  analyze IV.  analog-data  Section  of  emp i r i c a I  responses  U-wire  in  fall  the  even  rerecord in  the  th i s  wire  constant  used  empirical  consuming;  record,  technique and  time  wire  once  drawback  calibrate  determine  The  probes  takes  empirically wires  C,l\..  Section  C  of  is  Appendix  IV.  The  analysis  data  is  to  IV.II4.  A  discussed  spectra  fj25jj(f)  two  0.0|6  to  Serially  60  Hz,  from  digital  of  a  and  about  sections  the  Appendix of  the  the raw  were  single  points  took  for  X-wire  IV.  analog  Eqns.  A  values  of  the  results  of  the  carried  out  IV.9  analog  using  the  computer.  spectral  analyzed  of  derivation  0jj(k)  analysis  dozen  D  determinations  I . B .M.  normal  developed  Section  the  and  These  University's  about  in  outline  analyses.  A  technique  took  section  over two  a  days  less  of  data  frequency to  time,  gave  range  from  accomplish. since  one  setting  38  of  the  the  filters-was  same  effect wind  necessary  frequency.  on  Section  spec t r a I  direction  to  va I u e s  makes  E  of  with  analyze of  two  Appendix  to IV  varying/?,  the  verticaI  p I ane  the  four  runs  outlines:  angle,  at  the  the  mean  p a r a I IeI  to  the  X-wi r e s .  Samp Ie data  are  ca I cuI a t i o n s  outlined  discussed  in  Figs. II  A.I)  are  IV  both  shown.  used  B.I  with  It  Scales  B.IO  show  f.  For  the  U-wire be  fj#..(f) of  log  V.  analysis  Errors  of  to  be  X-  and  U-wire  expected  are  VI.  should  a I ong .the  data.  to  log  analog  Appendix  Appendix  versus  measured  in  for  (defined  comparison, and  noted  axis  f  fj25jj(f)  that  to  remain  the  values X-wire  a  of  the  the. same  fJZfj|(f)  of  a l l  each  scales  optimum  for  Section  during  variety  obtain  in  run are  display  runs.  of  The  /2TT_| origins  for  l o g k =" l o g / 2TT M  f  +  log  1  U I  and  log '  X  =  log  The  f  +  log  data.are  (Section  'IV  Four (Figs;..  IV  behaviour Section each  I I  plot  (  U.  /  a r e i n d i c a t e d  arranged A.  Figs.  i:n  the  A.I  to  representative B . II of  to  B..1I4.)  same  has  Numerical  and a  eqn.  plots are  -5/3  results  II  order,  Figure as  the  Captions mean  p 8 4 ) .  wind  data  A.10. of  log  Included  thejZljj(k)spectra  A,.5  (see  (kx^)  A  of  J0jj(k) to  high  5»')»  T  n  e  versus  -log  demonstrate  the  wave  numbers  straight  k  (see  line  on  slope.  obtained  from  the  X-  and  U-wire  data  39  are  shown  order  as  in  Table  before.  interpolated  2  IV  B.I,  The  at  the  The  mean  probe  data  velocity height.  are  grouped  quoted  is  Directly  in  the  the  same  one  measured  values  _ _  of  u-«-  = - U | U ^  by  summation  were  of  obtained  measured  by  a p p r o x i ma t i n g  spectral  eqn.  densities.  II  A I  .2  Indirect  2 estimates  of  u*  from  inertia I  subrange  obtained  using  used,  since  introduces  Table  B.I:  1965  of  21/6 20/9 29/6 29/6 22/7 22/7 22/7  data  the  of  theory  in  D l . l .  X-wire  from  X-  and  Section  the  26/6  Run  U-Wire  To  cm,sec  U-wires the  -1  cm,  138  1553-1625 1620-1652 1650-1715 2230-2258 2305-2336  fel 379 328 983 975  195 200 210 270 265  were bottom  the  0|j(k)  were  unnecessarily in  mean  Data:  336  Three  the  cup  Vertic I a  at  2  Iy  I2  heights  anemometer.  -13, From  -2 cm  2  -2 sec  55.9 190 220 190 308 f+05 375 2000 1510  r  3$ 11420 1214.0  Spaced  simi  sec  u#:from'0  30,8 131 179  195  Monin-Obukhov  mounted  cm  |60  202 168 192  check  in  were  of  changes  Spectral  2I4.7 3JI4. 289  from  values  with  1555-1629 2039-2122 2122-2206  Data  I I'D),  U-wire  associated  measured  u-"-:X-wire  II4I18-I525  2  0||(k)  U-wires«  20|0-203]i  I//?  to  of  values  T i me  Date  C.  II  variations  of  IV  (see  eqn.  use  response  the  U-Wlres:  1arity 67 each  and of  theory, 3^-0 the  c  m  three relative  three  (k)  simultaneously kx^0|j(kx  )  analyzed,  as  =  Figs.  IV  log  reasons  given  valid  C.3  and  ' '  :  M B .  C.5 were  s i m i l a r i t y "  Since  " .  eqn.  II  o n l y i n t h e i n e r t i a l  is  plotted  IV  C.2,  as  a  C.J4. a n d  .  Dl.l  of  log  C.6.  wave  - U | U ^ ( f r o m  =  plots in  of  this  k'x^JZfj | ( k x ^ ) fashion  for  C«  theory used  is  (kx^)  numbers  discussed; "' '  to  estimate  subrange,.the  function At  the  V  frequency  u-"-  plotted in  of  each  of  show  discussion  Monin-Obukhov  at  estimates  data  the  values  obtained  indirect  C.I,  in  responses,  were  (kx^).The  '  Section  f0||(f) were  against  The  recorded  in  " 2  u-*  is  quantity  for  each  high  run  enough  in to  Figs. be  in  2' the of  inertial Section  subrange, II  D.I  Procedures the  analog  Sample  data  in  Wind I V  A.1  I  to  the  u*-  ,  p r o v i ded  for  recording*rerecording  are  discussed are  quoted  profiles A.  =  a I I  f he  assumptions  hold.  calculations  expected  S  13.  for  i'n . . C h a p t e r .  outlined values  the  are  three  in  and I.I \  Appendix  discussed  runs  are  analyzing and  Appendix  V.  Errors  in  shown  Appendix  in  Figs.  IV.  to VI.  be  1+1  Numerical  values  f o r these  three  2 Table at  IV C , l .  the 5  Table  height  m  IV C . l :  1965  in  Data  u-*  f o r Three  I4.56  1501-1525  l|6u,  (in units  measurements,  in Table  U-wire  runs  are quoted  spaced  probes  U-wire  These U-wire  probe  sloping  Profile  Ij.28 122 126  )  determined  directly  ^11^'^  spectrum  the  t h e mean  last. of  Results  wind  p r o f i l e are  the three  vertically  Mean v e l o c i t i e s a n d the t h r e e  vertically  ( l a b e l l e d Sii., S3, a n d S9) f o r e a c h  excluding  are displayed at  - 2  before,  f o r each  U-"  run  array.,  results,  ones,  As  included  probe .heights  Numerical  cm^sec  and f r o m  IV D . I . are  of  „2 .  330 300 170  i n d i r e c t l y from  the i n e r t i a I•subrange,  speed  U-Wires:  U-wire  of P r o f i l e and H o t W i r e  X-wire  using;this  u-: ,2 :  I4.O8'  of.u-^  spaced  V e r t i c a l l y Spaced  UV  |607-|61|5  summarised  ./' T h e mean w i n d  ^ _. cm s e c "  Values  in  by U ^ . -  1550-1605  Summary  line  a r e cm s e c  denoted  Time  2I4./7 2I4./7 25/7  from  is  of  are given  2 - 2  . -  Date  D,  Units  runs  ii5°  is  the three  graphically  shown  f o r each  v e r t i c a I Iy  spaced  i n F i g . IV D . I , graph.  A  k-2 Table  IV  D.I:  Values  2 u*  of  Determined  A  T i me  1965  21/6 20/9 29/6 29/6 22/7 22/7 22/7 22/7 26/6 26/6 24/7  cm  l?8 247 334 289  1448-1525 1553-1625 1620-1652 I65O-I715 2230-2258 2305-2336  336 431 379 328  s4  975  in  157 237  s  3  S3  Values the IV  eqh.  II  D*2.  height  D.l.  at  the  the  C 2,1  All where  These IV  of  433  drag  coef f i c i ents  coefficients the  m  mean  values  Values 5  each  height  are  of  Cp are  annotated  according  determine-  them"'.  to  run, are  wind  arranged as  a  shown the  are  in  is  109 • 47.1 1320 645  1510  428  F i g .  300  122  170  126  determ i ned  summarized, to  a  same  of'the IV  measurement  in  from  Table  standard  d e n o t e d , by  the  function in  C^.,  referred  speed  2.8 128  330  459  for  356  405 375 343 2000  38JI 254 1420 1240  S9  S3  1.7 I 12  308  147 227  U  Prof i Ie  55.9  127  413 432  s  1501-1525  Runs  190 220 190  179  501 80 |60  s  25/7  30.8  131  457  s  1607-1645  Wire  0..(k)  X-wi r e  160 202 168 192 195 195 200 210 27O 265  983  S3 24/7  Hot  3  cm  sec'  2010-2034 1555-1629 2039-2122 2122-2206  1550-1605  All  -,2  U  Date  for  5  m  U^.  order mean  D*2,.and technique  in  Table  wind  speed  are used  to  hi  Table  IV D.2:  U  Values  o f GQ D e t e r m i n e d  '  5  cm s e c '  lii-5  The  0.2 1.57 2.36 .36 .5.0 0.0 0.61 0.65 0.39 1.17 0.57  1^58 1.80 0.78  Angle  two-dimensional  Profile  2.65 2.66 I .I16 1.76 2.2I1 1.95 2.25 2.88 1.77 1.35  -  The D i a g o n a I i z a t i o n  3  0||(k)  1.M  I+56 ij.08 k6k  Runs:  n  I .62 1.62 I.Ik 1.18 1.30 1.29 2.32 2; I-I 1.26  386 328 70 55 ii.08 3k3 1060 1057  E•  C xl0  X-wire  267  f o r A l l Hot Wire  '  2,05 0.73 0.58  9 of t h e R e y n o l d ' s  Reynold's  Stress  stress "tensor" is  Tensor:  discussed  i n S e c t i on I I A . 6 . Fig. II  A 6*1  IV E.I  shows  as a f u n c t i o n  the values  of f r e q u e n c y  /22/7/I965.  This  behaviour  9. I n r u n s  of  figure  typical,  9 increases  constant  value  numbers  frequency var iat i on.  but l i e s  from e q n .  X-wire  r u n s on  t y p i c a 1 a n d •' a t y p i c a I  1620-1652 a n d 165O-I715, w h i c h a r e increases,  f o r the frequencies  atypical  f o r three  demonstrates  as f r e q u e n c y  in the i n e r t i a l  one  of 9 d e t e r m i n e d  subrange.  run; in this  between about  corresponding The r u n  case  to an.almost  9 does  t o wave  1555~'625 was t h e not increase  1° a n d 1 0 ° , w i t h  with  no s y s t e m a t i c  F•  The M o n i n - O b u k h o v The  Values  Monin-Obukhov  of L ' , * t h e  calculated in  length  modified  foreach  the l a s t  eqn,  Length:  e q n . II  where  which,^air water  A><j i s  _  ^a i r -  Temperatures on Iy  the  estimate  not  included.  estimated probe  U-wires, and  would  of L '  x^.  ( o n p a g e 3^  above  t h e mean  ^a i r and "^water  )•  In  surface  be e x t r e m e l y  For the runs  in Section  degree  data  f o r most is  Celsius;  quoted  d i d not extend  sometimes  cannot  were  xj/L.'  is  the  magnitude  U-wire  any  the o r d e r  near  unity.  However,  of  a rather more  as t h e spaced  probes,  Sii  higher.  of  be c o n s i d e r e d  thus  a n d was  vertically  f o r t h e two l o w e r  runs,  measurements  three  IV A .  were  questionable  t h e same  with  at  ( t h e a i r and the  are given  was o f a b o u t  was c o m p u t e d  the r a t i o  numbers  summarized  F o r the run 2122-2206 / 2 9 / 6 / 1 9 6 5 ,  Although  temperature  and  f o r t h e r u n 1555-1629 /2O/9/1965  S 3 ; temperature  less,  I.I.  length, are  C I.3  to the n e a r e s t . o n e - h a I f  value  L'  A  respectively),  of. L '  height  B  "*"wa t e r xj  the height  was m e a s u r e d ,  temperatures  estimated  by e q n . II  theapproximation  "^5 used,  defined  of T a b I e. IV A , 2  dT  is  is  Monin-Obukhov  run using  two c o l u m n s  M C I . 3 ,  L  crude than  of 0 , 3 since  nature,  order  of  or the  the  1+5  magnitude  G.  The E f f e c t  An of  a  o f ft f  ana l y s i s  of  deviationyQ,  vertical A  estimates,  plane  0;  the effect  in  on m e a s u r e d  the d i r e c t i o n  parallel  to  of  spectral  t h e mean  the X-wires,  is  values,  wind  given  from  In  the  Appendices  I ,D a n d A I V . D .  To IV  i l l u s t r a t e  A.I)  with  a  this  small  (•= e s t i m a t e d v a l u e  effect,  average  2122-2206 /29/6/1965  met  these  and were  to  +15°  .13, a s a  fj^.-.'(f)  a r e shown  values  appropriate  i n F i g . IV  from as  changes,  eqns.  normally  ^ . . ' ( f )  /  A  G.I.  IV.l6  J0.-.(f)  From  it  is  level  frequencies  lower  Table  angle  error  9  r  Oj..  The  cr = l+.7°  best  r  G.I,  f o r each  higher  scatter  in  than  seen  0. . ( f ) about  signal-to-noise  is  0,2  the ratios ratio  to  from  spectral  j ' ( f )  IV.17, eqns,  at in  values  that  +  values  using  the  IV.10  A  10°,  and  to  plotted  oi /3 •  the proportional,  almost Hz  levels  (3 = + 5 ° ,  was c a l c u l a t e d  the three  F i g . IV  from  T h e f0.  computed  of  apparent  and  and A  functionof.fforeach  in  s t a ndard  9^* = - 3 . 5 °  with  the r e l a t i v e  levels  The r a t i o  change  the  of  caIcuI ated  f0..(f)  small  deviation  (from  c r i t e r i a .  Estimates fjZJ..(f)  r u n was c h o s e n  relative  o f ^ ) and a  run  a  (log  f>IOHz  constant  at  f~-0.7).  The  .was i n t r o d u c e d  the recorded  data  at  by these  46  frequencies. o f pf  is  0  At to  underestimate constant than  overestimate f0^(f)  percentage  this,  the  effect  on  higher  than  values  The  of  about  which on  the  proportional  in  fj^^j(f) is  but  given  in  Table  IV  G.I.  expressed  in  terms  of  the  this  again  ratios  than  IV  T a b Ie  The.  >  f0|j(f)  '0°  proportional  .  (f)  a  r  |  d  at  033 7 %  10  1.05  0.95  I .00  5  1.01  0.99  I ,00  theoretical as  are  frequencies  +  for  ' 5 °  ' J  I .01  calculated  i  changes  0.89  ratio  is  frequency-dependent.  5°» i  0. .'(f)/0.  The  frequencies  1.10  The  lower  P* 0:  Effect  ^II'/^T  The R a t i o  ratio,  a  + 15  ±  H.  almost  Hz,  0,2  G.I:  to  frequency,  iJ  h i gher  effect  frequencies  at  being  fory9= +  These  the  frequency-dependent.  below  changes  by  At  negligible  amount  and  case  on y9* is  Hz,  0,2  values.,  each  depends  Hz,  than  f0||(f)  f0|^(f)  0.2  with  higher  values,  effect  overestimated,  are  frequencies  of  -  0^/0\\  0jj/0n a l l  in  X-wire  predictions outlined  in  for  A l l  X-Wire  Runs  t h e " i s o t r o p i c" wave runs.  for  the  Section  II  This  was  numerical A.5.  number  done value  to of  range  check this  was  the  47  Table for  each  average  H.I  X-wire  frequency  9^T =  Table  1965 Date  21/6 20/9 29/6 29/6 22/7 22/7 22/7 22/7 26/6  26/6  /  the  estimated  H.I:  by  Hz  20  V  the  was  to Pond  was  set  B).  the  <Tf  G)  The R a t i o  /  0  I65O-I715 223O-2258  2305-2336  (1963)*  ( f )  of  was  was A  n  above upper  noise  suspected  that  produce  predicted  value  angular  included  M  f o r the  for  in  and  deviation the  X-Wire  table.  Runs:  033/01 I  Run  2010-2034 1555-1629 2039-2122 2122-2206 1448-1525 I553-I625 1620-1652  it  may  Time of  al  ratio  minimum,  This  because  measured  were  the  the  computed  et  Since IV  of  kx^>IO.  theoretically  observed, error  values  determine  ratio  (see Section  0  between  actually  to  corresponded  about  and standard  IV  order  (see Section  of  discrepancies value  of  the measured  values,  which  limit  effect  In  limit'  considerations  the  r u n .  range  'isotropic  the  outlines  a n d maximum  frequency the  IV  M i n i mum  <7"r  9.6 -2.7 3.5 -3.5 6.8 3.5 9.9  11.3 I.7  -2.8  0.86 0.97  6  It 7  I3 I l  35  7.1  7.9  I .06  1.08 0.75 0.62 0.87 0.96 0.55 0.58  Average  0.95  1.04  1.12 I  .14  0.82 O.69  0.9.5 I .00 0.67 0.6&  Ma x i mum  1.05 1.15 1.18 1.2. 0.8 0.82 1.02 1.09 0.75 0.82  kQ  V.  DISCUSSION  A,  Wind  AND  CONCLUSION  Direction  Mean  wind  displayed  in  summarized  The standard  data  Figs.  in  F  and  are IV  Tables  test  Cup  described  A.I IV  to A.I  (Fraser,  errors  directions  and  Data  Section  IV  Numerical  A.,  and  results  are  ,2.  PP  (see  CT  P  in  .13.  1958*  and  ty  Anemometer  was  IUI4--U4.6) Table  IV  A.I)  applied of  to  the  the  wind  3  measured  at  the  mast  and  instrument  hut  2 respectively. exceeded in 1$  k  that  cases;  level.  have  of  the  at  can  runs the  just  2  vanes  level  5$  exceeded  the  to  the  spatial  wind, be  F  ratio  (  /  0^  =  CTg  (95$  confidence  level)  that  allowed  the  have^ d i f f e r e n t  reasonably  regarding  tested,  response  such  a  expected;  homogeniety  at  times,  difference however,  and in  no  can  be  drawn  there  is  no  from  data. It  is  clear  relationship of  the  s t a b i l i t y HambIin'  slopes  of  conditions. (I 9 6 5 ) • of  sections  same  from  between  exception  linear the  li,  ten  exposures  variances  these  the  the  Since  conclusions  the  allowed  different  their  nor  Of  2  s i t e .  None the as  Table the  A.2  that  linearity  of  approximately This of run  found  Also,  IV  no  the  is  in  profiles  Iinear keeping  measured  with  p r o f i Ies,  obvious  often  (denoted  p r o f i Ies,  2305-2336/26/6/1965, reasonably  obvious  by  relationship  the  by  L),  and results  with exhibit  Hamblin exists  of  perhaps two  (I9&5) between  at  )  k9 the  slopes  of  the  linear  profiles  and  mean  wind  speeds.  p Much from  of  non-linear  probably  due  differences only  \%  error  and  wind  B.  near  B.I.  adjacent  of  N in Table in  speed  This  For  and  IV  of  each  the  A,2),  is  small  speed error  of  can  produce  an  speed  between  the  cup, in  case,  a speed  estimated  example,  difference is  u-«-  determining  cups.  the  of  for  an  example,  d i f f e r e n c e of  in a  10  cm.sec  in concord  with  earlier  workers,  that  of  (and  hence  drag  c o e f f i c i e n t s CQ)  from  very  unreliable.  stress are  should  U-Wire X-  values  conclude,  estimates  and  displayed  wire  the  l\. m . s e c " ' ,  profiles  X-and  (marked  inherent  100$  profiles  direct  in  cups.  must  summarized hot  between  estimates  The and  errors  third cups.  non-linear  with  profiles  to  the  One  linear  scatter  indetermining  between  the  large  approaching  second mean  the  in  be of  more stress  from  these  X-wires  are  from  the  compared  in Section  V  D.  Data U-wire  data  in F i g s ,  IV  Table  B.I.  signals  Performance  Comparisons  reliable;  Estimates  are  of  of  IV  are  B,l  to The  described  X-  cup  and  described .llj..  in S e c t i o n  Numerical  techniques  of  Appendix  IV,  in  IV  B,  results  are  analyzing  the  U-Wires  anemometer  and  U-wire  spectral  values  50  were  made  values  by  more  by  et  from  up  to  (19^5) •  al  showed  that  measurements  at  from  the spectral  values  cup anemometer  and measuring  Pond,  These  U-wire  35$  precise  calibration used  Pond  derived  differed much  by  and since  data.  techniques  my s p e c t r a l  low  Since  were  spectral  frequencies derived  my  U-wlre  similar  values  of  from  to  those  0||(k)  conform  _5/3 to  the k  IV  B.ll  to  by  Pond  (1963, I9&5)  have  behaviour  within  about  the IV  is  B.I  (f0|j(f)) shape runs.  those  the  level  that  from  measured  measured  levels  is  about  IV  B,2),  be  expected,  measuring  by  As  was  from  levels for  by  half  35$,  noted  absolute  in  consider  winds.  E.2),  confirmed one c a n  measurements  give  which  are  As  the r e l i a b i l i t y  c a n be s e e n  U-wire  both  the r u n s . maybe  well  are not  B,  probes  higher  or  are  spectral  than  between ( F i g ,  behaviour  instruments in  runs,  lower  difference  this  good  The agreement  in  for a l l  1555-1629/20/9/1965 IV  Figs,  For the other  T h e maximum  Section  agree  measurements  from  from  of  fluctuations  measurements  the run  hot wires  been  Figs.  ones.  the U-wire  for  (see  fluctuations  obtained  the X-wire,  since  spectral  the downwind  X-wire  obtained  t h e same  of  has  (see Section  precise to  subrange  which  measurements.  The s p e c t r a l  essentially  A.5)  the downwind  instructive  obtained  with  II  my U - w i r e  the spectra  .10,  inertia I  others  d  the  spectral  to  n  for  °f  35$  also  X-wire  a  that  estimates  It  the  .lli.and S e c t i o n  confidence  spectral  in  is  .  to  for shapes  51 (for  f0||)  from  confidence whole  that  been  The  measured  subrange, Figs.  IV  B.ll  confidence  over the  the  the  total  in  (b )  unreasonably  large  f0|^(f),  being flux  real. of  that  This  added,  the  to  changes  negative to  and  added  gives  inertial (see  provides  f0|^(f)  are  As  will  be  in  the  wire  factors  (K)  zero  values  the  the  downwind  added  measurements.  of  produce  conformed  but  measurements  behaviour of  the  in  Sect.  of  9,  indirect at  the  high  angle  "pseudo-tensor"  constant one  so  order  the  in  This  analyzed.  V B.3,  have  behaviour  A.5).  the  estimates.  k  X-wire  calibration  in  be  one  over  U-wires  (of  0^{k)  values  range  properly  the  to  gives  must  be  to  to  the  be  values  considered of  the  from  have  positive  expectations weight  seen  would  or  negative  as  downward  confidence  in  r e l i a b i l i t y  of  measurements.  An X-wire  and  T  momentum  X-wire  spectral  Section  of  II  of  probes  spectral  enough  Section  frequency  since  predicted  r e l i a b i l i t y  measured  discussion  levels  the  wire  operated  reliable  small  .lij. and  coefficients  of  give  exhibited  the  All  to  hot  interest,  scales  to  in  of  of  probes  spectral  at  again  types  X-wire  range  shown  fluctuations),  two  the  frequency  already  the  where  indirect  IV  E  value  (see in  significant confirmation  F i g ,  IV  variation  Sect.  E.I),  9  was  provided  of  in  subrange  the  is  orientation  inertial  of  of  frequencies  described  also the  of  indication  the  II  for  noted.  a l l  This  the  principal  A.6.  reached  by  As  an  was  axes seen  almost  runs, gives  excepting  52  the  proper  operation  one  questionable  was  anomalous;  of  run.  in  the In  all  X-wires,  that  other  run,  with only  respects  the the  exception  of  behaviour  the r u n appeared  to  the  of  9  behave  normally.  It•  appears'  operation spectrum But at  the most  ones. in  of is  the  properly  data  suitable  data  be  to  used  U-wires all  can  then  be  of  the  (see u-"-  probability  2  may  level  be  in  about the  frequencies cup  levels  give  since  anemometer VI), error  for  obtained  to  that by  approximating  of  spectra  can  recordings, the at  spectral  the  0.95'  most  more principle  wire X-  not  it  to  made.  and  spectral are  precise  proven  in  both  precise  to  outlined  much  hot  from  the  were  the  the  X-wires.  the  have  from  each  (within  wires  which  of  the  to  25$)  hot  the  shape  close  anemometers  calibrations  in  and  thus  IV,  measurements  the  U-  analysis  Appendix  However,  Section  within  of  adjusted  cup  the  the  reasonably  procedures  low  that  by  for  in  confidence  and  procedures  from  relative  from  assumed  at  f i e l d  frequencies.  available  values  derived  the  only  spectral  values  have  both  probably  the  the  obtain  responses;  are  outlined  for  precise  be  most  and  I,  can  measured,  The- c a l i b r a t i o n  Appendix  we  equipment,  levels  and  35$,  Spectral  at  X-wire  relative  rerecorded be  then,.that  values yet  will  levels  about  35$,  simply and a  ^  a  53  B.2.  Spectra  Both by  eqn*  "Low  have  one  of  the s p e c t r a l A  II  1.2,  while  and  is  0\\{k)  Figs.  a  general  from  upward  A  1.2)  displayed  estimates again  from to  at  n o t be  s t a b i l i t y  of  lower  frequencies,  the s p e c t r a  as  f o r  predicted IV  against  log  ^-5/3  B.ll k  expected  shapes  that of  will  the to  to  behaviour  (1963);  extends  from is  inertial  .15,  showing  to  the k  much  li-.5»  observed  discussed  J  J  larger  by  further  to  have  But  increasing  y  /  At  of  scales  high  behaviour  y  log  l a w , show  II  (  that  limit conforms  V B.I4..  A.5).  0| (k) the  (smaller  workers  in Section  three  spectral  may b e  isotropic  other  anaI yzed.  tend  (see Section  T.hi s • f e a t u r e  —2 '  s i nee the  plots l  that  of.-Uj  analyzed.  the k  four  so  the  which  analyzed.  subrange  the e s t i m a t e d  kx^^>  .10,  values  those  I.I.  f0||(f)  those  are  frequency  exhibit  demonstrate  spectra be  and  lowest  a l l  than  frequencies  than  A  the value  behaviour  ,7,  defined  I Hz.  to  too s i g n i f i c a n t , the  e q n . II  the spectra  lower  general  lowest  by  are  low f r e q u e n c i e s ,  Low, a n d t h e s p e c t r a l  frequencies  Figures  .10,  frequencies  B.3,  f0jj(f)  under  contributions  IV  the  those  towards  this  ^33)  defined  to  B.I  trend  Figs.  may  is  at  in  values  f a l l - o f f  IV  significant  exceptions  s t a t i s t i c a l  and  f0||(f)  seen  decreasing  than  and  As  Possible  this  values  (f0\\  are considered  e q n . II  runs  Energy  frequencies"  can expect  (see  Kinetic  of  k),  Pond to the  51+ As versus  seen log  measured zero The  from  f  exhibit  curves  values  In  maximum  frequencies The  occurs  showed  that  Since  in  shear  flows  ^ *2*  Spectrum  implies  in  of  seen  wind  tunnel value  f  ts  the  the  the at  et  by  toward  of  the  frequency  contribution  to  the  vertical  0,0l6  O.I  than  and  the  the  IV  is  60  and in  Hz'^  10  analyzed.  Hz.  The  u^-veloclty  the  and  B.I  at  lower  Is  scale  of  layer  (I96>5) my  (and  sizes  boundary  much  larger  directions. in  noted of  turbulent  in  f0\^(f)  at  Section were  observed.  downwards,  had  which  (f0|^)  frequencies  did  the  wind  surprising.  values  measurements  I Io t as  A,li),  made  hardly  ,10,  spectral  II  wind  were  f0j|(f)  the  to  vertical  of  with  (Section  Transfer  to  curves  keeping  mean  or  this  the  distance  transferred  range  2-3,.  In  observations  smallest  Comp t e - B e kx^-  of  the  lateral  observed  boundary of  Iy  ends  (1957)  al  Momentum  momentum in  three  both  thus  a boundary,  of  of  fft^if)  range  'maxima'  the  from F i g s .  that  same  Favre  cases  even  recent  the  log  the  near  fluctuations ;<-The  of  either  both  the  monotonicaI  fluctuations  d i r e c t i o n of  those  negative,  the  of  of  frequency  about  in  than  all  the  larger  scales  V B,l),  of  eddies  have  the  toward  between  against  results  of  curves  0||»  behaviour  tunnel  shapes  decreasing  ends  most  the  ,10,  smoothest  curves  to  to  between about  0^^ «  f05^(f)  As  both  that  occurs  B.t  f0jj(f),  contribution  component  IV  the  these  indicates  fluctuations  and  of  toward  decrease  range  Figs.  This  least  by  observed. at Rf5=2„3xlo5  made  k0^j  peaking  measurements.  at  in the  a  55  It  was  decided  negative.and the or  stress  A  the  they  (discussed wire  small,  at  whether  in  or  mean  change  b'  The  and of  G.I,  feature is  is  !  depends  on  the  horizontal.  Checks  that  b  the  geometry  remained  one in  a of  the  on the  the  spectral up  to  change  change over  o f  ail  factor  K  estimates on  as  wires  calculation 13%  the  as  of  X-array  at  15%  In  the  one  10%,  an  wire  and  of  one  to  zero, data  low  an  high  in  led  wire  summer  X-wire  wire to  of.  probes  change  of  The change  required  to  reduce  examined  by  doing  frequency  for  used  showed  to '  a  A  run  and  to  similar  that  a  maximum  one  simple  of less)  spectral  n  in  b'  I Hz),  I Hz).  some  the  showed  (or  showed  5%»  the  I.C).  (above  led  The  I 9&5  changes  10%  G,!  IV  to  coefficient  (below  c o e f f i c i e n t - b '  each  Section  each  frequencies  analyzed.  was  one  the  alignment.  Appendix  frequencies  average  wire,  at  15%  the  significant  \l\k&-1525/22/7/1965,  run  frequencies  observed  at  (see  in  errors  of  i n  r u n 2101-2034/2I/7/I9&5  large  level  for  of  the  of  (see eqn.  X-wires  improper  the  K  to  real,  estimate  no  of  were  result  factor  that  by  on  unchanged  a  the  the  inclination  wires  observed  contributions  discussed  throughout  data  :  change  changes  of  essentially  Calculations that  made  of  evident  introduced  the  as  in  c a l i b r a t i o n  misalignment  it  of  zero  introduced  the  of  frequencies  from  be  of  a l l  highest  could  value  0^  VI)  latter  IV  and  biassed  Appendix  F i g .  in  be  whether  non-zero,vaIues  lowest  because  wind.  and,from  but  may  coefficient  1.10),  to.check  levels  c a l i b r a t i o n ,  spectral calculations  56  223O-2258/26/6/1965.  The  factor  over  K  less .  required  than  +  3%  was and  (seeAppendix.Vl), unreasonable thus  show  in  that  spectral  the  the it  values  of  K  20%.  above  in  Since  in  at  b'  experience.  as  calibration  errors  in  unreasonable  f0j^(f)  the  than+||% changes  of  not  change  less  light  is  of  least  b'  the  and  95%  K  level  appear  These  to  are  calculations  consider  all  of  the  s i gn i f i c a n t I y r . n o n ' z e r o  being  and  negative..  flat  The  spectra  and  have  about  0.01  range to  of  broad  to  amounts'.of  fj#|^(f)  I  Hz  There  IV  B.I  f0  to  (f)  are  almost  than  10  above  to  0.5  of  wind  .10,  it  spectra  the  sea  surface,  is  in  of  and  seen  this  it  to  log  no  frequency  is  f  between  over  to  a  Figs,  the  waves -0.7  with  to  note  between  -0.3)  for  From  Figs.  occur  the  at  is  fall to  peaks  B.I  stress  encountered.  range,  IV  instructive  =  obvious  wide  turbulence  dominant  fetches  that  the  f a i r l y  significant'  (see  contribution  (equivalent  speeds  that  decades  Since  remain  range  downwards  two  Hz.  frequencies  Hz  showing  transferred  of  stress  frequency  runs,  higher  estimated  range  most  kinematic  the  l i t t l e  that  0.2  in  very  just  the  the  is  measured  the  for  frequencies  frequencies  about  maxima  momentum  .10).  of  in  the  exception  13 of  two  more  runs  pronounced  stress  is  however, is  /29/6/1965  on  maxima  present the  present  at  in  larger  (Figs.  near  this  these  which  of  8.3  and  which  frequencies.  frequency  proportion  frequencies  IV  interval  the  are  lower  Significant  in  totally than  have  every  observed wave  run; stress  frequencies.  57  The  spectral  regularity highest  in  shape,  frequencies  frequencies, significant  However,  with  lower  at  significant  values  is  of  drop-off Thus  further  show  contaminated  by  a  channels, coherent.  The  for  the  and  from  s t i l l  arise  from  analyzed.  runs  (Figs.  and  the  1448-1525, B.5,  reliable  in  IV  .7,  and  in  all  Moreover,  may  p o s s i b i l i t y  than  scatter  decrease that  lower  larger  p a r<t s of  proportion  derived which  about  because  frequencies  spectra (Figs.  extending  runs  I east  the  lowest  stress  interval  the  slow  of  general  at  there  s t i l l  may  be  frequencies  are  the of  the  -  20  Hz,  by  signals  contaminated  the  recorded  noise.  obtained  from  are  10  by  spectral  signal  Values  of  subtraction from  both  noise  was  of  two  wire  which  may  be  .  conditions maxima  high  both  the  ho  toward the  most  established.  is  higher,  to  e qua I  that  show  investigation.  began  a I mos t  towards  Reynolds'  in  are  well  contributions  at  the  frequencies,  not  frequencies  f013(f)  confidence to  values  t o w a r d  ;  estimates  frequencies.  At.  drop  1650-1715 / 2 2 / 7 / I 9 6 5 ,  and  rate  requires  a I I  ^ (f)  in most.cases  some  lower  drop-off  the  t h e -f0j  frequencies  spectral  I62O-I652,  runs  for  contributions  s t a t i s t i c a l l y  the  but and  giving  fluctuations  ,8)  curves  where  of IV to  Reynolds' B.l,  stress  .2,  larger  near-neutral  .5  scale or  to  observed .8  sizes  stable  and  in  ,10)  (smaller conditions  unstable have k)  broad  than exist  those  58  (Figs.  IV B . J , . i i ,  prediction produced those  values  by c o n v e c t i v e  A Ii3)  than  a l l runs  is  (<.I5)  than  half  imprecise  field  B.lj.  -O.73  about  IV B.I  larger  the runs,  near  /21/7/I965,  .5).  decreases  increases  of  values  to  5 or  increases  greater at  -0.2  and  near  value  -0.5 to  to q u i t e  '0  small  Hz, but f o r  towards  is believed  by e q n .  The e x t r e m e  and v a l u e s  IR|^I  increase  compensation  than  (defined  a l l numerically  and  the v a l u e  This  scales  I Hz s a y ) , o b s e r v e d  ( F i g . IV B . 3 ) ,  as f r e q u e n c y  stress,  stress.  20IO-203ii.  F o r a l l r,uns  still  t o be d u e t o  t h e two h o t w i r e s  under  conditions.  Evidence  f o r Non-Ext stence  A discussion anisotropy  II A 6.1a  in Sections  at very  eddies, holds,  it  of  Isotropy  the s t r u c t u r e  in general  turbulence  isotropic  of  is given  predictions the  at  are the smaller  (Figs.  • h i g h e r ...frequence es . the  occur  and a l m o s t  i n the runs  a r e common.  more  (below  Two e x c e p t i o n s  liuV8-i525/22/7/l965  values  produced  are a l l negative  0.3«  -0,6  to the general  the c o r r e l a t i o n c o e f f i c i e n t s R'j^(f)  low f r e q u e n c i e s  for  conforms  to the turbulent  effects,  low f r e q u e n c i e s of  This  contributions  of m e c h a n i c a l l y At  il  that  and .9).  have  of  II  been  A,3  based  smaI I s e a I e s  is predicted  so t h a t  is  at Small  turbulence to ,5«  Scales  and of  Theoretical  on t h e a s s u m p t i o n isotropic.  that 0  =0 5  In  and t h a t  i f 0, , ( k) <x k" ' °, '  that  then  equati  59 =  (4/3)0||•  limit' the  has  been  eddies  (Pond  et  that  are  a l ,  present  At  for  and  it  to  be  be  scale  near  a  boundary  near  a  wavenumber  isotropic sizes  expected non-zero  observations  are  unless  larger  'isotropic  is be  flow  to  the  will  f0|j,  shear  estimated  1963).  anisotropic  The  a  unlikely  estimated  stress,  In  at  k  in  the  that  4.5  k)  than  turbulence  lower  accord  such  k x -^y  contributions  these  well  'isotropic  (smaller  l i m i t ' ,  that  an  to  is  the  wavenumbers.  with  these  predictions.  My range  measurements  of  frequencies  are  described  .10  and  of  Figs.  values  highest is  in  not  reached  be  is  from  about  5  f0l1 o r f 0  5 5  .  10  displayed  B,  all B.3  V  at  it  runs  are  above  the  as It  of  anisotropy  more  IV  times  in  be  four  over  a  decades,  Figures  that  IV  B.I  to  is  the  appears  that  sizes, than  smaller  .10, than  at  nonthe  isotropy  (largest  the  r e l a t i v e l y to  the  negative even  scale  all  Calculations  real,  higher  B.I  seen  that  being  smallest  Figs.  almost  non-zero.  thus  wavenumbers  or  can  showed  at  in  of  spe'ctrum  B.3,  .10,  analyzed.  R|j(f) to  IV  considered  even  amount  sizes)  to  for  However,  the  are  B.I  (stress)  scale  Section  Section must  limit', seen  IV  frequencies  observed.  (or  in  f0|j(f)  the  Section  fjZf.-Jf)  discussed zero  in  discussed  From values  of  values  or  'isotropic  small;  values  k  of of  as f0 ^(f) (  6o  The region  data  for  which  isotropic X-wire  of  so  runs  average a  single were  0.6 from  IV  G.2,  kx^  10  and  where  serious.  ratio  a  estimate  more  merely  in  by  Q%  of  the  the  were  behaviour  and  of  in  of  a  V B.3), also the  most  equations  at A  a  change  of  (Eqn.  A  IV.i),  produces  0^^/01|.  Since  in  The A  in  range  was  effect  in  that  were  estimates  a of  too than  in  the  change  of  0.5P$  b'  better  of in  than  in  changed analysis  f0 j^ — 0 , K|  wire  Calculations  0 ^ / 0 1 |  factor  it of  discussed  and  10.)  the  whether  Furthermore, I  was  kx^ >  considered.  ratio  computed  (which  whether  changes  the  are  were  techniques  (partly  0^/0^^  ratio  around  not  or  b',  calibration  only  the  of  frequencies. for  a  real, by  as  greater  check  of  runs,  Pond's was  be  10  ratios  k x ^ ^ l O  be  to  the  ratios  noise  to  maximum  low  than  to  of  three  as  the  expected  The  above  order  I.10)  For  ratios  had  from  average  0.7.  by  ratio  showed  that  of  P$  ratio  change  IV.15  had  one.  introduced  high  that  the  signal  this  15$  show  requirement  made  Eqn.  be  than  and  chosen  might  ,  to,  cases,  of  analysis. 1  (  frequency  effects  (b ,  effect  at  all  (SignaI-fo-noise  coefficients  Section  I .24  (  were  runs  less  stringent  reflected  the  equal  was In  which  four  just  contamination  measurement  of  or  was  which  = [l\./~5)0 only  than,  Calculations observed  0^  observed.  as  >  analyzed,  observations  chosen and  Table  that  greater  033/011 the  in  shows  K 2 the +  I\%  ratio at  about  61  the  level  95%  changes  of  necessary  ratios  of  of  (Section  I4./5  probability in  b'  (see  0^/0^ II  and  (see K  IV  Table  A..5),  in  order G.2)  appear  VI),  Appendix to  to  then  bring  the  the  the  observed  theoretical  unreasonable  level  in  the  light  of  G.l),  the  effect  exper i ence.  As  seen  misaligning not  equal  ratio  in the  to,  0^/0^  observed  of  of  in  or  very  close  at  the  ratio  the  would  which  shows  0^/0]j quite  be of  ( those  (5°)  Indeed,  if  reduced the  to,  so  would  frequencies.  or  observed  is  observed  values  for seen  = j3  of  from of  the  wind  a l l  i n  the  15°, the  from  the  the  values IV  Table  the  1.0) w e r e  9~  decrease  mean  values  than of  to  of  was  9~|T = /3  However,  the  account  less  be  20%.  of  This  that  F o r f3~  almost  direction  smaller  close  wind  zero,  observed.  the  small.  to  IV  F i g .  mean  (0"") c a n n o t  ratios  that  (and  the  high  X-wires  the a c t u a l  G  X-wi re  observed, .deviationsplane  IV  Section  H.I,  ratio  associated  over  half  with  the  cases.  maximum'probabIe in  estimating  also  if  one  possible factors  took  values  maximum  allowed  changes (K),  one  a  in  a  liberal  o f ^  adjustments liberal  wire  is  found  /29/6/1965)  is  it  reasonable  ratios  conform  with  that  the  in  those to  adjustment  for tc  expect  predicted  for  ratios  two  and  value  each  to  run, and  allow  calibration  runs  that  the  j^j/j^M,  (^15%)  (b')  only  estimating  observed  the  coefficients  it  might  from  view  the of  (both  on  observed I4-/3.  The  for  62 observed  behaviour  interpreted the  as  that  the  we is  not  the  Since  the  is  reached  in  the  wavenumbers  supported  by  the  V  the  stress From  of  log  those  has  also  Pond  et  B. M  against  follow  the  to  by  k, |  a  \  can  0  m  u  c  h  e a r l i e r  1965).  Pond,  are  the  the  prediction  k""^/^  that  isotropy  is  d e f i n i t e l y f0|z,(f), values  of  zero.  that  the  scales  (Grant in  0  plots ^{k)  (smaller  isotropy.  seen  then  within  representative  seen  of  was  for  0^ ^  spectral  workers  As  of  spectra  larger  considerations by  view  the  be  structure  for  and  became  which  be  fluctuations  that  never  it  w  of  must  assumed  showing  This  seen  .li|.,  log  noticed  1963;  al,  is  that  of.  thus  the  required  as  f i e l d  runs  that  isotropy  behaviour it  k~5/3  allowed  been  of  frequencies  IV  from  examined.-::-  where  high  Figs.  0 j .(k)  spectra than  at  that  observed  B.3),  way  observed  other  suggests  observations  of  Sect.  all  assumption  was  range  (see  some  only  the  in  This  in  I4./3  interpret  ratio  r e a l .  differs  ratio  must  the  being  turbulence  prediction.  of  This  et  a l ,  II  Sect.  k),  behaviour 19^2;  A.5,  the  -5/3 k  law  for  using  the  assumption  ments  indicate  so  J  l  J  that  the  the  inertial  that  of  isotropy  anisotropy  assumption  unnecessarily  subrange  of  stringent  (plus  is  isotropy  II  (Eqn.  never  one  was  derived  other).  My  measure-  absent  appears  c r i t e r i o n  A3.I)  for  to  (at be  any  scales),  an  the  -::- T h e m e a s u r e m e n t s o f 0-z-z o f Comte . - B e I I 01 (1965) w e r e c o m p a r e d c to those c a l c u l a t e d from (assuming isotropy). F o r R e =2.3xl0 measured values were less than c a l c u l a t e d ones f o r k x z > ! } . by about 35$. T h i s g a v e 0T>T)/0\\~ O.9. O t h e r r u n s a t l o w e r R gave s i m i l a r resuIts.  0\\  e  ,  63  prediction  of  Direct  C.  and  C . l ,  the  and  the  -5/3 J  l  law.  J  Indirect  Drag  Direct  k  Estimates  Coefficient  and  Indirect  of  the  Kinematic  2  Stress'u-*  ,  Cp  Estimates  of  the  Kinematic  Stress  u-»-  p  Directly hot  wire  from X-  runs  p r o f i l e  and  and  indirectly  are  described  data  U-wire  are  data  estimated in  Section  summarized  in  Table  values  IV  in  IV  Table  B.I,  and  A  of  to  IV  u*-  IV  C,  A,2,  those  for  all  Values  those  from  from  the  three  2 vertically  spaced  are  for  listed  between values II  estimated  D,2)  and  plotted  the  X-wire There  from  the  appears  IV  C.  Table  IV  D.I.  F i g .  from 0^  to  be  the  D.I). the  l i t t l e wind  With line  the  at  The  results  V  A.  u*-  figure,  (Section  (Section  measured  are  thus not  and  exception 0  average.  Section  of  this  p r o f i l e  correlation  ij.5 ),  d i r e c 11 y • m e a s u r e d  profiles  In  spectrum  profiles  the  wind  values  Comparisons  D.I,  wind  values  estimates  on  the  \k)  against  IV  All  II  D,|)  d i r e c t l y  using  I V B ) .  from  above  Table  in  indirectly  (Sect ion  IV  in  shown  separately  (Fig,  points  are  those  determined  X-wire two  comparison  estimates  are  u-"-  U - w i r e s i n  the  stress  demonstrate  very  r e l i a b l e ,  between  those of  by that as  from  the  p r o f i l e  values  two  runs  noted  (the  underon  estimates was  the  method  about  of  the based  in  2  64  As  can  indirectly  be from  the  inertial  but  (except  measured the  I inear  the  (Moroney,  so  of  effects  the  more  fact  the  wind  the  p r o f i l e  mechanically  (b)  f i r s t ,  of  is  clear  holds  one  such  and  produced of  values  of  u*  ,.  (b)  than  of  test  the  of  profile  D.I,  that  the  valid rate  [6),  eqn.  when of  energy  the  the  two  that  Iy  the  different,  are  not  the  methods,  spectrum  method,  despite  stress.  II  the  0.53*  indirect  overestimation?  is  to  showed  two  form  were  error  profiles  the  is  overestimations,  an  energy  argue  F  of  which  A,2)  significant  the  the  turbulent  turbulent could  the  the Kolmogoroff  Section  values  of  that,  overestimates  of  average  not  runs  standard  with,  ratio  estimate  IV  in  directly  the  those  l44~l46),  1958, pp  of  Table  with  and  the  direct  in  two  It  cause  L  correlated  than,  only  0||(k)  spectrum  value  the  the  linearity  if  could  dissipation  to  to  on  the  estimated  strongly  If  1.34,  due  consistent  assumptions  estimate  was  227-233),  based  that  What  to  0\\)  (marked  test  of  The mean  0 v e r e s t i m a t i o n s were  technique  gives  t  values  all.greater  0,42.  (Fraser,  distinguished. the  values  are  error  D.I,  evidently  (from  ratio  pp  errors  average any  run)  IV  stresses.  the  1962,  are  profiles  average  Application  two  one  standard  exhibited  standard  subrange, for  F i g .  observed  estimates  with  used,  from  the  kinematic  former  I .1+2,  seen  According I I  (a)  D  I.I  the  used  of  equals  rate  Considering lack  of  to  logarithmic  production the  to  balance  of  assumption between  65  mechanical  production  estimation. II  C  dissipation some  other  energy  rate  would  source  it  energy other-  Hess  and Panofsky,  above  by  the  so  that  as  a  method  of  not  not  a  of  to  IV  2  i t .  u-»  Hence  of  the from  in  one.  in  different  U plotted  Ief t-hand it  is  from  as  was  that been  biassed  against be  and  has  not  figure),  has  the probable  ft  must  However,  and  120-125;  Also  (a)  both  production  pp  and  turbulent  that,  overes11 m a t i o n  well;  half  one can c o n c l u d e  assumption  D.I,  A 5«'  budgets  shown  i 96!+,  good  of  II  produced  energy  this,  fairly  not  estimated  underestimated  have  over-  or .advected,  significantly  From  the p r o f i l e  F i g .  about  energy  and Panofsky,  is  or  of  the  eqns.  be p r o d u c e d  the overestima11o n .  (see also has  are  the degree  conformity  before,  to  mechanically  1966).  above  that  of  to  equal  conditions  (see Lumley  linearity  cause  energy  estimates  that  dissipation  (b)  from  to  the mechanically  However,  appears  leads  c a n be shown  besides  each  assumption  dissipation  have  and non-neutral  general,  shown  it  turbulent  source.  neutral  and  However,  that  1.1  and  log  x^,  excluded noted  the  profile  consistently  cause  of  the  over-  2 estimation  of  u-"-  underestimation  from  by  t h e 0\ j  the p r o f i l e  (The  logarithmic  profile  appears  C.2.  The Drag  Coefficient  spectra I method in  va I ues  of  is  measuring  e q n . II  D  a  height  of  of 5  the drag  stress.  CQ -  coefficients  m a r e shown  general  I.I.)  2 Values  the  in  Table  IV  C  D  =  D..2,  2  u-"- / l l ^ and are  adjusted plotted  to  66  against IV  wind  D.2.  Values  scatter. greater  than  two  values  estimated  from  t h e 0||(k)  The  mean  calculated  directly  trend  were  necessary  wind  from  discernible  if  from  those  CQ  (extrapolated  calculated  Values  Values no  speeds  with  observed  from  profiles  direct  at  wind  are  )  F i g .  n  generally of  appear  speed;  higher  '  large  estimates  wind  speeds  m  show  estimated .stress  increasing  to 5  stress.  to  have  however,  than  only  m sec ' .  J4..6  ~3 value  is  I .I4.5  x  ,  10  and the standard  error  of the  ~3 observations A  is  substantial  range (see  part  expected Section  range  0.ii2  of  V.B). is  few ( t e n runs)  the  mean  of  Indirectly method,  trend  error  speeds  from  mean  values  speed  hot  I4. m s e c These  the  the  35%  total  direct are  s t i l l  estimates  of  speed.  Cp, using  the wind  values  0\\{k)  D),  values.  wires,  ',  the X-wire  wind  the spectral  wind  from  from  s t a t i s t i c a l  of  II  for ten  arises  two.  using  r e l i a b l e  (see Section  increasing  near  of  coefficient  with  t h e mean)  derived  factor  to give  of  probably  vaIues  a  estimated  subrange  with  about  any trend  and those  inertial  this  F o r wind  the drag  too  or  of  (~35%  in spectral  in values  estimates  10  x  also  of  showed  in the  no  f o r the ten X-wire  profile  obvious runs.  -3 The  profile  method  gave  a  mean  value  of  0.89  x  with  10  -3 standard  0\\{k)  error  spectral  standard  error  of  0.66  values of  O.53  x  gave x  (~75%  of  a  mean  value  -3  (~25%  10  10  of  t h e mean) of  2.10  the mean).  and the x  10  with  a  67  It  was  then  decided  to  apply  determine  whether  these  values  Cn  s t a t i s t i c a l l y  of  were  test  was  applied  test  can  be  found  that  observed  found all  profiles, under  a  from  d i r e c t l y  the the  three were  I ),  same  standard not  pp  I  of  1 i+6.)  Moroney,  values  of  measured  stress.  before. errors^  the  Iy  F  From  Cn  227-233*)  by  dtfferent  the  The  the  at  test  can  be  these  two  tests,  of  the  5$ in  one  this  was  at  from  the linear  obtained  Cn  F  three  the  found  of  c r i t e r i o n  result  of  t  indirectly  profiles  values  that  the  different,  from  AppIication showed  three  It  and  estimated  (chosen  against  the  F i r s t ,  directly  estimated  to  (A.description pp  of  tested  significant  description  values.  conditions  in  s i g n i f i c a n t .  were•significantIy  those  tests  differences  comparisons  were  as  J .  check,  near-neutral 0.  mean  M.  Cn  also  I xz/L ' I <  was  in  for  As  and  the  cross  means  level.  0.1$  to  observed  s t a t i s t i c a l  estimated of  these  test  to  D. A . S . must  the  standard  level.  tests  errors  (A Fraser,•  assume  that  1958, the  2 three  methods  significant  of  differences  determinations interpreting determining The lower  Section  of  II  Cn.  results  u-"-  between Hence,  from  the  give the  s t a t i s t i c a l l y corresponding  one  must  exercise  two  indirect  care  methods  when  of  stress.  directly  wind  determining  speeds  E.I|-),  measured than and  drag  those  coefficients  found  seemingly  do  by not  most  are  other  exhibit  the  higher  at  the  workers.(see increase  68  with  wind  drag  c o e f f i c i e n t measured  by  speed  Zubkovskii  wind 0.6  speed  found  by some  x 10  prof i I e measurements  D.  Data  spaced  U-wire  similarity numerical itself  from  values  The  wind  approximately the  two runs  /25/7/I965* reasonably II  C  used  in Section  to check  II  s  c  e  .  speed This  from is  keeping,with  (see Section  II  E.I4.).  three  vertically  :  IV C , a n d  IV C .  The t h e o r y  IV A . I I  to .13) a r e  B«  (Figs.  close  and n e u t r a l that  m  wind  to the  the Monin-Obukhov  in Table  Conditions.were  indicates  with  Section  linear.  /2I4./7/1965,  p, ( r e f e r r e d  U-Wires  observed  Table  approximately  it  c  i n which  are d e s c r i b e d i n  represented  w  to neutral  for  f o r t h e r u n on  the wind  by t h e l o g a r i t h m i c  profiles  may b e  expression (eqn.  I.I).  From  for  were  runs  are summarized  This  o  workers  profiles  on  n  of the  anemometer)  resu I t s , but i n  of o t h e r  the three  is discussed  s  Values  a sonic  at 5  J  V e r t i c a l l y Spaced  probes  theory  x 10  estimated  the  Results  ("1965) > •  t o I.I  t o my d i r e c t l y  from Three  (using  o f 2 m) i n c r e a s i n g  at J m sec  contrary  workers.  directly  and T i m a n o v s k i i  at a height  other  IV A . 2 ,  0.2  t h e r u n on  i t i s seen  f o r t h e two r u n s  /25/7/•9^5•  is appropriate  to take  From  that on  /2ii/7/l965,  remarks  the height  the ratios  x^/L' are and 0.01  in Section  x^, which  II  has the  B.3,  69  dimensions Since  k,  length, can  be  of the  wave  then  a  As is  structure can  z  actual  are  is is  be  sma I I #  physica I  According  scaling  the  In  a  well  single  curve  sizes  where  is  scales  at  scales  these  small  the  scales  of  Taylor's  that  to  is  when  the  height,  scales,  the  by  so  l/k,  grouping  If  theory,  by  the  one of  scales  and spatial  that  here  which  scales  whenever  they  describe  be  has  an  which  non-dimensional independent  of  represents  where  Taylor's  of has wave  actual  for  of  an  a  of is  a  of  unsealed  of  should run,  a  plot  of  (velocity) give at  turbulence; v a l i d .  the  properties.  Thus,  given  for  functions  functions  kx^,  scales  hypothesis  by  any  dimensions  number  height  then  height.  the  except  similarity  function  the  of  velocities  universal  corresponding  independent  flow,  turbulence, be  fhe  structure  turbulent  then the  the  will  l/k  length  actual  A.2,  kx^>>I;  compared  similarity  kx^0j |(kxj)(=f0| j(f ) ) , the  as  II  velocities  run,  will  Section  dimensionless  characteristic  given  against  a  involving  representing  approximated  determined  heights,  velocity  as  inverse  basis •  to  scaled  s e a Ied  long  At  parameters*.  velocity of  as  of  scale.  kx^,  in in  length  dimensions  grouping  l/k  small  quite  is  the  product  is  considered  turbulence  characteristic  has  discussed  valid  turbulence  anisotropy  kx  fhe  appropriate  hypothesis  the  dimensionless  :  turbulence?  as  number,  f o r m e d us ing  How  of  length,  a scale that  ,  70  This  wave  subrange, in  this  and  from  range  heights  (the  number  range  levels  three  the  same  for  curves  are  most  marked  where  a  turbulence  boundary,  and  hypothesis  hence  lacks  scales.  At  greater  than  Considering  there  invariant This  velocity  As  was  IV  C.I,  eqn. using scales D  these  u*  the  a  l.l  and  .  in  indirect  as  Section  estimates  IV  be  the  spectral to  C.I).  (kxj)  fhe  poor  where  the  by  the  sea  Taylor's of  spectral  which  the  are  about  the  measure  strong  of  than  Here,  limit',  three  (kx*))  shape  less  kxz.^10,  that  is  three  evidence  curves  for  the  point  of  hypothesis.  II  theory B . I ,  u-«- = y - u  a  fhe  IV  C,  | u*,  the  theory  w h i c h i s  scaling  stress  essentially  velocity  S,  in  the  (compare  was  in  fhe  by  by  range  Section  actual  for  defined  subrange  overestimated  layer".  indirectly  0 | | (k )  seen  predicted  boundary  quantity  densities  as  another  the  "viscous  kinematic  inertial  from  that  suitable  However,  estimates  in  influenced  a  provides  outside  s e a Ies  appropriate  log  is  z  velocity  used  measured  of  kx ,  Section  is  seen  Differences  k  similarity  height  veIocity  other  II  with  and  similarity  in  exists  log  (I 9 6 3 ) • ' i s o t r o p i c  the  seen  against  anisotropic.  of  the  kxz0||(kxz.)  strongly  This  seen  at  run.  of  is  spectra  values'  values  it  inertial  vertical  be  correctness  that  at  the  .5,  to  Pond's  was  given  and  .3,  expected  coincide.  it  of  validity,  higher  the  encompass  is  essentially  view,  of  curves  almost  I,  IV-C.I,  Figs.  fhe  should  of  eqns. V  stress  C.I,  71  present  (u-»- )  measured  d i r e c t l y  , on  the  that  S  average.  Thus,  should  constant  implies  that  subrange  be if  the  remains  u-«- a l s o  remains  S«1  with  with  invariant  in. t h i s  range  frequency  value  with  invariant,  X-wire,  by  about  ij.2%  2  ,lj.u-"- ,  measured  the  of  in  S  height  within  in  this the  for  the  of  a  scales, range.  This  i n e r t i a l  given  limits  so  of  run,  then  experimental  error. Figures by  eqn.  IV  function the  the  IV  C . l *  the  three It  ratios  At  of  the  .6 the  non-dimensional Values  seen  of  from  are  signals  of  to  wave  the a  wave  /25/7/1965  which  parts  of  the  are  experimental the  same  10  S  is  or  .  in be  .  over  the  the  is  least  greatest The  .  •  the  number  signal-to-noise  and  the  •  limits  height  scatter;  of  range  of  measurements.  The  measurements'  made  with  the  three  for  i n e r t i a l  ignored.  that,within  invariant  wave  the  S  within  kx^^2),  the  eqn. of  value  of  spectra  values  in  a  each  the  the  less,  .  as  using,  the  since  displays  .  ;5)  (log  therefore  demonstrate,  error,  to  (defined  S  for  from  average  enough  \ 1  kx^,  and  that  of  probes,  calculated,  to  on  measurements '" thus  number  increases,  run  values  U-wire  numbers  decrease  curves  three  C.l,..3,  small  S  the  figures,  for  highest  values  IV  the  converge  show  were  S  (Figs.  scales the  i n t h e  the  these  each  and  ( t o t a I .range)  which  of  for  heights  subrange. scatter  .I4.,  heights is  +15%  range ;in  for  the  C*2,  runs.  three  about  C*.|)  of  three  at  IV  v e r t i c a l l y  spaced  72  U-wires  thus  Mon i n - O b u k h o v range  of  which  the  provide  strong  similarity  heights  (about  measurements  support  for  th-eory •'(Sec11 on I  to  were  5  m  )  made.  above  the II the  validity  of  B~. I )  the  sea  for  surface  the  in  73  V I .  1.  SUMMARY  The  X-wire  velocity a  2.  wind  probes,  to  in  order  to  work  U-wire  and  both to  range  of  Pond  probes  fluctuations  can in  the  existence  and  the  of  of  Reynolds'  stress  technique  provides  tensor  in  The  kinetic  a  general  analyzed.  the  upward The  X|  and  energy  trend  spectral  2  of  analog  data  densities  (1965)  over  to  showed  and  in  the  values  of  angle  of  that on  the  velocity  inertial  spectral  showed  over  U-wires,  the  that  measure  downwind  the  subrange,  f$\j, the X-wire  velocity  directions.  spectral  towards  components  component  information x  on  measure  vertical  Pond  X-  all  (9),  ' .  X-wires  directly  diagonaIization  reliable  fluctuations  measured  negative  a  Hz.  velocity  both  over  cm.sec  the  cospectral  and  spectrum  fhe  to  60  shapes  with  1000  mount  successfully  the  only  behaviour  to  measure  directions  z  and  to  tape-recorded  and  (I963)  0||(k)  of  to  wires,  the  U|-wind  f0| | m e a s u r e d  the  the  x  II4.O t o  developed  used  spectra  the  about  0.016  al  be  and  horizontal  from  et  successfully  X|  spectral  Comparison  of  the  analyze  ocean.  behaviour  4«  to  used  from  were  extract  frequency  in  calibrate  response  velocity,  The  been  speeds  techniques  of  a  3.  of  Special  their  has  fluctuations  range  the  method  the  density,  density, lowest  f0**,  of  f0j|,  showed  frequencies the  fluctuating  71+  velocity at  the  its to  component, lowest  maximum TO  Hz.  At  is  et  al  (1957),  in  the  The  in  keeping  values  of  Checks  made  (b')  and  of  by  the  the  this  flat,  broad  two • r u n s  e s t i ma t e d • f r e q u e n c y experimentaI  at  s i t e . of  the  frequencies  frequencies.  The  The  all  were  spectral  of  of  Favre  turbulence  much  of  of  the  (K),  larger  ( f j # | 3) 0.01  runs,  b'.  even  and  K  were to  I  waves  the  stress,  than  curves  that  Hz.  at  no  did  For the the  larger was.  present  t h e - - e s t i ma t e d  had  the  f a i r l y  coincide.with  domi n a n t  observed lower  in  analyzed.  coefficients  showed  about  other  negative  wire  errors  the  had  frequencies  maximaroughly  totally  0.1  «  very  fj^jj,  spectra  between  For.the  which  at  large  range  -  had  from  results  scales  were  and  range $33  zero  i t .  factor  result.  did. the  the  value  unacceptably  maxima  Hz),  transfer,  the  analyzed,  tunnel  wind  to  sensitivity  not -change  that  densities  varying  ( < l  toward  Iy  frequency  wind  mean  momentum  of  with  the  the  showed  of  spectral  proportion  in  with  which  assumption  only  frequencies  perpendicular  spectrum  monotonicaI  low-frequencies,  direction  those  highest.  contribution  which  than  and  decreased  regularity  wave in  P shape:  they  frequencies, This the  gives  all  dropped  and  for  confidence  Reynolds'  stress  toward  most that  cases most  occurred  zero  at  at  the  lowest  of  the  contributions  from  the  highest  fluctuations  frequencies.  in  to the  75  frequency in  unstabIe  s e a Ie  analyzed.  conditions  sizes  s t a b Ie at  range  than  for  conditions,  larger  scales  In  had  their  those  showing  than  general,  in  broad  of  spectra  maxima  n e u t r a I,.  that  those  the  at  measured larger  near-neutraI,  or  convective ,eff ects ' occur mechanically  produced  turbulence*  The  correlation  values than  of I  My  magnitude  Hz..  Two  -0,2.  around  c o e f f i c i e n f s  runs  The  measurements  absent,  even  observed. values  behaviour usually  were  at  the is  that  of  0^^/0..  fhe  to  be  (kx^>I|..5)  values  the  greater'than  ratio or  t h e ,.,efxf e c ' t  and,in.  the  angle  direefion  from  two  could  cases  close the  I4./3  to  the ratio  of  the the  all  to  1,0,  in  of  the  observed  based  on  only  "and  wires, be  ;  range,  in  of  were Checks  b'  and  K,  wind that  considered  of  average  runs.  showed  assumption  scales  to the  mean  value  the  of  The  four  the  by  range  expected  of  ratio  non-zero  frequency  predicted the  the'  Iy•never  frequency:.^  and  (I963K.  than (/3)  less  values  apparent  according  al  for  deviation plane  with  ( h i ghes t  this  errors  theoretically is  et in  j  0^/0^  is  negative  ratio  ,  frequencies  frequencies,  Pond  larger of  s e a I es  ' i s o t r o p i c ' ,  equal  of  at  ;  negative  -O.73.  was  the  f$|z  c r i t e r i o n  of  by  ha d  for  0.3  anisotropy  sma I I es t shown  a I I  exceptions,  value  stress  assumed  of  than  the  maximum  show  This  of  greater  R|j(f)  as  l|./3«  in  only  being Since  isotropy,  Hz  76  then  the  observed  the  existence  The  observed  of  ratios  must  be  interpret,ed-as  showing  anisotropy.  Kolmogoroff  spectrum,  01  | ( k ),  behaviour  to  in  the  i n e r t i a l  -5/3 subrange  shows  greatly  predict.  which  This  workers  the  k  -5/3 J  I nd i r e c t wind  et  using  using  the  due  p r o f i l e  jZ5||(k)  The  the  also Pond  than  et  19^3;  the  original  by  other  1965),  Pond,  isotropy  for  and  would  noted  al,  of  c r i t e r i o n  the  isotropy, been  assumption  kinematic  l i t t l e  is  an  prediction  X-wire, stress  0 ^  and  by  (k)  about  the  by  of  to  s t a b i l i t y wind the  method.  of  about  estimated  h-0%,  the  the  on or  Indirect  estimates  i n e r t i a l  subrange,  estimates, the  values  indirect  more  of  average,  drag  of  is.  stress  methods,  consistent  the  and  the:non-existence  underestimation  gives  direct  T h e o v e r e s t i m a t i c n  two  the  average  ij-0/£.  conditions,  general  method  the  in  u-"-% f r o m  with  the- d i r e c t  p r o f i l e s ,  Of  on  spectrum  stress  stress,  c o r r e l a t i o n  with  spectral  d i r e c t l y  the  correlated  logarithmic  probably  the  the  strongly  irrespective  of  showed  overestimated  of  of  larger  law.  underestimated  were  the  stringent  p r o f i l e ,  u-»- ,  has  much  scales  that  1962;  a l ,  e s t i ma t e s  estimates  of  include  that  unnecessarily  turbulence  behaviour  (Grant  indicates  ;  k  anisotropic  assumptions,  and  the  the  r e s u l t s .  c o e f f i c i e n t  by  77  showed  no  average I J4.5  x  the  IO" ,  was  n  observed those  The  the  2.10  three  direct  by  provide  Monin-Obukhov heights  (about  standard  0.66.x I0"5 the  =  measurements  were  and  were are  with  )  0.1*2  x  from  the  that  from  x  10"?). in  the  in  general  The  height,  m  IO"  was (~  5  the  of  35$  profiles  was  values  S t a t i s t i c a l mean  s i g n i f i c a n t .  the  support  m  5  speed.  values  of  The  higher  than  workers.  s i m i l a r i t y 5  of  O.53  wind  the  differences  other  to  to  error  I0"5)  methods  made  mean  estimate  (cr  strong  i  with  corrected  .estimates  measurements  U-wires  the  x  that  measured  trend  indirect  (a~ =  showed  from  CQ,  The  I0"5  0  of with  5  x  tests Cp  value  mean).  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J  (I 9 6 2 ) :  Turbulence  F 1ui d Mech,  92,  pp  of  Near  B.C.,  |2,  ;  part  2,  the  301-305.  Canada, The  Ground:  of  July  1965.  Budget  of  Quart.  J . R o y .  277-280.  The  Incompressible Number.  Observations  Department  (I966):  Turbu I ence.  (I9lj-l):  Wind  Thesis,  Panofsky  Energy  (1959):  Reynolds'  pp  Study.  S t a t i s t i c s ;  Cup  Sea.  S o c ,  Ko I m o g o r o f f , . A , in  a  (19^5)*  and  Met. 0.  the  Stewart,  W..  Turbulent  J .  Deardorff,  Sons,  Physics  Hinze,  Stresses  Layer,  2k\-268,  Over  G.  Induced  Boundary  lj.75-Lj.89.  (1958):  R.  pp  Hess,  -  Space-  (1957)°  li+l-155.  A.  P.  Dumas  Turbulent  Tunnel  Above  Spectra  Hambli.n,  3LI1.-356 .  Humidity  D.  H.  pp  distribution  Wile y Grant,  Wind  J .  a  Vertical  PP Fraser,  A  R.  in  Wind  (1963):  Surfaces.  No,  5,  and  McGraw  Local Viscous  DOKLADY.  -  H i l l  Structure Fluid ANSSR.  for 50,.  Book of  Inc.  Turbulence  Very ,  Co.  Large  ... , .,  80  B,.(1966):  E .  Kraus,  be  (10  Lin,  C.  Lumley,  C.  I  pub  (1953): in  Math.  10,  Moroney, Pond,  R.  Hypothesis  C o l . Jan.  I966,  and the  Acceleration  Equations.  Quart.  AppI .  295-306.  pp  and H..A. Panofsky  (  Turbulence.  196J4.): John  The S t r u c t u r e  Wiley  of  and Sons.  Inc.  PP.  M . - J ,  S.,  Denver,  i shed.)  the Navier-Stokes  Atmospheric  239  Met. S o c ,  Taylor's  Terms  J . L.,  Amer.  (1962):  Facts  W. B u r l i n g ,  .Spectra  in  From  a n d R.  the Wind  Figures.  Penguin  (1963):  W. S t e w a r t  Over  Waves.,  Books L t d . Turbulence  J . A:tm. S c i , . ,  V o l , 20, No.. l u p p 319-324. Pond,:.S.  (I965):  Turbulence  Boundary of Pond,  S..,  S,  the  Priestley,  ,  D...Smith, of  P.  C.  H.  S c i . B,  (195  Atmosphere. Sheppard.,. . P . - A , and  (1963):  Humidity  Aug. paper)  Univ. F.  of  the 'A tmospher i c 1  Ph.D. Thesis,  B.C.,  Hamblin,  Velocity  Atmospheric A t m.  in  Over t h e S e a ,  Physics  Spectra  J .  Layer  Spectra  June,  a n d R.  and Temperature  Boundary  Layer  Over  W.  Department  I9&5*  (1966):  Burling  FIuctuations  in  the S e a .  ( i n p r e s s . ) Turbulent  9)s  University  of  Distribution i n A i r  19-30, 1965,  Transfer  Chicago of  Wind  in  the  Lower  Press, Speed,  Temperature  Flowing  O v e r - Wa t e r .  I . U ,G , G . ,  Berkeley,  C a l i f o r n i a .  (Verbal  :  81  Stewart,  R,  (I96l):  W.  Math.  Hydr.  Meereskunde Stewart,  R.  W.  Japan. Zubkovskii,  der  S.  V o l . and  Experimental  Comte  et  Gibson,  I36-1I4.2.  D.  F.  Timanovskii  Layer  (I9&5)  of  :  the  A i r , Okt.  du  reference  Waves.  on  fur  A  at  Soc.,  n  Regime  Akad.  given  J . Oc.  (I965)j  Izv.  Nauk.  in  the  U.S.S.R.  1965*  available  at  the  Turbulent  P u b I i c a t i 0ns  Ministere  was  course  Turbulent  ^ c o u I ernent  Paralleles.  Techniques  following  externa!  pp  r e f e r e n c e became the thesis.  G.  Sea  19.  of  Institut  Ie c t u r e  Over  Atm. Okeana.,  I 01,  A  Profiles  Study  Proc... Symp.  Hamburg.  C o l .  Fis,  -3eI  Oc..  Brit.  Water  Parois  The  of  Near  The following c o m p l e t i o n of  Phys.  Turbulence,  Wind  L.,  of  on W a t e r .  Universitat  University  (1963):  A.  Stress  Methods  (I963):  the Takeda,  Wind  de  suggested  date  Entre  Scientifi  L'Air.  for  No.  of  Deux  gues I4.19 •  inclusion  by  the  exa m i n e r .  M.M.  (1962):  Number.  Spectra  Mature,  of  195,  pp  Turbulence  1281-1283.  at  High  Reynolds'  82  EQUIPMENT  Ampex  MANUALS  Corp.,  CPIOO  1963:  magnetic  tape  recorder.  Redwood  City  C a l i f o r n i a . Donner  S c i e n t i f i c  multiplier. Flow  Corporation, wire  1961:  Division,  Concord,  anemometer  3732P  electronic  C a l i f o r n i a .  Bulletin  1956:  Model  Selected  25,  theory.  ,  1958:  Model  HWB  2  hot  wire  ,  I962:  Bull.  68,  Tech.  Mem.  3  hot  wire  Cambridge,  topics  in  hot  Mass.  anemometer. X-wire  Turbulence  Measure-  ments. ,  , Hewlett  1962:  Model  HWB  1962:  B u l l .  16 A ,  1963:  B u l l . 1 9 ,  Packard, Pa I 0  ,  I96I:  Honeywell,  A I10,  H  Philbrick:  K  7  (containing Boston, UJ  -  533  vacumn V  CR  tube  D.C.  sum  electronic  difference  unit.  counter.  voltmeter.  d i f f e r e n t i a l  Model  1958:  f i l t e r .  Model  Mod'el  wire  amplifier.  Co I o r a d o .  Corporation,  •pass  Hot  C a l i f o r n i a .  Accudata  Denver,  — - - ,  Model  k.00  Model  HWI3  ModelMM3Micromanometer.  1959:  1962:  Krohn-Hite  Model  anemometer.  Cambridge, ~ 10  A  10  U.S.A.  integrator.  -  A  ultra  low  frequency  Mass,  stabilized  Mass. 2  $00  3  operational  operational  manifold  amplifiers.)  83  Sanborn  (Hew I e t t - P a c k a r d ) : thermal  Thornthwaite  writing  p r o f i l e  Centerton, Associates: Pa I 0  Alto,  Model  channel  Waltham,  Operating  register  New  Two  320  recorder.  Associates,  wind  Varian  Model  system,  protable  Mass.  instructions  Model  106.  Jersey. G-! I  A  C a l i f orn i a ,  strip  chart  recorder.  for  84  FIGURE  CAPTIONS  (All  logs  Fig.  Ill  are  to  base  10.)  .1  Experimental  .2  Photograph  A .  I9&5  88  Experimental  88  Site  of  for  89  Mean Mean  W i nd  Mean  W i nd , D i r e c t i o n  e  a  9  r  P r o f i 1e a n d  -direction Pt.  (9  a  relative  and  6 ): r  to  Atkinson  - d i r e c t i o n . r e 1 a t i ve  top r o b e .  Relative to the lowest c u p , the cup h e i g h t s w e r e 0, 30, 80,. 150, 2I4.I, a n d « Height of bottom cup f o r each r u n is included in brack ets .  35'  c  m  2010-2034/21/7/1965  ( 95)  ....  89  .2  1555-1629/20/9/I965  (137)  ....  90  .3  2039-2122/29/6/1965  (103)  ....  91  .4  2122-2206/29/6/1965  (127)  ....  92  •5  1448-1525/22/7/1965  (130)  ....  93  .6  1553-1625/22/7/I965  (130)  ....  94  1620-1652/22/7/I965  (135)  ....  95  .8  1650-1715/22/7/1965  (145)  ....  96  •9  2230-2258/26/6/1965  (205)  ....  97  .10  2305-2336/26/6/1965  (200)  1550-1605/24/7/I965  (170)  .. . . . .  .12  1607-1645/24/7/1965  (160)  ....  100  .13  1501-1525/25/7/1965  ( 95)  ....  101  A.I  . 1  Run  I  ?  98 99  85  Fig.  IV  B.  X-  and  U-Wire  Spectrum  Data:  :  1  f0\\{f)  of  ^  u  Downwind  Fluctuations fjZS*z(f) J  Cospectrum:  J  of Vertical Velocity Fluctuations  f0|z(f)  of H o r i z o n t a l and Vertical Velocity Fluctuations  R|z(f)  of H o r i z o n t a l and V e r t i c a l V e l o c i t y  Correlation Coefficients:  Fluctuations. Org i n  of  Origin  of  (Scales for  log  second,  . B.l  Run  log  k  log  of f; k  scale (kx^)  both  are  scale the  f  is  in  is  in  radians  same  cycles  as  per  per  cm)  2010-2034/21/7/1965  1  0  2  .2  1555-1629/20/9/1965  103  ..3  2039-2122/29/6/1965  I04  .-4  2122-2206/29/6/1965  .5.  1448-1525/22/7/1965  ,6  1553-1625/22/7/1965  .7  1620-1652/22/7/1965  .8,  1650-1715/22/7/1965  ...9  2230-2258/26/6/1965  no  ,.l..o  2305-2336/26/6/1965  I N  — .  105 I °  ........  l 0  6  7  108 ....  . . . . . 109  :86  Log-log 01  I ( k)  and  B. l l  F i g ,  IV  of  Run  plots  of  a n d 0*3  (k.).  "01|(k)  Wave  Number  from  from  Spectra  X-Wire  U-Wire  Data,  Data.  20IO-203lj./2l/7/!965  .'•  I  1  2  .12  2039-2122/29/6/1965  113  .13  2122-2206/2.9/6/1965  I llj.  .Ill  IU4.8-I525/22/7/I965  115  C.  Data  for  Three  V e r t i c a l l y  Spaced  U-Wi r e s Figs.  I I  I,  3»  6  Spectra  5°  kx30 1 1 ( k X3) (='f 0 1 j ( f ) ) of D o w n w i n d Velocity F I u c t ua f i ons f o r A l l Three Probes  Figs.  2,  k,  Values  6:  f or C. l  Run  Fig.  IV  IV  (eqn.  Three  IV  C.l)  Probes  .............  ||6  I550-I605M/7/I965  .............  117  1607-1614-5/214./7/1965  •  .............  ||8  .1|  l607-l6l4.5/2l|./7/l965  .............  119  .5  1501-1525/25/7/1965  .v...........  120  .6  1501-1525/25/7/1965  .............  121  D.I  .2 Fig.  AI I  S  I55O-I605/2I1/7/1965  .2 .3  of  E.I  Comparison  pf  and  IndirectIy  u*  for  2  All  Directly  (u-«- ,  Determined  X-Wire  Runs  'lines'  slope  at  I4.5.)  Drag  Coefficient  at  5  DiagonaIization  the  Reynolds'  a  Function  Runs  of  Recorded  Stress  m  Height  Angle  9  Tensor  Frequency During  of 122  (The  The  X-Wire)  VaIues  for  123  of as Three  /22/7/1965  I2I4.  87  Fig,  IV  6.1  The  Effect  pt  o  on  Spectral  Values  of  125  jZSjj'(f)  :  Spectral  level  for/3?  0  jZSj.(f)  :  Spectral  level  for/3=  0 .  (FROM  FIG. III.I  EXPERIMENTAL  SITE  i Main instrument mast  FIG. III.2 PHOTOGRAPH  C.H.S. CHART 3001)  FOR  1965  r  J Platform  Rover mast  OF EXPERIMENTAL SITE  3.0 log  x  :  0a  9r  70  +20  60  +10  2.8  2.6H  2.4 50 Probes  2.2  40 2.0  -IO-  1  ~ i —  140 U  150  (cm/sec)  FIG. IVA.I  MEAN  WIND  DATA  2010-2034/21/7/1965  3.0-1 log x  3  da X  12.8 H  \  280 2.6 270 2.4 H Probes  260  2.2  2.0 240  260 U  FIG.  (cm/sec)  IVA.2  MEAN  WIND  DATA  3.0  X  2.8  2.6  9  0Q  logxj  r  o  |  |  260  0  250  -I0H  2 7 0 + 10-  A  ZA-\ Probes  Time  2.2 2120  2.0  — i r 300 U (cm/sec) FIG.  IVA.4  MEAN  2140  400 WIND  DATA  2122- 2 2 0 6 /  29/6/1965  2200  3.0 logx. 2.8  do  ft  X  o  J  J  2 8 0 +10-  zeA 270  0 XXX  x  x  2.4 260  -I0H  Probes 2.2 Time 1600 2.0  I  i  400  500 U (cm/sec) F I G . IV A. 6 MEAN  WIND  DATA  1553-1625 / 22/7/1965  1620  3.0 logx.  da  x  9r o  \ I  2.8  285  +10-  275  0  2.6  x X  x XX  X  X X  2.4 H Probes  265  X  X  -lOH  22  1700 2.0 300  400 U  (cm/sec)  FIG. IV A.8  MEAN  WIND  DATA  1 6 5 0 - 1715/ 22/7/1965  1720  Time  3  0  2.8  da  i  -I  3 , 0  Probes  —i  1  900  1000 U  a  1 0  300  0  290  10  1— 1100  (cm/sec)  FIG. I V A . 9  MEAN  WIND  DATA  2230-2258/26/6/1965  I  1  9 0 0  1000 U  1— 1100  (cm/ s e c ) FIG.  IV A . 1 0  M E A N  WIND  D A T A  2 3 0 5 -  2 3 3 6 / 2 6 / 6 / 1 9 6 5  100 H • 80 -\  '  f C  rV  f )  fdb(f)  wire  • 9 • • (crrfVsec) 2  60  40  *  .  Af^  H  •  (f)  • f<£„.f.  h- U-wire  E  H  • 20  l 3  H  o  o o o  I  o o  -I A  2  o  o  •  ° fl  o @ 6  * A  • .  A  A  A  A  A  A  A  A  A  E  © H  A  A  A  -B—@—Hlog f  0  -20 0  R if): Correlation R  -1.0  Coefficient  »' > f  FIG.  IV B. I  X- and  U-wire  data  2010-2034/21/7/1965  3001  f^(f) (cm / s e c ) 2  2  • f  •  if)  o f(/) (f)  —X-wire  33  •  200-  •  •  • •  A f <£ (f) |3  • •  • •  lOOH  o o o o  -2  A  A  A  A  A  •  •  •  o  A  A  A  A  A  A  A  0  A~^T  A  A  A  A  f^.tf)  |  h-U -wire  U g j B ^ logf  -IOOH B  R (f) |3  -l.0  ^i3 ^ 1  r  :  Correlation  Coefficient  J  FIG.  IVB.2  X- and  U-wire  data  •  1555 - 1 6 2 9 / 2 0 / 9 / 1 9 6 5  2  2 0 0  "ftp• f <£„ i f ) f ^  (f)  O f C^3 (f)  (crrrVsec )  3  2  •  •  00H  •  •  • a  •  •  •  •  A  f <£ lf)  •  f ^ . l f )  — X - w i r e  l3  •  •  h  U-wire  •  o o o  o  • 0  8  Q  go O  o  —Q-  0  2  A  A  A  A  fl 9  O  fl a  o  -I A  Q  0  A  A  g A  A  CJ A  log f A  •50H  A  A  o-  • R  -I.Q-  1  ( f 1 3  .  •  •  •  •  * F I G . I V B. 3  R| (f) 3  X-  and  U-  wire  data  2 0 3 9 -  !  Correlation  Coefficient  2122/29/6/1965  20CH f</>.(f>  f<  V»  o f c ^  (cm /sec ) 2  • f<£||(f)  • 2  3  ( f )  •X-wire  D  • A f c£ (f) l3  •  roo  B  g  B •  •  \— U - w i r e  f (jf>„lf)  fi  ° _Q_  0  A  O  o  °.  °  •  5 g  0  8  O  8 o g A  A  A  , A  9  9  A — A  A  A  2  I  0  - |  I  log f  A  A  A  A  -50-  o-  • R  -i.o-  R  ,  3  ,  f  »  FIG.  I V B .4  X - a n d  U - w i r e  data  | 3  (f)=  •  c  Correlation  Coefficient  2122- 2206/29/6/1965  0  4 0 0 1  f^.lf) • f <£>„lf) •  fc^if, 3 0 0 1  (cm /sec ) 2  2  •  •  o f<£ if)  h—X-wire  33  fi  A f <£, if)  •  3  13  -U-wire  • f<jf>,,lf>  0  200H  0 1 0 0 1 0  o  o  o  o  o  °  °  o  o  gg  0  o  E  0  A  -2  A  A A  A  A  A  A 0  0  @  A A A | A A A A  A  logf  A  -100-J  0"  • • R  -l.0  J  .3  •  • •  R if) s C o r r e l a t i o n  •  |3  Coefficient  ( f )  FIG.  IVB.5  X- and  U-wire data  1448-1525/22/7/1965  2  f </>„«*>  fc/),f,  2 2 (cm / s e c )  600  •  0  O f<£ (f)  •  —X— wire  33  •  Af<jfc (f) l3  •  400i  •  M  •  •  •  •  200H  o  0  -2  o  o  o  o  o  o  o  o  •  o  O  O  • o  0  -I A  A  A  0  5•  A A A — A  I A  U-wire  • f <jf> if)  *  *  A  A  AO*  • fi |A A A  A  A log f  •20 0  J  o-  •  o  R, (f) 3  1.0  R (f) | 3  FIG.  IVB.6  X-and  U-wire  data  c  !  •  "  e  c  Correlation  » c Coefficient  1553-1625/22/7/1965  f  <f>  (t)  (cm /sec ) 2  2  f <£„({>.  6 0 OH a  o f ^33^  •  f <^ (f)  A  4001  •  •  •  •  •  • •  u  •  2001  o o  0-2  A  o o  o  0  •  o o.  • 0  0  9 0  ^  o • A  A A A  A  h-U -wire  •  ° -I  A  3  • f cf> (f) •  o o  -X-wire  A  A  S  8 %  g  A  A  —  A | A  A  A  T" 2  A O A  A  A  logf  A  2001 0  a a  a  a  a  a  R, if) 3  R  -I.CH  '3  l f )  ' FIG.-IVB. 7  X-and  U-wire  a  •  •  data  :  Correlotion  1620-1652/22/7/1965  Coefficient  <rV f  '  1  • f ^>„if)  J .  6 0 ( H (cm /sec ) 2  2  o f c/) (f) 33  400 H  | 3  •  • f <^>||lf)  0 200 O  O  O  0  A  o o  O  O  g  0  B  .fl  A  A  A  A  A  A  AnA ^ O  "  n  y  A  U - wire  0 9  o o o o ° •2  -X-wire  Af<£ (f)  •  o-  )f  A  A  Q Q A  A  Q g A |A log f  200-  1  0 c • R  -1.0-  .3  l f )  F I G . IV B. 8  o  c  o  R (f) :  c  X-and  )3  U-wire  data  Correlation  Coefficient  1650-1715/22/7/I965  f(/),(f)  tci 3000H  J 2  • f <£l,lf)  (t)  2  o f c/) f, 33t  (cm / s e c )  D  D  |3  •  •  2 0 0 0  •  u  \— U - w i r e  •  •  •  1000-  •  a  o o o o o o o o o o o o o o o - 2  A  A  A  A  A-|  A  A A  A  A  A  A  0  A  A  fi  D  0  0  A  A  A  | A  A  o  e  o  R , (f) 3  •i.o-i  1 3  A — &  :  e  c  o  0  o  o  °  Correlation  (t) FIG.  I V B . 9  X -  a n d  U-wire  &  log f  0-  e  A  A  A  - 5 0 0 i  R  wire  A f Cjb (f)  •  0  — X -  data  2 2 3 0 - 2 2 5 8 / 2 6 / 6 / 1 9 6 5  «  >  Coefficient  f<f>..<f)  icb  (f)  • f (£„(f>  (cm / s e c ) 2  3000  O f c/^lfl  2  -X-wire  Afc/) (f) |3  0 2 000-  •  •  •  •  •  •  •  •  •  U -wire  f<fr,lf>  •  e  fl  IOOOH  0  "2  H  -500  o o o  A  1  A  X  A  A  o o o o o o o o o o  I A  A  A-l A  1  A  I  A  A  A >  °  o  A  A  QA  8B  8  A—A A  A  A I  A  9 e  |A  e  A  A—A—A  A  logf  0R (f) l3  -l.0  R J  (3  :  Correlation  Coefficient  (f) FIG. IV  B. 10  X - and  U-wire  data  2305-2336/26/6/1965  500k X  3 / ll C  )  l k X  3  c  )  (cm /sec ) 2  o  2  400-  o  s~  A  S-9  3  6 A  300  O  o  A o  O  9  O c  A  200-  A O  O A o  O  8  100-  &  oFIG.IV C.l  S-4  FOR  THREE  VERTICALLY  &  A log(kxJ  0 DATA  &  SPACED  U-WIRES  1550-1605/24/7/1965  50 CH  .  S  o  A  (cm^sec ) 2  S-4  S-9  o  4001  •  O° A A O O °A° . t ^A A A AA 0  0  300 H  A  200 O  •a  100  A  A  o R  °  Q b  o  S-3 Q  •  A A A A  *  O O A  9  o  0 FIGIVC.2  i - I DATA  1—  1—  0 FOR  THREE  VERTICALLY  I  SPACED  U-WIRES  r 2  log(kx ) 3  1550-1605/24/7/1965  5001  kx 9 3  t l  ikx )  o  3  (cm /sec ) 2  2  S-3 S-.9  A  °  400H  o °^  O  O  A  A  3001  A  o  O  0  O  r£ e  200-  A o  o  * A  •  100  oFIG. IV C.3  O c •  A  9  A  ^  — , —  - i  :  .  .  D A T A . FOR  1  :  >  0 THREE  *  ^  I VERTICALLY  SPACED  '  *  *  I  I  2 U-WIRES  A  A  A  A  log(kx ) 3  1607-1645/24/7/1965  500-  S (cm /sec ) 2  2  .  S-4  o  S-3  A  S- 9  4001 A A  3001  ^ & A  200"  A O °  A  A o  0  A  A  o °.  A  A  ° -o *  A o  A  A  A A  .  0  •  °  A  0  A A  o  A G O O  I00  . O  , .  .A  .o  o-  I  -I FIG. IV C . 4 D A T A  T  FOR  0 THREE  1  VERTICALLY  :  I SPACED  1  U-WIRES  ;  2 logtkx^ I607-I645/24/7/I965  kX3^>iiikx ) 3  lcm /sec ) 2  2  c  o  S  "  4  S-3  AS-9 2001  o  o  o  ° ° A  °  A  O  A A  A  c °  100  ^ A '  * O O A  A  0  c  A  O A o  A  °o  A O  AO Ac?  0-  -I FIG. IV C . 5  DATA  i  :  FOR  r~—• 0 THREE  VERTICALLY  AoAg A  1  I SPACED  U-WIRES  2  log(kx ) 3  1501-1525/25/7/1965  A  A  s  - S-4  (cm /sec ) 2  2  Q o  o S- 3  o  A S-9 .  200A 00  0  0  A  0 •  A A°  A.  • ^0  •  • 0 A A  .  A A  • A  o A  •  O 0 A  A  °O  A  A  A A  a 100-  o  .A' A o °'A A  A  o  •  .  *  o  A  FIG. IV C . 6  A A  OA  •A AO 1  I  1 DATA  FOR  0 THREE  VERTICALLY  SPACED  1  1  1  2  U-WIRES  log(kx ) 3  I50I-I525/25/7/I965  Uj FIG. IV D.I  COMPARISON VALUES  OF OF  DIRECTLY uf  FOR  AND ALL  INDIRECTLY X-WIRE  2000  X-WIRE DETERMINED RUNS = ( ul  in cm /sec ) 2  2  "°  3.0 C  D  X-and  o  x 10'  runs  o  o  3  o 2.0  U-wire  U-wire  runs  From  ><[-wire  <P(,(k)  A  From  From  wind  •  From  0  From  (j6|(k)  o  spectrum  profile  (  wind  spectrum  profile  o 0  -  o  •  o A  o  o  • o o  .0  A  -  c  0  •  A A  U  (m/sec)  •A-  0  1.0  2.0 FIG. I V D . 2  3.0  40 DRAG  5.0  70  6.0  COEFFICIENT  AT  5IVL  8.0 HEIGHT  9.0  10.0  @  • 1553 - 1625  o  A 50 0- 1715 o 1 16 62 1652 A  A  A  A A  A  •  A O  A  A  O  °  o  A O  A ^ O  A O  "  A  A  A  A  A  A A  / O  o  A  O O  O  O  O  O  *_ 1  FIG'.IVE.I.  o  O °  T H E DIAGONALIZATION AS A FUNCTION  ANGLE 0 OF T H E R E Y N O L D ' S  OF F R E Q U E N C Y  FOR T H R E E  RUNS  A  STRESS  logf TENSOR  ON / 2 2 / 7 / I 9 6 5  O  •  ICH  AA  A  „  A  A  A A A  A  1.0 H  A A A  0  A  A  A  A  ^  .  A  A  A  A  .  A  A  »  A  A  A  A  A  O O ± 15°  o °  0.9CH  °  °  °  O  O  A 0  1.05  A  A  c  A  c  o  A  A  c  o  A  o  o  o  o  o  o  c  «  c  o  o  o  n  o  O  O  o O  o O  o  l  o  >  c  o C  0  A  A  A  A  A  A  A  A  n o  o o  ^ o  o  o  A  A  9  t  >  A  A  A  A  n  o  o  A  ° o  0.95-1 P=  o „  A  1.0  o  0  A  A  0  ±10°  0  °  O  O  O  o  O  /  O u  O u  n °  u  ^ o  o  o  o  o  A  A  A  A  A  o  o  A o  o  o  1.05 A  1.0 0.95-  A  A  o  A  A  °  o  A o  A o  o  A  A  A  o  o  A o  A o  A o  A o  A o  A  A o  o  o  o  o  o  »  A  o  o  /3 = ± 5 ° I  i  I  I  -2  - I  0  I  FIG. IVG.I  THE  EFFECT  ON  SPECTRAL  VALUES  OF  fit  logf 0  APPEND ICES  Al  APPENDIX  I:  THE  CONSTRUCTION  AND  CALIBRATION  OF  HOT  WIRE  PROBES  A.  The  Wind  In wire  Tunnel  order  to  Mechanical tunnel  by  of  level  fhe  infrequent  and to  hot  low  is  obtain  a  a.wind  wind  in  use  wind  and  tunnel  tunnel  employed,  students  irregular  probes  to  measure  with  a  the  low  necessary.  speed was  System  wire  X-wire,  \%)  Engineering graduate  necessary  an  ( «  I n i t i a l l y ,  Manometer  calibrate  coefficients  turbulence  and  that  of  but  the  tunnel  for  Department  increasing  department  the  tunnel  in  use  allowed  that in  use  the  it  of  of the  such  became  Institute  of  Oceanography.  With Model  this  WTlj.)  was  Corporation speeds  in  supplied that To  in  3"  lower  the  MMJ 3"  x  proved high  a  small  purchased  Model  the  very  view,  to and  together  test  have  sharp  level,  constructed,  version  the  intake  areal  final  r e d u c t i on . r a t i o  to  a  in  of  two  the  (Flow  determine  mean  wind  tunnel  as  edges  (see  11.9:1,  on  the  levels  of  a  wind  F i g .  and  the  dimensional  form  a  A  Corporation  micromanometer  turbulence a  (Flow  However,  non-return  design  a to  leading  unacceptable  turbulence  The  with  section.  was  University.  tunnel  Micromanometer)  plexiglass of  wind  fine  were  so  present.  intake  of  scaled-down  tunnel 1,1  intake,  and nylon  at  McGill  .2) mesh  has of  an  5"  A2  meshes/mm s t i l l  stretched  further.  Pressure of  the  test  The  U  taps  is  the  -  O.OOOij.  wind  is  manometer  -  mercury.  the  to  a  is  the  and  units  of  m.sec  atmospheric Since was  placed  atmospheric  wire  wind probe.  Mechanical between  the  satisfactory.  test  were  P  a  relating  section  middle  of  the  the  mean  FIow  d i f f erence Ap  temperature  s p e c i f i c is  (in  IO"  in.  5  the  in  u ..,.)•  [  d  ° F . ,  gravity  butyl  atmospheric  O.8176  =  alcohol  pressure  in  in  the  inches  .  constant,  i n . )  the  screen.  for  pressure  in  with  having the  a  value  reference  0,5822  of  pressure  (in  tap  at  pressure. in  the  just  modified  behind  the  pressure.  longer ,v a I i d . Corp.  is  the  turbu I ence  by  housing  50)  K  be  equation"  a of  minimize  i m ^ ^ ^ m ^  1  system,  to  behind  in  given  to  micromanometer  just  tunnel  manometer (T  and  intake  proved  "velocity  butylalcohol)  T  the  m.sec""')  , ^  the  design  for  section  (in  Corporation of  This  standard  velocity  across  To  tunnel  F i r s t ,  Engineering probe's  the  the  probe wind  wire  it  reference was  constant  appropriate  calibrated  the  the  screen,  Hence  obtain was  tunnel  as  was  K  follows  to  and  longer  with  K, a  was  no  the  Flow  single  calibrated  obtain the  of  mean  the wind  tap  at  0.5822  =  value  carefully  tunnel  current  no  pressure  in  hot the  relationship velocity  A3  in  the  Next, wind  tunnel; the  this  probe  tunnel,  is  was  and  given  by  immediately  the  wire  King's taken  currents  Law to  (suitab Iy  corrected  for  atmospheric  pressure)  were  observed  wind  v e l o c i t i e s .  performed  The each/** p was from for of  This  numerical observed  value in  the  each A p  from  values value  of  temperature at  calibration  was  pressure  and  several'-  different  procedure  I.I,  no  and  calculated  Corporation changes  Engineering  A  from  K  Flow  (assuming  the Mechanical  average  Corporation  was  twice.  transferred  a l l  complete  the Flow  1.12).  a n d m i c r o m a t e r  differences  both  (eqn. A  in  tunnel .  the r e s u l t s  the repeated  as  follows.  funnel,  a  the hot  wire  Then  K  value  was  averaged.  calibration  gave  For for U  system)  calculated Combination  a  weighted  of  K = 0,5606 cr= 0.0179 for  31  paired  The  B•  B,I,  values  error  The S i n g I e,  of £p,  is.discussed  or  U-Wire  where o"is  in  the standard  Appendix  VI I ,  Section  deviation.  A,  Probe  C o n s t r u c t i on  The  probes  Corporation  used  Model  for  HWP-B  a l l  measurements  probes  using  were  Wollaston  standard  Flow  platinum  wire  of  0.0003  of  etching  was  similar  Initially soldering Experience  solder  were  readily  To a  ends; the  joints  remedy  comm.), of  a  a  tweezer,  etched  in  adequate  B.2.  pulling  them  taut  a  was  etched  steel  prongs. f o r two  insufficient  parts  the wires of  in Fig. of  tip  and  of  the  for  wires  vibrations.  Grant  and then  wire  were  Pacific. A  section  minimizing  Naval  in  about  by  I9&5  soldering ,  ZD  the  along  manipulation mm l o n g  I.5  in ,  Laboratory  the form  removed  This  mounted  After  1.3.  bent  were  portion.  while  the  method  configuration  >  was  had  breakages •  C a I i b r a t i on  performed  The  of  taut  the wire  the c e n t r a l  1965,,  During  the  the  defects,  length  r i g i d i t y  the s t a i n l e s s  of  The  (1965)•  Pond  ends  of  by H .  in  by  by  area  and shown  kinks  used  diameter.  mounted  by' p r o n g  these  short  prongs,  with  broken  core  t h i s;;\ t e c h n i q u e w a s . u n s u . l t a b I e  (2)  way s u g g e s t e d  (pers.  the  the/small  (I)  that  were  that  A  microns)  to  across  s howed  good  in  wires  them  reasons:  7»5  in,. (abou t  in  the Flow  c a I i b r at i on  single  wire  measurements  correct  mos t  to  of  Corporation  procedure  v e r t i c a l l y of  within  the ca  i bra t ions  I .5°  cons i s t e d of  showed •  of  wires  were  tunnel.  in. t h e . t e s t  the angles about  I  visually  section.  that  (The method  placing  Comparison  such  alignment  was  of  m e a s u r i ng  wire  A5  angles - i s ' o u t l i n e d I962.)  This  as  is  was  points  measured  procedure  Flow  accuracy  Calibration speeds  in  by  considered  were  the  outlined  Corporation  in  -Bui l e t i n  sufficient  obtained  at  manual  for  about  micromanometer. the  16-A,  provided  f i e l d  mean  10  The  Feb. use.  wind  calibration  with  the  HWB-2  2 hot  wire  U ,  where  2  speed the  bridge.  in  I  was  form  Frequent  the  the  to  C.  The  C l *  a  of  few  wire A  current  King's  tunnel  had  were  plotted  in  line  Law  of  this  1965,  were  straight  of  calibrations  one  results  repetition  small  summer  runs,  the  m.sec''.  standard  since  The  ma., on  (eqn.  was  been  not  A  I U  against the  plot  mean  wind  represents  1.12). was  set  up  always  performed  and  this  calibration not  as  desirable, at  the  possible.  before  and  after  but  beginning For a  later  set  of  runs.  X-Wire  Probe  C o n s t r u c t i on  The Model  X-wire  HWP-X  probes  probes  21+  used in.  were  long;  standard the  same  Flow  Corporation  length  as  the  U-wire.  probes.  The to  of  fhe  center  wires  U-wire of  each  were  attached  probes; wire  the  but  on  and  etched the  etched parts  upwind  in were  half  a  similar not  of  fashion  quite  each  to  in  the  A6  minimize  interf erance.  shown  Fig,  in  A  Although lack  careful  it  method was  handling  When  the  of  found wire  angle  a 9  single to  hot  the  with  a  construction by  repeated  angles  in  If  parallel  the  the  plane  direction  misalignment), velocity  If  this  cooling  the  is  the  the  did  to  the  mean  at  assumed  component  finished  array  is  at  f i r s t  seemed  to  calibrations  not  the  that  change  two  in  given  a  then  and  that  during  a  (see can  turbulent  sensitive  horizonta I  t i l t e d  same  the  in  becomes  with  use.  wires  AI.D be  for used  is a  to  flow  to  velocity  directions. parallel  to  discussion  on  measure  two  wire to the  turbulent  is the  cooled wire  only (we  effective  flow  of  by  the  will  return  instantaneous  mean  horizontal  by  (A  where the wire  u,  x,  y  v  and  and  makes  z  with  w are  the  directions the  at  time.  perpendicular  velocity is  if  array  later),  C  placed  flow  assumption  v e l o c i t y U  is  vertical  X-wire  components  it  ve I o c i t y  both  of  wire  horizontal,  fluctuations  to  tip  Theory  C.2,  an  probe  I  this  r i g i d i t y ,  A  fIucfuating  veIocity  respectively.  horizontal,  is  The  normally  components angle  about  97 t h a t li-5 * 0  1,1)  in the  A7  The  above  C  =  expression  Us i n.9 [l  +  +  can also  (2/U) (u  i  ( u  ?  be  +  written  w/tan9)  .+ w c o t 9  2  as  2  +  2  u  2  csc  2  9  +  2uwcot9)  1.2)  (A  In  the atmosphere,  of  t h e mean  are  of  flow,  turbulence, levels  that  order,  contributions a n d wi I I  be  The to  =  bridge balance  Us i n 9 , s o  that  of  about  the  or  \0%  quadratic giving,  less terms  by  *  Usin9[l  +  (l/U)(u  in  out  contribution  the  a  +  network  the  are  neglected,  expansion  C  used  so  the second  binomial  rms  2  w/tan9)  hot-wire  fluctuating  +  . . . ]  anemometer of  velocity  the  (A  system  mean  1.3)  i s  ve l o c i t y ,  component  is  a p p r o x i ma f e I y  c  -  sin9.u  +  cos©.w  i,  •  which the  is  a  plane  Iinear of  the  However, temperature  Champagne  to  R.  W.  More  at  Stewart,  recently, Sciences  Laboratories;  velocity  a  have  results  a  -  '  components  made  (personal  shown  have  wire  that  appeared  Ph.D. dissertation,  of  •  '  in  U.  the  by  communication  the cooling  L a b o r a t o r y , ' B o e I n.g S c i e n t i f i c  and as  «  measurements  heated  Corporation  1965)'*  these  the  experimental along  Boeing in  of  .  wire..  distribution  H.  Flight  t i l t e d  unpublished  F.  ^  combination  I.I).)'  (A  in  Report  effect  N o . 103,  Research of  W a s h . (Dec.1965).  A8  of.the As  a  veIocity  result,  considered  compohent  the  above  valid,  and  along  the  expression a  more  wire  for  c  empirical  cannot can  no  be  neglected.  longer  relationship  be  has  to  be  empIoyed .  If  is  C  the  h o r i z o n t a I w i nd and, a  verticaI  horizontal; to  cooling  velocity  ve I oc i t y Iine,  then  a  and  taken 9  is  of  to  the  be  the  in  angle  generalization  of  wire, the of  the  U  is  plane the  case  a of  wire  steady the  to  wire,,  the  a b o v e . a I Iows  us  write  C  where  f(9,P)  other  geometrical  with  A  small  a  change  is  an  unknown wire  change and  c  =  f(9,P)U  function  parameters  dC  in  the  t i l t  in  U  =  =  dC  of  wire  angle  9  and  P.  cooling  is  the  thus  f(9,P)dU  +  velocity  C  represented  associated by  df(9,P)Ud9  (A  I.5)  d9  In  a  fluctuating  velocity  where  fluctuations turbulence component  wind  we  have,  levels,  c  represents  assume  only  second  the  a  in  the  change  eqn.  order  A  cooling transverse  I.3,  e f f e c t .  vertica I f|uctuating  in  For  wind  small  velocity  is  w = =  (U Ud9  +  u)tand9 (A  1.6)  A9  where  d9  is  in  radians.  C  For  a  properly  ac.ross  t h e wi r e  latter  is  there  is  a  depends  function  of  of  Corporation  e  is  on the  Bulletin  wave dU/dC  ms  is  current =  the  f(9,P)  the  (A  bridge,  current  the I,  velocity  coo l i n g  while  C.,  of  I .7)  voltage  a  E ,1*-*  the  Hence,  v e l o c i t y ,  the wire  calibration  if  voltage  magnitude  procedure  (Flow  gives  rms s q u a r e  ,  wire  across  37B)  amplitude  df(9,P)w IS  cooiing  | |  where  +  u. = d U ,  hot wire  in  produced  u  the  dC  the regular  since  f(9,P)  balanced  a , f l u c t u a t i o n  fluctuation  Use  =  Hence,  of  =  and using  ..(A  s  wave i .  e  m /i  calibration  Putting eqn. A  =  K(u  +  I'  I.7  = in  voltage  for  1.9)  square  dl/dU, eqn. A  b'w)  1.8  gives  (A  I . 10)  where  K  =  K t b  The  quantities  ( m / i ) I ' s  I'  df(9 P)  fT97PT d9  determining  K  /A I  #  '  c a n be  (  easily  A  obtained  * a \  A 10  A  normal  tunnel  calibration  shows  that  of  the  King's  wire  Law  at  an  remains  angle  true  9  in  (Fig.  the  A  wind  1.5),  s  o  that  \  = A + BT^U".  %  (A 1 . 1 2 )  Thus  I,  the  run,  mean  the  wire  current,  quantities  m  is  and  s  determined  i  are  obtained  corresponding  square  wave  from  tunneI  caIibrations .  the  wind  determination  C»3«  of  b'  C a I i b r a t i on  The  is  of  the  calibration  similarly  to  that  of  for  calibration  described  X-Wi  each  a  in  in  The  in  setting from  the  up  for  each  the  f i e l d ,  and  B  empirical  Section  C;l+...  re  wire  single  of  wire,  the  X-wire  with  the  was  made  following  add i t i ons .  A screw,  brass to  smooth,  the  flat  carpenter's  The both  rectangle probe face level,  probe  wires  made  was  was  arm  could to  fastened,  pear be  visually  as  a  before  bolts  connector  aligned  serve  turned  its  by  and  end.  v e r t i c a l l y ,  reference  its  f i r s t  approximately  the  a Its  using  locking one a  surface.  calibration same  angle  until to  the  All  horizontal  and  surface.  Vertical  adjustment the  of  same  ,ln  probe  the  Flow  Corporation  by  a  clamp  protractor,  of  The  the  angle  determined  time  the  wire  geometry  wires  I9&5,  wire  probe  to  wire the  had  not  changed  the  use  order during  wire.was. in  order  example  shown  in  were  9 /  between  were  of  the  of  accuracy  one  then to  F i g .  A  A  l.5)«  and  B  arm.  fastened  A  removable angular  horizontal  was  determined  unchanged  obtain  was  angle  was to  last  ensure  of  it  1°or in was  during  this of  that  before  less.  each the  assumed all  A  that  runs.  9 I.IH  to  and  Since  successive  angle  eqn.  in  c a l i b r a t i o n .  cal ibrations  obtained  at  plane  was  outlined  order  calibrated  probe  procedure  caIibration,  remained  a  was  d i r e c t i o n .  measure  the  the  in  wind  which  calibrated  since  geometry  provided  the  to  vertical  axis.  with  This  wire  probe  long  the  horizontal  mean  on  used  standard  probe  of  was  made  |6A.  the  the  and  the  tunnel,  on  to  runs,  stand^  its  the  horizontal is  about  Bulletin  geometries  Each  probe,  each  that  f i e l d  wind  retort  locked  surface  contained  centered  variations  determinations  and  of  period of  a  the  according  Corporation  the  to  that  Flow  was  also  to  the  ensured  wires  rotations  this  arm  of  calibrations  polnter,.fastened  a  permanently  both  standard  after  was  to  supported  During  it  alignment  the  during  parallel  a  then  the (an  AI2  C .Ij..  Empirical  If wind  a  hot  tunnel,  Determination  wire so  probe  that  one  horizontal,  then  the  constant  as  long  as  However,  if  the  the  voltage  determined w to  wire  across from  determine  voltage which  the  eqn.  U d 9 ^ ... H e n c e , K,  by the  variations  are  produced  increments.  This  placed  of  its  Wire  in  a  wires  I.10.  U  through  an  this  case  the  probe  value  can  be  dE  =  by  turning  the  be  from  can  e  b'  across  seen  the  not  as  remain  angle  =  wire  in  the  d9,  e  dU  0,  outlined  part  the  measured  from  For was  these  used.  determined speed  was  range  5  voItage  eqn.  to  A  I.10  eqn.  A  measurements,  the  The  procedure  was  as  (as  described  following  set 7  at  a  m.sec  c a l i b r a t i o n .  Then  the  =  A9  +3°,  Flow  Corporation  follows. eqn.  A  wind  F i r s t ,  K  l . l l ) ;  then  '  reasonably  order  •  This  the  wire  +5 ° ,  to  was  +8°,  obtain  was  foI  I owed  t i l t e d +1°°  ••«'*'••*>  1.6.  velocity  in  wire  relation  constant'caIibration  s e n s i t i v i t i e s )  ang I es  and  the  angular  '  derived  and  before  from  of  then  as =  determined*:,  etched  a  change.  amount u  level  the  will  small  calibrating of  to  wire  change  (in  9  does a  b'  turbulence  at  the  velocity  will  Constant  low  is  across  t i l t e d wire  A  E  mean  is  the  is  voltage the  of  by  a  U  from  9,  was  c  the  (in  wind  the  high  square  successively  tunnel  wave  through  wh I c h • w e r e  A 13  measured DC  voltage  with  a  successive  20-50 t i m e s values the  protractor  output  recorder, each  the  on  of  for  averages  visually  appropriate squares  values  quite  value  of  The  used  or  b'  =  large.  F*" use  for/^9 of  a  It were  must  wire  This  was  and  increment  as  A  shown  in  0.  This  was  were  F i g .  weighted  according  was  were  bT  used  | t h A 9  w  w  is  used  all  for  much  was  to  the  A  smaller about  a  least-  F"  versus  number  1.6  of  appears  than  u,  and  occa-  5  Hence  computations,  of  one  average.  F i g .  less.  the  f i t t i n g  the  most  drawn 1.6.  values  in  much  at  A  and  the  thus  value  of  avoiding  procedure.  at  probe  this in  point  the  assumed  to  assumption  configuration  shown  reach be  was  last  as  typically  can  the  determine  normally  noted the  to  averaged was  purposes by  about  calculated  curve  obtained  The  after  repeated  the  46  A 9 .  computational  b'  was  direction  X-wires. the  with  A9,  established  of  of  be  of  pointer.  dual-channel  to  will 0  procedure  for  linearization  made  stream  =  being  0)  "b~T v e r s u s  points,  Sanborn  function  Since  and  The  angular  t h e n A© sionally,  (A9  a  detachable  quadratic  that  change  =  as  the  t o A9  line  Each  ^9.  plotted  value  line  increment  each  through  The  on  AQ.  each  the  recorded  zero turn  for  b'  was  using  was  set  that  mean lie  all  stream,, in  is  in  by  eye  the  calibrations  and  the  plane  r e a l i t y and  the  not  of  mean the  unverified, checked  by  since  A|J+  measurement.,  During  the  mean  wind  also  the  wind  vector  measurements. but  exists  f i e l d  measurements  varied,  direction This  so also  e f f e c t ,  nevertheless,  that  a  must  will  the  horizontal have  however,  and  a Iso,  variation  of  of  affected.the  was  be  direction  not  compensated  discussed  in  the  for,  next  section.  D.  Effect from  If  the  the  containing an the  of  Deviation Plane  of  the  direction one  velocity  of  sloping  a n g l e ^ w i t h  the  in  +  a  and  and  in  +  of  the  positive  perpendicular  from  to  x  plane  vcos^a -  If  the  wire  cooling  C  slopes  velocity  =  £[(U  +  +  at C  of  Mean  -  mean  plane  Velocity  in  the  plane  plumb  line  velocity  U,  makes  then  are  horizontally v e r t i c a l l y  axis.  The  component  is  (U +  u ) s i r\jS  angle  is  given  ujcos^  [vcosyg  line  vertical  the  ,  the  the  a  vsinyg,  w  with/3  total  horizontal  direction  u)cos^3  Direction  X-Wires  X-wire  components  (U  the  +  -  9  to by  the  h o r i z o n t a I,  (compare  vsin0]sin9  +  (U + u ) s i n £ j  2  with  wcos9j  then  eqn.  A  the I.I)  2  (A  1.15)  A  By  expanding  2 u  2 2 /U  ,v  C  =  2  eqn.  A  and  1.15  etc.,  then  the  U si n 9-(fcos ^ 2  A  I ,i|)  2 |7c  the  Binomial  reduces  eqn.  2  t_ lcos£ Us i n ©  reduces  osyS  +  s i r\S\u  +  cos/3w  sTn^Q/ expansion A  I-. 16  order  +  in  2 \~  "  sin  the  expressions  the  the  I.16)  .(A  of  eqn.  +  c o s ^  w  Jcos/9  +  s i n >g ]  ^  tan©  Sin ©/ 2  +  >  s i n g  a n  2  (A  e  I  .17)  sin ©/ 2  component  procedure  for  derivation  -y—j-  9/  \  following  I s i n£  2tan2(  s i n(2/3) y 2 2 T f  /  fluctuating  -  tan©  (as  s i n ^ T u+  ^ #  \  to  to  2|cos/3  the  of  2  \  for  terms  sin ^)  +  2  2  equation  U [I of  all  2 /U  .  Use  neglecting  15  of  leading  the to  eqn.  two  fluctuating  K,f  M,u  e '  =  e. 2  = K- f 2  -  M- u + 2  a  coo Iing A  wire  cpsfl  w  -  b cos/3 w M  L  I.10  we  voltage  .  By  derive signals  N,v  V  (A  I.l8)  N^v  J  (A  I .19)  (A  1.20)  M  2  veIocjty  2  ]  where  [  c o s y9+ p  sinjfi  TTn^0 . r  A 16  N  -iilaiM  R  * where  r  equals  By A  p u t t i n g ^ is  I.I 0  It range  I or  fan 9  ( A I . 2 1 )  2  r  2*  =  the  0,  original  form  of  the  equation  obta i ned.  may  30°  be  noted the  70°,  to  fory9as  that  value  high  changes  of  Mr  on  Hot  15°,  as  only  9  and from  in  r  O.97  the to  1.07. E.  The ' E f f e c t  Changes can  produce  velocity changes speed.  mean  wire  a  change rate,  w h i e h i n wire.  produced  turn  in  a  uses  change  the  same  Uj  a  fluctuation  a  component.  a  in  in  in  temperature  The way  wire  resultant as  a  change to  change  change the  changes  fact  due  a in  the  the in  of  voltage  in  wind  wire  wind  speed in  resistance,  voltage  the  utilizes  constant  change  temperature  "velocity"  of  technique  velocity,  temperature  a  wire  turbulent that  fluctuations  measurements  indicate  produces  shows the  to  causes  wire.  to  the  wire  the  in  of  hot  Measurements  temperature  to  which • then  However, by  the  temperature  surrounding up  since  Wire  and  contributions  measurements  technique  coo Iing  temperature  spurious  in. the  current  the  in  Temperature  fluctuations,  For  causes  of  is  across also  f l u i d .  fluctuation  contribution  A  The mean  effect  temperature  velocities  The by  of  the  temperature  on  canbe  fluctuations  the measured  estimated  resistance  R  of  as  a  spectra  outlined  wire  at  a  and changes  of  below.  temperature  2  T  0  is  is  0  (Hinze, only  and  used  the wire P  1959,  about  will  <T i 3*5  jfo  0  the  neglected.)  10  ^  ( ° C ) " ' ,  resistance  common  ratio  way o f  linear For  that  R/R  Q  Both and  wire a  .23  temperature  =  T  given  change  in  wire  equivalent  to  a  temperature  =  1.8  (AI.22)  for  was  the squared  conditions wires for  Law  encountered  used, the  normally  is  by  the  (a+bi/U) ( T - T )  equation  (Al .23)  0  I959>  term  230°C.  about  King's  temperature  7^,  P  and comparison  Eqn.  of  2-7).  equations  AI.I2  that  B  The  of  the overheat  (Hinze,  and b are constants show  term  expressing  2  a  is  ]  the reference  the platinum  so  i R  for  at  (The mangitude  78).  of  0  resistance  be  x  A  T  expression  0  R  in  fluctuating  R=R [l+cr(T-T )+<r'(T-T ) +...  where  16a  =  temperature  change  fluctuations  in  mean show  ( A l .21+)  b(T-T )/R 0  produced wind up a s  by  speed  a  change  dU s i n c e  variations  in  dT  is  ambient U,  Then  16b  A  from  equations  AI .22,  and  .23,  dT  B ( T - T j ( l+cr(T-Tj) o _ ——-Q-  =  measurements  calculations  I  2  from  made, data  -0.3.  dT/dU'~-0.2  to  temperature  generated  about  9  estimated  1  flow  to  from  the  atmosphere,  allows  not  in  rms  measured rms  one  9  was  length  for rms  velocity of  the  level  importance  the  velocity  as  L ~ L '  using  of  in  fluctuation  fluctuation  analyzed  value  the  estimated  runs  wire  fluctuation  turbulence  guage  and  ten  and  2.0  fluctuation  temperature  to  or  1.8  all  comparison  temperature  available,  the  'contaminating'  the  Monin-Obukhov  an  either  that  9',  Hence,  estimated  fluctuations  Since  by  the  was  0  showed  Then  0.2u'.  9'<~  is  R/R  .25)  (Al  21. YD  dU  For  ,2i|.  of the  9  of  u'  of  the  the  latter  signal.  measurements  follows.  shear  Taking  equation  II  were  the B  2.1  gives  dU  u-::-  d(Inxj)  .  K  u.% K  L'  t  so  that  at  the  two  heights  d U  I  L  \dUnx )/ 5  where from for  ^  ~-5  (Lumley  equations estimating  II the  and  B2.I  I , (d(  x^  and  d U  \  Inxj)/  Panofsky, and  AI.26  temperature  x^  = »*sL{  KL'  196I+, an  flux  xiix,) 5  pp  IO7-IO8).  approximate can  be  (A I  5  .26)  Then  expression  obtained:  A 16c  2 9U7  The  ^  expresses  a  'Figures  IV  9  estimated  to  be  For shown  all  in  gives  Hence,  for  ; ;  from  these  would  about  1$,  an  other  runs  t h i s .  The  The  worst  an  error  neglect thus  of  mean  air  is  would  necessitate  at  .27)  in allowing  ;;  except  u  it  was  it  is  seen  error  the  in  most  the  effect lead  uj  runs  that  cm.sec""',  9'^26-28°C.  of  temperature at  in  was  two  found  that  &fo  the  I3O-II4.O  —  1  in  temperature  percentage  not  shown  9u^^-9u. -,  that  cases,  the  does  temperature  calibrated a  and  the  Flow  u t i l i z e s  the  constant  Flow  when  is it  systematic  However,  in  of  data  where  wire  an  so  less,  .10,  cases,  the  (Al  very  of  turbulent  to  very  the  most  For  all  much  less  than  temperature  large  errors  in  estimates.  probe  out  rms  produce  recorded,  fluctuations spectral  two  worst  fluctuations or  and  these to  or  C.9  AX3  \ x^;/  AI.27.  equation  9~.07°C IV  rise  From  dU  " \ ^ ' 0 9  2,3c*'g  . IO,'J/uj^—u. .,  runs,  For  3  *V  T  p - j - r -  d i f f e r e n c e .  to  Figures  9-~-0.9°C. which  B.I  ^  Corporation  is  B u l l .  corrections  are  necessary  temperature  are  a u t o m a t i c a I Iy  different  used  in  correction constant  resistance  Corporation  usually  25,  since  ratio p  5,  changes  corrected  the to  when  f i e l d .  spectral  the  This levels.  current  anemometer  method.  As  n  such  o  in for  pointed  temperature  ambient if  is  fhe  mean anemometer  A  is  used  that for by  properly.  proper the  due  square  "damping"  conduction  important or  less. to  Also,  to  for (My  provided  the  wave  the  wires in  on  wire with  had  b u l l e t i n nearly  velocity  supports.  this  is  ratio  mean used  points  out  completely  fluctuations This  length/diameter  ambient  anemometer  same  alignment  effect  wires  changes  the  about  19)  compensates  produced  "damping"  becomes  ratios  200  200.)  temperature properly.  (p  l6d  can  of  Hence be  effects  neglected,  APPENDIX  A  THE  block  shown were  II;  in  three  diagram  F i g .  either  A  two  U-wire  The remove  amplified recorded  DC by  on  magnetic  X-wire  channels  across a  a  was  f i l t e r i n g  probe..  WIRE  used set  in  of  and  one  led  to  The  Accudata'V  F.M.  record  I  the  were  SYSTEM  each  channel  observations,  U-wire  a  is there  channel,  DC  or  potentiometer  r e s u I t i ng DC  s i gna I  amplifier  channel  on  added  a  a  and I  to  was then  in.  the  the  use  Although  procedure  C  was  compensation  +  \%  is  0  to  recorder  as  much  DC  as  s u f f i c i e n t l y  resulted  in  used  by  Pond  from  the  in  F i g .  amplifier  kc.  amplifiers,  low  l6  frequencies.)  possible  quite  a m p l i f i e r .  provided  shown  10  the  the  and  c i r c u i t ,  from  of  increased  tape  a  of  that  the  remove  and  as  DC  compensation  compensation  saturating  to  same  attainable  within  the  output,  capacitance  with  of  inertia  proportion  was  the  thermal  stage  kc.(It  potentiometer this  output  probe  the  to  the  the  flat  taken  for  to  curve  Without  be  to  that  lower  avoid  adjust  c i r c u i t  response  responses  to  above  to  11.2.  had  the  signal  except  pf  to  added  differentiated  To  HOT  tape.  compensation  A  bridge  separate  The  Typical  each  the  Honeywell  wire  26  THE  c i r c u i t  During  from  hot  to  the  I I.I.  Compensation  (I965),  of  OF  channels.  output  the  ELECTRONICS  with  voltage  low  care the  gain*  signal-to-noise  A I 8  ratios,  noise  (0>02  interest  The was  record  range,  the  total  voltage  frequencies the  shorter  runs  signal  higher  velocity  thesis)  signal  levels  Improved.  s u f f i c i e n t l y  60  s e c " ' ) .  of  the  limited  system  frequencies  higher  to  response  e f f e c t i v e l y  F.M.  the  was  made were  of  recording by  the  the  0  tape  sec  s e c " ' ,  the  which  there  was  usually  small, was  lost steady  and  the  in  no the  wind  of  channel  bandwidth  recorder.  60  was  each  '  than  (in  possible  625  for  better  correlations  very  frequencies  was  about  during  at  system  to  magnetic  linearity than  small  1%,  In  of  the  this  At and  at  somewhat  interest  for  this  noise.  For  some  conditions,  signal-to-noise  higher ratio  A 19  APPENDIX Section  III:  AUXILIARY pp25-27,  III,  MEASURING  contributes  EQUIPMENT an  introduction  to  this  Appendix.  A.  The  A . I»  Cup  The  The array (C. were  six  the  Normally cm  the  below  edge  from  of  the  at  recorded  and  one  via  system, which  for  the  the  were  mounted  cm,  a  the  for  and  assembly  about  multiplexing pulses  in  frems  cups  on  the  cm  35'  the  anemometers  channel The on  separated  a  by  (to  17  35  and  fire  which  was  pulses  were  magnetic a  tape.  Schmitt  oscillator  instrument steps.  cm  cm.  amplified  the  2.0%  level  was  seven  the  a  pulse  These on  at  extended  was  counter,  system  o s c i l l a t o r .  were  was  camera.  each  arms  once,  pulse  an  Rover,  The  cross-wind  diameter  rotated  This  automatic  cm  |6  anemometer  electro-mechanical an  gates 6  80  photocell.  using  and  probes  assembly  photographed  frequencies^  U-wire  cup  an  movable 2l±\  and  activate  an  cup.  at  cup  by  1965)*  150,  cup  frame,  Hamblin,  80,  The  a  trigger  30,  cups).  from  this  0,  measured  anemometers  v e r t i c a l l y  the  generated  In  1961,  the  was  cup  cup  the  also  speed  the  time  to  on  heights  X-and  Each  used  wind  Associates  lowest  the  mean  Thornthwaite  v e r t i c a l l y  mast  to  the  sensitive  mounted  instrument  15  of  Thornthwaite  relative  System  System  p r o f i l e  of  W.  Anemometer  mast The  7  A20  gated  -outputs'were  Channel  -of  To  t  the  ensure  available, A  cup  the  reading  occasions the  every  The base,  anemometer  visually  on  the  was  2  counter  3  thus  of  the  low  The  g a v e ,an  its  expected  wind  of  of  the  in  be  Record  turn  the  data  minute.  (from  was  always  into  every  read  anemometer  mast  was  the at  log,  On  most  lowest  least  to  once  relative  determined  against  error,  Cup  ref I ective  using  cm  25  to  for. each tape  a run  markers  marker  spacings,  tunnel  at  the  in  the  were  summer  linear  f a i r l y  calibrations slow  out  at  For  of leak  large the had  individually of  the  all  2  to  cups  each cpm  discrepancies  been  cup  the  m.sec""'.  13  beginning,  between  same  in  Mechanical  between  relationship  between  a  speeds  1965*  of  3,5$  that  Department  carried  However,  found  c a I i b r a ted  different  I+.-5  expected  Anemometers  were  speed.  was  once  cup  level  wind  It  would  entered  counter  bottom  anemometers  Calibrations end  were  read  each  Direct  cm,  Engineering,  and  the  sighting  cup  speed  data  least  instrument  Calibration  The  at  were  one  •  readings  entered  on  mi n u t e s ,  mast. to  cup  counters  on  by  A ,2,  that  height  level  recorded  tape-,  cups),  seven  and  magnetic  Was  the  highest  summed  middle  calibration and of  average up  anemometer  present  in  the  to  occurred.  A2I manometer  system  a result,  the  1965,  which  general  of  end  Th:  followed  the  repair  of  were  are  the  top  the  movable  of  the  hot  wire  on  the  display  no m o r e  these  leak,  cups  in  our  As  19,  October used.  From  program,  the  2^,  than  Indicators  of  frame  the  w|nd  vane  was  instrument  hut.  On  about" a meter  probes.  p e r p e n d i c u l a r "to direction  of  the  mounted the  I ' I g h f ' r w e l g h t ' p o t e n t I ometr.i.c w i n d  on  "N"  in'use  platform, a Casella  nthwaite  mid-summer.  of  Direction  above  to  calibrations  B,.  feet  up  summer  errors  the  and  the  expected  At  prior  of  experience  Wind  the,tunnel  dial  the  This  vane  and  a half  was  so  corresponded  probe  shafts.  taken  as  deviations from  meter  dials  of  the  ;  was  above  the  3  a mounted  the  adjusted  Deviations  were  mast  vane  to a ' w i n d  about  ends  that  the  direction from  plane  this  of  the  X-wTres •  The  photographed sheets  C .-  and  once p e r  also  would  was  have  difficulties  readings  recorded  in  were the  data  log  Measurements  hoped been  their  indicators  minute.  Temperature It  direction  that  the  operational  prevented  its  temperature by  the  proper  profile  summer  of  operation.  equipment  I9&5,  b  u  *  Reliance  various thus  A22  had  to  be p l a c e d  thermistor,  with  temperature  was  surface,  plus  This  The  readout*  measured  the wafer  measured  at  at  With  various  was  far  time a r e  Temperature  data  wereobtained  long  air  above  below as  the  the an  surface.  absolute  between  probably  water  different  significant.  to 0 . 1 ° C o n ' the r e a d o u t at  determinations  least  once  were made at  during  dial. each  about I4.O-6O  intervals.  Tide  Measurements  Tidal meter  runs,  the  differences  estimated  For  just  from a c c u r a t e  temperature a given  this',  heights  temperature  were  minute  streams  raised  or  displayed  a I so' r e c o r d e d  Tidal averages  of  on the main  were measured  lowered by  from one c o r n e r were  a dial  However  a bead ^  ;  temperatures  run.  D.  :  instrument  instrument. heights  on a commerc i a I' thermometer 'us'ihg  of,the on  the d a t a  heights wave  a winch.  pI a t f o r m .  two p a n e l  in  log  heights  read  mast,.  rotor  The meter  Current  meters  was  speed  which were  sheet  were e s t i m a t e d  instrument  by a S a v o n i u s  about 3  once e v e r y  reflecting  m  direction  photographed  to w i t h i n + 5  against  and  current  and  minute.  c  m  from tape  markers  A23  APPENDIX  A•  IV:  ANALYSIS OF HOT WIRE DATA  I n t r o d u c t i on As  each of  seen  from e q u a t i o n s  the w i r e s  of  A I.IO,  an X - w i r e  the  array  voltage  are  signals  of  the  form  into  the  wind;  from  ej=Kj(u-aw)  e  e.| r e f e r s  to  refers  the w i r e  to  the w i r e  2  ^(u  =  sloping  sloping  +  b w  )  downward  upward.  Both  contain  u and w.  ~2  —2 In and  former X-wire  uw were o b t a i n e d 1.  analysis by one of of  knowledge  b allow  the u and w p o r t i o n s  be at  are  need  not  This  method demands  accurately. easy are  If the  to a c h i e v e .  both  wires  horizontal  formed.  that  « 2 and a and  not  always  If  changed must  the  of  an  these X-array  the h o r i z o n t a l . be known  possible  values  of  and  the  very  never  constants  be c o m p l e t e l y r e a n a l y z e d .  an X - a r r a y . a r e  and have  to be  From  The w i r e s to  u , w  the s i g n a l  the c o n s t a n t s  is  the d a t a  of  K|,  and s u b t r a c t i o n .  the same a n g l e  This  necessary  of  of  methods:  the c o n s t a n t s  by a d d i t i o n  the c o r r e l a t i o n s  the v a l u e s  two g e n e r a l  Precise  separated  2.  work,  at  the  same a n g l e  same s a . n s i t i v i t y  to  to  the  A2i| . . . . .  w  fluctuations  (i.e.  m a n i p u I a t e d -to extracting  u  often  assumed,  outer  wire  Builetin  This  are  well  make  known  their  dubious.  to  ,It  was  analysis.';  After  be  was  out  worked  applicable similar checks  to  designed  p a r a m e t e r s • d-i d ana  to  at  best  a  methods  Flow  described  method in  Corporation  serious  work  suggestion  by  R.  t r i e d .  proved  s e n s i t i ve  investigafe  w  to  w of  tunnels,  an  analysis  Stewart,  to  be  were  effects  repetition  D  of  this  of  the  both  X-wire appendix.  which  and  a  which  extremely  alternative  method  third  successful, not  of of  data  of  method and  geometrically  fluctuations.  the  necessitate  horizontal.  Furthermore,  observations  W.  wires  to  the  disadvantages  in.wind  atmospheric  whose  to  approximation*  find  Section  the  geometrically  angle  s e n s i t i v i t i e s  have  It  be  achieve.  crude  who to  to  to  for  is  of  Furthermore,  changes the  is  in  analog  I y s i.s .  This  readily  equality  s e n s i t i v i t y  wires  same  decided  not  are  without  This  (See  the  the  similar  X-array  o r - e q u a I Iy  that  d i f f i c u l t  thus  and an  set  those  a  c o r re I a t i o n s  w separately..  demands  application  signals  68.).  assumptionof  these  the  both.  very  of  the  for  This  Both  b),  is.used  and  at  =  observed  l6A,  is  a  the  s i m i l a r  wires  . . . . .  and  method  is  give  and  ^  i-  fully  the  A25  B,  Selection  and  Normally than  20  a  Rerecordihg  continuously  minutes  was  broken  of  Data  recorded into  one  accept  a  section  or  more  of  data  longer  subsections  for  analysis.  The were  c r i t e r i a  as  foI  1.  A  used  reasonably  the  that  as  over  seven  wind  the  interval.  within  +  for  up  one  to  the  lowest  reasonable  run  15°  subsection  a  end  runs,  analysis  plane  of  In  wider in  which the  contained frequency  statistical  range  at to  to  was  least be  however, three, instead  steady were  extend meteorological directions  used,  15  complete  analysed  r e l i a b i l i t y  was  throughout  were  observed  mean  of  means.)  steady  of  run  excepting  X-wires  order  speed  no t e d ,  which  the  in  available,  minute  reasonably  present  the  is  were  directions  from  of  present  I  over  change  (It  preferred  the  was  limit.  acceptable.  conditions,  and  only  was  speed  A. n e t  minutes  Wind of  10°  observations  of  the  direction  considered  varied  upper of  n o r m a I Iy  The  The  an  a l l  the  wind  beginning  during  means  mean  interval.  the  considered  of  steady  between  15$  3.  subsection  lows:  throughout  2.  to  at  to low  cycles  provide frequencies.  A26  This  frequency  was  to  a  period  6I4.  at  least  The  of  16  norma sec.  minutes  subsection  Thus  during  the  sec"  corresponding  subsection  had  to  be  long.  contained  discontInuities,which used  I Iy 0,0156  no  "spikes"  would  analysis  to  cause  ring  and  or  other  electronic introduce  f i l t e r s spurious  res uIts •  5;  For  an  wire  The provide For  be  X-wires, about  serially  to  6Ij.  analysis  both  chosen  times was  since real  Rerecording  of  s i g n a I, s p e e d e d  up  recording,  passed  pass" the  was  (0.02  original  sec"'  tape  analyses  either  to  signal.  simultaneously second  the  speeds,  done  o r „16  Ij.  through  the  rerecorded,  the be  wire  made  the  were  signals.  could  analysis  performed  time  to  coincident  s ubsections  into  r e c o r d e r , a f t e r  as  at  required  f rom  rates  of  for  )  to  F.M,  remove  least  5  s  e  c  reproduced  original  tape  f i l t e r  on  any  present  signals  recording  Each  the  Krohn-Hite  filtered  at  follows.  t i mes  a  sec"'  These  switched  to  of  the  both  shortened,  was  2000  were  could  setting  on  subsection.  severaI  one  data  existed  end  signals  Since  substantially  the  and  for  time  signaI  analysis  beginning  sec.  analysed and  for  reproduced  +0,1  a  throughout  well-defined  equipment, l6  analysis  channels  subsections a  within  X-wire  DC  " a l l -  were channels  of  a  o f s i g n a l f r o m  in  A 27  the  start  filters  of  to  as  Ahead  each  of  the  separated  run  The  timed with  outputs.  recorded.  wave  down.  interval  several was  were  filter  same  selected  settle  intervals the  each  had  lengths  The  U-wire  two  X-w i r e  signal  to  'the  subsections,  an  followed  was  recorded  over  consisting  of  itself  by  a short  from  Subsections  were  separated  a zero-signal  end  of  wave  the  each  original  were  shorting the  the  section  original  run,  of  square-  data.  of  square  wave  reasonable waves  recorded,  f o I I owed  by  Krohn-Hite  filters,  set  from  the  another  sine  identification.  Transfer pass  with  made  at  curves  actual  the  of  beginning  Included  the  loads;, are  indistinguishable. not  rerecorded  run  by  i d e n t i f i c a t i o n sine  calibration)  FoiIowihg  rerecorded ended  (for  length.  the  and  signal  by  allow  signals,  run,  was  of  a stopwatch,  rerecorded  This  passed,  since  of  The  shown  I9&I- a n d sections  the r e s p o n s e  in  Fig.  the  A  end  between curves  at  Measurements  IV.I.  of '1965-are I and  were  100  flat  a l l -  ;  ..  sec"'  in  were  that  i nterva I •  Recording rerecording which the  procedures  procedures  contaminated  turbulent  the  signals  at  in the  the  and  laboratory,  turbulent for  field,  noise,  signal. the  noise  introduced In  order  signals  to  noise correct  recorded  A28  in  the  f i e I d-«- w e r e  containing serially nearly  rerecorded  rerecorded  a l l  of  the  interval  was  This  shown  the  was field  inputs  of  recording  •»-The  generated  by  data,  sections.  noise  the  output  signal  the  of  beyond  Pond's  (I965)  showed  that  the  the  that  analysis  in  probe, point of  the hot-wire  by  or  the  for a  generated  noise  rerecorded by  from  shorting  the  and  signal.  was  p r o d u c e d , by  a l l  generated  ;  procedure.  noise  f i e l d  two  that  rerecording,  the measuring  itself  showed  produced  recording  noise  between  rerecorded  levels  as  sections  else  rerecording  used  the  and  the  the  levels  f i l t e r s  of  ana I y s i s  noise  fitters  recorded  hot-wire  in the  noise  the K r o h n - H i t e  end  Later  during  the  the  signals  present  comparing  and  at  turbulent  introduced  noise  shorting  rerecorded  the  noise  equipment. by  the  negligible  equipment, noise.  A29  C.  Single,  of  total from  in  U-wire  fIuctuating  The only  or  the  eqn.  change  A  A  I.3  so  voltage  is  9  of  not  a  voltage is  rerecorded e  p  which  uncorrelated  averaged  signal  added  with  the  The  true  mean  s  square  =  =  consists  provided  This case,  velocity  can dU TJC  u  the  be  =  seen  | and  produces  (e  +  signal  2  .  b'  =0  a  e  contains  ?  sensing  then  e  f n  2  level  =  (A  signal.  e  2  s  that  in  Ku  after wind  e  so  this  signal  contains  e  large.  In  change  voltage  s  essentially  magnitude  is  e  U-wire  components,  too  e  The  the  TT/2.  =  that e  on  down-wind  level with  1.10,  in  signa I  horizontal  turbulence eqn.  Analysis  the A  wind,,  squared  signal  and  =  e '  "e^ +  a  I V . I)  noise and and  noise,  which time  so  that  n  is  -  e  2  n  (A  IV.2)  A30  where  C  and  K  is  To  given  find  amplified, block  of  and  such  rerecorded  Krohn-Hite  central The  f i l t e r  A  then an  (A  2  IV  I .1 I •  density,  each  signal  integrated  analysis  the  four  were  V*~2 I n or  32  V DC  used  f i r s t  to  system  to  law  average  boost  +  in  the  100  v.  The  effect  of  times  the  real  data  run  must  find is  and  filtered,  be  an  shown  of  the  Donner  db  3  average. in  A  Fig.  to  signal  to  an  is  at  l6  ^0-l\.0  v,  some  Donner  squaring  FF/2), separated these TwentyThe  pre-ampIifier  average  undes i rab I e,  the  Is  samp I e d .  band-pass  Square  of  points  with  frequencies.  Iinear  saturation  ( i . e .  through  |02lj. s e c " ' ,  n o r m a I Iy  level  passed  successively  pIecewise  exceeds  the  to  0.25  ar e  and  band-pass  Philbrick  signal  back  were  were  amp I i t u d e s  level  of  bandwidth  frequencies  the  through  octave  range  Lower  signal  occur  2  at  played  the  per  break-point  square  set  amplifier  3O-I4.O v o l t s .  peaks  6I4.  frequencies  Accudata  was  (centraI)  ratio 16,  signal  F F , the  frequency  analysis  being  at  spectral  squared  diagram  The  by  a  equation  K"  IV.2.  A  a  by'  =  amplitude  since  approximation v.  Also,  if  clipping  operational  circuit  on  of  of  the to  the  the signal  amplifiers  the  output  A3!  signal  was  discussed  Pond  output  (I9&5,  voltages  PP*  measured  values  with  IdeaI .response  for  inputs  squared  was  integrated  the  of  by  I 36-1 3 7 ) •  were  in  between  good  '  H  S  agreement  about  and  15  105  volts.  The  (designated A to  reset  on  on  computer  the  noise  to  ( i . e .  level  noise  s i g n a I,  was  on  used  to  100  volts  paper). be  a  to  treated  combined  An  were  squared  (T  and  timed  It  Hz  and  obtaining  a  rms the  TN), with  a  each  setting  measured  *  to  (XK)  feeding  timed  chart  to  recorder. automatically  the  offset  a  system  gain  obtained  and  integral  integrator  under  similarly,  for  input,  paper  integrator out  c i r c u i t s ,  25  the  (corresponding  multiplying  frequency  the  analysis  durations,  signals,  by  Varian  reset  balanced  input  and  full  allowed  zero-signal shorted).  ,  The  obtain  an  integrated  of  hot  wire  and  to  0.1  XN.*-  total  level  The  was  chart  noise  The  recorded  reaching  condition  noise  X)  c i r c u i t  zero  scale  by  signal  '  the  stopwatch  of  t h e ' amp-M f i e r s  of  the  caIibration  voltage average  Je  system,  .sine  into  voItage  +  the  level  wave  and  was of  Accudata  V  V  the  d  from  integral.  is  noted  instructions s i gnaI•  to  that the  sec.  the terminology is that used for digital c o m p u t e r so t h a t XN i s a  single  A  32  Thus:  2  e  A filter ratio when  it  each  desired  was  (analysis) under  transfer  (amplitude  denoted response  at  octave  of  by  A.  square  to  that  A "unit  between  FF  0.5  FF,  normally  of  2  of 1  The  this  an  Ideal  filter"  is  and  FF,  1.5  measuring  This each  used.  of  by  input)  .  for  for was  of  ratio  "unit  defined  the  the  filter  done  the  response  and  IV.5)  (A.  c  obtained  bandpass  frequency  the  frequency,  V  output/amplitude  central  curve  (XK)  t e r m A was  frequencies  the  against  set  of  =  c  central  25  of  for  the  area  ratio/'pIotted filter",  to  have  zero  is  unit  response  elsewhere.  A "% b a n d w i d t h " relative  amplitude  frequency,  (It under  which  Measured 60%  is  for  The  be  defined,  response  of  F  %  the  such  that  filter  at  if  the  F  is  the  central  then  noted the  values the  may  that  area, of  F  is  2  when  the  "$  Krohn-Hites  measured  2  values  bandwidth  the  (A  maximum  value  plotted against bandwidth"  were  of  the  frequency, all  IV.6)  curve is  A.)  b e t w e e n 50  and  used.  of  A varied  by  as  much  as  5%  between  A33  different "%  days,  bandwidth"  for of  each the  was  f i l t e r to  The  gains  The  signal  of  their  A  amplitude  used  If then  the  the  loss  of  flat  300  on  central  output  combined  from  over eqn.  however,  Hz  (see  A  these  frequencies  result  of  IV.5  T  is  e  A  similar  recorded v a I ue  analysis signal  XN  of  the  during  2 s  n  result,  %  bandwidth"  frequency  squarers,  rated used  5  boost kHz.  A  IV.3).  Above  were  order applied  greater  is  to  than  the  mean  ( f j  =  the  time  TN,  noise.  Hz.  by  e ( f ) , s  and  signal  X,  of  .  voltage  .  thejValues  300  recorded  value  (XK)X  'noise'  a  Hz,  reduce  amplification, squaring produce  gains  300  to  represented  the The  (measured)  in  from  performance.  to  about  range  flat  f i l t e r  to  has  a  had  off  curves  the  to  Fig.  dropped  from  time  zero  the  A,  frequency  amplifiers  from  response  based  at  integration which  were  about  Corrections of  without  preamplifiers, to  0,1  a  V  the  multipliers, over  As  f i l t e r  for  used  Accudata  and  each  values  (i.e. be  at  whiIe  (<2%).  measured,  individual  kHz,  2  the  levels.,  Philbrick from  least  was  beforehand  could  frequency,  variation  F  system  etc.)  central  l i t t l e  measured  analysis  at  given  setting  compute  integrators to  a  showed  f i l t e r  used  zero  at  (A  e , n  which  results has  the  in mean  IV.7a)  a  k3k  7?{f)  The  means  and  noise  the  discussion  of  that  to  the  and  part  of  the  from  a  which  to  e  to  of  f,  are  through A a  It  follows  (A IV. b) 7  those the  IV.6)  in  passes  of  II  which  of  signal (from  eqns,  width A  Al.l).  spectrum  in  A  equal  IV.I  to  that  the  the  band  of  is  IV.7 ic\ - C( XK) f x XN 1 f0,,(O = — — [ T -TFT]  , .. ,.. -9)  rri  so  the  the f r a c t i o n  band  from  (eqn.  velocity  parts  f i l t e r ,  frequency  j#||(f)  downwind  at  (f)  eqn,  spectrum  the  T n  pass  frequency.  centered  A  and  definition  contribution  and  (f)  leading  central  f,  s  spectra  from  width  ~~2 e  .  > (XK)B  { A  l v  that  from  Sect ion  II  A.I,  Computa t i ons:  Since nature,  the  some  electronic  expression  computations  calculator.  for were  f0^{f) carried  was out  of  a  using  straightforward a  Friden  130  SJOB  70045  S T I ME $ I 5FTC  UWIRE  WEILER 5  FREQ DIMENSION  SPECTRA  AT(12)  PI=3.1415926 R E A D ( 5 » 1 )  AT  1  V-/RITE ( 6 * 2 ) AT FORMAT(12 A 6)  2  FORMAT( IX ? 1 2 A 6 / )  3  READ<5,3) C , U , S , Z FORMAT) E10.3»3F10.3) WR I T E ( 6 > 4 ) C »U »S » Z  4  FORMAT(1X,2HC=>E14.4,1X,2HU=,E14.4,1X,2HS=,E14.4,2HZ=,E14.4/).  2001 5  READ(5,5) F F , A » X K , X » T » X N » T N FORMAT ( 2 F 1 0 . 3 J E 10 . 3 ? 4 F 1 0 . 3 )  :<o=o WR I T E ( 6 > 7 7 )  77  /  "" ..  FF » A » XK , X , T , XN , TN'  FORMAT(IXJ7E10.3/)  '  '  RF=FF/S RFLG=ALQG10(RF)  6  V/ V N B R = 2 . 0 * P I » R F / U WL06=AL0G10(WVNBR) WRITE(6*6) F F»RF » R F L G FORMAT(IX?3HFF=,E14.4,IX,3HRF=,E14.4,IX,5HRFl_G WRITE(6*7)  7  =,E14.4/)  WVNBR,WLOG  FORMAT(IX,7HWVNBR=,E14.4,IX,5HWLOG=,E14.4/) •ZK = W V N 3 R * Z ZKLOG = ALOG10(Z!<) V.'RI T E ( 6 » 1 2 )  ;  12  ZK,ZKLOG  * ;  F O R M A T ( I X » 3 H Z K = , E 1 4 . 4 , 2 X , 6 H Z K L 0 G - , E 1 4 . 4 / )  FORTRAN  I V PROGRAM  FOR" U - W I R E  ANALYSIS  8 9  10 ; 13  FPHIU=(C*XK/A)*(X/T-XN/TN) PHIUK=FPHIU/WVNBR • P U L 0 G = A L 0 G 1 P ( PH I UK ) ' WRITE(6»8) FPHIU FORMAT(IX»6HFPHIU=,E14.4/) / . . WR-ITE(6>9) P H I U K » P U L Q G ' • FORMAT!1X>6HPHIUK=,E14.4,1X>6HPUL0G=.E14.4/) . SQKPHI=WVNBR*WVNBR*PHIUK WRITE ( 6 ? 1 0 ) ' S Q K P H I • FORMAT ( 1X» 7HSQKPH I = , E 1 4 . 4 / ) • R=((ZK)**0.667)*FPHIU ' ' UW=1.13»R ' WRI T E ( 6 » 13 ). R , UW • F O R M A T { 4 X » 3HR =,E14.4,4X,4HUW KO.= K O + l  11  •  WRITE(6»11)' KO FORMAT(iX>32HNUMBER GO TO 2 0 0 1 •  =>E14.4/) "  •  OF F R E Q U E N C I E S A N A L Y S E D  END  . \  =.16//) -  SENTRY  FORTRAN  I V ^RO^RAM  FOR .U-WIRE A N A L Y S I S  (Cont'd.)  A 35  To and in  for  speed  up  future  Fortram  following  IV  the  computation  U-wire  analysis,  language.  pages.  A  This  for a  some  computer  program  glossary  of  necessary  the  is  program  included  printed  checks, was  written  on  outputs  the Is  given  below:  FF  f i l t e r  RF  rea1  RFLG  log  WVNBR  wave  WLOG  log  ZK  kXj  ZKLOG  1  FPHIU  f 0 M ( f )  cm,  PHI UK  .011  cm.^sec"  PULOG  log  SQKPHI  k 0\|(k)  R  ( k x  input  D |, t  f  sec"'  f number  cm."'  k  (k)  (kx^)  og  )  constants,  X-Wire  plus  printed  to  2  -2  sec  2  (011(k)) cm.sec"  3  )  2  /  5  f ^ , , ( f )  cm,  „2  f r e q u e n c y , were  D.  frequency  2  UW  All  sec  frequency  cm,  all  values  f a c i l i t a t e  used the  for  2 2  sec sec  each  location  2  -2 -2  f i l t e r of  errors*  Analysis  I n t r o d u c t i on  The  two  signals  from  the  two  wires  of  an  X-wire  array  can  A36  be  represented  us i n g e q n s . A signal and  e  given  ej  I,10  arises  arises  2  by  by  e|  =  e  = K (u+bw)  2  (see also  from  from  K|(u-aw)  Section  the wire  the wire  (A  2  A  IV.A).  sloping  sipping  Thevoltage  downward  upward.  IV.10)  K  r  into  the wind,  (r=l,2)  is  e q n . A I . I I .  The  object  of  the present  analysis  is  to find  the  contributions,  ~7(f)  to  =  fjZJ,,(f); ii  the various  centered on  signals  f0||(f) e  2  at  spectra  =  in  the frequency e  fj*L_(f);  ^ ( f )  33  the frequency f.  By  I V . 2 a n d .3)  eqns.  A  in e q n .A  IV.9,  we c a n o p e r a t e  Thus  s  I V , 10,  to  find  f0,_(f) i3  with  from  a  the  -  2auw(f)  A(2)  =  u^(f).+  b w^(f)  +  2buw(f)  A(3)  =  u^(f) -  a b w ^ ( f ) •+  2  2  signals  (b-a)uw(f)  in e q n .A  frequency,  in such  a  to ej and  equations  .  IV.IO  f  operations  U-wire,  simultaneous  a w^(f)  central  width  the three  = " ? ( f ) +  t h e same  of  (A1V.II)  on t h e s i g n a l s  A(I)  the two voltage at  =  .bands'  analogy  (In  in e q n .A  f i l t e r e d  w^'tf)  ( A I V . I 2 )  mus t b e way  that  A37  both  active  frequency be  f i l t e r s  within  correctly  produce  the  band  multiplied  an  identical  phase  pass  intervaI.  In  without  introducing  change  this phase  at  way  every  they  errors  can into  t h e p r o d u c t .  Using pass  and  each  wire  and  the  two  carefully is  integrated  A  IV.9,  we  f i l t e r s  matched  phase,  obtained.  integrated,  5  Krohn-Hite  and  find  Each  their  outputs the  in  a  f i l t e r e d  product  XI(l)-«-, three  set  signal  also  (compare  eqns.  C(l)  ( K , ) "  =  A  2  of  IV.I  A(I)*-,  Every  other  symbol  (e.g.  XA(I))  has  a  symbol  "(e.g.  XA)  in  in  for  from  then  squared From  finding  the  eqn.  I = 1,2,3  ( A I V . 13)  XN(I)1  C(I.)  the  are,  from  eqn.  A  IV,10,  and  C(2)  ;  signal  is  as  band  l-TTTT ' TNTTTJ  XATTI definitions  octave  integrated.  A ( I) = C(I) x X K ( I ) T x i ( I )  The  ^  f i l t e r e d  proceeding  numbers  at  on  =  ( K  the  ) "  2  right  meaning eqn.  2  ;  hand  identical  C(3)  =  side to  ( K , K  of  that  2  ) " ' .  eqns. of  a  A  (A  IV,  I V . 11+)  13  corresponding  A IV.9'.  /  S i nee in the X - w i r e analysis, two s i g n a l s are used a subscripted notation is used. Although the symbol I is used elsewhere to denote t h e mean w i r e c u r r e n t (see e q n . A 1.12), it will a l s o be u s e d in brackets in f o l l o w i n g sections, as an identifying symbol. This makes it compatible with the digital computer. The d i f f e r e n c e s h o u l d be n o t e d t o avoid confusion.  A38  The s o l u t i o n s  to eqns.  f0 (f)  =B»(b A(l) 2  M  f0  5 5  A IV.12 are,  ( f ) = B'(  + a A(2) + 2abA(3)) 2  A( I ) +  f 0, ( f ) = B ' ( - b A ( I) 5  A (2) - 2  :  A (3))  + a A(2) + (b-a)A(3))  (A  I V . 15)  -2  where B ' = (a + b) Use  of  spectra I  .  t h e d e f i n i t i o n of  k (Section  where k -  Treatment  explained Fig.  of  The  A IV. 1+ shows  The  X-wire  octave  wave was  set first  input  = f0(f) k  the R e r e c o r d e d recorded  in Section A  used to a n a l y z e  and was  gives  the  (A  IV.16)  2TTf/U..  The X - w i r e s i g n a l s as  A.I)  vaIue 0(k)  D.2..  II  at  in  the f i e l d  were  rerecorded  IV,B.  the b l o c k  diagram  of  the a n a l o g  system  signals.  filters  were m a t c h e d as  the f i l t e r i n g  frequency  fed from a s i g n a l  signal  Data  to the f i l t e r ,  by u s i n g  generator and  the P h i l b r i c k p r e a m p l i f i e r f o l l o w i n g  follows.  A  sine  a counter,  into a f i l t e r  the output the f i l t e r  signal (see  input, from  Fig.  A39  A  IV .1+),  upper  were  and  fed  lower  maintained  at  while  were  zero  both phase  manner. inputs zero  and  could the  The  curves  differ  central  as  Initial  showed  that,  much  as  frequency  on  the  same  visually  observed.  The  preamplifiers  the  were  signal  frequency  and  the  to  the  f i l t e r  obtain  f i l t e r ,  and  The inputs  to  enough, B.2).  the  but For  integrals I02l|. s e c "  1  =  each  the  sides),  and  same  as  and  large  piece  of  obtained  ,  obtai n  was  of  same  f i l t e r test  for outputs  dia I  f i l t e r s  the  transfer  far  as  it  loads  readings  (2.5$ curves  could of  from were  be  both  f i l t e r s  analysis.  set  measured (I  to  the  (see  eqn.  1,2)  for  =  ensuring  multiplying to  each of  produce three  f i l t e r i n g  IV.6),  A  each  f i l t e r XI ( I )  that  the  signal  circuits  were  large  clipping  (see  Section  signal  and  frequency and  a  t h e f l i t e r  fi I ter  again  ana I y s e d ,  va l u e s  to  the  2  data, at  band  during  XA(I) j. XA(2)) .  .  as  both  two  output  as  responses  then  were to  between  in  to  pass,  indicated  preamplifier  the  corrections  were  so  although  band  figure  measurements  input  (XA(I)  correct  fed  for  were  matched  frequency  generator  squaring  not  was  then  controls  points)  obtain  Philbrick  both  the  The  Lissajou  frequency,  f i l t e r  XA(3)  signals  5$  the  wide  band.  to  was  between  about  Next,  a  (3-db  f i l t e r  generator  centered  and  until  second  through  pass  oscilloscope.  frequency  adjusted  signal  X-Y  ' f r e q u e n t i es  common  difference  the  transfer  a  swept  phase  an  cut-off  s h i f t .  The  across  into  X N ( I) .  three from  noise 0.25  Their  to '  Alj.0  respective stopwatch  The as  for  D.3»  time to  intervaIs  within  squared  +  gain  the U-wire  thence  from  the  of  the  the system,  for  analog  For  X-Wire  three  the solutions  results  of  and TN(I)  were  measured  with  a  s e c .  analysis.  Calculations  Initially,  0.1  T(D  XK(I)  this  see  was  eqn. A  obtained  IV.5«  Analysis  values eqn. A  analysis,  of  A(l)  in  IV.lIj.  were  using  an  eqn. A  IV.13 and  computed  electronic  from  the  desk  calculator.  This  method  consuming,  as  proved  well  as  to  be  prone  unduly  to  human  laborious errors.  and As  time-  a  result,  for  *  the  I.B.M.  JOl+O d i g i t a l  member  of  Analog  results  one-half  the s t a f f  of  of  were  computer,  a  program  the U n i v e r s i t y ' s  entered  the so I utions  on p u n c h e d  were  computed  was  written  Computing cards, by  a  Center.  a n d more  means  by  of  than  this  program. The outlined outputs  detailed on is  fina I  version  the f o l l o w i n g given  below:  pages.  of  the Fortram A  glossary  of  IV  program  the  is  printed  AJLJ. I  FF  f i Iter  RF  real  RFLG  log  WVNBR.  wave  WLOG  log  ZK  kx.  ZKLG  log  sec"  frequency  frequency  1  sec"'  f  f number  k  cm."'  k  (kx^)  FSQU  era.  FSQW  cm.  0, (f)  cm.  FUW  f  RUW  R, (f)  PH 1 UK  0,,(k)  PH 1 WK  ^33  PH1UWK  |0, (k)|  PULOG  1og ' 0 , , ( k )  PWLOG  log  PUWLOG  log  SQKPHU  k  5  2 2  - 2 sec sec  2  -2  -2 sec ^  3  3 -2 cm.?sec  cm.3sec"  (k)  cm  5  2  0  0  5 5  .3s  e c "  2  2  (k)  jZf, (k) 5  M  (k)  cm.sec  -2 ^  PWOVPU TAN2T  tan  THETA2  9/2  All fiIter were the  gains  and f i l t e r  frequency,  printed location  frequencies  (26)  and a l l  out along of used  transfer values  with  any e r r o r s . about  1.5  functions  such  spectral A  X(I),  values,  typical  minutes  as  of  f o r each XN(l), to  T(I),  f a c i l i t a t e  r u n f o r 25 computer  central  f i i t e r  time.  etc.  SJOB ST I ME SIBFTC  70045  WEILER 5  XWIRE  SPECTRA  FREQ . D I M E N S I O N C ( 5 ) , T < 3 ) , AT ( 12 ) ,XA ( 3 ) ,XK ( 3.) , X I ( 3 ) »XN ( 3 ) , TN ( 3 ) ,A ( 3 ) P I= 3.1415926 1 A S S I G N 2 0 0 0 TO M '• '' • CALL EOF(5,M) FORMAT ( 1 2 A 6 ) / ; 1 F O R M A T ( 3 E 1 0 . 3 , 5 F 1 0 . 3 / 3 F 1 0 . 3) 2 FORMAT ( 2 F 1 0 . 4 ) 500 FORMAT ( I X , 1 2 A 6 / ) FORMAT(F10.3,E10.3,3F10.3) 4 FORMAT(IX,SHU =»E14.4,3X,3HS =,E14.4,3X,3HZ =»E14.4/) 5 FORMAT(IX,5HC(1)=,E14.4,IX,5HC(2)=,E14.4,IX,5HC(3)=,E14.4/) • . 700 FORMAT ( I X , 5HC ( 4 ) = , E14 . 4,4X , 5HC ( 5 ) = , E 1 4 . 4 / ) • 800 OFORMAT ( 1 X , 4 H F R F R , E 1 4 . 4 , 4 H R E F R , E 1 4 . 4 , 7 H L 0 G R E F R , E 1 4 . 4 , 5 H W V N B R , E 1 4 . 4 6 1,10H LOG W V N B R , E 1 4 . 4 / ) FORMAT ( 1 X , 4 H F S Q U , E 1 4 . 4 , 4 H F S Q W , E 1 4 . 4 , 4 H FUW,E14.4,4H RUW,E14.4/) ' .. ' 7 FORMAT (1X,6HSQKPHU,E14.4>6HPW0VPU,E14.4/) 9 OFORMAT ( IX , 5 H P H I U ' K , E 1 4 . 4 , 3 H L 0 G P H I U K , E 1 4 . 4 , 5 H P H I W K , E 1 4 . 4 , 8 H L 0 G P H I W K 8 .1 , E 1 4 . 4 / I X , 6 H P H I U W K , E 1 4 . 4 , 1 0 H L O G P H I U W K , E 1 4 . 4 / ) • READ ( 5 , 1 ) AT • .. s • 2000 WRITE(6,3) AT KO =0 ' . R E A D ( 5 , 2 ) C. T, U , S, Z . WRITE(6,700) C(1), C ( 2 ) , C ( 3 ) WRITE(6,800) C ( 4 ) , C ( 5 ) WRITE ( 6 , 3 8 ) T ( l ) , 1 ( 2 ) , T ( 3 ) > • FORMAT ( I X , 5HT ( 1 ) = , F 1 4 . 4 , I X , 5HT ( 2 ) = , F 1 4 . 4 , I X , 5 H T- ('3 ) = , F 1 4 . 4 / ) 38 WRIT.E ( 6 , 5 ) U,S, Z " • C4 5SQ. = l . / ( C ( 4 ) + C ( 5 ) )**2 . C4SQ = C ( 4 ) * C < 4) " . • C 5 SQ = C(5)*C(5) . _ . .' . ___ >  .FORTRAN  I V PROGRAM  FOR X-VJIRE  ANALYSIS  READ ( 5 » 5 0 0 ) FF DO 1 0 1 I = 1 »3 ' . • .... R E A D ( 5 , 4 ) X A ( I ) , X K ( I ) . X I ( I ) , XN ( \ ) , TN ( I ) ' *: WRITE(6,11) X A ( I ) , XK(I),XI(I),XN(I),TN(I) FORMAT ( I X , 5 E 2 0 . 5 / ) 11 . A( I ) = ( C ( I ) * X K ( I ) )/XA( I ) * ( X I ( I ) / T ( I )-XN( I )/TN( I ) ) 101 555 FORMAT ( 1X,5HA( 1 ) = , E 1 4 . 4, 2X , 5HA ( 2 ) = , E 1 4 . 4 ,2X»5HA ( 3 ) = , t l 4 . 4 / ) W R I T E ( 6 » 555 ) A ( 1 ) , A ( 2 ) , A ( 3 ) "• RF=FF/ S RFLG = ALOGIO(RF) - K0= KO + 1 FSQU = C 4 5 S Q * ( C 5 S Q * A ( 1 ) + C 4 S Q * A < 2 ) + 2 . 0 * C ( 4 ) * C ( 5 ) * A ( 3 ) ) FSQW = C 4 5 S Q * ( A ( l . ) + A ( 2 ) - 2 . 0 * A ( 3 ) ) FUW = C 4 5 S Q * ( - C ( 5 ) * A ( 1 ) + C ( 4 ) * A ( 2 ) + ( C ( 5 ) - C ( 4 ) )*A(3') ) RUW = FUW/SQRT(FSQU*FSQW) WVN5R= 2 . * P I * R F / U WLOG = A L O G 1 0 ( W V N B R ) ' > ZK=WVN8R*Z . . . ZKLG=AL0G10(ZK) W R I T E ( 6 , 6 ) F F , R F , R F L G , W V N B R » WLOG ' 41 FORMAT(IX,3HZK=,E14.4,2X,5HZKLG=,E14.4/) WRITE(6,41) ZK,ZKLG . • WRITE ( 6 , 7 ) F S Q U , FSQW, FUW,^.R'JW ' ' ' 2001  - - -  •  •  F O R T R A N I V PROGRAM FOR  X - V J I R E A N A L Y S I S ("Cont'd.)  ,  . . .  P H I U K = -FSQU/WVNBR " * " ' ' . . """*""" PUL06= ALOGIO(PHIUK) PHIWK= FSOW/WVNBR P H I W K = A 3 S ( P H I WK ) / PWLOG= A L O G I O ( P H I W K ) PHIUWK=FUW/WVNBR PHIUWK=ABS(PHIUWK) PUWLOG= A L O G 1 0 ( P H I U W K ) W R I T E ( 6 » 8 ) PHIUK, PULOG, PHIWKtPWLOG»PHIUWK»PUWLOG SQKPHU= WVNBR*WVNBR*PHIUK • PWOVPU= P H I W K / P H I U K . W R I T E ( 6 » 9 ) S Q K P H U , PWOVPU T A N 2 T =(1.7321*FUW)/(0..75*FSQW-FSQU) . • THETA2 = 0.5*ATAN(TAN2T ) THETA2=180.0*THETA2/PI 600 FORMAT(IX*5HTAN2T,E14.4,2X,6HTHETA2*E14.4/) WRITE<6*600) TAN2T, THETA2 W R I T E ( 6 * 1 0 ) KO 10 FORMAT ( I X , 3 2 H N U M B E R OF F R E Q U E N C I E S A N A L Y S E D = 1 6 / / ) GO TO 2 0 0 1 END SENTRY . ^ ; • _  FORTRAN  I V PROGRAM  FOR X-VJIRE A N A L Y S I S  (Cont'd..)  E•  Changes  In  in  Appendix  fluctuating wind  I,  signal  given  If  from a  A  both  wires  are  plane,  eqns.  A  the  1.18 X-wire  since  extremely  is  geometry  during  calibrated, velocity wind to  the  probe  vertical do the  not  make  probe  this  arm  planes  f0jj(f),  in  is  now  which  than  5°  instructive me sured a  the  mean  vertical  voltage  ensure  plane  signals  with say,  actually  precise  and  conditions plane  two  which  can  w(=u^) where  long  wires  plane  are  the  mean  perpendicular  As  the  angular  expressions  probes  u(=uj)  same  unwarranted,  such  probe).  actual  the  -For is  the  vertical the  the  to  to  the  signals.  under  horizontal  probe  the  into  However,  of  angles  actual  are  to  the  axis  the  when  paralled  assumption  measured,  (long  the  be  both  this  case,Arepresented to  modified  sensitivities  always  (less  a n g l e ^ t o  to  d i f f i c u l t  large  their  perpendicular  It  for  containing  too  arm  practice), In  is  modified  angIeft enters  arrays,  their  is  that  .I9«)  assumed  J9)  fluctuations  direction  seen  was  (The  construction.  and  it  wire  and  same  constructed it  each  I.l8  and  0  D,  wire.  eqns.  for/Q/  horizontal  sloping  by  vertical (see  the  Values  Section  di r e c t i on- m a k e s  containing are  Spectral  of  as  the  the  X-array  perpendicular be  achieved  directions  can  deviations  from  be  to  in ignored.  the  plane  arm.  to  calculate  f o r =  0,  how are  the  spectral  modified  to  values  give  the  Alj-3  spectral A  IV.D,  one  eqns.'A case  values  f0'jj(f)  can  IV,12)  derive for  wherey3^0.  the  the  By  when/3^0.  expressions  fi Itered  using  Proceeding  and  eqns.  A  A'(l)  averaged one  1.19,  as  =  M  2  u  ( f )  2  +  a  2  c  o  M  1  |i  f  to  signa I s  the  obtains  N  l  2 w  (f)  -  cos£  2a  f)  T7w(  +  2 (  2 A'(2)  A'(3)  =  =  M  2  2  u  ( f )  2  2f )  +  f  cos*uw(f)  2b  2  M M 1  +. h c o s ^ M  u~ (f) 2  -  ab£°4^J7(f)  .M •  +  *,M .:  2  +  ^  M  values  2  (f) 2  v ^ f )  2  2  2  " ¥j" a  the  1  »  r  for  AS Mj  N  2  Section  (equivalent  2 A» ( I )  in  COSyfl uw( f )  2  N.N 2  M.M  ( A IV.17)  y^fj.  "2 • where u ( f ) , w (f) and uw(f) are defined in eqn, A I V . I I f (^= 0), and where v ( f ) =J022^ ^* l ' IV,17 reduce to eqns, A IV.12 whenyS = 0. T h e extra contributions produced -2"  '  2  E c  n s  A  by having/S^ 0 is thus given by 8A(I)  using  eqns.  A  IV,17  and  .12,  =  A'(I)  These  -  (A  A(I)  values  are  given  IV.18)  below  AUI*. 2  8A( I ) = ( M . - I ) 7 ( f ) + a 2  2  1  +  8A(2)  = (M  2  -  l)u (f) + 2  - 2a (cos/3 -l)TJw(f)  ( ^ # - l)w (f) M|  2  b (^i2  N  2  I  V  -~  v (f) 2  l)^(f)  - l)TTw(f)  + 2b(cos£  + _2 v ( f ) M ^ ..• 2  2  _  - «  2  8A(3) = ( M , M 2 - I ) u ( f )  - ab(£°^ -  2  b( — L c o s y S + | b( L • M_  l)w (f) 2  I) - a(' -=cos/3 - I) u w ( f ) M. J  2  + V_2 The s p e c t r a l Substitution  v  ( f )  .  (A IV.19)  v a l u e s a r e s i m i l a r l y m o d i f i e d when»£/ 0 .  of t h e v a l u e s A ' ( l ) ( e q n . A IV. l 8 )  e q n s . A IV. 15, g i v e s  the new s p e c t r a l  into  f 0 . ' j ( f ) , such  values  that  fitf'jjU) = f 0 . j(f) (fif  0)  The v a l u e s of S[f0. replacing by  the v a l u e s  (fi  = 0)  + 8 - [ f 0 , j ('"f)] • ( ^  (A IV.20)  0)  . ( f ) ] a r e e a s i l y o b t a i n e d by  of A ( l ) , A ( 2 )  and A ( 3 )  t h e i r r e s p e c t i v e v a l u e s of & A ( I ) , & A ( 2 )  i n e q n s . A IV.15 and & A ( 3 ) .  In-order ft ?  a  0,  between  to  run the  obtain  must mean  perpendicular  be  chosen  wind  to  numerical  the  direction probe  spectral  from  the  actual  measured  non-zero  values  of  f0j (f) 3  arrays  can  and  f0|j(f)  IV.19, a  A  value  According (S.  values  ^9  to  Smith,  into  /3 ?  0,  carry an  out  comm.),  programs.  two  These, parts  be  a  a  fair  were  and  B)  angle plane  calculated  introducing  and  However,  .20.  f0||(f),  values to  use  assumed  using  of  The  be  by  eqns.  or  thrust  estimated.  anemometer,  approximation.wouId  +  f j % ( f ) )  computations  parts (A  then  order  (£)(f0,,(f)  =  numerical  additional  small.  in  effect  measured  quite  spectral  estimated  the  vertical  IV',19  must  of  the  can  A  hence, v  f022(O To  the  the  f0jj(f)  eqns.  f022 ^  pers .  1966,  army/ is  values  only;  spectra  and  ?  measure  for  that  f0' j(f)  modified  X-wire  such  estimates  for  written  are  •  (A  the for  outlined  IV.21)  effect the  on  be  of  Fortran  the  IV  following  pages.  Part of  the  A  includes  constants  'effective' This eqn. in  value  l . l l ,  Appendix  by I,  calculations  formed of  relationship A  all  9  is  from is  before  the  first  before  the  I«B.M.  step card  with C.2. of  the  by  using  putting  arguments This  section  and  p  the  eqn.  f(9,P)  leading  computation  reading.  produce  containing  estimated  obtained  analogy Section  terms  which  is  to  The  9. tan  9  sin  9  eqn.  A  =  placed  loop;  values  that  =  l/b'.  in I.I  just is  just  READ(5'',500) F F  2001 Part computed  B  spectral  frequency card  of  includes  FF.  the  calculations  (f0||(.O  values  This  loop;  all  section  that  is,  Is  which  etc.)  placed  just  before  TO  2001  depend  for  each  on  f i l t e r i n g  just  before  the  I.B.M.  the  last  card  reading  GO  lossary  of  the  extra  .  printed  outputs  o  T2  0  BETA  6A(I)  D(I) DELTA  1  DELTA  2  DELTA  J  1 1  b0 • 6  5 5  cm .  FPI3  1  RA2 RA3 RATIO  -2  cm •  2 _ -2 sec C  -2  2  -2  C  sec  2 cm . s e c  F)/f0,|(f) 5 5  (f)  f0i3'(i )/f0, (f) :  5  ;  sec  2 cm . s e c cm .  F)  )/f0 *(f) M  -2  2  3 (*  F)/f0  sec  -2  cm .  f ^ l i ' d F)  2  2 cm . s e c  (f  FP33  RA  given  0  Tl  FP  i s  the  -2  T NT 1= 1.0/C(4) TNT2 = 1 . 0 / C ( 5 ) Tl= ATAN(TNTl) T2= A T A N ( T N T 2 ) Tl = (180.*T1)/PI  l 5 2  *  T2= (180.*T2)/PI / WRITE(6i52) T l » T2 , BETA FORMAT(2X,3HT1=,F14.4»2X,3HT2=»F14.4»2X»5HBETA=»F14.4//) T1=(PI*T1)/180. T2 =(PI*T 2 )/180. BETA=(PI*SETA)/180. • CSB=COS(BETA) SN3=SINlBETA) . SNT1=SIN(Tl1 SNT2=SIN(T2) TNT 1 = T A N ( T l ) TNT2=TAN(T2) SN2B=SIN(2.0*BETA) P ( l ) = CSB*CSB + ( SNB*SNB) / (SNT1*SNT1 ) • P ( 1 )' = P ( 1 ) * * 0 . 5 P(2)= C S B * C S B ' + (S N B * S N B ) / ( S N T 2 * S N T 2 1 P(2) = P(2)**0.5 P (3 )= (0.5*SN2B)/(TNTl*tNTl) P(4)=(0.5*SN2B)/(TNT2*TNT2) P(5) = ( C S 3 * C S B 1 / ( P ( 1 1*-P ( 1 1 1 1.0 P(6) = ( C S B * C S B J / ' ( P ( 2 ) * P ( 2 ) ) •" 1.0 P(7) = (CSB*CSB)/(P(1)*P(2)) 1.0  FORTRAN  IV  PROGRAM  ^OR  .  •  •  .  . '•- > .  •  /»  EFFECT:  •. ' . "' .-  PART  A.  —  ,Q(1)= P ( l ) * P ( 1 ) 1.0 Q(2)= P(2)*P(2) 1.0 Q(3)= P(1)»P<2) 1.0 R(1) = C(4)*C(4)*P(5) R(2) = C(5)*C(5)*P(6) R(3) = C(4)*C(5)*P(7) E ( l ) E(2)  =•2.0*C(4)*(GSB = 2.0#C(5)*(CSB  -  1.0) 1.0)  E(3)  =  C(5)*(P(1)»CS3/P(2)-1.Q)  F ( l ) F(2) F(3)  = = =  ( P ( 3 ) / P ( i n * * 2 . 0 (P(4)/P(2))**2.0 ( P ( 3 )/P( 1 ) ) * ( P ( 4 ) / P ( 2 ) )  -  C(4)»(P(2)»CSB/P(1)-1.0)  FORTRAN. I V PROGRAM FOR fl EFFECT: PART  A (Cont'd.  II  ro < rH  II  LL.  r-H  (NJ  LL  +  LL  (\J  (NJ  —  Q  *  # ~  *>  rH  »»  Q  O  X <)• X cN C J  +  <  •—  <  CC  UJ IINJ C C O CO CM < _UJ LQU LQ X  —  33  in  CJ  (NJ  + +  II CO  U. X XNJ C  o-  CO  •»  CL  CN!  I  in  rH LL  r n  x  CJ  o  co-  «r  o * X X  U_  * *  CO  r-~i  Q  oo  o o co co  LU II  LU X  LU  > >  m <t  u;  rH  LL  t- _J  CO CO a.  CO • <r rO OO O r X X +C NJ CNJ O — CO - OM- + * CNJ i -HJ O CS U C N J C O LU <r I3 + + in 3 —u Q I QQ O OO3 O 3O Q + + X\ LU 3 -~ rin in in O3-3 X <f <r <f ro u_ OO—O— X I I C O II < < < II II — —< III n — > -~ ~ I O O ^> <CNJ<CO cc IU CO CO — IU QJXO I— I — O Oco I UJ — r~ CO — cc X a a ru_ 3 LU < I + + —  CNJ  co tO  —  LL  LL  *  *  +  I  CNJ  —  CO  •  —  Q  rH  CO  rH  Li_ —  —  ~  rH —  CM  —  —  CC CC CC  +  I  rH  -  LL  CJ  Q  <  •>  r -  <T  _ l  •  in —  '  i-O  LU LU  rH  rH  CO LL — *  m  co LL *  LO LL  I/)  rH  o o o CO CO cO  * — —  •H  CL CO Li- U _  rH  Q  LO *-  cO  LL  Lf\  ll  •—•  rH  #.  LL  r-l  r -  rH  LO  —  rH rH  CL  f\J  CJ <J CJ  ll  r -  UJ  LL  _J  >—i  Q  DC  _J _J  CNI —  Q  in  LU  o  I—  LL  _ l  LU m  Q  ' CN IJ < • cc<X r  n  r -  UN  «.  |— m  i — s: —> of  cc o  3  LL  <  v  •  CC L L  > • II r-H  rH  < <  X O X— — LU <I 3O oc Ct: —  <f  ON  —• CC CC  LI-  rH  rin H  —  rH  CC  ro x < CNJ cc CO C NJ O <  LL  ON  AU-7  APPENDIX  A«  V:  Glossary  (i)  SAMPLE  of  Terms  CALCULATIONS  Terms  used  Used  for  for  calculations  R.R.  Resistance  B.N,  "Bridge  Null"  the  wire  I i  hof  Wire  ratio  current  Rms  square  Rms  B  Slope  S  Analysis  used  for  probe.  reading  for  "Cold  bridge for  wave  c a l i b r a t i o n ms  Calculations  square  of  probe current  wire  wave  Balance"  of  c i r c u i t .  in  in  ma.  for ma  voltage  square  wave  rms.  in  volts  rms.  2  (ii)  of  the  I  versus  speed-up  rate  V  'U  c a l i b r a t i o n  line.  _ / Real t i me \ \Ana lysis time/  .  Equations:  g  I'  =  ±  k  1U  .  I . I  3)  and  2  3.05 ~  1  .  (eqn, A  2  I  +  (B.N.)(R.R.) £0T5  I  +  ( B. N. M  I  2.SO  =  1  anemometers  I + WR. 1600  R . ))  anemometer  3  2 C  =  C ( I )  X  =  K]"  JT)  2  =  K  "  2  U-wire  X-wi r e  (eqn. A  ( eqn.A  I.II)  I »I I  A!L8  B.  Data  U  of  =  K "  C(3)  =  (K,K )"'  cm.sec"  of  1.8  B.N.  \k3  k  •  '  I  B  ( e q n . " AI . I I )  X-wire  (eqn.  U-wire  A  I.I  I)  Calculation:  1  0.351(6)  volts  3kj  ma x  2.00 *  s ( i !)  2  X-wire  Constants  R.R.  m  ;  S3  Values  ; s  •;  2  2  cm.  192  Probe  (i)  =  I 5 5 0 - I 629/29/6/1 9651  289 =  C(2)  rms  ma^(cm/sec)  10  16  Coef f i c i ent  C .2  p  =  2  -0° ^  0  i = I  c  ( i i i )  =  Data  X  =  321  T  =  I  +  2.30  lij 3( I r  (0T3F1F  for  1I4..9  =0.0338(8)  +  sec.'  = I •kk-3 x  ?  m a  r m s  I .of  TOTW)  X  F i l t e r i n g  volts  k  ToTJo  ma(cm/sec)  2  =  L , 1 + 6 ( 7 )  Frequency  (FF)  X  L0  ^"  C  M  ^  =2.8  Hz.  (See  Sect.  V  O  A  L  T  S  2  S  E  IV.C)  2  sec.  (signal (signal  integral) integral  duration)  C  2  )  Ak3 2  =  0.9  volts  TN  =  60.0  sec.  (noise  2  XK  =  3.9^2  x  (gain  factor)'  A  (i v)  =  sec.  2  XN  ( n o i s e  10"^ ,  ( f i l t e r  j  0.1592  integral) integral  duration)  "  response)  CaIcuI at ions  ~~  ^ 1 1 '  A  I  U  01  k  j(k)  =  kx^  =  101 f  0|I ^ ( f  O..OO581  x  (eqn. A  3.9J4-2  o.j592  x I0"^/52,I  '  £_jM  \ I i t . 9• "" "~"070 W,  =  x  =  2.65  x  l(A  cm sec~ 5  2  (eqn. A  0.OO38I c m '  192 =  C .  log  k  O.73I  -2.ij.l9  log  kz  log  0, , ( k ) = t.1+23  =  j  -2  l o g f = -O.757 =  IV.9)  cm sec  2_JLJI_^_dli  =  TN J  IcA  .lj-67 x 2  =  "  -0.I36  555-1629/29/6/19^5:  Data  of  I  Run  2:  2122-2206  U =  289  cm s e c "  1  X-wire  Calculations;  I V.I  5)  ASO  x  =  192 cm  5 Probe  X3  Values  of  Inner  Wi r e ( S i g n a 1 1  R.R.  1.8  B.N.  98  m  0.510(1)  volts  k 1  It-09  ma  B  2.o'9.(8) x  ma (cm/sec)  s  S  16  b'  1.06(8)  Values  of  1.8  B.N.  9k  s  k  1  Outer  I0  X  ma  2  (  0.825(2)  C o e f f i c i e n t 2.098  I'  • 1  C ( l ) : x  _J(cm/sec)"  2  2  =  b  in eqn.  Wire _1  =  5.05  f  rms  2  Q  « 3°t 5) 0  _  9B x I 75 -  " T+  (Signal  ^2 IO  -Jfoq—^289  -  Inner  2  in eqn.  Wi r e  ma  16  =  a  k*k  S 1  =  volts  2.38(2)  b  (  0.351(6)  B  rms  2  Consfants:  R.R.  m  ( i i i )  C*onsfants:  f  ..„  0  2  ,  1  1  ma(cm/sec)  .  7  ma  r m s  14.00  OTjfoT  l 2 X  O.O3O15  =  °-5l2('8)  x  I0 (cmsec*%>lt) 5  A51 (Iv)  C o e f f i c i e n t  C(2):  2 _ 2.?82 x 10 k2k 289  ] t  ' ~ 1 + 9il°x"~nB  Outer  Wire  .  maUm/sec)"  1  =  0 # 0 5 5 0 { 2 )  =  2  -'^  m a  -  r m s  too  2.11+3  C(2)  =  (v)  Coefficient  O.3516  = o.3l|.o(7)  0.03302  = (CCD x  (vi)  Data  for  R '  sec  Fi Itering  =  5  #  Wire:  X|(l)  =  986  T  =  159.8  XN(I)  =  2.0  TN( I )  =  7I4.. I  volts  2  r  Frequency  sec.  voIts  2  (FF)  2  (Signal (signal  sec.  =  T  308  (noi se  =  TN(2)  = 7I4..I  0.5  sec.  sec.  v o l t s  2  (noise  3t0  integral) duration)  v o l t s  duration)  i ntegraI) integral  i ntegraI)  (noise  integral  length)  factor)  (f i I t e r  sec.  length)  2  (ga i n  2  response)  (noi se  sec.  = 0.08'3( I )  =  Hz.  integral  (s i gnaI  sec.  Mu11 i p I i e d s i g n a I : XI(J)  l\..0  (eqn.A  i ntegra I )  (signal  XK(2) = 1.02(5) x 10"^ XA(2)  / v o l t )  (gain-factor)  volts  (2) = 159.8  XN(2)  p  2  integral  (f i Iter  XI(2)  /volt)  sec.  X A ( I ) = 0.123(6) Wire:  -1  2  sec.  X K ( I ) = 9.80(5) x 10'  Outer  ( cm- s e c  I  C ( 2 ) ) = 0 Ii l8(0)xl0 ( cm 2  Inner  (I)  5  10  C(3)  _L  C(3)  x  (s i gna I  response)  2  i ntegraI)  IV.13)  A52  (vii)  1(3)  =  159.8  XN(3)  =  1.0  TN(3)  = 7t,« 1  XK(3)  = 1 .00(5)  XA(3)  =  sec. p  volts  sec.  i ntegra1  (noise  i ntegra1)  (noise  sec.  x .10""^  (gain  0.103(0)  integral  (eqn.  A  1 eng t h )  factor)  (filter,  Calculations:  1eng t h )  ( s i gna1  response)  IV.II)  i5 o Q - fine; y n~5 ( I ) = 0.5128 x- 10^ x 9.805 x 11 0 ^ / 986 _ _ 2 ^ a \ A.U; u.1236 \J597B A  =  w  2  250  _  / K [ Z )  =  k  '/ . ^3)  -  2  0.5^07 x I O  =  )  cm sec""  8O.7  cm  2  x 1.025 07083!  x \Q"  3  sec""  k  2  ' 0>Jj.l80 x to5 x I .005 x l O " ^ 0.1030  = " 86.2  c m s ec 2  (a  + b ) ~ = 0.2790  fj#  M  ( 508 _0_5\ ^159.8 " T i f t T j  f 3JJ-0 „ ^159.8  I .0\  WTTj  2  2  (f)  =  (a  +  b ) "  ( b  2  2  A ( l )  +  a A(2) 2  + 2abA(3)) (eqn.  =0.2790 -  I  fjZL_(f)  I  *  I  16 =  (0.6810x250+ ~  2  cm  (a  +  I.ltlx80.7+  1.763x86.2)  2  b)" (A(l)  +  ?  •  A(2) - 2 A ( 3 ) ) • •  = 0.2790(.250 + 80.7 - 2x86.2) cm  sec  33  = 44.I  A  sec  (eqn.A  A53 fJZf^U)  =  (a  b)  +  (-bA(  l)+aA.(2)+(b-a)A.(3))  (eqns.  A  IV. l i p  = o.2790(-o.8252 x 250 + 1.068x80.7 - 0.2^28x86.2) 2 -2 - -39•I cm s e c f = | £ = i±^2 = 0.25 Hz , _ 2 x HT x 0.25 k 289' kx  -  5  O.OO544 x 192 = I . 0 4  0, , ( k ) II  =  ^ ' , '^  f  k  }  =  o.uup44  2.13  x  f0zz(O •Jili I _ ^ = 0.00544 = 8-I2  0_ ( ) 5  1  O.OO544 cm  n  k  10^ cm3 ec-  2  (eqn.A  S  z X  1  0  z c  m  ?  s  e  _p  3  *  =  -39.3  f0,z(O —  "  = O.6054V = " 7 A  f  i  = 0.620  l o g k = 2,264  =  0.I46  l o g 0 ( k ) = 4.328 M  log  0  log  |0, (k)|  5 5  (k)  5  =  3.910  =  3.860  A  IV.  15>  3 3 - 2 x 10* cm^sec (eqn.  log f  .  c  (eqn.  0| (k)  IV.  A  IV.15)  15)  Apt  APPENDIX  In  VI:  THE  estimating  calculated estimate  be  independent i.e.Q* as  =2  P"'  i=l which  20",  When about  made.  •  (or  2cr  The  maximum  observed  which the  had  "maximum  of  Mean  The  "maximum  of  was  error  95$•  Wind  in  ' of  as  error"  often  (which  is  by  thus  at  error  equal  cal led  by  halving  many  95$  be  the  factors.  probability are  (often  confidence  data  Section  is V  described A.  in  Section  IV  of  error  for  the  "maximum  The  final  level  in  substantial) level.  Data  wind  the  than  each  total all  mean  larger  factors,  adding  the a  to  to  a  estimated  they  the  level.  the  error",  have  is  expressed  of  expected  for  an  is  normally  percantage  simply  words,  error  a  This  contained  estimated  other  the  ' ' confidence  available,  should n  quoted  not  several  treated  error  estimated.  this  involving  the  are  is  allow  were  " . 95%  RESULTS  was  (c)  to  the  obtained  errors"  errors  expressed  range  error  to  was  NUMERICAL  expression  standard cases  IN  existed  given  (percentage)  mean  discussed  data  a  overestimates  A.  standard  which  (percentage)  excess  EXPECTED  expression  expression  estimate  and  a  such  errors  error",  an  the  greater)-  value.  1  n  For  corresponds  standard  "maximum  For  '  BE  the  sufficient  factors,  N  TO  errors,  where  to  ERRORS  A  and  ASS  Calibrations outlined counts  by  per  velocity  each  measured  in  the  of  overlapped  a  (I9&5)«  Hamblin  wind  cup  averages  run  cup  of  individual  the  the  minute  estimates  The  of  speed  from  by  duration.  "maximum  error"  maximum  error  between  cups  Section  V  of is  wind  were  of  the  than  about  estimate  taken  to  be  of  the  about  each  mean  differe-nce of  1$  the  minutes  7 and  with  contribute wind. in  mean  in  minutes.  other  the  mean  error  of  to  the  runs,  7  multiples  the  to  most  every  2%  less  The  speed  wind  (see  A),  to  Corporation in  the  wind  Calibration  of  Calibration  corrected  over  in  expected  used  relating  cups  once  For  is  was  The  read  \%,  method  relate  standard  procedure  Department  described  than  The  This  tunnel  B,  tunnel.  the  assembly,  with  wind  appears  cup  LL m i n u t e s  the  Flow  curves  than  Since  the  Calibration  less  different  less  followed  individual  is  counters  anemometers  in  tunnel), speeds  constant  K  the  wind  mean  manometer  in  cup  in  pressure  in  error  that  Wind  of  wind  (and  also  about<l$ tunnel,  Tunnel  wind  funnel  is  A.  "velocity  speed  Engineering  anemometers  systematic  Corporation  Section  the  the  Corporation  Flow  I,  a  MechanicaI  determined  Flow  the  Appendix  the  calibrate  the  of  in  the  equation" test  difference  (eqn,  section readings,  to  A the  was  I.I)  A5'6  determined values)  to  error  0,0179  was  quantities of  in  than  determination  in  The.standard  3»2$.  or  eqn. A  less  systematic  0,5606.  be  I.I,  at  an  The standard  the wind  error  The a c c u r a c y  introduces  1.5$.  error  tunnel  t h e 95$  is  of  paired  reading  additional error  thus  confidence  31  (of  in  less  the standard  o n e mean  wind  3.5$»  The  than  level  is  thus  less  Section  IV  B and  than  7$.  C.  U-Wire  The  U-wire  discussed outlined  Data  in in  King's the  measured  A^easured of  where  V  Appendix  I,  described B,  Law r e l a t e s velocity  wire  procedures  procedures  the hot wire  (balance)  B  showed  Calibration  and a n a l y s i s  U,  in  in  by  the  I  =  2  A +  B  in  Appendix  current  I  IV.  to  relationship  between  that  are  BVU  two s u c c e s s i v e  would  be  1,12)  (A  known  to  calibrations about  5$  at  worst.  The each  is  Section  differences  t h e same  the  data  equation  frequency  used  to  analyzed,  determine is  given  by  spectra I  va I ues  fj#||(f)  at  A57  c  = Rrf" 1 x  and  ! '  =  '  1+  s  The  maximum  in  is  I'  tabulated  O.S  (for  f i e l d  measurements)  2.  (for  f i e Id  measurements)  total  systematic  confidence  error  error  in  in B  I'  =  would  (eqn. A  7»5% be  e q n . A 1.12)  3.5$.at'  the  1.13).  95$  level.  maximum  percentage  error  in  C  is  t a b u I a t e d ' be Iow:  0.5 %  i m  (from  below:  I (from cup anemometers)  %  iVu  5.  Maximum  The  error  (each  3»  g  measured  from  more'consecutive I' Total The thus  maximum about  values  of  error  error  in  in  C =  the  2  x  II.  10  %  calibration  =  22%  factor  (eqn. A K  I.I  (eqn. A  I) I.II)  I\%,  maximum f0,  ,  is  percentage tabulated  error below:  or  square  waves)  7*5  maximum  The  I.13)  M l ) . , (A  B  U  The  percentage  (A  -in  the  individual  spectral  is  A 58  (XK)  2$  (see  S e c t i on  A  IV.C)  (XA)  2  (see  Sect ion  A  IV.C)  (X/T)  I  (see  Section  A  IV.C)  22  C Total  maximum  The due  to  using  the  maximum These with hot  systematic  mean  The  error  in  maximum  wire  in  27$.  f0||(f)  Engineering,  error  in  values  errors  in  differences spectral  =  measurements,  Mechanical  maximum  f0^{f)  errors  velocity  error  the  in  k  of  0||(k)  f ^ j ^ f )  obtained  values  wind  due  a  given  to  run  errors  in  tunnel.  1 $ , so  is  f0||(f)/k  and by  (see  =  in  7$  plus<l$  2TTf/u  =  are  0|j(k)  V  is  thus  comparing  Section  that  cup  the  about roughly  total 3'$» conform  anemometer  and  B.I).  ( D.  X-Wire —  —  —  Data —  —  '  l  ,  —  t  i  X-wire in and  Section to  V  The A  I.  The  described,  their  Analysis  largest 1.12)  calibrated  is  Procedures  B.  measure  Appendix  (eqn.  data  and  value  was  wire  used  techniques  difference found  the  in- S e c t i o n  to  wire  to  in be  -are  the 3$,  within  IV  and  B  calibrate  coefficients  recalibrated  of  •  b , 1  X-wire  are  outlined  constant for  a  the  coefficients  wire same  b'.  discussed  B  probes,  outlined  in  in  Appendix  of  King's  which  IV.:  Law  was  day.  for  each  wire  is  A59  obtained  from  which  Obtained  is  eqn.  A  each  term  the  l.lli.  appear, velocity  equation  by  The  is  substituting  maximum  tabulated  since  b'  percentage  below.  measures  m  relative  random  no  I.13  into  errors  in  systematic  response  to  errors  two  ( e s t i m a t e d ' f rom-,. s t a n d a r d  2.  $  I  0.5  B  3»  10  (wire  !•  VO"  AE '  more  current  square in  calibration for  (using  2  King's  o r ' more  wire  error  waves)  f i e l d  (using  (from  3.  or  points per  use)  with Law  or  15  calibration)  determinations  calibration) or  20  readings  30  at  Gj)  each  maximum  error  b'  in  was  b'  =  ;  10.  $  calculated  f i t t e d  readings  at  included  with  the  other  which  has  maximum  of  thus  to  from  function  is  A  0.5%  for  each  that  and  I.II  rangeof  Note  the  A  components.  i  Total  eqns.  10  10/VTo,  or  least-square  estimates  different  10  a  I ess  values angles error  than  +  of  the  of  9j  3.2$.  or  b'.  of  mean (+  mentioned 10$.  line  The  7° in  was  quadratic 20  30  also  Section  maximum  or  A  error  I.C.IL) in  b'  A60  In  order  values data  determine  computer  for  the run  calculations various  constants were  (2)  in  eqns.  A  study  the c a l i b r a t i o n to  the estimated  (J4.)  rotating  the whole  errors  error  frequency divided  frequency  range  the  from  from  in.the  0.05  Hz  spectral  outlined  As array  I  from  in  was  set  The  to  I  upward. values  Hz,  0.05  A  As  L  and the  and  in  The  of  one wire  by  error,  ( b ' ) o f  one wire  by  3$  error,  by  3°, and  IV.I.  The  in  a  by  covers the  calculations  the above  result,  groups  Hz;  The average f $ j j ,  analog  by 3 ° .  rough  letter  to  0.01  t h e tajole  noted  three  the  errors  .15*  introduced  dependent.  into  convention.  range  X-array  the percentage  of  maximum  X-array  in.Table  f0 I I owing  range  the  spectral  separate  (K)  maximum  are summarized  were were  of  the  of:  coefficient  one w i r e  to  factor  the estimated  rotating  effects  IV.13  the e f f e c t  equal  that  Four  used  (3)  showed  using  the e f f e c t s  the wire  results  made  were  study  changing to  in  to  equal  11$  calculations  errors  made  to  changing  (1)  t h e maximum  I Ui-8-1525/22/7/1965.  were  calculations  The  to  the  estimated  according errors  letter  letter  H,  four  to the  in the M,  those  those  in  in the  maximum  percentage  the r a t i o  0z.z/0| |  errors  are  below.  in  Section  up  on  A  I.C.3,  the mast  at  it  low  was tide  felt  that  within  an  the angle  X-wire of  A6I  1°  at  the  extra an  t i l t i n g  extra  1t of the of  worst.  the  of  degree  may  the  of  3°  Table  A  but  VI  a  was  is  si  nee  wou1d  be  then  the  field  to  margin  that  quite  large  to  include  tidal  for  streams,  c r u c i a 1, in  since  that  this  a  the  of  2°  easily  mast  observed  t i l t  a  +  of  levels  spectral  however,  of  and  a 1i g n m e n t  proper  b e 1i e v e d , t i l t  any  error.  the  changes  Ma x i mum P e r c e n t a g e  .1:  due  table  is  doubled  mast  further  produce  It  o v e r e s t i ma t i o n ,  as  from  the  can  angle  instrument  added  in  stress.  not i c e d ,  the  noted  be  X-array  array  This  is  a n not  was  visually.  Errors  in  Percentage  Values:  Spectral Errors  In:  Effect  f0,, (1)  (2)  3$ i n  (3)  L  \\% change in K  22 15 10  65  I  H  5 5 5  0  l l  3 - 8  L  5  8  30  H  5 5  7  15 35  "  L  5  o.  3  M  65. 35 70  L  change  M  (t)-Tilting X-array  M  3  f0\|  are  Table  A  affected  least  of  a l l .  large  errors;  V 1 . ,\ i t s  l i f t le  Spectral however  no  k  k  8  7  can by  be  seen  errors,  values change  of in  —  5  65  6  $  H  From  3  16 l6 l6  M H  b •  Ti 1 t i n g one w i r e  fj0,  that  and  f0|z sign  the are  5 ...5 .  .1 I  7 7  spectral ratio most  (from  —  values 0  of  Z Z  sensi f i v e  negative  to  to  A62  positive)  was  The as  produced  systematic  before:  +  Corporation  determinations Engineering  E.  the  Errors  .in  estimating  u-*  obtained  in  the  the  spectral  calibration  and  wind  frequencies.  +<\%  due  tunnel  of  to  in  values the  are  Flow  errors  the  fjZSjj  in  the.  speed  I.I  is  Mechanical  Department.  Maximum  In  to  tunnel,  in  high  errors  "1% d u e  wind  at  from  about  Determination  2  d i r e c t l y ,  25  measured  of  the  u»  p  integral  values  of  II  A  fj$|j»  Since  most  2 of the  the  contribution  frequency  labelled errors  M  in  in  to  the  range  from  Table  A  that  kinematic  about  VI.I),  frequency  0.05  it  range  to  is to  stress I  (u*  Hz  occurs  (the  reasonable be  )  in  range  to  consider  representative  of  the  the  2 errors  encountered  errors  estimated  in  in  the  the  doubtlessly  overestimate  encounter.  Also,  and  calibrating  the  them,  estimates  table the  care and  are  of  the  maximum  errors  one  exercised  in  stress  u-»-  .  estimates,  normally of  which  expects  setting  seIf-consistency  The  up  the  the  to probes  results  2 described are  smaller  errors the  in  Section than  that  introduced  angular  t i l t  considerations unreasonable  to  IV,  by of.  into  points  indicated maximum  the  whole  account,  consider  toward by  errors,  a  simple in  X-array. it  values  seems of  errors  the  u-»-  K's,  Taking  to  u-"-  which  summing  then,  2  in  be  not  of  the  the  b''s,  these too  known  say  to  and  A63  wi t h i n  about  For  the  velocity cup.  is  U  50$.  logarithmic  is  available  The height  This the  +  is  also  the  distance drawn  and  within  a  bottom  cup  maximum  between  error  cups  is  value  maximum  in  is an  known  known  +  I  experimental  points,  slopes  are  drawn  the  Xz  (+  5  drawn  which  the points  order  cm).  visually  differences  in  to  f i t  exhibited  35$»  of  T h e maximum  For  slope  the a  are  of  the  and  the of  of  with  less  of  +  5 cm.  in  but line  greatest  error  of  slope  U  of  cases  scatter,  is  in  of  scatter, as  25$  each  b e s t - f i t  the worst  amount  order  h$> a t  height, A  in  mean  within  cm.  limits  points,  the p r o f i l e s  of  to  difference  large  the  individual  to  within  of  error  the  lines  the  the  the  through  least and  of  p r o f i l e ,  an  appropriate 2  upper  l i m i t .  (from  the  cases,  This  logarithmic  a n d 60$  maximum  gives  cases.  a n d JOfo  the runs  with  non-linear  to  the slope  estimate had run  of  ij.0$,  between  (see  p r o f i l e ) ,  typical  differences  which  total  of  errors  For  for  the  very  small  cups  2  (log  slopes  in  1)448-1525/22/7/1965  of  about  80$  This  is  estimation for  the  equivalent  of  worst to.  p r o f i l e s , from  x^) the  f °  r  the  velocity  the bottom  of  e q n . II  wind  p r o f i l e  example),  give  were  C  I.I. at  used Runs  this  height  differences 2  slope  of  a  compIeteIy  factor unreIi  of  two  abIe.  to  u-*  respectively.  and 3  dtl/d  range  five,  making  estimates  o f u-«-  in  A64  The jZf||(k) the  maximum  spectrum  average  account  F,  error in  of  10  or  (eqn.  inertial  more  individual  in  various  Maximum  Errors  in  Determining  give  an  an  error  error  coefficient This  does  CQ as  value from  from  x  10 I  x  10  by  measurements  of  to  standard  near  the  of  2  is  x  10  the of  of about  the  spectra 19$  eqn.  of  and  an  the  X-wire  -3  D l . l .  II  Section of  u*  E would  drag  observed  +_ 50$  from  takes  on  c o e f f i c i e n t to  l\.Q% of  38%.  drag to  drag in  into  range the  mean  values  ).  drag  4  from  measurements.  the  CQ  30$  the  Coefficient  of  about  from  taking  start  since  estimates  of  about  Drag  values  D.2  of  factors  0\\{k)  the  the  from  errors  gives  of  U~lj- m / s e c ,  about  have  error  I eve I .  IV  is  determinations  directly  estimates  the  in in  estimates  profiles  indirect  60$  Figs.  profiles  d i f f e r  conf i dence  -3  50$  at  determined  values,  the  unreasonable,  ( i . e .  indirect  can  a  about  noted  wind  The  about  appear  non-linear which  of  terms  discussion  determined  about  linear  of  not  1.5  The  the  C . l )  IV  subrange  errors  above,  have  the  S  the  Considering  in  in  Use  from of  coefficients  25.  c o e f f i c i e n t  the  error  inertial of  38$  at  from subrange, the  95$  A65  FIGURE  Fig.  A  CAPTIONS  I  FOR  APPENDICES  .1  Entrance  ,2  Scaled  for  Flow  Throat  Corporation  Design  for  Wind  Flow  Tunne I . . .  Corp.  Wind  T u n n e l . . . . . . .  . . A 68  .3  U-Wi r e  Probe  A69  .Ii  X-Wire  Probe  A69  .5  Ca I i b r a t i o n (No  Curves  experimental  for  X-Wire  points  J-  U  2  a*  speed  .6 A  II.I  No.  measured  2  A70  between  -L  1.8  to  i n s t a b i l i t y  Fig.  .A67  2.3 of  (m/sec)  wind  because  2  tunnel  fan  of  motor  in  this  range.)  Value  of  Tj~  Block  Diagram  r  as  a  Function  of  One  ....A7'  0  of  Channel  of  Hot  Wire  C i rcui t .2  The  A72  Average  Amplifiers  Fig.  A  III.I  Block  Gain with  Diagram  Anemometer  and  of  the  Three  Accudata  V  D.C.  « 73 A  Compensation.  of  Instrument  Rover  Cup  Mast,  Cup  Anemometer  E l e c t r o n i c s . . . . . . .  Fig.  A  IV.I  Krohn-Hite Pass:  F i l t e r s  Channels ,2  Block  F i l t e r  at  Analyzing  Transfer  Loaded  Input  Diagram  «A7^  of  U-Wire  and  With  Curves the  Tape  Output,....  Analog  System  Signals.  on  A l l Recorder A75  for A7&  A66  ,3  ,li  Squared  Voltage  at  High  Frequencies,  at  Low  Block of  Response  of  Preamplifiers  Relative  to  Response  F r e q u e n c i e s , , . , . . . . . ,,.. Diagram  X-Wire  of  Signals  Analog  Spectral  A?? Analysis ,  . 7 A  8  V  •1.78'  SCALING  FIG-AI.2  FACTOR  0-395  X (in)  Y (in)  0 •91 I -90 2-39 2-63 2-98 3-28 3-48 . 3-57 3-67 3-77 3-87 8-iO  1 -58 1 -59 1 -63 1-67 1 -70 1 -75 1 -84 1 88 1 -92 1 -97 2-02 2 09 6-37  SCALED FLOW  THROAT CORP.  DESIGN WIND  FOR  TUNNEL  (a)  PROBE  BODY  (b)  PRONGS  (c)  SOLDER  (d)  WOLLASTON  (•)  ETCHED  JOINT  PORTION  OF  0-00075  DIAMETER  FIG.AL3  WIRE  U-WIRE  (a)  PROBE  (b)  PRONGS  (c)  SOLDER  (d)  WOLLASTON  (e)  ETCHED  WITH  SLIGHT  BOW  cms  PROBE  BODY  JOINT WIRE  PORTION  DIAMETER  OF  000075  it  FIG. A1.4  WIRE  X— WIRE  PROBE  WIRE cms  WITH  SLIGHT  BOW  b'  • INNER WIRE o OUTER WIRE  1.3o  1.2i i 1 .i  1.0.90  r  .71  1  -10°  C) °  -5°  PROBE  5°  X N°3  CALIBRATION  DATE  S E P T . 13-14, 1965  b' = 1.050 FOR  A  8=  INNER  • t  VALUE  WIRE  0° = 0.825  F I G . AI.6  10° £.Q  OF  b  1  AS  OUTER WIRE  A  FUNCTION  OF  A 9  iwwvW  PROBE  BRIDGE CIRCUIT  V  X  D.C. POTENTIOMETER CIRCUIT  1  V  A C C U DATA V D.C. AMPLIFIER WITH COMPENSATION  •F. M. R E C O R D TAPE RECORDER CHANNEL  FIG. A II. I  BLOCK OF  DIAGRAM HOT  WIRE  OF  ONE. C H A N N E L  CIRCUIT  0  100  200  300  400  500  Frequency (sec ) 1  FIG. AII. 2  THE AVERAGE ACCUDATA  GAIN  OF  THE  V D.C. AMPLIFIERS  THREE  WITH  COMPENSATION  6 MAIN MAST CUP ANEMOMETERS  6 ELECTROMECHANICAL COUNTERS  6 AMPLIFIER  :  SYSTEMS  WET C E L L POWER SUPPLIES  7 CHANNEL MULTIPLEX  "ROVER" CUP  AMPLIFIER  ANEMOMETER  SYSTEM  ELECTROMECHANICAL COUNTER N°7  FIG. A III. I = BLOCK ROVER  DIAGRAM CUP  OF  ANEMOMETER  T. R. CHANNEL  SYSTEM  INSTRUMENT  MAST  CUP  ELECTRONICS  DIRECT RECORD  ANEMOMETER  AND  : VOLTAGE  i.oH  O  GAIN A  & &  £ 4 )  o  O  o A O  o  A  A  O  O  0.8 H •  0.61  1201 O  100-1  NO.  I  2  A  .  NO.  O  u  NO. 3  FOR X - WIRE ANALYSIS  ]  FOR U-WIRE ANALYSIS  O  A  A  0.44  KROHN-HITE  A  B>  PHASE  {OUTPUT  REFERRED  TO  INPUT)  80 H  60 H  0.2H  401  20 A  0.0 .01  0.1  A  / /  100  T  I  I  I  I  I I I  1000  FREQUENCY  FIG. AIV.I  KROHN-HITE FILTER TRANSFER CURVES ON A L L - P A S S « FILTERS TAPE RECORDER C H A N N E L S AT INPUT AND OUTPUT  LOADED  WITH  I— (Hz)  THE  A  TAPE  RECORDER  (Rerecorded  Signal)  -  KROHN - HITE (l/2  FILTER  Octave)  ADJUSTABLE•  GAIN  ACCUDATA V AMPLIFIER  ADJUSTABLE  GAIN  PREAMPLIFIER  PHILBRICK SQUARING  CIRCUIT (O.OI X ) 2  OPERATIONAL AMPLIFIERS  INTEGRATOR ( J dt)  <'  CHART  RECORDER  (Varian)  FIG.AIV.2'  BLOCK DIAGRAM OF ANALOG S Y S T E M FOR ANALYZING U-WIRE SIGNALS  i.o-  & B &a  0  A Q ia  A' a  Am  A  a *  D  .  A  ^ A A  /HIGH FREQUENCY G A I N ] LLOW FREQUENCY GAIN J  2  0.8-  o  0.6-  0.4-  •  GAIN  x 10 '  O  GAIN  x 74 .  A  GAIN  x 10  •  GAIN  x72 .  PREAMPLIFIER  No. 28  4  • A . O *A . • * on • on o * •  PREAMPLIFIER  No.29  0.2-  -  •  O.O — • —  •  20  FIG.AIV.3  •  1  I  I  I  '  '  100  1  1  1  1  T  1000 FREQUENCY  SQUARED VOLTAGE RESPONSE OF PREAMPLIFIERS AT HIGH R E L A T I V E TO R E S P O N S E AT LOW F R E Q U E N C I E S  (Hz)  FREQUENCIES,  I e.  FILTER  ACCUDATA V  I  AMPLIFIER  1/2 O C T A V E  I  PRE-  -+> I AMPLIFIER  SQUARER .OIX  2  XI (I)  INTEGRATOR  VARIAN j  n  TAPE  VARIAN  RECOR-  MULTIPLIER - .OIXY  DER  INTEGRATOR  CHART RECORDER  CHANN r  i  CHART  XI13)  (Rerecorded  RECORDER  Signals)  FILTER  A CCUDATA V  2  1/2 O C T A V E  SQUARER  PREAMPLIFIER  AMPLIFIER  PHILBRICK  FIG. A IV. 4  DUAL  BLOCK (FILTERS  DIAGRAM I  AND  OF 2  ANALOG WERE  -.01 Y  INTEGRATOR  XI (2)  2  OPERATIONAL  AMPLIFIER-  S P E C T R A L ANALYSIS OF X - WIRE  PHASE - MATCHED)  SIGNALS  


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