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UBC Theses and Dissertations

Fluxatron and sonic anemometer measurements of the momentum flux at a height of 4 metres in the atmospheric… McDonald, John William 1972

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FLUXATRON AND SONIC ANEMOMETER MEASUREMENTS OF THE MOMENTUM FLUX AT A HEIGHT OF 4 METRES IN THE ATMOSPHERIC BOUNDARY LAYER JOHN WILLIAM MCDONALD B.Sc, University of V i c t o r i a , 1969 A-THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Physics and the In s t i t u t e of Oceanography We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1972 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver 8, Canada ABSTRACT At the International Comparison of Turbulence Measuring Instruments, 1970, v e l o c i t y components and momen-tum f l u x measurements were compared using propeller-type Fluxatrons (Hicks, 1970) and sonic anemometers from Kaijo-•Denki, Japan and the Insti t u t e of Atmospheric Physics, U.S.S.R. There were d i s t i n c t differences found i n the measurements of the v e r t i c a l v e l o c i t y from the propeller sensors. The propeller's momentum f l u x measurements computed from i t s v e l o c i t y components were also d i f f e r e n t . The U 1 propeller was found to be l i n e a r for lower frequencies with an associated distance constant of about f metre. Measurement of the variance of U' for f < 0.16 hz. showed the U 1 propeller i n excess of both sonics by 20%. However, with the propeller's high frequency loss beyond f = 0.2 hz. the discrepancy was reduced to only an 8% excess for .00055 hz. < f < 10.8 hz. The W propeller response was non-linear and had an upper cut-off frequency of 4 hz. Because of i t s non-linear response and s t a l l i n g c h a r a c t e r i s t i c s at low wind speeds and also i t s high frequency cut-off the W propeller was observed to measure only about 50% of the t o t a l f l u c t u a t i n g W energy av a i l a b l e . Analysis of the sonic cospectra of momentum showed that s i g n i f i c a n t contributions to the momentum f l u x were to I i i be found i n the frequency domain 0.001 hz. < f < 5.0 hz. The combined response e f f e c t s of the propeller were enough to reduce the Fluxatron 1s estimate of t h i s momentum f l u x by 32.5%. TABLE OF CONTENTS Page ABSTRACT ± i-TABLE OF CONTENTS i v LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS 3.2.2 Measurements o f v e r t i c a l v e l o c i t y 3.2.3 Measurements o f momentum f l u x IX Chapter 1. INTRODUCTION 1 1.1 P r e v i o u s work and purpose 1 o f t h i s s t u d y 1.2 D e s c r i p t i o n o f experiment ^ 2. ANALYSIS PROCEDURES 1 0 2.1 Data r e c o r d i n g ^ 2.2 S p e c t r a l a n a l y s i s 10 3. DISCUSSION OF RESULTS 14 3.1 R e s p o n s e - c h a r a c t e r i s t i c s 1^ 3.1.1 G e n e r a l comments on p r o p e l l e r 1^ response t o d i f f e r e n t wind speeds 3.1.2 C a l i b r a t i o n p r o c e d u r e s 19 3.2 D i s c u s s i o n o f d a t a 21 3.2.1 Measurements o f h o r i z o n t a l ^1 v e l o c i t y 34 55 Chapter 4. CONCLUSIONS LIST OF REFERENCES LIST OF TABLES T a b l e Page 1. VCO C h a r a c t e r i s t i c s 11 2. U 1 c u m u l a t i v e i n t e g r a l s 27 3. W c u m u l a t i v e i n t e g r a l s 45 4. U'W c u m u l a t i v e i n t e g r a l s 59 5. C a l c u l a t i o n s o f C^ and r 64 LIST OF FIGURES F i g u r e Page 1. S i t e diagram 2. Photo o f R u s s i a n and UBC s o n i c anemometers 6 3. Photo o f F l u x a t r o n 8 4. B l o c k diagram o f s p e c t r a l a n a l y s i s 12 programmes 5. Response o f f o u r b l a d e p r o p e l l e r 15 6. H y p o t h e s i z e d r e s p o n s e )of G i l l - t y p e anemometers 1 7. P r o p e l l e r r e s p o n s e v s . wind a n g l e 20 8. Time t r a c e s o f U' 22 9. U' s p e c t r a - Run T013 24 10. U' s p e c t r a - Run TO26 25 11. U' s p e c t r a - Run TO29 26 12. R a t i o o f G i l l and s o n i c U' s p e c t r a l 28 e s t i m a t e s - T013 13. R a t i o o f G i l l and s o n i c U' s p e c t r a l e s t i m a t e s - T026 14. R a t i o o f G i l l and s o n i c U' s p e c t r a l e s t i m a t e s - T029 17. Coherence and phase l a g o f U' G i l l and U' s o n i c 18. Time t r a c e s o f W 19. F i l t e r e d t i m e t r a c e s o f W (6, 5, and 4 hz.) 20. F i l t e r e d t i m e t r a c e s o f W (3, 2, and 1 hz.) 29 30 15. J o i n t p r o b a b i l i t y d e n s i t y o f U* G i l l ^2 and U' s o n i c 16. P r o b a b i l i t y d i s t r i b u t i o n o f U' G i l l 1 6 and U 1 s o n i c 35 36 38 39 V I X I Figure Page 21. F i l t e r e d time traces of W 40 (0.7, 0.5, and 0.3 hz.) 22. W spectra - Run T013 , 42 23. W spectra - Run T026 43 24. W spectra - Run TO29 44 25. Rationof G i l l and sonic W spectral 47 estimates - T013 26. Ratio of G i l l and sonic W spectral 48 estimates - TO26 27. Ratio of G i l l and sonic W spectral 49 estimates - T029 28. Joint p r o b a b i l i t y density of W G i l l 50 and W sonic 29. P r o b a b i l i t y d i s t r i b u t i o n of W G i l l 52 and W sonic 30. T v e r i f p r o b a b i l i t y d i s t r i b u t i o n s of 53 W sonic 31. Coherence and phase lag of W G i l l 54 and W sonic 32. U 1W,cospectra - Run T013 56 33. U'W cospectra - Run T026 57 34. U'W cospectra - Run T029 58 35. Ratio of G i l l and sonic U'W cospectral 61 estimates - T013 36. Ratio of G i l l and sonic U'W cospectral estimates - T026 62 37. Ratio of G i l l and sonic U'W cospectral ^3 estimates - T029 ACKNOWLEDGEMENTS The w r i t e r e x p r e s s e s h i s i n d e b t e d n e s s t o h i s t h e s i s s u p e r v i s o r , Dr. M. Miyake, f o r h e l p f u l s u g g e s t i o n s and guid a n c e d u r i n g t h e p e r i o d o f s t u d y a t U.B.C. He a l s o r e c o g n i z e s t h e e f f o r t s o f a l l t h e s t u d e n t s i n t h e A i r - S e a I n t e r a c t i o n Programme who h e l p e d i n t h e p r o c e s s i n g o f t h e d a t a . The many c o n t r i b u t i o n s i n b o t h t i m e and a d v i c e o f Mr. Dominique R o s s i g n o l d e s e r v e s s p e c i a l m e n t i o n . A l s o Mr. Don Hume who worked l o n g h o u r s t a k i n g d a t a and k e e p i n g t h e e l e c t r o n i c s w o r k i n g and M i s s Daphne F r i e s e n f o r h e r h e l p i n t h e a n a l y s i s . D r s . A. Dyer and B. H i c k s from C.S.I.R.O. o f A u s t r a l i a d e s e r v e s p e c i a l r e c o g n i t i o n f o r t h e i r many c o u r t e s i e s and s c i e n t i f i c a d v i c e d u r i n g t h e e x p e r i m e n t . Without s i m u l t a n e o u s measurements from t h e i r F l u x a t r o n t o match t h e s o n i c o u t p u t s t h i s t h e s i s c o u l d not have been a t t e m p t e d . The experiment i t s e l f was conducted a t t h e T s i m l y a n s k F i e l d S t a t i o n o f t h e Academy o f S c i e n c e o f t h e U.S.S.R. and s p e c i a l t h a n k s and r e c o g n i t i o n must go t o a l l our R u s s i a n c o l l e a g u e s who made t h e experiment p o s s i b l e . Dr. Obukov, Dr. Tsvang, Dr. Koprov/ and Dr. Zubkovsky d e s e r v e s p e c i a l t h a n k s . W h i l e w o r k i n g i n Graduate S t u d i e s a t t h e I n s t i t u t e o f Oceanography t h e a u t h o r r e c e i v e d p e r s o n a l f i n a n c i a l s u p p o r t from t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada. CHAPTER I INTRODUCTION 1.1 P r e v i o u s Work and Purpose o f t h i s Study I n t h e p a s t s e v e r a l y e a r s many s i g n i f i c a n t s t e p s have been t a k e n i n t h e a r e a o f equipment d e s i g n f o r t h e measurement o f a t m o s p h e r i c t u r b u l e n c e . Of most s i g n i f i c a n c e r e c e n t l y was t h e development o f t h e s o n i c anemometer-thermo-meter (Bovsherov, 1960 and M i t s u t a e t a l , 1967). The s o n i c anemometer d e v e l o p e d by M i t s u t a a t K y o t o U n i v e r s i t y i n Japan o p e r a t e d on a p u l s e - t y p e o f t r a n s m i s s i o n w h i l e t h e i n s t r u m e n t d e v e l o p e d by t h e I n s t i t u t e o f A t m o s p h e r i c P h y s i c s , Academy of S c i e n c e , U.S.S.R. o p e r a t e d on a c o n t i n u o u s wave p r i n c i p l e . Both t y p e s o f t h e s o n i c anemometer a r e r a t h e r e l a b o r a t e e l e c t r o n i c d e v i c e s , hence a r e c o s t l y t o b u i l d and r e q u i r e much t i m e and e f f o r t t o m a i n t a i n i n p r o p e r w o r k i n g o r d e r under f i e l d c o n d i t i o n s . Meanwhile much u s e f u l t u r b u l e n c e d a t a have been o b t a i n e d i n A u s t r a l i a by an i n s t r u m e n t u s i n g two p r o p e l l e r s e n s o r s . I t was d e v e l o p e d a t t h e Met. D i v i s i o n o f C.S.I.R.O. by Dyer e t a l (1967) and c a l l e d a. F l u x a t r o n . The most r e c e n t v e r s i o n ( H i c k s , 1970) used two G i l l anemometers and a wind vane t o measure h o r i z o n t a l and v e r t i c a l components o f t h e wind. A t h e r m i s t o r bead was used t o g i v e t h e a s s o c i a t e d f l u c t u a t i o n s o f t e m p e r a t u r e . T h i s i n s t r u m e n t was t h e n c a p a b l e o f m u l t i p l y i n g and i n t e g r a t i n g i n s t a n t a n e o u s l y t o g i v e t h e h e a t and momentum f l u x . The p r o p e l l e r s e n s o r s were 2 v e r y s i m p l e i n d e s i g n and, under f i e l d c o n d i t i o n s , l e s s t i m e consuming t o m a i n t a i n t h a n were t h e s o n i c anemometers. The c o s t o f such a system was a l s o much l e s s . I n e a r l y comparisons o f s o n i c anemometer measurements t h e r e s u l t s o b t a i n e d by d i f f e r e n t groups f r e q u e n t l y r e v e a l e d some d i s a g r e e m e n t . T h i s d i s a g r e e m e n t was t h o u g h t due t o e i t h e r an improper e v a l u a t i o n o f m e t e o r o l o g i c a l phenomena or i n c o r r e c t c o n s i d e r a t i o n o f t h e f a c t o r s a f f e c t i n g c a l i b r a t i o n and r e s p o n s e o f t h e m e a s u r i n g i n s t r u m e n t s . I n o r d e r t o check t h e l a t t e r t h e r e have been s e v e r a l j o i n t i n t e r c o m p a r i s o n s s i n c e 1966. M i y a k e e t a l (1970) and Tsvang e t a l (1971) were two such ones h e l d a t U.B.C. T h i s t h e s i s was a t t e m p t e d i n o r d e r t o s t u d y d a t a o b t a i n e d from a s o n i c anemometer and t h a t from a F l u x a t r o n ' s p r o p e l l e r s . Causes, i f any, f o r d i s c r e p a n c i e s i n t h e h o r i z o n t a l and v e r t i c a l wind components (U' and W ) were t o be found i n terms o f t h e s p e c t r a and c o s p e c t r a f o r each o f t h e v e l o c i t y components. 1.2 D e s c r i p t i o n o f Experiment D u r i n g t h e p e r i o d o f June 15 t o J u l y 20, 1970, an e x p e d i t i o n f o r t h e comparison o f a t m o s p h e r i c t u r b u l e n c e s e n s o r s was conducted a t t h e T s i m l y a n s k F i e l d S t a t i o n o f t h e I n s t i t u t e o f A t m o s p h e r i c P h y s i c s , U.S.S.R. T h i s p a r t i c u -l a r s i t e was l o c a t e d about 200 m i l e s e a s t o f R o s t o v on t h e Don R i v e r and was where most o f t h e t u r b u l e n c e measurements r e p o r t e d by t h e I.F.A. groups had been produced i n t h e p a s t 3 f i f t e e n y e a r s . S c i e n t i f i c p a r t i c i p a n t s i n t h e experiment came from f o u r d i f f e r e n t c o u n t r i e s . They i n c l u d e d Drs. Dyer and H i c k s from A u s t r a l i a ; D r s . Tsvang, Zubkovsky, Koprov, P e r e p e l k i n a , Timanovsky, and o t h e r s from t h e U.S.S.R.; D r s . B u s i n g e r , F r e n z e n and P a u l s e n from t h e U.S.A.; and Dr. M i y a k e and m y s e l f from Canada. There were a v a s t number of t u r b u l e n c e m e a s u r i n g i n s t r u m e n t s used and compared d u r i n g t h i s e x p e r i m e n t . A l l were i n s t r u m e n t s used i n t h e p a s t t o s u p p l y t h e t u r b u l e n c e knowledge we have t o d a y . To measure t h e f l u c t u a t i n g com-ponents o f the wind f i e l d , a c o u s t i c anemometers from I.F.A. (U.S.S.R.) and K a i j o - D e n k i ( J a p a n ) ; F l u x a t r o n s from C.S.I.R.O. ( A u s t r a l i a ) ; m i n i a t u r e cup anemometers from Argonne N a t i o n a l Lab (U.S.A.); and h o t w i r e s from D.I.S.A. (Denmark) were a l l used. To measure t h e f l u c t u a t i o n o f t e m p e r a t u r e , t h e A u s t r a l i a n s used t h e r m i s t o r s , t h e R u s s i a n s used f i n e w i r e r e s i s t a n c e thermometers, ; and t h e U.B.C. group used a c o u s t i c .anemometer-thermometers from K a i j o - D e n k i . The f l u c t u a t i o n s o f h u m i d i t y were measured by t h e U.B.C. group u s i n g an u l t r a v i o l e t Lyman-Alpha humidiometer and by t h e R u s s i a n group u s i n g an i n f r a r e d h umidiometer. The a c t u a l e x p e r i m e n t a t i o n was conducted on a r e l a t i v e l y even s e c t i o n o f t h e R u s s i a n Steppes w i t h a s l o p e o f 1/100 i n i t s southwest p a r t . The a r e a was o f d i m e n s i o n 600 by 900 m e t r e s c o v e r e d w i t h s h o r t g r a s s and surrounded 4 by an a r a b l e p a r t o f t h e s t e p p e s p l a n t e d w i t h c l o v e r and c o r n . To t h e s o u t h - e a s t a u n i f o r m l y u n c u l t i v a t e d p a r t o f t h e s t e p p e s extended out some 1500 metres from t h e measure^ ment a r e a . S i n c e t h i s was t h e d i r e c t i o n o f t h e p r e v a i l i n g wind f o r June and J u l y a l l t h e measurements were made w i t h r e l a t i v e l y good f e t c h c o n d i t i o n s . A rough s k e t c h o f t h e s i t e i s shown i n F i g u r e 1. A l l r e c o r d i n g equipment o t h e r t h a n sensor heads were l o c a t e d i n an underground bunker about 30 m e t r e s downwind from t h e main mast. The I.F.A. group based t h e i r own equipment some 50 m e t r e s downstream from, t h e mast on a t r u c k . A n o t h e r s m a l l e r underground bunker was used f o r p r o f i l e measurements o f t h e U n i v e r s i t y of Washington and I.F.A. The base camp was l o c a t e d about 500 m e t r e s away where a c a f e t e r i a , r e c r e a t i o n a l f a c i l i t i e s , computer c e n t r e , work houses, and s l e e p i n g a r e a c o u l d be f o u n d . The e n t i r e s i t e was t h o u g h t t o be an adequate l o c a t i o n t o b o t h measure, r e c o r d , and a n a l y z e t u r b u l e n t a t m o s p h e r i c d a t a , e s p e c i a l l y f o r t h e i n t e r c o m p a r i s o n o f s e n s o r s when s u r f a c e h o r i z o n t a l homogeneity i s not so i m p o r t a n t . F i g u r e 2 g i v e s a p i c t o r i a l view o f t h e s o n i c anemome-t e r s ( K a i j o - D e n k i and I.F.A.) as t h e y were used i n t h e f i e l d . On t h e f a r r i g h t o f t h e mast t h e 20 cm. sound p a t h K a i j o -Denki s o n i c anemometer was mounted. There were t h r e e p a i r s o f sound p a t h s used t o d e t e r m i n e a l l wind components. One of t h e p a i r s was mounted v e r t i c a l l y and t h e o t h e r two i n a ( ! FIGURE trl, SITE DIAGRAM 01 7 h o r i z o n t a l p l a n e ( t h e h o r i z o n t a l p a t h s were s e p a r a t e d 120° t o a v o i d s t r u c t u r a l i n t e r f e r e n c e ) . The p a t h l e n g t h l i m i t e d t h e wave number r e s o l u t i o n o f t h e s o n i c anemometer t o s c a l e s i z e s o f about 1 m etre. Each p a i r c o n t a i n e d two s e t s o f t r a n s m i s s i o n and r e c e i v i n g t r a n s d u c e r s , one s e t t r a n s m i t t i n g one way and t h e o t h e r s e t t h e r e v e r s e d i r e c t i o n . S i n c e b o t h t r a n s m i t t e d a t t h e same t i m e , t h e d i f f e r e n c e of t h e two t r a n s i t t i m e s gave an a b s o l u t e measure o f t h e v e l o c i t y f l u c t u a t i o n . The sum o f t h e two gave an i n d i c a t i o n o f t h e i n s t a n t a n e o u s sound speed i n a i r and t h u s t h e t e m p e r a t u r e , assuming t h e speed of sound depends m a i n l y on t h e t e m p e r a t u r e , and not t h e h u m i d i t y . On t h e l e f t o f F i g u r e 2 a r e two I.F.A. s e n s o r s each c o n t a i n i n g 1 t r a n s d u c e r f o r t r a n s m i s s i o n ( t h e c e n t r e one), 3 t r a n s d u c e r s f o r r e c e i v i n g (2 upper ones 1 f o r U 1 and 2 o u t e r ones f o r W ) , and a f i n e w i r e a r r a y f o r m e a s u r i n g t e m p e r a t u r e . The I.F.A. s e n s o r s d i d not have any p r o v i s i o n t o measure t h e V component o f t h e wind. The F l u x a t r o n , as used by t h e A u s t r a l i a n group, i s shown i n F i g u r e 3. Two such d e v i c e s were used d u r i n g t h e e x p e d i t i o n i n o r d e r t o measure s p a t i a l v a r i a b i l i t y o f t h e momentum f l u x and h e a t f l u x (Dyer and H i c k s , 1970). The b a s i c d e s i g n was s i m p l e . Two p r o p e l l e r ( G i l l t y p e ) anemome-t e r s and a vane were used f o r m e a s u r i n g v e r t i c a l and t o t a l h o r i z o n t a l v e l o c i t y components. Temperature f l u c t u a t i o n s were d e t e c t e d by a s m a l l t h e r m i s t o r bead. Long t i m e c o n s t a n t R-C f i l t e r s were employed t o remove b o t h t h e mean l e v e l s and 8 9 t h e l o n g p e r i o d f l u c t u a t i o n s . I n t e r n a l e l e c t r o n i c s g e n e r a t e d a c o n s t a n t v o l t a g e o u t p u t o f two square wave s i g n a l s w h i c h were used t o c a l i b r a t e t h e f l u c t u a t i o n s o f t h e l o n g i t u d i n a l and v e r t i c a l v e l o c i t y components when t h e d a t a was p l a y e d back. For t h e e x p e r i m e n t a l d a t a used i n t h i s t h e s i s one of t h e R u s s i a n s o n i c s i n F i g u r e 2 was r e p l a c e d w i t h t h e F l u x a t r o n i n an attempt t o make a t h r e e way i n t e r c o m p a r i s o n w i t h t h e s m a l l e s t s p a t i a l s e p a r a t i o n . 1 The d a t a were g a t h e r e d d u r i n g t h e p e r i o d June 23 t o J u l y 21, 1970. Each r e c o r d e d t a p e was d e s i g n a t e d w i t h a T ( f o r T s i m l y a n s k ) and t h e n a 3 d i g i t numeral t o i n d i c a t e w h i c h r u n . F o r t h i s s t u d y t h r e e s e p a r a t e c a s e s were a n a l y z e d i n d e t a i l . One case was from measurements on June 29 and two c a s e s were from measurements on J u l y 5. The r u n on June 29 was d e s i g n a t e d as T013 w h i l e t h e runs on J u l y 5 were d e s i g n a t e d T026 and T029 r e s p e c t i v e l y . Run T013 began a t 21:36 and ended a t 22:08 L.S.T.; Run T026 began a t 10:30 and ended a t 11:10 L.S.T.? and Run TO29 began a t 16:45 and ended a t 17:17 L.S.T. CHAPTER 2 ANALYSIS PROCEDURES 2.1 Data R e c o r d i n g The e l e c t r i c a l s i g n a l s from each s e n s o r were r e c o r d e d i n a f r e q u e n c y modulated form u s i n g a bank o f 12 v o l t a g e c o n t r o l l e d o s c i l l a t o r s . The c h a r a c t e r i s t i c s o f each o s c i l l a t o r a r e shown i n t a b l e 1. Each c h a n n e l was a l l i g n e d so t h a t a i 1.00 v o l t i n p u t c o r r e s p o n d e d t o an ou t p u t o f i 7.5% f r e q u e n c y d e v i a t i o n from t h e c e n t r e f r e q u e n c y o f t h a t p a r t i c u l a r c h a n n e l . The f r e q u e n c y o u t p u t i n c r e a s e s as t h e i n p u t v o l t a g e changes i n a p o s i t i v e d i r e c -t i o n . A l l t h e c h a n n e l o u t p u t s were t h e n m u l t i p l e x e d and r e c o r d e d on one d i r e c t r e c o r d c h a n n e l o f a H e w l e t t P a c k a r d t a p e r e c o r d e r . The t a p e s were t h e n s h i p p e d back t o Vancouver f o r a n a l y s i s . 2.2 S p e c t r a l A n a l y s i s A t U.B.C. t h e m u l t i p l e x e d s i g n a l was p a s s e d t h r o u g h a 12 c h a n n e l d i s c r i m i n a t o r network which r e c o n v e r t e d t h e d a t a back t o o r i g i n a l c o n d i t i o n . Then s i g n a l s were d i g i t i z e d on an A-D c o n v e r t e r . F i g u r e 4 shows a b l o c k diagram o f t h e U.B.C. s p e c t r a l p r o c e s s i n g scheme. The f u l l s c a l e v o l t a g e l e v e l p r e s e n t a t t h e Analogue t o D i g i t a l C o n v e r t e r i s changed t o a 10 b i t b i n a r y number. T h i s means t h e f u l l s c a l e v o l t a g e i s q u a n t i z e d i n t o 1024 ( 2 1 0 ) l e v e l s . 11 Table 1 V.C.O. CHARACTERISTICS ±7.5% CHANNELS x, Lower Upper Nom. Center Deviation Deviation Freq. Freq. Limit Limit Response Channel (c/s). . ' (c/s) (c/s) (c/s) 1 400 370 430 6 2 560 518 602 8 3 730 675 785 11 4 960 888 1,032 14 5 1,300 1,202 1,398 20 6 1,700 1,572 1,828 25 7 2,300 2,127 2,473 35 8 3,000 2,775 3, 225 45 9 3,900 3,607 4,193 59 10 5,400 4,995 5,805 81 11 7,350 6,799 7,901 110 12 10,500 9,712 11,288 160 12 H£UIL£7T 7~/?P£ Tpr£ A-C? Con/i/£KTfR • 5P££D C/P Xg POP- •/2 7, TP T/r>7£ S£/?/£S PJLOTS P/?OG/?/?/?7 PL/A/OP r77£TO^ SP£CT/?#L PLOTS £ST/09/?r£S AJOXrr>fiL/2£0 SP£CT/?P? FIGURE 'A mom GAITS AA/O V/STfi/ear/OA/S SCO/? *srpcr< p/^oa/f/?/r? sry?rc S r p r / s r / c s 13 The d a t a were d i g i t i z e d i n 32 o r 40 minu t e g r o u p i n g s a t 75 h z . ( r e a l t i m e ) . The PDP-12 wrote t h e s e q u e n t i a l l y sampled d a t a on d i g i t a l t a p e w h i c h made i t c o m p a t i b l e w i t h t h e I.B.M. 360 system a t U.B.C. The program "TVERIF" a c t e d as a check t o see whether or not t h e d i g i t i z a t i o n p r o c e s s was done p r o p e r l y . V o l t a g e d i s t r i b u t i o n s f o r each c h a n n e l and t h e i r f i r s t , second, t h i r d and f o u r t h moments were d i s p l a y e d by t h e program. "FLINOP" was an o p e r a t i o n a l program w h i c h a l l o w e d c h a n n e l s t o be s e p a r a t e l y o p e r a t e d on. Such a c t i v i t i e s as a d d i n g , sub-t r a c t i n g , m u l t i p l y i n g , d i f f e r e n t i a t i n g , b o x - c a r a v e r a g i n g and f i n d i n g t h e square r o o t o f each c h a n n e l c o u l d be done b e f o r e making s p e c t r a l e s t i m a t e s . The program "FTOR" used t h e f a s t F o u r i e r t r a n s f o r m method t o c o n v e r t each c h a n n e l i n t o F o u r i e r c o e f f i c i e n t s . The c o e f f i c i e n t s were s t o r e d on t a p e and s e n t t h r o u g h t h e program "SCOR" w h i c h produced s p e c t r a l and c r o s s - s p e c t r a l e s t i m a t e s . "SIMPLOT" a c c e p t e d t h e s p e c t r a l e s t i m a t e s from "SCOR" and gave t h e c u m u l a t i v e i n t e g r a l under t h e s p e c t r a as a f u n c t i o n o f d e c r e a s i n g f r e -quency and a l s o p l o t t e d t h e s p e c t r a and c o s p e c t r a on a calcomp p l o t t e r . CHAPTER 3 DISCUSSION OF RESULTS 3,1 Response C h a r a c t e r i s t i c s The S o n i c Anemometer and. t h e F l u x a t r o n measure wind components by d i f f e r e n t methods. C o n s e q u e n t l y , t h e r e s p o n s e c h a r a c t e r i s t i c s o f each may not be t h e same and some comments a r e n e c e s s a r y b e f o r e d i s c u s s i n g t h e r e s u l t s . 3.1.1 G e n e r a l Comments on P r o p e l l e r Response t o D i f f e r e n t  Wind Speeds F i g u r e 5 shows t h e r e s p o n s e o f a f o u r b l a d e p r o p e l l e r t o w ind speeds from t h r e s h o l d t o 5 f t / s e c as g i v e n i n t h e G i l l P r o p e l l e r Anemometer Manual. The r e s p o n s e was z e r o w i t h i n t h e t h r e s h o l d r e g i o n and n o n - l i n e a r from t h r e s h o l d t o about 3.5 f t / s e c . Then a f t e r t h e r e s p o n s e was 0.96 r e v / f t . The n o n - l i n e a r r e g i o n was t h e r e s u l t o f s l i p p a g e and c h a n g i n g dynamic f r i c t i o n a t low wind speeds. F r i c t i o n a l d r a g was r e s p o n s i b l e f o r t h e t h r e s h o l d r e g i o n e f f e c t s and a?:0.96 r e v / f t . r e s p o n s e a t h i g h wind speeds. Measurements o f U' s h o u l d not be a f f e c t e d by t h e s e r e s p o n s e c h a r a c t e r i s t i c s where U i s l a r g e enough t o keep t h e g i l l a t speeds g r e a t e r t h a t 1.2 m/sec. F i g u r e 6 shows a p r o p o s e d s c h e m a t i c r e s p o n s e c u r v e f o r t h e p r o p e l l e r where U Q i s t h e g i l l w ind speed and U i s t h e t r u e w i n d speed. The t h r e s h o l d and n o n - l i n e a r r e g i o n s a r e marked and t h e dashed s t r a i g h t l i n e r e p r e s e n t s a 1:1 s l o p e . U. 1 <r O at a 0 J ^ 0 UJ ^ \ 5 * Q- * h ol o 0 ^ z <E 2 o J O cj 1)1 C( u It 1/7 1 \ \ i \ o lS 3 ul £ Ul o " C HI S n ? 1 » 1 \ 1 \ 1 \ '\ \ </> o £ H 1 \ »\ \ l \ \ \\ \ \f \ of ,« 11 * \ & \ \ u \ X \ to \ \ \ a of w z w 1 9 o a o. o U 5 0-1 I W \ \ \ \ \ V \ \ \ \ V Ul 9S 3 i \ \ V N V \ T T 16 ACTORL A c T o K L fcESPoHSE \*.\ R E S P O N S E FIGURE7/6 . SCHEMATIC RESPONSE OF GILL ANBIOfiETERS One can a p p r o x i m a t e . t h e c u r v e by making U „ T T T dependent on 1/U i n t h e n o n - l i n e a r r e g i o n : U Q = U - b/U (1) where: U i s a c t u a l w i n d and b i s a c o n s t a n t , R e w r i t i n g i n q u a d r a t i c f orm we have: U 2 - U_U - b = 0 (2) Or U = Ug/2 ± j U 2 + 4b/2 (3) To d e t e r m i n e b we l o o k a t t h e t h r e s h o l d c o n d i t i o n s : U = 0 when |u| < U where: U^ , i s t h e t h r e s h o l d wind T h e r e f o r e from (2) we g e t : - °2 Thus (3) becomes ( f o r > u T ) ; U = 0.5 ( U Q ±Ju 2 + 4 U 2 ) (4) where under t h e square r o o t s i g n t h e + s i g n i s used when U > 0 and t h e - s i g n i s used when U < 0. As an example o f t h e above f o r m u l a t i o n we can l o o k a t t h e c a s e where U G = 0.50 m/sec. and U T = 0.2 m/sec. 18 The actual wind U i s calculated by (4) to be 0.57 m/sec. Thus the amplitude of the G i l l has dropped by 12%. When U„ f i r s t reaches zero the actual wind w i l l s t i l l be 0.2 m/sec. The frequency response of the G i l l anemometer i s expected to be more l i m i t e d . In practice we can approximate i t s response by a low pass R-C f i l t e r i n i t s output. R-C f i l t e r theory defines the capacitive reactance as X , the resistance as R, the output pote n t i a l as e c, the input p o t e n t i a l as e . and the phase s h i f t as e . X = J^-n fC e = e X / V R 2 + X 2 c c s c' y c 9 = arctan (R/X) When the signal frequency i s such that X c = R we define the cut off frequency f . The power dissipated across the r e s i s t o r R i s exactly h a l f the apparent power, the output potential e i s 0.707 e , and the phase s h i f t i s 45°. When the G i l l anemometer i s used as a U 1 sensor the response c h a r a c t e r i s t i c s are given i n the terms of a distant constant X^ where X^ i s defined as the distance a i r must tr a v e l past the propeller before i t turns at 0.707 the speed of the actual wind. The distance constant can be converted into a time constant by di v i d i n g by the mean wind ( t L = X^/u). This time constant i s analogous to the R-C time constant discussed e a r l i e r . Thus at the distance constant point the amplitude of t h e G i l l output' would be 0.707 t h e t r u e a m p l i t u d e , t h e phase s h i f t between G i l l and t r u e would be 45° and t h e power spectrum a t t e n u a t i o n would be 0.50. 3.1.2 C a l i b r a t i o n P r o c e d u r e s  S o n i c Anemometer The s o n i c anemometer i s an a b s o l u t e i n s t r u m e n t where f l u c t u a t i o n s i n sound speed a r e used t o measure v e l o c i t y -f l u c t u a t i o n s . A check o f t h e c a l i b r a t i o n can be done i n a wind t u n n e l . The c a l i b r a t i o n i s m a i n t a i n e d by p e r i o d i c measurement o f t h e t i m e bases i n analogue s e c t i o n s o f t h e e l e c t r o n i c s . The r e s p o n s e i s l i n e a r f o r a l l w i n d speeds and i t s f r e q u e n c y r e s p o n s e i s good f o r f r e q u e n c i e s up t o 10 h z . where p a t h l e n g t h r e s o l u t i o n becomes i m p o r t a n t . F l u x a t r o n The f l u x a t r o n employs a G i l l p r o p e l l e r anemometer w i t h vane t o measure U' and a n o t h e r p r o p e l l e r s e n s o r t o measure W. I n o r d e r t o c a l i b r a t e a g i l l t y p e anemometer t h e a n g u l a r r e s p o n s e o f t h e s e n s o r t o t h e wind becomes v e r y i m p o r t a n t . F i g u r e 7 shows how t h e p r o p e l l e r r esponds t o d i f f e r e n t w ind a n g l e s . When t h e wind a n g l e i s z e r o (wind b l o w i n g d i r e c t l y i n t o p r o p e l l e r ) t h e r e s p o n s e i s 100%. However beyond 30° t h e a c t u a l r e s p o n s e i s below t h e i d e a l cos 0 r e s p o n s e . S i n c e normal wind f l o w s do not exceed ± 30° from t h e h o r i z o n t a l t h e e f f e c t would be m i n i m a l when th e p r o p e l l e r i s used f o r U' measurements. A t i 30° t h e 21 r e s p o n s e i s down an e x t r a 6% The a c t u a l c a l i b r a t i o n o f each U 1 g i l l can be done i n t h e wind t u n n e l . T h i s a l l o w s t h e e s t i m a t i o n o f t h e t h r e s h o l d r e g i o n , t h e n o n - l i n e a r r e g i o n , and t h e l i n e a r r e g i o n . The c a l i b r a t i o n i s good f o r t h e t o t a l component o f t h e h o r i z o n t a l wind. For t h e v e r t i c a l g i l l c a l i b r a t i o n t h e c o s i n e r e s p o n s e o f t h e p r o p e l l e r i s needed s i n c e i n o p e r a t i o n t h e v e r t i c a l s e n s o r i s c o n s i s t e n t l y m e a s u r i n g components o f t h e wind. I n p r a c t i c e t h e s o n i c W s i g n a l and ,the F l u x a t r o n W s h o u l d agree f o r l a r g e a m p l i t u d e low f r e q u e n c y f l u c t u a -t i o n s i f b o t h a r e c a l i b r a t e d p r o p e r l y . - T h i s p a r t i c u l a r p r o c e d u r e was used i n t h i s s t u d y t o check t h e c a l i b r a t i o n o f t h e s i g n a l s from t h e T s i m l y a n s k f i e l d d a t a . 3.2 D i s c u s s i o n o f Data 3.2.1 Measurements o f H o r i z o n t a l V e l o c i t y The t i m e t r a c e s o f U 1 from t h e F l u x a t r o n s h o u l d be v o i d o f n o n - l i n e a r e f f e c t s when mean winds a r e i n e x c e s s o f about 3 m/sec. To check t h i s t h e l i n e a r s o n i c U 1 t r a c e was compared t o t h e F l u x a t r o n o u t p u t . F i g u r e 8 shows t i m e domain t r a c e s o f U' f o r Run T029. A c t u a l o u t p u t s a r e shown from b o t h i n s t r u m e n t s and a l s o t h r e e f i l t e r e d t r a c e s o f t h e s o n i c U 1. A K r o h n h i t e F i l t e r (model 3340) w i t h a sh a r p low-pass f i l t e r i n g c h a r a c t e r i s t i c was used. The f i l t e r e d o u t p u t was s p e c i f i e d t o be down 18.5 db. a t c u t - o f f and t o have a 48 db. p e r o c t a v e a t t e n u a t i o n s l o p e . The b a s i c 22 S 0 NI C U 10 S O N I C U 2 H Z . F I L T E R FIGURE 8 - Tift TRACES OF' U* 23 agreement i n shape and magnitude of t h e s o n i c and p r o p e l l e r was good as shown i n F i g u r e 8. Best v i s u a l shape agreement was observed when frequencies greater than about,6 hz. had been removed by the Krohnhite from the SonicU'. si g n a l . The cut-off frequency f c at h a l f power turns out to be at lA hz. for a Krohnhite,setting of 6 hz. (checked by f i l t e r i n g the sonic espectra separately),. The distant cpns,tant for t h i s case would then be of the order ^ = 3£ = m . fc 1-4 F i g u r e s 9, 10 and 11 show s p e c t r a l c o m p u t a t i o n s f o r t h r e e r u n s . P l o t s d e s i g n a t e d w i t h a 1 r e p r e s e n t U.B.C. s o n i c measurements, t h o s e w i t h a 2 R u s s i a n S o n i c Measurements, and t h o s e w i t h a 3 t h e F l u x a t r o n Measurements. I n t h e r e g i o n below about f = 2 x lO-"*" h z . t h e s p e c t r a agreed c l o s e l y i n shape and magnitude. For f r e q u e n c i e s g r e a t e r t h a n 2 x 10 1 h z . , t h e h i g h f r e q u e n c y a t t e n u a t i o n o f t h e g i l l began t o a f f e c t t h e r e s u l t s . The F l u x a t r o n s p e c t r a was a t t e n u a t e d by , 2 a f a c t o r o f h a t about 1 h z . T a b l e 2 shows e s t i m a t e o f U c u m u l a t i v e i n t e g r a l s f o r t h e s e r e g i o n s . The average r a t i o o f t h e t o t a l v a r i a n c e s f o r t h e F l u x a t r o n / s o n i c was 1.08. The F l u x a t r o n i n g e n e r a l appeared t o o v e r e s t i m a t e t h e wind s l i g h t l y , a p o s s i b l e c a l i b r a t i o n problem. F i g u r e s 12, 13 and 14 show r a t i o s o f t h e s p e c t r a l a m p l i t u d e s p l o t t e d a g a i n s t f r e q u e n c y f o r t h e t h r e e r u n s . The agreement below f = 2 x lO -" 1" was a p p r o x i m a t e l y 1.2:1 except a t v e r y low f r e q u e n c i e s where h i g h pass f i l t e r s i n t h e F l u x a t r o n e l e c t r o n i c s became s i g n i f i c a n t . Above 24 1 . 0 T013 LONG\T\ JD\N P\L V E L O C I T Y U 1 0 . 0 CO % - i . o u LJ Ll_ O - 3 . 0 3 3 3 1 3 I 3 U = 4.7 M/SEC TS?= 0.8313 *v*«c«-S a m e — 3 4 T 3 3 * | a 3 u3 1§. 3 * i . . 3 3 J - 4 . 0 I U B C S 0 H » C 2. U S S R S 6 f » * c 3 F U J X * T « O M •5.0 - 4 . 0 - 3 . 0 •2.0 - 1 . 0 0 . 0 LOG F ( H Z . ) 1 . 0 2 . 0 FIGURE 9 25 1.0 i T02 6 . L .ONG\TUDtNM_ V E L O C I T Y U 1 4.0 U = 6.3 M/SEC £ °-0 UJ ' CO K - 1 . 0 u ui a C O X LL.-2.0 CD O ,1,007 w V s e c * Ul= 0.9819 i s 1 ! I i 4 t 5 2. *** 3 * 4 3 * i 3 e. 3 - I 3 £ 3 3 3 3 3 -5.0 \ UBC s a m e 2. USSR 56*>c-3 •4.0 -3.0 -2.Q -1.0 0.0 1.0 E.O LOG F ( H Z . ) FIGURE .10 26 l.O-i 0.0 ni (_> UJ CO -1.0 LJ LU O-LO >K U— £.0 g.3.0 -4.0 •5.0 -4.0 T029 LONG lTUD lMf tV- V E L O C \ T Y U' U = 5.8 M/SEC 3 l U*= 1.: PUOX. IT^  1.2415 3 i •3.0 Some I S 3 U 3 3 * t use s o m e 2, USSR s o m e 3 F U O X . I V T K . O V t •2.0 -1.0 0,0 LOG F ( H Z . ) 1.0 *AVSEC?-a.o FIGURE 11 27 TABLE U'u' CUMULATIVE INTEGRALS . 0 0 0 5 5 h z. <f ' t . 1 5 8 h z . RUN FLUXATRON T013 0.67*44 T026 0.7820 T029 1 .205 (M.K.S. UNITS) SONIC(UBC) 0.5192 0.7086 1.005 SONIC(USSR) 0.5077 0.7350 1.066 FLUX./SONIC(UBC) 1.29 ' 1.10 1.20 .158hz.^f< lO.ohz. RUN FLUXATRON SONIC(UBC) SONIC(USSR) FLUX./SONIC(UBC) T013 0 .1569 0 .2095 0.2026 0.7^9 T026 0 .2250 0 .2733 0.2750 0.823 T029 0.1880 0.2^00 O.236O 0 .783 .00055hz.<f< 1 0 . 8 h z . RUN FLUXATRON SONIC(UBC) SONIC(USSR) FLUX./SONIC(UBC) T013 0 .8313 0.7^87 0.7103 1.11 T026 1 . 0 0 7 0.9819 1.010 1.02 T029 1.393 1.245 1.302 1.12 28 CO r-l O (X o d O* O d LL H d O o uJ UJ _J u UJ CL o g fe cr al LU cr 10.0 1.0 X X. X X X x _V _-RUN T026 x X „ X "~*x X. * \ x \ \ \ \ X \ •• —x • -0.001 o.oi o.l 1.0 io.0 LOG F F I G U R E 1 3 - R A T I O O F S P E C T R A L E S T I M A T E S X x * * v X X * « "X ~ * — ^ x RUN T029 25 X X X * x z \ \ \ X \ O.OOl O.Ol o.i 1.0 lo.o LOG F . F I G U R E 1 4 - R A T I O O F S P E C T R A L E S T ^ M f t T E S f = 2 x 10 h z . t h e r a t i o began t o drop. The F l u x a t r o n power was r e d u c e d t o % a t f = 0.70 hz., f = 0.85 hz, and f = 0.90 h z . f o r Runs T013, T026, T029 r e s p e c t i v e l y . The mean winds from p r o f i l e measurements were 4.7 m/sec, 6 i 3 m/ sec, and 5.8 m/sec r e s p e c t i v e l y . Thus, t h e a s s o c i a t e d d i s t a n t c o n s t a n t s would be 6.72 m., 7.54- m., and 6.47., (from = U / $ r r f ) f o r Runs T013, T026, and T029 r e s p e c -t i v e l y . F i g u r e 15 shows t h e j o i n t p r o b a b i l i t y d e n s i t y o f U 1 s o n i c a c r o s s and U' p r o p e l l e r down. The c o n t o u r s r e p r e s e n t l i n e s o f c o n s t a n t d e n s i t y a t i n t e r v a l s o f 200. The r i d g e of h i g h e s t d e n s i t y marked w i t h a d o t t e d l i n e r e p r e s e n t s a b e s t a p p r o x i m a t i o n o f t h e a c t u a l r e s p o n s e o f t h e two i n s t r u m e n t s . The r e s p o n s e was 1:1 and l i n e a r between o u t -p u t s o f i 1.0 and then.showed a s l i g h t t e n d e n c y f o r h i g h e r s o n i c v a l u e s a t l a r g e r o u t p u t s . T h i s c h a r a c t e r i s t i c o f t h e signal's was p r o b a b l y a r e s u l t o f - t h e h i g h f r e q u e n c y l i m i t a t i o n s o f t h e G i l l . Peak v a l u e s o f t h e h i g h e r f r e -quency S o n i c F l u c t u a t i o n s s h o u l d be g r e a t e r t h a n t h e G i l l beyond c u t - o f f . F i g u r e 16 shows t h e p r o b a b i l i t y d i s t r i b u t i o n o f b o t h U' s i g n a l s . The skewed n a t u r e o f t h e v e l o c i t y d i s t r i -b u t i o n was n o t e d . B o t h t h e s o n i c and G i l l p r o p e l l e r showed peak d i s t r i b u t i o n i n t h e same r e g i o n w i t h t h e S o n i c showing a h i g h e r p r o b a b i l i t y . The h o r i z o n t a l a x i s i s such t h a t h i g h e r v e l o c i t i e s were t o t h e r i g h t ( i n t h e p o s i t i v e r e g i o n ) 32 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 i 0.0 10 0.5 1.0 1.5 2.0 2.5 3.0 3.5 G Uscm.c -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 ' 0 0 19 16 j 0 i 0 ! 0 i 0 6 15 i 0 . 0 . 0 | •-- \- : - --4-- ! 21 i 10 i 25\ 67 ; 16 = 1 i 10 0 • 11 : 43 .94 17 0 : 0 0 25 0 0 I 0 0 ; 5 55 0 0 ; 0 0 ' 0 0 0 0 0 0 0 0 0 0 > 0 0 14 j , 0 , 0 0 0 0 0 0 ' 0 0 : 0 0 0 0 0 0 0 4 0 0 0 5 0 0 0 39 18 0 0 .48 7 4 ) 0 0 0 1 0 0 0 0 0 0 I 0 0 0 i 0 0 0 f 0 0 0 ' : 0 0 0 , 1 0 0 0\ 8 0 0 28 0 0 0 0 0 NORMALIZED FIGURE 15 - JOINT PROBABILITY DENSITY OF U GILL Ait) U SONIC 33 5 o o o FIGURE '16 - PROBABILITY DISTRIBUTION OF U GILL AND U SONIC 34 and lower v e l o c i t i e s to the l e f t (negative region). Both sonic and G i l l observed a second peak i n d i s t r i b u t i o n i n the p o s i t i v e or higher wind speed area of the v e l o c i t y f i e l d . Figure 17 shows a plot of the coherence and phase for the Fluxatron U' and sonic U' (U.S.S.R.) signals of Run T029. One defines coherence as: / S 2 (n) + Q 2 (n) Y%. Coherence: coh_.(n) = ( ; S ^ . y x g X y ( n 0 ) xvK ' \ ,S (n) x S (n)' * xx yy where and Q Xy(n) are the cospectrum and quadspectrum respectively. The coherence was near 1 at £ = 0.01 hz. and had f a l l e n o f f to 0.5 at f = 0.9 hz. The phase lag of the propeller was near zero at the lowest frequencies and reached 45° by about f = 0.75 hz. If we assume t h i s was the point of frequency cut-off according to theory, t h i s corresponded U 5 8 to a distance constant of •sr== - -— 0 f > > ' = 7-.91 m. which 2£r 6 - 2SD.>75J.»75 compared with the r e s u l t attained by looking at the r a t i o s of power spectra (.6.91 metres) respectively. 3.2.2 Measurements of V e r t i c a l V e l o c i t y Figure 18 shows time domain traces of W signals. Actual voltage outputs are shown from the Fluxatron and the U.B.C. Sonic and also three f i l t e r e d traces of the Sonic W. The v i s u a l agreement i n both shape and magnitude i s less than i t was for the U' traces. Spacing of the sensors can sometimes introduce sampling problems. However, the cross-stream separation for these runs was always i n the order of 1 metre so that larger scale a. x <r in u -i<tcs 36 S O N I C W S O N I C W 6 HZ . F I L T E R S O N I C W 4 H Z . F I L T E R .LAJUI M I^shdA/lHm ml Art iv/Hl. HiAity i fl S O N I C W 2 HZ . F I L T E R FIGURE 18 37 v e r t i c a l gusts should s t i l l have agreed i f the instrument responses were si m i l a r . Comparison with the two acoustic anemometers indicated t h i s to be the case. Figure 18 showed that i n general the best agreement i n shape was attained using 2l-4hz, K r o h n h i t e - f i l t e r s . on Sonic W. Comparing i t with the propeller W, i t was observed that near where W = 0, there was l i t t l e f l u c t u a t i n g energy from the propeller but s t i l l considerable energy associated with sonic W. Areas A and B on the traces emphasize t h i s statement. Part A indicates a loss i n amplitude of higher frequency fluctuations i n the propeller signal as c f . to the sonic. Part B shows a loss i n amplitude of both higher and lower frequency fluctuations associated with the pro p e l l e r . In Part B, a d e f i n i t e low frequency trend i n sonic W was not seen at a l l by the propeller. As pointed out by the scale of the traces a large percentage of the time was spent operating i n the non-linear range (1 1.00 m/sec). This p a r t i c u l a r loss of W information from the propeller had a d i r e c t e f f e c t on the computation of the momentum f l u x as w i l l be shown l a t e r i n a discussion of the cospectra of U' and W. In order to look at the energy contributions at a l l frequency l e v e l s for both sonic and Fluxatron W signals, Figures 19, 20 and 21 were shown. Each W signal was d i s -played at d i f f e r e n t f i l t e r i n g stages down to 0.3 hz. low 38 F L U X A T R O N W 6 H Z . F I L T E R S O N I C W - 6 H Z . F I L T E R F L U X A T R O N W 5 HZ . F I L T E R S 0 N I C W 5 H Z . F I L T E R F L U X A T R O N W M H Z . F I L T E R S O N I C W 4 H Z . F I L T E R FIGURE 19 39, F L U X A T R O N - W-3-HZ.- F I L T E R -SON I C W 3 HZ . F I LTE'R F L U X A T R O N W 2 H Z . F I L T E R S ON IC W 2 H Z . F I LT E R F L U X A T R O N W I HZ . F I L T E R S O N I C W I H Z . F I L T E R FIGURE 20 F L U X A T R O N W 0.7 H Z . F I L T E R S O N I C W 0.7 H Z V F I L T E R F L U X A T R O N . W 0.5 H Z . F I L T E R S O N I C W 0.5 H Z . F I L T E R F L U X A T R O N W 0.3 H Z . F I L T E R S O N I C W 0.3 H Z . F I L T E R 20 sec. FIGURE 21 41 p ass f i l t e r i n g . A t a l l s t a g e s t h e r e appeared t o be s t r o n g e r f l u c t u a t i o n s a s s o c i a t e d w i t h t h e SONIC W t h a n w i t h t h e f l u x a t r o n . T h i s i n d i c a t e d a s i g n i f i c a n t l o s s o f energy-measurement by t h e f l u x a t r o n o v e r t h e whole spectrum 0.3 h z . £ f £ 10 h z . F i g u r e s 22, 23 and 24 show W s p e c t r a l c o m p u t a t i o n s f o r t h e t h r e e r u n s . The U.S.S.R. and U.B.C. s o n i c always agree c l o s e l y f o r t h e f u l l f r e q u e n c y range. The p r o p e l l e r W s p e c t r a c o n s i s t e n t l y f a l l s below t h e s o n i c s p e c t r a e s p e c i a l l y i n t h e h i g h f r e q u e n c y a r e a above f = 2.0 x lO-''" h z . The f a c t t h a t t h e p r o p e l l e r a b s o l u t e magnitude i s s t i l l l ower t h a n b o t h s o n i c measurements below f = 2 x 1 0 - ^ h z . i l l u s -t r a t e s t h e e f f e c t o f t h e t h r e s h o l d and n o n - l i n e a r r e s p o n s e f e a t u r e s o f G i l l anemometers. A r e d u c t i o n i n t h e energy measured a t a l l f r e q u e n c i e s was e x p e r i e n c e d by t h e F l u x a t r o n as a t o t a l e f f e c t . 2 T a b l e 3 shows e s t i m a t e s o f t h e W c u m u l a t i v e i n t e -g r a l s from t h e t h r e e r u n s . I n t h e low f r e q u e n c y range 0.00055 h z . < f < .158 h z . t h e average r a t i o o f c u m u l a t i v e . ^ . (FLUXATRON ) . . n ,,, . ., . . , „„ ~ i n t e g r a l s ( S 0' N' I C ( U B@) ) w a s about 0.745 i n d i c a t i n g a l o s s o f about 25% o f t h e t o t a l energy i n t h e FLUXATRON SIGNAL due t o t h r e s h o l d arid n o n - l i n e a r e f f e c t s . T h i s means t h a t t h e r e would be an average a m p l i t u d e l o s s o f about 12% i n t h e W G i l l s i g n a l below 0.158 h z . I n t h e h i g h f r e q u e n c y range where about 2/3 of t h e t o t a l f l u c t u a t i o n e n e rgy was t o be found, (0.158 hz < F < 10.8 h z . ) , t h e h i g h f r e q u e n c y 43 R V J N T 0 2 6 V E R T I C A L V E L O C I T Y U a 6.3 M / S E C . PtOX. W^ —I 0.ife96 • A V S E C 2 -3 12, 3 - 4 3 3 ' i 3 3 3 3 3 3 3 3 3 I use S O N I C £ USSR SoWlC 3 FUJXftTRoN -e.o - i . o o.o i . o 2 . LOG F <«o x - l FIGURE. 2 3 % 44 1.0 l o.o Ul 1 CJ a. en x -e.o o -3.01 -4.04 - 5 . 0 - 1 — -4.0 RUN T0E9 VERTICAL VELOCITY ^ 1 i t * * 3 3 £ 0- 5.8 r * / S E C . V 0 4 | L O X = 0 . 1 E 1 6 M V S E C * ^ ' S O M . C " 0 . ^ 4 7 9 M ' / S E C 8 3 3 i 3 * 3 * \ U6C SO^IC 2. USSR SortlC 3 FLOK.ATB.OVl - 3 . 0 2 . 0 - 1 . 0 LOG F 0 . 0 1 . 0 2.0 FIGURE 24 ; M 45 'TABLE W W CUMULATIVE INTEGRALS .• (M.K.S. UNITS) . 0 0 0 5 5 h z.<f^ . l 5 8 h z . RUN FLUXATRON T013 O.O36QI T026 0.0533 T029 0.0581 SONIC(UBC) 0.0474 0 . 0 7 5 8 0.0753 SONIC(USSR) 0 . 0 5 0 6 0 . 0 7 1 3 0 . 0 7 2 5 FLUX./SONIC(UBC) 0 . 7 6 0 0 . 7 0 3 0.771 . 1 5 8 h z.^f <• 1 0 . 8 h z . RUN FLUXATRON T013 0.04680 T026 0 . 0 7 0 5 T029 O.O635 SONIC(UBC) 0.1272 0 . 1 9 3 8 0.1726 SONIC(USSR) 0.1371 0 .1913 0 . 1 6 5 0 FLUX./SONIC(UBC) O .368 0 . 3 6 4 O .368 . 0 0 0 5 5 h z.^f< 1 0 . 8 h z . RUN FLUXATRON T013 0.08281 ••T026 0 . 1 2 3 8 T029 0.1216 SONIC(UBC) 0.1746 0.2696 0.2479 SONIC(USSR) 0.1877 0.2626 0 . 2 3 7 5 FLUX./SONIC(UBC) 0 . 4 7 4 0 . 4 5 9 0 . 4 9 1 attenuation of the propeller also affected i t s r e s u l t s . In t h i s range the average r a t i o of cumulative integ r a l s propeller energy was l o s t due to i t s li m i t e d high frequency response. The o v e r a l l r e s u l t was a 0.475 r a t i o of W cumulative integrals of FLUXATRON VS. SONIC f o r the entire frequency range studied. A t o t a l loss then of about 52% of the t o t a l f l u c t u a t i n g W energy is- experienced by the FLUXATRON. t i v e l y . Below f = 2 x 10 hz. the agreement was about 0.75:1.0 except at lowest frequencies where the high pass f i l t e r s i n the Fluxatron (Dyer and Hicks, 1970) became s i g n i f i c a n t (especially i n Run T013) and where the signal sample time was small. In the higher frequency area, the GILL/SONIC r a t i o becomes ha l f of the mean r a t i o at f = 0.70 hz., f •= 0.60 hz., and f = 0.60 hz. respectively f o r the three runs. This would correspond to a KroTapJai&e f i l t e r with a cut-off frequency of Rear f = 3 hz. i n the system. This r e s u l t was v i s u a l l y observed i n the study of the time traces. The random var i a t i o n of the ratio'from the mean in the mid-frequency range was probably a function of how much energy at each frequency was l o s t while i n threshold or non-linear conditions during each run. Figure 28 shows the j o i n t p r o b a b i l i t y density of W SONIC across and W FLUXATRON down. The contours (FLUXATRON ) (SONIC(UBC)) was about 0.367 in d i c a t i n g about 63% of the Figures 25, 26 and 27 show r a t i o s of the spectral estimates X X X RUN T013 X. •«i x X \ X X X * X NX \ • \ \ X \ 0.001 o.oi. o-l i.o lO.O L06 F F I G U R E . ^ 5 - R p f H O O F S P E C T R A L - E S T I M A T E S $ 48 Cfi> ol O V z X X } y X r If kX" 4 / X" / X X X X X X X X X o 6 6 o H 6 CD o H o o o CP Ld 10.0 l.o W SONIC o.i o.oa. X X X RUN TOe9 X X X . X "x \ X X X X A. x " « X * ~ " * \ x \ x\ X V V\-| ^ \ \ X FIGURE LOG F 2 7 - R A T I O O F S P E C T R A L E S T I M A T E S 50 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 i 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0 5 1.0 1.5 2.0 2.5 3.0 3.5 0 12 43 99 0 : 3 7 i 0 4 6 0 i 1 ! 0 23 1 21 119 27 13 3 0 ^32 38 ! 59 51 '46 10 •s N 0 13 N51s9Z^-lIB 176 122-o 1 5 7 1 i a 0 13 50 114 0 5 15 ; 57 \2X£ 0 0 0 ,45 114\26K^1 0 0 ; 3 21 70 \138v258 0 4 6 0 10 66"SL15. 0 0 0 0 5 21 36 0 0 0 0 0 7 12 0 0 0 0 0 3 2 513 525//291 U99 105 28 7 m^im^mjmm 1 9 1 7 L28 168 IB^98 vv93 15 4 ~- — ^ N, • ~ - X • -33 51 34 79 26 ^ 9 2 16 : 51 . 49 8 27 ' 1 29 128 i 8 1 0 0 i l l 0 NORMALIZED FIGURE 28 - JOINT PROBABILITY DENSITY OF W GILL AND W SONIC 51 represent l i n e s of constant density at i n t e r v a l s of 100. The raHge of highest density marked with a dotted l i n e represents a best approximation of the two instrument responses. I f both signals were exactly the same, a density d i s t r i b u t i o n would show a straight l i n e of slope 1 through the centre. The fact i s that they are not the same. The dotted l i n e i n fa c t follows very c l o s e l y the hypothesized response outlined i n Figure 6. The zero l e v e l of the FLUXATRON'S propeller was o f f s e t -0.25 i n recording which explains the v e r t i c a l o f f s e t on the graph. It would appear that a threshold area was observed between t. 0.6 v o l t s 'on the sonic scale and a non-linear range out to about -1.5 v o l t s . There was a much larger spread i n the r e s u l t s than for the U' measure-ments i n d i c a t i n g a smaller c o r r e l a t i o n between the W signals than f o r U' signals. Figure 29 shows the p r o b a b i l i t y d i s t r i b u t i o n of the W signals f o r Run T029. The G i l l shows a higher p r o b a b i l i t y of f i n d i n g no fluctuations than does the sonic. Also i t would appear for t h i s observation that the d i s t r i b u t i o n of the sonic W i s non-gaussian i n the p o s i t i v e (updraft region) e s p e c i a l l y . A check with another independent means for c a l c u l a t i n g the p r o b a b i l i t y d i s t r i b u t i o n revealed the same f a c t . Figure 30 shows the p r o b a b i l i t y d i s t r i b u t i o n for a l l 32 minutes of Run T029. Figure 31 shows a plot of the coherence and phase for the Fluxatron W and Sonic (U.B.C.) W signals for 52 FIGURE'#29 - PROBABILITY DISTRIBUTION OF W GILL AND W SONIC F I G U R E . 30 _ T V E R 1 F P R O B A B I L I T Y D I S T R I B U T I O N O F S O N I C W o o O a> o o 9^ w 'O 4- o J0 54 Run T029. The coherence was about 0.91 a t f = 0.01 h z . and had f a l l e n o f f t o 0.5 by about f = 0.3 h z . The phase l a g of t h e p r o p e l l e r was near z e r o a t low f r e q u e n c i e s and began t o i n c r e a s e by f = 0.04 h z . A t f = 0.3 h z . t h e phase l a g was about 45°. A c c o r d i n g t o specsv t h e n , t h i s c o r r e s p o n d e d t o a Ki>nhi>te~: f r e q u e n c y c(Atr,pff o f about 1 h z . 3.2.3 Measurements o f Momentum F l u x F i g u r e s 32, 33 and 34 show t h e c o s p e c t r a o f U'W as c a l c u l a t e d f o r RUNS T013, T026 and T029. The i n t e g r a l o f t h e a r e a under t h e c o s p e c t r a is> t h e k i n e m a t i c momentum f l u x . The c o s p e c t r a l shapes and magnitudes were a l m o s t i d e n t i c a l f o r t h e two s o n i c anemometers.:: and v e r y s i m i l a r i n shape t o momentum c o s p e c t r a measured i n 1969 a t Ladner, B.C. (McBean, 1970). However, t h e f l u x a t r o n c o s p e c t r a were r e -duced i n b o t h shape and magnitude a t h i g h e r f r e q u e n c i e s . T a b l e 4 l i s t s v a l u e s o f t h e U'W c u m u l a t i v e i n t e g r a l s f o r t h e d i f f e r e n t f r e q u e n c y r a n g e s . I n t h e h i g h f r e q u e n c y range ( f > .158 hz.) where about 1/3 o f t h e momentum f l u x was f o u n d t h e FLUXATRON was o b s e r v e d t o have measured o n l y about 50% o f t h e t o t a l f l u x a v a i l a b l e . T h i s was a r e s u l t o f t h e upper f r e q u e n c y l i m i t a t i o n s o f t h e p r o p e l l e r . I n t h e low f r e q u e n c y range ( f > .158 hz.) where t h e o t h e r 2/3 of t h e momentum f l u x was found t h e FLUXATRON m i s s e d o n l y about 25% of t h e t o t a l f l u x a v a i l a b l e . There was a l a r g e s c a t t e r i n t h e s p e c t r a l p o i n t s , however, p r o b a b l y due t o t h e n o n - l i n e a r r e s p o n s e o f t h e W s i g n a l s . 5 6 l . O - i Ui 0 . 0 R U N T 0 1 3 U = 4.7 YYv/SGC. V/U'^ U** = - o. OT5lE M V 5 E C . 1 Fu>x. some p -i.o-u Cu >K - 2 . 0 -O - 3 . 0 -? * A 3* I t 3 I 33 a - 4 . 0 - ^ 3 3 =» • 1 - 5 . 0 -4.0 -j$—,—$—3-I U 6 C S O K V C £ ussa S O N I C 3 F L 0 * A T R 0 M •3.0 -2.0 -1.0 0 . 0 L O G F c « o ' FIGURE 32 - U'W COSPECTRA - RUN T013 1 . 0 2 . 0 57 1 0 i RUN J O Z B % 0.0 Ul U = 6,3 w v / S E C Vg U = U * * - 0 . 1 2 4 - 5 KAVSBC*-vu>x. TTjTTT = U * - * = - 0 . 1 7 3 5 N* 1-/SEC 1 p - i . o Lu Q . x -2.0 Lu O -3.0 4 4.01 - 5 . 0 4 - 4 . 0 ( 3 d 3 3 3 5 3 3 3 e l -2 l_ 3 3 .? I 2 ' 3 2 I I U B C S O N I C 2. U S S R S O H I C 3 FLOXPiTRQVl g 5 2 jt 2 3.0 • 2 . 0 - 1 . 0 0 . 0 LOG F l . o 2 . 0 FIGURE 33 - U'W'COSPECTRA 58 R U N T 0 £ 9 1 . 0 i 0 III o.o p -1.0 LU Q -, X - 2 . 0 Li_ O - 3 . O H -4.0 H • 5 . 0 - 4 . 0 2 I | § 3 U •= 5 . 8 >N'U' - u * = - 0 .14 - 5 3 MVsec' VAJ'O' = U**' = ~ 0.1913 *AVsec*-SftkttC 3 3 E fe 3 3 £ USSfc. "oOKXC 3 - s — I — - 3 . 0 - 2 . 0 - 1 . 0 0 - 0 LOG F ^ 1.0 2.0 FIGURE .34 - UVCOSPECTRA 59 TABLE U'W' . 0 0 0 5 5 h z.<f< . 1 5 8 h z . RUN FLUXATRON T013 T026 T029 - 0 . 0 5 4 0 9 - 0 . 0 8 9 0 - 0 . 1 2 0 7 CUMULATIVE INTEGRALS (M.K.S. UNITS) SONIC(UBC) -0.0843 -0.1145 -0.1410 SONIC(USSR) - 0 . 0 7 5 6 - 0 . 1 3 7 2 -O .I63O FLUX./SONIC(UBC) 0.642 0 . 7 7 8 0 . 8 5 5 . 1 5 8 h z.<f^ 1 0 . 8 h z . RUN FLUXATRON SONIC(UBC) SONIC(USSR) FLUX./SONIC(UBC) T013 - 0 . 0 2 1 0 3 - 0 . 0 5 2 9 - 0 . 0 4 5 1 0 . 3 9 8 T026 - 0 . 0 3 5 5 - 0 . 0 5 9 1 -O.O657 0 . 6 0 1 T029 -0.0246 - 0 . 0 5 0 3 -0.0464 0 . 4 8 9 .00055hz.<f «• 10.8hz. RUN FLUXATRON SONIC(UBC) SONIC(USSR) FLUX./SONIC(UBC) T0135 -0 .07512 -0.1=372 - 0 . 1 2 0 7 0.548 T026 -0.1245 -0 . 1735 - 0 . 2 0 2 9 0.717 T029 -0.1453 -0.1913 - 0 . 2 0 9 4 0.760 60 The o v e r a l l e f f e c t was a r e d u c e d momentum f l u x measurement o f about 0.675 f o r t h e F l u x a t r o n when compared t o a s o n i c t y p e anemometer. I n d i v i d u a l r a t i o s o f t h e f l u x measurements by FLUXATRON VS. THE U.B.C. s o n i c were 0.548, 0.717 and 0.760 f o r t h e t h r e e r u n s T013, T026 and T029 r e s p e c t i v e l y . I t must be noted t h a t Run T013 was t a k e n i n t h e e v e n i n g under more s t a b l e c o n d i t i o n s t h a n were TO26 and U'W FLUX T029. The average r a t i o o f jp-^p S O N I C f o r t ' i e t w o u n s t a b l e c a s e s would be 0.739. F i g u r e s 35, 36 and -37 show r a t i o s o f t h e c o s p e c t r a l f-U1 W G i l l ) e s t i m a t e s ^^Trm e 7 ( f o r Runs T013, T026 and T029. The (U'W S o n i c ) ' s t a b l e c a s e (RUN T013) showed much more s p r e a d e s p e c i a l l y i n t h e low f r e q u e n c y r e g i o n t h a n d i d t h e more u n s t a b l e c a s e s , T026 and T029. T a b l e 5 shows some c a l c u l a t i o n s o f t h e d r a g c o e f -f i c i e n t c ^ and t h e c o r r e l a t i o n c o e f f i c i e n t r wu f o r t h e FLUXATRON and two s o n i c anemometers. lo.o 1.0 U'W S O N I C O.l. o.oxl O.OOL X X X X X X R U N TOL?> v <. \ x X X X X X > v X x\ X \. X O.l L O G F 1.0 10.0 F I G U R E '• 3 5 - R K T \ 0 O F S P E C T R A L E S T I M A T E S O.OlL O.OOl o.oi. O.l 10.0 LOG F F I G U R E 3 6 - R A T I O O F S P E C T R A L E S T I M A T E S lO.O 1.0 U'W' & M U U'W some O.l o.oxl x * X X R U N T o e 9 X Xs \ X Y X x x X * X X lo.o LOG F F I G U R E 37 - R A T I O O F S P E C T R A L E S T I M A T E S TABLE % CALCULATIONS OF T W U AND C D (M.K.S. UNITS)' P w u = U* /;(-sigma U)(sigma w) RUN FLUXATRON SONIC(UBC) SONIC(USSR) T013 0.286 O .379 0 . 3 3 1 T026 0 . 3 5 3 O .337 0 . 3 9 ^ T029 0 . 3 5 3 0.3MJ- OS377 C D - u* 2/!* 2 RUN FLUXATRON SONIC(UBC) SONIC(USSR) T013 0 .003^8 O.OO635 0.00558 T026 0 . 0 0 3 1 ^ 0.00437 0 .00511 T029 0 . 0 0 ^ 3 2 0 . 0 0 5 6 9 0.00622 CHAPTER 4 CONCLUSIONS The turbulent horizontal and v e r t i c a l components of the wind were measured and compared using a sonic-type anemometer and G i l l p r o pellers. Measurements of the horizontal v e l o c i t y fluctuations showed good agreement between sonics and propeller i n both the time domain and frequency domain. Best shape agreement i n the time traces occured when frequencies f>6 hz.' hacU-been removed,, by -the. Ksohnhite /.filter from'-Sonic W>. .(f c = l . 4 hz.). This meant the propeller had an associated distant constant of about 4 metre considering the mean wind at the time. Spectral computations revealed the Fluxatron i n general tended to overestimate the t o t a l U' variance by about 20% f o r f r e -quencies below f = 0.2 hz. i n d i c a t i n g a possible c a l i b r a t i o n discrepancy. By looking at where the r a t i o of the power spectral estimates (propeller vs. sonic) f e l l to about 0.50 i t was possible to reconfirm the value of the distant con-stant for the propeller. The average for the three runs was 6.90 metres. The j o i n t p r o b a b i l i t y density of U1 sonic and U 1 G i l l confirmed the l i n e a r response of the U' G i l l p r o p e l l e r . Measurements of the v e r t i c a l v e l o c i t y fluctuations showed poorer agreement between sonic and propeller i n both the time and frequency domains. Time traces of sonic W and propeller W showed best agreement when a 3hz. Kroftnhite f i l t e r 66 was used on the S o n i c ^ W,' -.Cfc^Oi^hzi 1). By f i l t e r i n g b o t h p r o p e l l e r and s o n i c s i g n a l s f o r 0.2 h z . < f < 10 h z . a s i g n i f i c a n t l o s s o f p r o p e l l e r energy measurement was o b s e r v e d o v e r t h e f u l l range o f f r e q u e n c y . S p e c t r a l com-p u t a t i o n s showed a l s o t h a t t h e W f l u c t u a t i n g e n e rgy o f t h e p r o p e l l e r was always l e s s t h a n t h a t from t h e s o n i c s . Non-l i n e a r and t h r e s h o l d e f f e c t s were a l l e g e d t o have caused an average 25% r e d u c t i o n o f t h e t o t a l W energy measured by t h e p r o p e l l e r i n t h e f r e q u e n c y r e g i o n f < 0.158 h z . The p r o p e l l e r ' s h i g h f r e q u e n c y c u t - o f f a t f c f 0.9 h z . and i t s n o n - l i n e a r r e sponse a t low wind speeds t h e n r e s u l t e d i n a t o t a l l o s s o f 52% o f W f l u c t u a t i n g energy over t h e f u l l f r e q u e n c y range s t u d i e d . The j o i n t p r o b a b i l i t y d e n s i t y d i s t r i b u t i o n a g a i n c o n f i r m e d t h e n o n - l i n e a r r e s p o n s e o f t h e W p r o p e l l e r and i n d i c a t e d a n o n - g a u s s i a n d i s t r i b u t i o n even f o r t h e s o n i c W. A n a l y s i s o f t h e c o s p e c t r a o f U'W showed t h a t s i g -n i f i c a n t c o n t r i b u t i o n s t o t h e momentum f l u x were t o be found i n t h e f r e q u e n c y domain 0.001 h:z. < f• <5.0 h z . Below f = 0.158 h z . t h e n o n - l i n e a r r e s p o n s e and s t a l l i n g e f f e c t s i n t h e W p r o p e l l e r s i g n a l were t h e p r o b a b l e r e a s o n s f o r t h e average r a t i o o f (U'W G i l l / U'W s o n i c ) b e i n g 0.76. Above f = 0.158 h z . t h e h i g h f r e q u e n c y l o s s e s o f b o t h t h e G i l l U' and W s i g n a l s h e l p e d a t t e n u a t e i t s U'W c o s p e c t r a more q u i c k l y t h a n t h a t f o r t h e s o n i c s r e s u l t i n g i n a measured l o s s o f momentum f l u x . The combined r e s p o n s e e f f e c t s o f t h e propeller were enough to reduce the Fluxatron's estimate of the t o t a l momentum f l u x by 32.5%. Both sonic types of anemometers agreed c l o s e l y as to shapes and absolute magnitudes of the spectra and co-spectra of U' and W. In the f i e l d , one method of minimizing the non-l i n e a r i t y and threshold e f f e c t s at low v e r t i c a l wind speeds would be to t i l t the v e r t i c a l sensor into the wind by 40°, or so, to always keep the propeller moving i n one d i r e c t i o n . This would assume the mean wind U near 5.0 m/sec. I t could be mounted on the same assembly as the horizontal G i l l so as to always face the mean wind. REFERENCES Bovsherov, V.M. and V.P. Voronov, I960, ' A c o u s t i c ; W i n d Vane', I z v . Acad, o f S c i . U.S.S.R., Geophys. S e r i e s , No. 6. Dyer, A.J.., B.B. H i c k s and K.M. K i n g , 1967, The F l u x a t r o n -A R e v i s e d Approach t o t h e Measurement of Eddy F l u x e s i n t h e Lower Atmosphere, J o u r n a l A p p l . M e t e r o r o l . , 6, 408-413. Dyer, A . J . and B.B. H i c k s , 1970, The S p a t i a l V a r i a b i l i t y o f Eddy F l u x e s i n , t h e C o n s t a n t F l u x L a y e r , Quart. J . Roy. M e t e o r o l . S o c , I n p r e s s . H i c k s , B.B., 1970, The Measurement o f A t m o s p h e r i c F l u x e s Near t h e S u r f a c e : A G e n e r a l i z e d Approach, J . A p p l . M e t e o r o l . , 9, 386-388. McBean, G.A., 1970, The T u r b u l e n t T r a n s f e r Mechanisms i n t h e A t m o s p h e r i c S u r f a c e L a y e r . Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia. M i t s u t a , Y., M. Miyake and Y. K o b o v i , 1967, Three d i m e n s i o n a l s o n i c anemometer-thermometer f o r a t m o s p h e r i c t u r b u l e n c e measurements. Kyoto U n i v . I n t e r n . Rep., 10 pp. Miyake, M., M. Donelan, G. McBean, C. P a u l s e n , F. Badgley, and E. L e a v i t t , 1970, Comparison o f T u r b u l e n t F l u x e s o v e r Water Determined by P r o f i l e and E d d y - c o r r e l a t i o n T e c h n i q u e s . Quart. J . Roy. M e t e o r . S o c , 96, pp. 132-137. Tsvang, L.R., B.M. Koprov, O.A. Kuznetzov, M. M i y a k e , R.W. S t e w a r t , and R.W. B u r l i n g , 1971, Comparison o f A c o u s t i c I n s t r u m e n t s i n A t m o s p h e r i c T u r b u l e n c e over Water. Boundary-Layer M e t e o r o l o g y , V o l . 2-2, 20-37. 

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