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An airborne investigation of the structure of the atmospheric boundary layer over the tropical ocean 1970

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AN AIRBORNE INVESTIGATION OF THE STRUCTURE OF THE ATMOSPHERIC BOUNDARY LAYER.• OVER THE TROPICAL OCEAN by MARK ANTHONY DONELAN B.Eng., M c G i l l U n i v e r s i t y , 1964 A THESIS SUBMITTED. •IN PARTIAL"FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF : DOCTOR OF. PHILOSOPHY i n the Department of P h y s i c s and the I n s t i t u t e of Oceanography A . We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October, 19 70 In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission for extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s repre s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of physics and the I n s t i t u t e of Oceanography The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date October 15, 1970 ABSTRACT Across the a i r - s e a i n t e r f a c e there i s a tr a n s f e r of momentum, heat and moisture. Knowledge of these i s e s s e n t i a l to the understanding of oceanic and atmospheric c i r c u l a t i o n s . This study i s an i n v e s t i g a t i o n of the v e r t i c a l turbulent transfers of momentum, heat and moisture i n the boundary layer of the atmosphere using an instrumented l i g h t a i r c r a f t . The data were c o l l e c t e d at several a l t i t u d e s between 18 m and 500 m i n the A t l a n t i c trade wind zone east of the i s l a n d of Barbados. Since the t r o p i c a l ocean i s the primary source of heat input to the atmospheric heat engine, good estimates, i n t h i s region, of the transfers of heat and moisture and t h e i r v e r t i c a l v a r i a t i o n s are e s s e n t i a l to any gl o b a l numerical atmospheric p r e d i c t i o n scheme. The f l u c t u a t i o n s of the v e l o c i t y components, temperature and humidity and the tran s f e r s of momentum, heat and moisture were investigated, p r i m a r i l y by means of t n e i r spectra and cospectra. I t was found that: ninety percent of the heat input to the atmosphere was i n the form of l a t e n t heat; the sen s i b l e heat f l u x was p o s i t i v e (upward) at the small scales generated near the surface and negative at the large scales due to subsiding a i r ; the lat e n t heat f l u x was p o s i t i v e at a l l scales and s i m i l a r i n s p e c t r a l d i s t r i - bution to the momentum f l u x ; the flow appeared to be an i s o t r o p i c even at scales one hundred times smaller than the distance from the boundary; the drag c o e f f i c i e n t , from d i r e c t measurements of the momentum f l u x ( or stress ), _3 was (l-45±0.08) x 10 ; shear generated turbulence was not e n t i r e l y d i s s i p a t e d l o c a l l y . TABLE OF CONTENTS ABSTRACT TABLE OF'CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS CHAPTER 1: INTRODUCTION 1.1 Airborne turbulence measurements 1.2 Previous work 1.3 Obj e c t i v e s of t h i s study CHAPTER 2: OBSERVATIONAL SCHEME AND ANALYSIS METHODS 2.1 The experiment 2.2 F l i g h t p a t t e r n s 2.3 Data g a t h e r i n g procedure 2.4 Data p r o c e s s i n g CHAPTER 3: EXPERIMENTAL RESULTS AND DISCUSSION 3.1 I n t r o d u c t i o n 3.1.1 The data 3.1.2 Synoptic c o n d i t i o n s 3.1.3 Methods of p r e s e n t a t i o n 3.2 Measurements along the wind 3.2.1 V e r t i c a l v e l o c i t y 3.2.2 H o r i z o n t a l v e l o c i t y 3.2.3 Temperature 3.2.4 Humidity 3.. 2.5 Momentum f l u x X V 3.2.6 Heat f l u x 59 3.2.7 Moisture f l u x 65 3.3 Comparison of crosswind measurements with measurements along the wind 73 3.3.1 Introduction 73 3.3.2 V e r t i c a l v e l o c i t y 74 3.3.3 H o r i z o n t a l v e l o c i t y 78 3.3.4 Temperature and humidity 80 3.3.5 Heat f l u x 80 3.3.6 Mois ture f l u x 85 3.4 The turbulent k i n e t i c energy budget 88 3.4.1 Introduction 88 3.4.2 Height dependence of terms i n k i n e t i c energy budget 90 3.4.2.1 Mechanical production 90 3.4.2.2 Buoyancy production 90 3.4.2.3 D i s s i p a t i o n 90 3.4.2.4 The r e s i d u a l term 93 3.4.3 The budget f o r f l i g h t s 1 and 3 95 3.5 The temperature-humidity correspondence 98 3.6 Discussion of a possible pattern of convective organization 108. CHAPTER 4: SUMMARY OF CONCLUSIONS 112 LIST OF REFERENCES " 117 APPENDIX A: THE INSTRUMENTS 120' A . l Introduction 120 A.2 The temperature sensor 120 A.3 The humidiometer 124 APPENDIX B: DATA PROCESSING 128 B . l Introduction B.2 S e l e c t i o n of data segments B. 3 Machine processing APPENDIX C: COMPARISON OF SIMULTANEOUS MEASUREMENTS FROM FLIP AND THE AIRCRAFT C l Introduction C. 2 Data o u t l i n e C.3 Spectra and cospectra APPENDIX D: STATISTICS v i LIST OF TABLES page 1. F l i g h t summary 14 2. Normalizers f o r s p e c t r a and cospectra of f l i g h t s 1 and 3 20 3. S t a t i s t i c s of f l i g h t s 1 and 3 27 4. Drag c o e f f i c i e n t s . 3 7 5. The data used i n the F l i p / A i r c r a f t comparison 136 6. Variances 143 7. S t a b i l i t y 144 8. S i m i l a r i t y r a t i o s 145 9. The K i n e t i c Energy Budget 146 v i i L I S T OF FIGURES page 1. The Bomex a r r a y 5 2. The r e s e a r c h a i r c r a f t , B e e c h r a f t Queen A i r 304D 6 3. F L I P 7 4. The f l i g h t p a t t e r n s • 9 5. T e m p e r a t u r e and h u m i d i t y p r o f i l e s ; 15 6. Wind p r o f i l e s f r o m t h e a i r b o r n e D o p p l e r r a d a r 16 7. S a t e l l i t e p h o t o g r a p h s o f t h e Bomex a r e a 17 8. V e r t i c a l v e l o c i t y s p e c t r a (upwind) 24 9. V e r t i c a l v e l o c i t y t r a c e s (upwind) 25 10. fj* v s . Z (upwind) 26 w 11. ( k j i ^ v s * ^ (upwind) 28 12. B v s . Z (upwind) 30 w 13. L o n g i t u d i n a l v e l o c i t y t r a c e s 32 14. L o n g i t u d i n a l v e l o c i t y s p e c t r a 33 15. '4/3' t e s t f o r i s o t r o p y 35 16. 0"/u* v s . Z 39 17. Temperature s p e c t r a (upwind) 41 18. 0"T v s . Z (upwind) 42 19. ( L M ) T v s . Z (upwind) 43 20. Tem p e r a t u r e t r a c e s (upwind) 45 21. H u m i d i t y s p e c t r a (upwind) 47 22. CT̂  v s . Z (upwind) ' 48 23. H u m i d i t y t r a c e s (upwind) 49 24. Momentum t r a c e s (upwind) 51 v i i i 25. Momentum cospectra . (upwind) 52 26. u^ vs. Z 53 •27. - r vs. Z 55 uw 2 8« (Vuw V S- Z 5 7 29. B vs. Z 58 uw 30. Heat f l u x traces (upwind) 60 31. Heat f l u x cospectra (upwind) 62 32. Heat f l u x vs. Z (upwind) 64 33. Moisture f l u x traces (upwind) 66 34. Moisture f l u x cospectra (upwind) 67 35. ( L J J ) ^ vs. Z (upwind) 69 36. r n vs. Z (upwind) 70 wQ r ' 37. Moisture f l u x vs. Z (upwind) 71 38. V e r t i c a l v e l o c i t y traces (crosswind) 75 39. V e r t i c a l v e l o c i t y spectra (crosswind) 76 40. L a t e r a l v e l o c i t y spectra 79 41. CT*T vs. Z (crosswind) 81 42. Q""Q- vs. Z (crosswind) 82 43. (kj^Q v s - ^ (crosswind) 83 44. Heat f l u x cospectra (crosswind) 84 45. Moisture f l u x traces (crosswind) 86 46. ( L ^ ) ^ v s « z (crosswind) 87 47. Mechanical production vs. Z 91 48. D i s s i p a t i o n vs. Z , _ 92 49. Divergence vs. Z 94 50. K i n e t i c Energy Budget f o r f l i g h t # 1 96 51. K i n e t i c Energy Budget f o r f l i g h t // 3 97 i x 52. T'Q' Ct) (upwind) 99 53. T'Q' (t) (crosswind) 100 54. r T Q(.k) (upwind) 101 55. r ^ (k^) (crosswind) 103 56. ( L + ) T Q vs. Z (upwind) 104 57. (L + ) T Q v s < z (crosswind) 105 58. Cross-spectra of T' and Q' (upwind) 107 59. A p o s s i b l e pattern of convactive organization 110 60. The frequency response of the thermistor 122 61. The frequency response of the humidiometer 126 62. Block diagram of machine processing steps 130 63. Comparison of w spectra from the a i r c r a f t and F l i p 138 64. Comparison of u spectra from the a i r c r a f t and F l i p 139 65. Comparison of the momentum cospectra from the a i r c r a f t and F l i p 140 X ACKNOWLEDGEMENTS The w r i t e r wishes to express h i s indebtedness to the many members of this I n s t i t u t e who i n one way or another helped make th i s thesis p o s s i b l e : i n p a r t i c u l a r to Dr. M. Miyake whose guidance shortened many paths, Dr. R.W. Stewart and Dr. R.W. B u r l i n g from whom help and encouragement were never wanting, Ron Wilson, John Garrett, Gordon McBean and Mary Lou Marotte who put many painstaking hours i n t o computer, programming f o r the general good, and to Ernie Jerome with whom data c o l l e c t i n g was never a chore. Mr. Don Hume designed and b u i l t some of the e l e c t r o n i c packages and Mr. Heinz Heckl did much of the s t r u c t u r a l construction and r e p a i r s . This thesis i s based on information c o l l e c t e d from an a i r c r a f t owned and operated by the U.S. National Centre for Atmospheric Research. The author would l i k e to thank a l l the p i l o t s who were involved i n t h i s programme and e s p e c i a l l y Mr. L.M. Zinser and Mr. R. Burris who flew an average of one mission a day f o r 30 long, hot, consecutive daj's i n sunny Barbados. The a n c i l l a r y data was c o l l e c t e d with NCAR instruments using NCAR recording equipment, and some preliminary data preparation was handled by NCAR personnel. Consequently, the l i s t of persons who have co n t r i b - uted to the groundwork of t h i s thesis i s long; the author i s g r a t e f u l to them and e s p e c i a l l y to Mr. Richard G a r r e l l t s , who did much outside the l i n e of duty and whose patience appeared to be inexhaustible. To my wife, June, I o f f e r my gratitude for the many ways i n which she has made my years as a graduate student happy ones. x i This study was d i r e c t l y supported by contract E22-78-7Q (N) of the U.S. Environmental Science Services Administration. The research i s conducted as part of the Air-Sea I n t e r a c t i o n programme of th i s I n s t i t u t e , which receives general support from: the National Research Council of Canada, the Defence Research Board of Canada, the Meteorological Branch of the Canadian Department of Transport, and the U.S. O f f i c e of Naval Research. While engaged i n th i s study the author received personal support from the National Research Council of Canada. CHAPTER 1 INTRODUCTION 1.1 A i r b o r n e t u r b u l e n c e measurements The a i r p l a n e i s an e m i n e n t l y s u i t a b l e p l a t f o r m f o r t h e i n v e s t i - g a t i o n o f a t m o s p h e r i c t u r b u l e n c e p r i m a r i l y b e c a u s e o f i t s m o b i l i t y . P a r a d o x i c a l l y enough, i t i s j u s t t h i s m o b i l i t y w h i c h poses t h e most s e r i o u s p r o b l e m s i n t h e i n t e r p r e t a t i o n o f a i r b o r n e t u r b u l e n c e measurements. That i s , the d a t a must be c o r r e c t e d f o r t h e m o t i o n o f t h e p l a t f o r m . The c e n t r a l p r o b l e m , however, i s t h e measurement of v e r t i c a l v e l o c i t y ; a t a s k w h i c h has been t a c k l e d i n s e v e r a l d i f f e r e n t ways o v e r t h e p a s t f i f t e e n y e a r s . 1.2 P r e v i o u s work . B u n k e r (1955, 1957, 1960) used an ' a i r p l a n e a c c e l e r a t i o n ' t e c h n i q u e t o e s t i m a t e t h e v e r t i c a l v e l o c i t y . I n t h i s method t h e a i r p l a n e i t s e l f i s t h e s e n s o r and t h e r e l a t i v e v e r t i c a l a i r v e l o c i t y i s r e l a t e d t o t h e v e r t i c a l a c c e l e r a t i o n o f t h e a i r c r a f t t h r o u g h t h e l i f t e q u a t i o n ( v o n M i s e s , 1945). Of c o u r s e t h i s method i s s e v e r e l y band l i m i t e d by the a i r c r a f t ' s p h u g o i d a l o s c i l l a t i o n s a t low f r e q u e n c i e s and i t s i n e r t i a a t h i g h f r e q u e n c i e s . I n terms o f m e a s u r a b l e g u s t s i z e s , B u n k e r (1957) e s t i m a t e d a range o f 20 m t o 2000 m f o r t h e Woods H o l d O c e a n o g r a p h i c I n s t i t u t i o n ' s PBY-6A ( C a t a l i n a ) a i r c r a f t . Lappe e t a l ( 1 9 5 9 ) , T e l f o r d and Warner ( 1 9 6 2 ) , D u t t o n and Lens chow (1962) and Myrup (1965) a l l used e i t h e r a vane o r p i t o t tube a r r a y a n g l e o f a t t a c k s e n s o r t o e s t i m a t e t h e v e r t i c a l v e l o c i t y components down t o much s m a l l e r s c a l e s i z e s . 2 The development o f t h e s o n i c anemometer p r o v i d e d a n o t h e r method o f g e t t i n g a t t h e c r o s s - s t r e a m ' v e l o c i t y components (Kuprov and Tsvang, 1965; M i y a k e e t a l 1970b), and, s i n c e t h e i n s t r u m e n t ' s c a l i b r a t i o n i s u n i q u e l y r e l a t e d t o t h e s p e e d o f sound i n a i r and t h e a c o u s t i c p a t h l e n g t h , t h i s method i s p a r t i c u l a r l y w e l l s u i t e d t o t h e d e l i c a t e s t u d y of i s o t r o p i c t u r b u l e n c e . The q u e s t i o n o f c o r r e c t i o n o f " t h e measured v e l o c i t y components f o r t h e a i r c r a f t ' s m o t i o n has been h a n d l e d by t h e p r e v i o u s i n v e s t i g a t o r s c i t e d i n much th e same manner: t h e d e t a i l s o f e a c h method and t h e d i f f e r e n c e s among them can be f o u n d i n many o f t h e r e f e r e n c e s l i s t e d . I n g e n e r a l t h e i n t e - g r a t e d o u t p u t s o f a c c e l e r o m e t e r s f u r n i s h the a i r c r a f t ' s v e l o c i t y components • and a g y r o s c o p e s e n s e s t h e v a r i a t i o n s o f a t t i t u d e a n g l e . I n t h i s way t h e a i r v e l o c i t y components a r e deduced w i t h i n an a c c u r a c y o f a few p e r c e n t ; however, c o r r e c t i o n s a t f r e q u e n c i e s l o w e r t h a n 0.005 Hz a r e r a t h e r u n c e r t a i n due t o g y r o s c o p i c d r i f t . Today t h e s e p r o b l e m s a r e b e i n g e l i m i n a t e d by t h e use o f i n e r t i a l p l a t f o r m s on t u r b u l e n t f l u x m e a s u r i n g a i r c r a f t . 1.3 O b j e c t i v e s o f t h i s s t u d y I n 1967 a programme o f development o f t u r b u l e n c e s e n s o r s f o r use on l i g h t a i r c r a f t was l a u n c h e d a t t h e I n s t i t u t e o f Oceanography o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . The programme c u l m i n a t e d i n A p r i l 1969 w i t h t h e s e n s o r s y s t e m d e s c r i b e d by M i y a k e e t a l (1970b) and used i n t h i s i n v e s t i g a t i o n . A t t h a t t i m e i t was c o n s i d e r e d t h a t t h e d e v e l o p m e n t a l programme h a d a c h i e v e d i t s o b j e c t i v e , w h i c h was t h e c a p a b i l i t y o f measurement o f t h e v e r t i c a l t u r b u l e n t f l u x e s o f momentum, h e a t and m o i s t u r e o v e r s c a l e s i z e s f r o m 2 m t o 20 km. A s u b s e q u e n t c o m p a r i s o n a g a i n s t o t h e r f l u x measurements (see A p p e n d i x C) i n d i c a t e d t h a t t h i s was i n d e e d t h e c a s e . The use o f h o t - w i r e anemometry e x t e n d e d t h e measurement o f t h e h o r i z o n t a l v e l o c i t y f l u c t u a t i o n s t o s c a l e s as s m a l l as 5 ram. The c o m p l e t i o n o f t h e d e v e l o p m e n t a l programme c o i n c i d e d w i t h t h e commencement o f a l a r g e m e t e o r o l o g i c a l and o c e a n o g r a p h i c f i e l d e x p e r i m e n t n e a r t h e i s l a n d o f B a r b a d o s . The c e n t r a l p u r p o s e o f t h e Barbados O c e a n o g r a p h i c and M e t e o r o l o g i c a l E x p e r i m e n t 'BOMEX' ( D a v i d s o n , 1968) was th e measurement of t h e i n t e r c h a n g e o f mass, momentum and e n e r g y a c r o s s t h e a i r - s e a i n t e r f a c e . Thus t h i s e x p e r i m e n t p r o v i d e d an e x c e l l e n t o p p o r t u n i t y t o d i r e c t l y measure t h e t u r b u l e n t t r a n s f e r s i n a r e g i o n where t h e upward f l u x o f h e a t i s t h e p r i m a r y d r i v i n g f o r c e f o r t h e a t m o s p h e r i c h e a t e n g i n e . I n a d d i t i o n , t h e Bomex o r g a n i z a t i o n h a n d l e d many o f t h e l o g i s t i c a l f i e l d p r o b l e m s i n h e r e n t i n any l a r g e e x p e r i m e n t a l programme, and f a c i l i t a t e d t h e exchange o f i n f o r m a t i o n between t h e v a r i o u s p a r t i c i p a n t s . T h i s s t u d y i s an e x p e r i m e n t a l i n v e s t i g a t i o n i n t o t h e s t r u c t u r e o f t h e a t m o s p h e r i c b o u n d a r y l a y e r i n t h e A t l a n t i c t r a d e w i n d zone, u s i n g d a t a g a t h e r e d d u r i n g Bomex. Measurements were made a t s e v e r a l a l t i t u d e s between 18 m and 500 m. Ground b a s e d measurements i n d i c a t e t h a t a f l i g h t a l t i t u d e o f 18 m i s s u f f i c i e n t l y low t o o b t a i n good e s t i m a t e s o f the t r a n s p o r t s i n t h e s u r f a c e b o undary l a y e r . D a t a were c o l l e c t e d a t h i g h e r a l t i t u d e s t o i n v e s t i g a t e t h e v a r i a b i l i t y w i t h h e i g h t o f t h e t u r b u l e n t f l u x e s and o f t h e mechanisms r e s p o n s i b l e f o r t h e i r v a r i a b i l i t y . The d a t a a r e a n a l y s e d t h r o u g h t h e c o s p e c t r a o f t h e f l u x e s o f h e a t , m o i s t u r e and momentum and t h e s p e c t r a o f t he f o u r t u r b u l e n t p a r a m e t e r s r e q u i r e d t o compute t h e s e f l u x e s . B o t h t h e t o t a l i n t e g r a l under t h e s p e c t r a and c o s p e c t r a and t h e d i s t r i b u t i o n o f t h e ene r g y among s c a l e s i z e s a r e examined f o r t h e d a t a g a t h e r e d d u r i n g f l i g h t s i n t h e w i n d d i r e c t i o n . S e v e r a l c r o s s w i n d t r a v e r s e s were a l s o made t o e x p l o r e t h e . p o s s i b i l i t y o f c o n v e c t i v e o r g a n i z a t i o n . CHAPTER 2 OBSERVATIONAL SCHEME AND ANALYSIS METHODS 2.1 The E x p e r i m e n t I n May 1969, some 1500 s c i e n t i s t s and t e c h n i c i a n s c o n v e r g e d on t h e i s l a n d o f Barbados t o p a r t i c i p a t e i n t h e Barbados O c e a n o g r a p h i c and M e t e o r o l o g i c a l E x p e r i m e n t (BOMEX). The o r g a n i z a t i o n and o b j e c t i v e s o f Bomex a r e d e s c r i b e d by D a v i d s o n (1968) and K u e t t n e r and H o l l a n d ( 1 9 6 9 ) , b u t t h e a s p e c t s w h i c h p e r t a i n d i r e c t l y t o t h i s work a r e summarized b r i e f l y h e r e . Bomex's p r i m a r y o b j e c t i v e was a t h o r o u g h i n v e s t i g a t i o n o f t h e a i r - s e a i n t e r a c t i o n p r o b l e m o v e r an a r e a o f 500 km x 500 km ( s e e F i g u r e 1 ) . V a r i o u s w e l l i n s t r u m e n t e d r e s e a r c h p l a t f o r m s i n c l u d i n g 25 a i r c r a f t p r o b e d t h e atmos- p h e r e t o an a l t i t u d e o f 20 km and t h e ocean t o a d e p t h o f 500 m. S e v e r a l o f t h e p l a t f o r m s were e q u i p p e d t o measure v e r t i c a l t u r b u l e n t t r a n s p o r t s b e n e a t h c l o u d b a s e . Of t h e s e o n l y a few were c a p a b l e o f s i m u l t a n e o u s d i r e c t measurement o f t h e f l u x e s o f momentum, s e n s i b l e h e a t and m o i s t u r e : NCAR'S a i r c r a f t , B e e c h r a f t Queen A i r 304D ( s e e F i g u r e 2) i n s t r u m e n t e d as d e s c r i b e d i n M i y a k e e t a l (19 70b) and A p p e n d i x A; ' F L I P ' ( s e e F i g u r e 3) t h e manned s p a r buoy o f S c r i p p s O c e a n o g r a p h i c I n s t i t u t i o n (Pvudnick, 1964), i n s t r u m e n t e d w i t h t u r b u l e n c e s e n s o r s s i m i l a r t o t h o s e on the Queen A i r ; and a DC-6 o f t h e R e s e a r c h F l i g h t F a c i l i t y o f t h e U.S. E n v i r o n m e n t a l S c i e n c e S e r v i c e s A d m i n i s t r a t i o n . 2.2 F l i g h t P a t t e r n s The e x p e r i m e n t was d e s i g n e d t o i n v e s t i g a t e t h e ' v e r t i c a l s t r u c t u r e o f t h e boundary l a y e r . T h e r e f o r e e a c h f l i g h t was d i v i d e d i n t o s e c t i o n s o f l e v e l f l i g h t ( h e n c e f o r t h c a l l e d ' l e v e l s ' ) a t t h r e e o r f o u r d i f f e r e n t 5 FIGURE 1. THE BOMEX ARRAY (from Bomex B u l l e t i n No.3, 1969) FIGURE 2. THE RESEARCH AIRCRAFT, BEECHCRAFT QUEEN AIR 304D FIGURE 3. FLIP 8 a l t i t u d e s . And, because i t was b e l i e v e d t h a t t h e t u r b u l e n c e s t r u c t u r e changes l e s s r a p i d l y w i t h h e i g h t t h e g r e a t e r t h e d i s t a n c e from t h e boundary, t h e a l t i t u d e o f s u c c e s s i v e l e v e l s was chosen t o i n c r e a s e i n e q u a l l o g a r i t h m i c s t e p s f r o m t h e l o w e s t l e v e l o f about 18 m. To a v o i d t h e p o s s i b i l i t y o f c o n f u s i n g t e m p o r a l v a r i a t i o n w i t h s y s t e m a t i c h e i g h t dependence, t h e p a t t e r n s were n o t f l o w n a t s t e a d i l y i n c r e a s i n g o r d e c r e a s i n g a l t i t u d e . G e n e r a l l y t h e f i r s t l e v e l f l o w n was a t an a l t i t u d e o f a p p r o x i m a t e l y 50 m b e c a u s e i t was a t t h i s l e v e l t h a t t h e p i l o t and o b s e r v e r e s t i m a t e d t h e w i n d d i r e c t i o n . T h i s was done i n t h e f o l l o w i n g f a s h i o n . As t h e a i r c r a f t a p p r o a c h e d t h e s u r f a c e c r a f t , o v e r w h i c h t h e p a t t e r n was t o be flown., t h e a l t i t u d e was h e l d a t about 50 m and t h e p i l o t a l t e r e d t h e h e a d i n g t o c o i n c i d e w i t h the d i r e c t i o n o f t h e wi n d r o w s . The D o p p l e r r a d a r d r i f t a n g l e was t h e n a m p l i f i e d and m o n i t o r e d on t h e c h a r t r e c o r d e r i n t h e c a b i n . F o l l o w i n g the o b s e r v e r ' s i n s t r u c t i o n s t h e p i l o t made f i n e a d j u s t m e n t s t o t h e h e a d i n g u n t i l t h e t r a c e o f t h e d r i f t a n g l e a v e r a g e d z e r o o v e r a p e r i o d o f about 30 s e c o n d s . A t t h i s p o i n t t h e a i r c r a f t had alw a y s j u s t p a s s e d o v e r t h e v e s s e l , and i t s h e a d i n g was t a k e n t o be r e p r e s e n t a t i v e o f t h e w i n d d i r e c t i o n a t t h a t l e v e l i n t h e v i c i n i t y . As t h e a i r c r a f t made a s t a n d a r d 180 degree t u r n t o b e g i n t h e f i r s t downwind l e g , t h e o b s e r v e r h a s t e n e d t o make a d j u s t m e n t s t o t h e i n s t r u m e n t s . The p i l o t t h e n g u i d e d t h e a i r c r a f t i n one o f the f l i g h t p a t t e r n s o f F i g u r e 4 by c h a n g i n g t h e h e a d i n g i n 90 degr e e s t a n d a r d t u r n s t o p o r t . A t t h e c o m p l e t i o n o f a t u r n t h e a i r c r a f t a u t o p i l o t was s e t t o t h e ' a l t i t u d e h o l d ' mode e x c e p t a l o n g t h e l e g 'A' i n w h i c h t h e p i l o t a l t e r e d -the a l t i t u d e t o e n t e r t h e p a t t e r n a t a new l e v e l . E a c h l e v e l was c o m p l e t e d w i t h l e g s e i t h e r p a r a l l e l w i t h o r p e r p e n d i c u l a r t o t h e p r e v i o u s l y PATTERN I PATTERN 2 D U D A = ALTITUDE CHANGE D = DOWNWIND C = CROSSWIND U = UPWIND WIND DIRECTION AT 50 m TI 10 km FIGURE 4. THE FLIGHT PATTERNS d e t e r m i n e d w i n d d i r e c t i o n a t 50 m. To compensate for t h e d i f f e r e n c e i n ground s p e e d between t h e upwind and downwind l e g s , t h e l a t t e r o c c u p i e d a s h o r t e r t i m e i n t e r v a l t h a n t h e f o r m e r . E a c h f l i g h t was i n t h e v i c i n i t y o f e i t h e r F l i p o r t h e s h i p , "Mt. M i t c h e l l " ( s e e F i g u r e 1 ) . Throughout t h e month o f May a b o a r d F l i p a team o f i n v e s t i g a t o r s f r o m t h i s I n s t i t u t e c o l l e c t e d t u r b u l e n c e d a t a ; t h e r e f o r e t h e f l i g h t s o v e r F l i p were d e s i g n e d t o p r o v i d e d i r e c t c o m p a r i s o n s o f s t a t i s t i c s o f t h e t u r b u l e n c e n e a r t h e s u r f a c e ( s e e A p p e n d i x C) as w e l l as t o o b t a i n d a t a a t h i g h e r l e v e l s . S i n c e t h e f l i g h t s t o F l i p s e v e r e l y t a x e d t h e Queen A i r ' s range c a p a b i l i t i e s , t h e s h i p "Mt. M i t c h e l l " was s e l e c t e d as an a l t e r n a t e 1 ground t r u t h ' s t a t i o n . One o f t h e i m p o r t a n t c o n s i d e r a t i o n s i n t h e d e s i g n o f t h e f l i g h t p a t t e r n s i s t h e c h o i c e o f a s u i t a b l e l e n g t h f o r b o t h t h e a l o n g w i n d and c r o s s w i n d l e g s . V e r y l o n g l e g s a r e d e s i r a b l e t o be a b l e t o c o n s i d e r t h e l a r g e r t u r b u l e n t s c a l e s . On t h e o t h e r hand, s i n c e t e m p o r a l v a r i a t i o n s a r e n o t b e i n g c o n s i d e r e d , t h e s h o r t e r t h e i n t e r v a l between l e v e l s the b e t t e r . The d u r a t i o n o f f l i g h t s o v e r F l i p was l i m i t e d " by the range o f t h e Queen A i r ; h e a v i l y l o a d e d as she was i t was j u s t p o s s i b l e t o f l y t o F l i p , spend an h o u r t h e r e g a t h e r i n g d a t a and r e t u r n t o B a r b a d o s . The c h o i c e o f 20 km f o r t h e a l o n g w i n d l e g s was s e l e c t e d as a b a l a n c e between t h e s e c o n s i d e r - a t i o n s and b e c a u s e g y r o s c o p i c l i m i t a t i o n s make f o r u n c e r t a i n t y i n t h e c o m p u t a t i o n o f t h e v e l o c i t y components o v e r l o n g e r d i s t a n c e s ; a l s o i t i s known f r o m ground b a s e d measurements t h a t s a m p l i n g i n t e r v a l s c o r r e s p o n d i n g t o a s c a l e s i z e o f 10 km a r e adequate t o e s t i m a t e t h e f l u x e s n e a r t h e s u r f a c e . A somewhat s h o r t e r d i s t a n c e was t r a v e r s e d a c r o s s the w i n d F i g u r e 4) so t h a t the f l i g h t d u r a t i o n o f each l e v e l was l i m i t e d t o f i f t e e n m i n u t e s o r t h e - c o m p l e t e f l i g h t t o one h o u r , and so t h a t n e i t h e r t h e upwind n o r t h e downwind l e g s w o u l d be f a r f r o m t h e s u r f a c e v e s s e l . 11 2.3 D a t a g a t h e r i n g p r o c e d u r e The d a t a were r e c o r d e d on m a g n e t i c t a p e i n b o t h d i g i t a l and a n a l o g u e form on two s e p a r a t e t a p e r e c o r d e r s . T h i r t y two c h a n n e l s o f i n f o r m a t i o n were d i g i t i z e d a t 32 Hz p e r c h a n n e l ( w i t h a t a p e t r a n s p o r t speed o f 7 1/2 i . p . s . ) and r e c o r d e d on NCAR'S ARIS I d i g i t a l d a t a l o g g i n g s y s t e m ( D a s c h e r , 1966). The a n a l o g u e t a p e r e c o r d e r a c c e p t e d 14 v o l t a g e s i g n a l s and r e c o r d e d them i n f r e q u e n c y m o d u l a t e d form w i t h an upper f r e q u e n c y c u t - o f f o f 2.5 kHz Cat 7 1/2 i . p . s . a l s o ) . The s i g n a l s r e c o r d e d i n a n a l o g u e form were ' p r e - c o n d i t i o n e d ' i n t h e f o l l o w i n g way: each s i g n a l was, when n e c e s s a r y , added t o an a d j u s t a b l e DC v o l t a g e , so as t o remove i t s mean v a l u e , t h e n a m p l i f i e d by a se c o n d o p e r a t i o n a l a m p l i f i e r u s i n g one o f two g a i n s e t t i n g s i n o r d e r t o use as much of t h e t a p e r e c o r d e r ' s dynamic range C+ 1.5 v o l t s ) as p o s s i b l e . The d i g i t a l d a t a l o g g i n g s y s t e m was used t o r e c o r d t h e o u t p u t s f r o m t h e mean v a l u e s e n s o r s d i r e c t l y i n a d d i t i o n t o s i g n a l s from t h e t u r b u l e n c e s e n s o r s p r e - c o n d i t i o n e d as d e s c r i b e d above. T h i s redundancy p r o v i d e d b o t h a s a f e g u a r d a g a i n s t o u t r i g h t l o s s o f t h e r e c o r d e d i n f o r m a t i o n , and a l s o p e r m i t t e d r e c o r d e r c a l i b r a t i o n checks on many o f t h e c h a n n e l s . In v i e w o f t h e h e c t i c pace o f a i r - b o r n e d a t a c o l l e c t i o n , i t i s i m p o r t a n t f o r t h e o b s e r v e r t o be a b l e t o q u i c k l y d e t e r m i n e t h e s t a t u s o f any o f t h e r e c o r d e d s i g n a l s . T h i s f a c i l i t y was p r o v i d e d by s e v e r a l t y p e s o f m o n i t o r i n g equipment. A l l o f t h e t u r b u l e n c e s i g n a l l e v e l s c o u l d be v i e w e d a t a g l a n c e on a p a n e l o f v o l t m e t e r s , and any o f t h e d i g i t a l l y r e c o r d e d c h a n n e l s c o u l d be s e l e c t e d f o r d i s p l a y on a d i g i t a l v o l t m e t e r . In a d d i t i o n a t w o - c h a n n e l c h a r t r e c o r d e r was used t o m o n i t o r e i t h e r t h e i n p u t t o o r p l a y b a c k f r o m t h e a n a l o g u e r e c o r d e r . L a r g e l y as a t r o u b l e s h o o t i n g a i d a s m a l l d u a l beam o s c i l l o s c o p e was a l s o u s e d . 12 In the course of a f l i g h t the degree of DC bias had to be a l t e r e d frequently on some channels, the gain s e t t i n g s l e s s frequently, to achieve the best p o s s i b l e s i g n a l to noise r a t i o without s a t u r a t i n g the tape recorder. To keep track of these changes and to record v i s u a l synoptic observations, the observer kept a c a r e f u l f l i g h t l o g on paper and a s i m i l a r voice l og on an edge track of the analogue recorder. The voice log was kept as an emergency measure only, as this observer regards the a f t e r - t h e - f a c t separation of occasional c r y p t i c comments from the constant drone of an a i r c r a f t as among the most tedious of tasks. Fortunately, the w r i t t e n l og proved adequate. The logs were t i e d to the recorded data by means of a d i g i t a l l y recorded clock which also provided a v i s u a l output. 2.4 Data Processing ' The d i g i t a l data tapes were made a v a i l a b l e to us i n two forms by the National Centre f o r Atmospheric Research: 1) Copies of the o r i g i n a l tapes i n an acceptable I B M format; 2) Smoothed time s e r i e s of each s i g n a l on mi c r o f i l m i n which each frame covered 10 minutes. The microfilm was us e f u l i n l o c a t i n g each run on the analogue tape by comparison of the r o l l angle s i g n a l s , and i n obtaining the mean value of various parameters f o r each run. The d i g i t a l tape was used to compute sev e r a l spectra merely to check the c a l i b r a t i o n of the analogue tape recorder and subsequent conversion to d i g i t a l format. A l l the spectra and time s e r i e s presented herein were computed from the o r i g i n a l analogue recorded data, which contained information up to frequencies i n excess of 2 kHz, whereas the maximum d i g i t i z a t i o n rate used was 128 Hz. The d i g i t i z a t i o n and subsequent processing of the analogue recorded data i s described i n Appendix B. 13 CHAPTER 3 EXPERIMENTAL RESULTS AND DISCUSSION 3.1 I n t r o d u c t i o n : 3.1.1 The D a t a The d a t a a n a l y s e d h e r e were g a t h e r e d d u r i n g s i x f l i g h t s on f i v e c o n s e c u t i v e days (May 2 5 t h t o May 29th) and t h e n i g h t o f the f i f t h day. The f l i g h t s a r e numbered 1 t o 6 i n c h r o n o l o g i c a l o r d e r and T a b l e 1 summarizes the f l i g h t p a t t e r n s ( F i g u r e 4) used and p r o v i d e s d e t a i l s o f t h e runs w i t h i n f l i g h t s 1 and 3, w h i c h a r e t o be d i s c u s s e d i n d e t a i l . The t e r m ' r u n ' r e f e r s t o a s i n g l e c o n t i n u o u s d a t a segment a t c o n s t a n t a l t i t u d e . I n t h e t e x t and f i g u r e s a p a r t i c u l a r r u n w i l l be d e n o t e d by x/y, where x i s t h e f l i g h t number and y t h e r u n number. 3.1.2 S y n o p t i c c o n d i t i o n s D u r i n g t h e 'A' l e g s o f the f l i g h t p l a n s o f F i g u r e 4 t h e mean v a l u e s e n s o r s ( M i y a k e e t a l 19 70b) y i e l d e d s e c t i o n s o f t h e p r o f i l e s o f t e m p e r a t u r e and h u m i d i t y o f F i g u r e 5. The s e c t i o n s were t h e n p i e c e d t o g e t h e r and t h e p r o f i l e s combined t o g i v e t h e v i r t u a l p o t e n t i a l temp- e r a t u r e p r o f i l e . The mean w i n d s p e e d p r o f i l e s were d e r i v e d f r o m D o p p l e r r a d a r measurements a v e r a g e d o v e r a l l t h e runs a t any l e v e l . They a r e d i s p l a y e d i n F i g u r e 6, and the d e v i a t i o n o f the w i n d d i r e c t i o n f r o m t h e o r i e n t a t i o n o f t h e f l i g h t p l a n i s i n d i c a t e d a t e a c h l e v e l i n t h e t a b l e o f F i g u r e 6. However, s u c h s h o r t t e r m a v e r a g e s o f D o p p l e r r a d a r measurements a r e q u i t e l i k e l y t o v a r y by 3% o f t h e ground s p e e d , w h i c h i n t h i s c a s e i s an a c c u r a c y o f - 2 m/sec. Thus, a l t h o u g h the d e t a i l e d b e h a v i o u r o f t h e p r o f i l e s cannot be r e g a r d e d as r e a l , they p r o v i d e a rough e s t i m a t e o f the mean w i n d speed. I n a d d i t i o n t o t h e s e p r o f i l e s , t h e d a i l y s a t e l l i t e p h o t o g r a p h s ( F i g u r e FLIGHT DATE LOCAL TIME START END 1 25/6/'69 10.50 12.00 2 26/5/'69 10.15 11.20 3 27/5/'69 14.40 15.50. 4 28/5/'69 15.15 16.20 5 29/5/'69 17.15 18.30 6 29/5/'69 22.00 23.10 LOCATION Mt. M i t c h e l l WIND DIRECTION AT 50 m 100° FLIGHT RUN PATTERN 2 3 5 6 7 11 12 LEVEL i n m e t r e s 43 43 20 20 150 150 500 500 * * DURATION i n s e e s . C U C U D C C u 80 270 60 320 190 60 75 210 Mt. M i t c h e l l 108° 18, 46 150, 460 FLI P 100 c 2 3 5 6 8 9 11 12 49 49 18 18 150 150 500 500 C U c u C u c u 75 210 55 280 60 240 45 165 F L I P =95' 18, 52 150, 460 Mt. M i t c h e l l Mt. M i t c h e l l 90 c 88° 26, 49 88, 140 29, 98, 480 U = Upwind D = Downwind C = C r o s s w i n d TABLE 1. FLIGHT SUMMARY ZS-o a g o x 7 . s 400 200 T — " r- T" 15 /3 4-00 tV4 200 . . . 1 r ~ — 1 — — J — — 1 1 > 1 r——1 13 13, I S /S- 2"? C n — p - 3© *C 1 1 r- T I • 1 400 T 1 r IQ'c 32'C 31^ potential v i r t u a l temperature = ® + .183 Q FIGURE 5. TEMPERATURE AND HUMIDITY PROFILES 16 6 oo.. CO cu M •u CD B 0 •rl IS3 4-00- 2. 00- I 4- MEAN WIND SPEED (m/sec) ^ F L I G H T APPROX^ ALTITUDE \ 1 2 3 4 5 6 18 m 12 11 2 2 27 m 3 3 50 m 9 13 1 6 90 m 3 3 150 m 9 12 3 1 7 500 m 6 -3 9 6 The numbers shown are the wind d i r e c t i o n s i n degrees r e l a t i v e to the o r i e n t a t i o n of the f l i g h t pattern. Clockwise i s p o s i t i v e . FIGURE 6. WIND PROFILES FROM THE AIRBORNE DOPPLER RADAR 28/5/'69 29/5/'69 30/5/'69 FIGURE 7. SATELLITE PHOTOGRAPHS OF THE BOMEX AREA These photographs were taken soon a f t e r l o c a l noon. The Bomex array i s shown i n the l a s t photograph; In each of the others an ' x* marks the l o c a t i o n of the f l i g h t pattern on that day. i n d i c a t e t h e p r e v a i l l i n g s y n o p t i c c o n d i t i o n s i n t h e a r e a . F i g u r e 7 c o n s i s t s o f 6 e n l a r g e m e n t s o f t h e Bomex a r e a d u r i n g t h e f i v e days o f f l i g h t s 1 t o 6 and t h e f o l l o w i n g day. These p h o t o g r a p h s were made fr o m computer composed panoramas o f v i s u a l range s a t e l l i t e p h o t o g r a p h s t a k e n by ESSA 9, a s a t e l l i t e o f t h e E n v i r o n m e n t a l S c i e n c e S e r v i c e s A d m i n i s t r a t i o n , U.S.A. ESSA 9 p a s s e d o v e r t h e Bomex a r r a y i n t h e e a r l y a f t e r n o o n . From F i g u r e s 5 t o 7 i t i s e v i d e n t t h a t c o n d i t i o n s d u r i n g t h e s i x f l i g h t s were q u i t e s i m i l a r e x c e p t w i t h r e g a r d t o mean w i n d s p e e d . D u r i n g a l l o f t h e f l i g h t s t h e p o t e n t i a l v i r t u a l t e m p e r a t u r e was n e a r l y c o n s t a n t w i t h h e i g h t , and m e t e o r o l o g i c a l c o n d i t i o n s were s i m i l a r e x c e p t d u r i n g f l i g h t #6 w h i c h was made a t n i g h t . Thus t h e mean s u r f a c e w i n d s p e e d i s t a k e n as t h e b a s i s f o r g r o u p i n g t h e s e f l i g h t s . I t i s see n t h a t t h e y f a l l q u i t e n a t u r a l l y i n t o two gr o u p s : (a) f l i g h t s 1 and 2, h a v i n g w i n d speeds l o w e r t h a n 7 m/sec, a r e c a l l e d t h e 'low w i n d s p e e d group'; (b) f l i g h t s 3, 4, 5, and 6, h a v i n g w i n d speeds i n e x c e s s o f 8 m/sec ; a r e l a b e l l e d t h e ' h i g h w i n d speed' group. 3.1.3 Methods o f p r e s e n t a t i o n I n t h e f o l l o w i n g s e c t i o n s o f t h i s C h a p t e r , f l i g h t s 1 and 3 a r e \ised, as examples o f t h e low and h i g h w i n d s p e e d g r o u p s , i n t h e p r e s e n t a t i o n o f t i m e domain and s p e c t r a l r e p r e s e n t a t i o n s o f t h e f l u c t u a t i o n s o f t h e v e r t i c a l and h o r i z o n t a l v e l o c i t y components, t e m p e r a t u r e , h u m i d i t y and t h e f l u x e s o f momentum, h e a t and m o i s t u r e . S p e c t r a a r e p r e s e n t e d i n terms o f t h e p r o d u c t o f f r e q u e n c y w i t h the s p e c t r a l e s t i m a t e s nS (n) v e r s u s t h e l o g a r i t h m o f f r e q u e n c y . I n s u c h X X p l o t s e q u a l a r e a i n c r e m e n t s r e p r e s e n t e q u a l i n c r e m e n t s o f t h e v a r i a n c e o f the d a t a . S i n c e i t i s t h e p r o d u c t nS (n) r a t h e r t h a n s p e c t r u m i t s e l f r x x w h i c h i s used e x c l u s i v e l y i n t h e sub s e q u e n t c h a p t e r s , i t i s c o n v e n i e n t and 19 unambiguous to r e f e r to nS (n) as the 'n-spectrum'. The corresponding wave number spectrum times wave number kS (k) w i l l be c a l l e d the 'k-spectrum'. X X 2TFxi Normalized k-spectra are presented versus the wave number k = • fadlatis/m; where V i n the true a i r speed of the a i r c r a f t averaged over each run. The ordinate i s normalized by the ind i c a t e d parameter evaluated at the lowest upwind run i n that f l i g h t ; see Table 2 for the values of the normalizers. B i - l o g a r i t h m i c axes are u s e f u l , e s p e c i a l l y i n i l l u s t r a t i n g the high wave number power law dependence and i n showing d e t a i l i n the le s s energetic spectra on a composite p l o t . These are used f o r the k-spectra (f o r example as i n Figure 8), and to avoid confusion the ordinate values are separated by a decade f o r each successive f l i g h t l e v e l . On the other hand, l o g - l i n e a r kS^^k) (see Figure 25) are used f o r the k-cospectra, because cospectral estimates may be e i t h e r p o s i t i v e or negative and because i t i s extremely important to be able to assess the r e l a t i v e importance to the t o t a l f l u x of various s c a l e s i z e s . In these s p e c t r a l representations the l e v e l s 18 m, 50 m, 150 m, 500 m are i d e n t i f i e d by the symbols L, C, V, T r e s p e c t i v e l y f o r f l i g h t # 1 and J ,0 , A , ± f o r f l i g h t // 3. From each f l i g h t a s i n g l e run i n the wind d i r e c t i o n at each l e v e l i s select e d . Because of t h e i r greater length, the upwind runs are chosen i n a l l but one case: run #1/7 which i s a downwind run (Table 1). Run # 1/7 replaced run # 1/9 (upwind) because the l a t t e r suffered from radio pick-up i n the thermistor c i r c u i t . Thus, i n t h i s case only, the sig n of the h o r i z o n t a l v e l o c i t y component, i n the time domain p l o t s i s opposite to the mean wind d i r e c t i o n , and as a r e s u l t the corresponding instantaneous momentum i s shown as p o s i t i v e (Figure 24). Due, again, to thermistor pick-up on both upwind and downwind runs, no temperature spectra or heat fluxes appear f o r run // 3/12. The time s e r i e s of run # 3/12 have been truncated to exclude the noisy s e c t i o n . FLIGHT [„2] L I ^ ] L t t T ^ [0- H^T !L ! ] L I C T ^ " Q ! L #1 497 .011 .085 .033 .032 .031 #3 1140 .014 .092 .047 .053 .036 R A T I 0 # 3 / # l 2 , 3 1 ' 2 4 1 , 0 8 1 A 5 1 * 6 6 1 , 1 6 LOG Q RATIO .36 .093 .033 .16 .22 .064 TABLE 2. NORMALIZERS FOR SPECTRA AND COSPECTRA OF FLIGHTS 1 AND 3. 21 Crosswind runs at each l e v e l are also presented to i l l u s t r a t e d i f f e r - ences between the data thus obtained and the data c o l l e c t e d during f l i g h t s i n the wind d i r e c t i o n . The widespread p r a c t i c e of computing the turbulent fluxes from the averages, over 'some' period, of the instantaneous values of the meteorological v a r i a b l e s i s rather l i k e walking on t h i n i c e - you do not know a p r i o r i how f a r to go. I t i s considerably more enlightening to compute the spectra and cross-spectra of the variables concerned; on the basis of t h e i r behaviour and from a thorough determination of the l i m i t a t i o n s of the instrumentation and i t s operation, the measurements can be properly evaluated.- • . There are two factors which are most e a s i l y dealt with by c a r e f u l .inspection of the relevant spectra and cross-spectra. The f i r s t , general to a l l turbulent f l u x computations by the eddy c o r r e l a t i o n method, i s the question of j u s t what i s a s u i t a b l e time i n t e r v a l or what s c a l e s i z e s should be included i n the f l u x computation. The second, p e c u l i a r to observation platforms which are not f i x e d to t e r r a firma, i s the question of whether the e f f e c t of platform motion can be removed from the data. I t i s p r i m a r i l y the second f a c t o r which prompts i n v e s t i g a t o r s , seeking to e s t a b l i s h the v a l i d i t y of t h e i r method, to compare r e s u l t s from t h e i r moving platform with those obtained from another type of platform. I f the r e s u l t s agree, a reasonable conclusion may be that they are both correct. Such a comparison, between data gathered from the a i r c r a f t used i n t h i s study and those obtained simultaneously by a manned spar buoy, i s presented i n Appendix C. The d e c i s i o n as to what range of scale s i z e s should be included i n the computation of fluxes hinges on the existence of the s o - c a l l e d ' s p e c t r a l gap', separating turbulent from mesoscale. e f f e c t s . However, i n the atmospheric boundary l a y e r the spectra of seve r a l meteorological v a r i a b l e s sometimes display a 'plateau' at large scales rather than a d i s t i n c t gap. Under these conditions the choice of an upper l i m i t of the turbulent scale s i z e s greatly a f f e c t s the computed s t a t i s t i c a l q u a n t i t i e s at low frequencies. 0 For t h i s reason the author chose to define the upper l i m i t to the turbulent flux s c a l e s i z e s i n terms of the v e r t i c a l v e l o c i t y . The v e r t i c a l v e l o c i t y i s , of course, common to the three v e r t i c a l fluxes (momentum, heat and moisture) being considered and i t s spectrum times frequency nS (n) WW contains a d i s t i n c t peak i n the turbulent region. The upper scale s i z e l i m i t i n terms of measured frequency n i s taken to be that frequency below which nS (n) i s less than one tenth of i t s value at the peak. I f the value ww r of nS^O^) increases as r a p i d l y as i s frequently found at sub-peak frequencies (Lumley and Panofsky, 1964), then very l i t t l e of the variance of v e r t i c a l v e l o c i t y i s l o s t and the estimates of other meteorological v a r i a b l e s , i n p a r t i c u l a r the v e r t i c a l fluxes, are defined i n a consistent manner among themselves and between runs. 23 3.2 Measurements a l o n g t h e w i n d 3.2.1 V e r t i c a l v e l o c i t y F i g u r e 8 d i s p l a y s t h e k - s p e c t r a l b e h a v i o u r o f t h e v e r t i c a l v e l o c i t y f o r f l i g h t s 1 and 3. The k - s p e c t r a l e s t i m a t e s a r e n o r m a l i z e d by t h e 2 s q u a r e o f t h e f r i c t i o n v e l o c i t y u^ a t t h e l o w e s t l e v e l , d e s i g n a t e d [ u ^ ] . I t i s c l e a r t h a t a t t h e l o w e r two l e v e l s the h i g h wave number v a l u e s a r e v e r y n e a r l y e q u a l ; whereas a t t h e 150 m l e v e l f l i g h t # 1 i s much l a r g e r t h a n f l i g h t # 3. T h i s d i f f e r e n c e i s e v i d e n t a l s o i n t h e t r a c e s o f F i g u r e 9, i n w h i c h i t appears t h a t t h e e x t r a e n e r g y i n kS (k) o f f l i g h t // 1 i s WW a s s o c i a t e d w i t h a s e r i e s o f r a t h e r e v e n l y s p a c e d u p d r a f t s . The c l o s e c o r r e s p o n d e n c e o f t h e n o r m a l i z e d k - s p e c t r a a t l a r g e k between t h e two f l i g h t s and b e l o w 100 m i s a consequence o f t h e r e l a t i o n between t h e e n e r g y a t s m a l l s c a l e s and t h e r a t e o f d i s s i p a t i o n , w h i c h i n t u r n i s r e l a t e d t o t h e f r i c t i o n v e l o c i t y n e a r t h e s u r f a c e . A l l t h e k - s p e c t r a o f v e r t i c a l v e l o c i t y a n a l y s e d d i s p l a y e d a -2/3 power law dependence on k above t h e peak o f t h e k - s p e c t r a . T h i s '-2/3 r e g i o n ' i s d i s c u s s e d i n t h e n e x t s e c t i o n ( 3 . 2 . 2 ) . I n F i g u r e 10 t h e s t a n d a r d d e v i a t i o n o f t h e v e r t i c a l v e l o c i t y f l u c t u a t i o n s CTw i s p l o t t e d a g a i n s t log-^Q Z . T h e r e seems t o be no s y s t e m a t i c h e i g h t dependence. The r a t i o C T w/u Ais shown i n T a b l e 3 f o r each l e v e l o f f l i g h t s 1 and 3; t h e o t h e r f l i g h t s a r e t a b u l a t e d i n A p p e n d i x D. I t i s seen t h a t CJ w / u * does i n c r e a s e w i t h h e i g h t , b u t t h e s c a t t e r i s c o n s i d e r a b l e above t h e 50 m l e v e l . F i g u r e 11 i l l u s t r a t e s t h e dependence o f t h e wave l e n g t h a t t h e k - s p e c t r a l peak on h e i g h t . I n s p i t e o f t h e s c a t t e r i t i s e v i d e n t t h a t i n t h i s s t u d y t h e wave l e n g t h o f the peak o f t h e k - s p e c t r u m o f v e r t i c a l v e l o c i t y v a r i e s a p p r o x i m a t e l y as Z^' 7^ and e x t r a p o l a t e d t o a h e i g h t o f 10 met r e s the peak wave 24 FIGURE 8. VERTICAL VELOCITY SPECTRA (UPWIKD) tn FIGURE 9. VERTICAL VELOCITY TRACES (UPWIND) 26 VERT ICHL VELOCITY UPWIND 4 9 1 1 "I 1 I Q. l 0.2 0.3 0.4 0.5 0.6 STANDARD DEVIATION f.MKS) FIGURE 10. CTWVS. Z (UPWIND) 27 RUN ** 2 m 2 u * (m/s) 2 w'T *' (m/s)C° -Z/L T w'Q' 0 & s kgm -Z/LQ -Z/L 1/6 1/3 1/7 1/12 u u D U 20 43 150 500 .0497 .0237 .0448 .0061 .0059 .0058 -.00083 -.0094 .14 .89 -.17 -130. .0318 .0293 .0483 .0605 .14 .83 1.9 150. .28 1.72 1.73 20. 3/6 3/3 3/9 3/12 . U U U U 18 49 150 500 .114 .0712 .061 .0391 -.00042 .0049 .0039 -.025 .16 .51 .0529 .0237 .025 .0286 .059 .15 .61 4.4 .034 .31 1.12 4.4 RUN <r w «q T ^zx FH FQ cm/s cm/s C° gm/kgm dynes cm2 mW/cm 2 mW/cm2 1/6 1/3 1/7 1/12 30.8 31.0 47.3 33.8 52.2 37.8 38.5 42.9 .105 .071 .063 ,155 .291 .188 .223 .499 .643 .306 .579 .079 .77 .75 -.11 -1.22 10.30 9.49 15.65 19.60 3/6 3/3 3/9 3/12 40.2 41.5 31.5 42.0 74.6 59.5 56.6 44.4 .117 .093 .066 .527 .302 .252 .184 .198 1.47 .921 .789 .504 -.05 .64 .51 17.14 7.68 8.10 9.27 RUN u* -T _ C T T / T A - O Q / Q cm/s C° gm/kgm 1/6 22.3 .066 .357 1.38 2.34 1.59 .82 1/3 15.4 .094 " .476 2.01 2.45 .76 .39 1/7 21.2 -.010 .570 2.33 1.82 -6.30 . .39 1/12 7.8 -.301 1.939 4.33 5.50 -.51 .26 3/6 33.8 -.003 .391 1.19 2.21 -39.0 .77 3/3 26.7 .046 .222 1.55 2.23 2.02 1.14 3/9 24.7 .039 .253 1.28 2.29 1.69 .73 3/12 19.8 — .361 2.12 2.24 — .55 U = Upwind, D = Downwind TABLE 3 - STATISTICS OF FLIGHTS 1 and 3 28 V E R T I C A L V E L O C I T Y w' UPWIND / / z 4 * » / / / / / / J.0 1.5 ^.0 2.<i 3.0 3 5 L O G 1 0 ( L T N M E T R E S 1 FIGURE 11. CL M) W VS. Z (UPWIND) 29 l e n g t h i s r o u g h l y 55 m e t r e s ; .'. L^. = 55 ( Z / 1 0 ) ^ * ^ m e t r e s , which, r e p r e s e n t s t h e l i n e shown i n F i g u r e 11. Or i n terms o f t h e measured f r e q u e n c y n k 0.018 V ( Z / 1 0 ) 0 , 7 5 Hz. F a r f r o m t h e b o u n d a r y where most o f t h e m e c h a n i c a l t u r b u l e n c e i s g e n e r a t e d , t h e i n f l u e n c e o f c o n v e c t i v e e f f e c t s i s e v i d e n t i n t h e v e r t i c a l v e l o c i t y s p e c t r a ( F i g u r e 8 ) . The s p e c t r a become n a r r o w e r , b o t h b e c a u s e t h e b u o y a n t i n p u t t e n d s t o have a n a r r o w b a n d w i d t h and b e c a u s e t h e boundary i s no l o n g e r e f f e c t i v e i n r e s t r i c t i n g t h e l a r g e s c a l e s i z e g e n e r - a t i o n n e a r t h e b u o y a n t i n p u t peak. I n t h i s and s u b s e q u e n t s e c t i o n s t h e n a t u r a l l o g a r i t h m i c b a n d w i d t h B i s d e f i n e d as t h e r a t i o o f t h e v a r i a n c e t o t h e k - s p e c t r a l peak e s t i m a t e . The b a n d w i d t h v a r i a t i o n s o f t h e s p e c t r a a r e summarized i n F i g u r e 12, i n w h i c h i t i s seen t h a t t h e b a n d w i d t h d e c r e a s e s up t o t h e 150 m l e v e l ; a t g r e a t e r h e i g h t s any change i s l e s s d e f i n i t e l y o b s e r v e d . V E R T I C R L V E L O C I T Y W U P W I N D 3 c ' I « 3 8 1 ' 1 ' — 1 1 1 1 0.0 2.0 4.0 6.0 8.0 10. B — N R T . L O G . B A N D W I D T H FIGURE 12. B VS. Z (UPWIND) 31 3.2.2 H o r i z o n t a l V e l o c i t y F i g u r e 13 and t h e k - s p e c t r a o f F i g u r e 14 p r o v i d e a c l e a r d e s c r i p t i o n o f t h e e v o l u t i o n o f t h e h o r i z o n t a l v e l o c i t y component w i t h h e i g h t . I n g e n e r a l t h e r e i s an o v e r a l l d e c r e a s e i n t h e e n e r g y o f a l l s c a l e s i z e s , b u t t h e r a t e o f d e c r e a s e o f t h e s m a l l s c a l e s i s f a s t e r t h a n t h a t o f t h e l a r g e r s c a l e s . T h i s g i v e s t h e i m p r e s s i o n i n t h e t i m e s e r i e s ( F i g u r e 13) t h a t t h e e n e r g y a t l a r g e s c a l e s i n c r e a s e s w i t h h e i g h t . I n F i g u r e 14 i t i s s e e n t h a t t h e h i g h wave number e s t i m a t e s f o r f l i g h t s 1 and 3 a g r e e w e l l e x c e p t i n t h e case o f t h e runs a t 150 m e t r e s . However, t h e d i f f e r e n c e h e r e i s much s m a l l e r t h a n i n t h e v e r t i c a l v e l o c i t y s p e c t r a and a p p e a r s Only above k = 0.01 m \ whereas t h e d i f f e r e n c e i n t h e v e r t i c a l v e l o c i t y s p e c t r a was l a r g e s t n e a r t h i s wave number. I f t h e d i f f e r e n c e i s due t o t h e f r e q u e n c y o f u p d r a f t s , t h e n i t i s r e a s o n a b l e t o e x p e c t t h e v e r t i c a l v e l o c i t y s p e c t r a t o e x h i b i t a l a r g e r d i f f e r e n c e e s p e c i a l l y i n t h e energy o f s c a l e s i z e s a t w h i c h the e f f e c t s o f buoyancy a r e most p r o n o u n c e d . The k - s p e c t r a o f F i g u r e 14, and a l l o t h e r s computed, d i s p l a y a -2/3 s l o p e a t h i g h wave numbers. T h i s s l o p e a l s o o b t a i n s a t wave numbers c o r r e s - p o n d i n g t o s c a l e s i z e s w h i c h a r e t h r e e o r f o u r t i m e s l a r g e r t h a n t h e d i s t a n c e f r o m t h e b o u n d a r y , and w h i c h t r a n s p o r t momentum ( S e c t i o n 3.2.5) and hence a r e a n i s o t r o p i c . Thus t h e -2/3 s l o p e o f t h e downwind v e l o c i t y component's k - s p e c t r a i s n o t s u f f i c i e n t e v i d e n c e f o r t h e e x i s t e n c e o f an ' i n e r t i a l s ub- r a n g e ' , w h i c h depends on t h e f l o w b e i n g l o c a l l y i s o t r o p i c ( K o l m o g o r o f f , 1941). B u t a t s u f f i c i e n t l y h i g h wave numbers, where t h e k - s p e c t r a o f b o t h v e r t i c a l and h o r i z o n t a l v e l o c i t y components d i s p l a y a -2/3 s l o p e and where t h e momentum t r a n s f e r i s n e g l i g i b l e , i s o t r o p y may e x i s t . I t c a n be shown Cfor example H i n z e , 1959) t h a t i f t h e f l o w i s i s o t r o p i c t h e r a t i o o f S (k) t o S ( k ) , where k i s the wave number component i n t h e TiTT.T 1111 ' " FIGURE 13. LONGITUDINAL VELOCITY ""RACES FIGURE 14 . ' LONGITUDINAL VELOCITY SPECTRA 34 d i r e c t i o n o f t h e u component, i s 4:3. T h i s r a t i o i s shown i n F i g u r e 15, i n w h i c h i t can be s e e n t h a t , a l t h o u g h t h e r e i s s c a t t e r , a l l o f t h e p o i n t s c o r r e s p o n d t o a r a t i o s m a l l e r t h a n 4/3. There i s a tendency f o r t h e r a t i o t o i n c r e a s e s l i g h t l y w i t h h e i g h t , r e f l e c t i n g a r e d u c t i o n i n a n i s o t r o p y as the l o c a l s h e a r weakens. However t h e r e a p p ears t o be no l o c a l l y i s o t r o p i c r e g i o n i n t h e range o f s c a l e s i n v e s t i g a t e d 0 < k < 1 m \ c o r r e s p o n d i n g t o a maximum v a l u e o f kZ o f 500. W e i l e r and B u r l i n g (1967) o b t a i n e d s i m i l a r v a l u e s o f t h e r a t i o o f s p e c t r a l d e n s i t i e s u s i n g X - w i r e s n e a r t h e s u r f a c e o v e r w a t e r . Payne and Lumley (1965) used a s i n g l e h o t w i r e mounted on t h e w i n g t i p o f an a i r c r a f t t o make measurements b o t h a l o n g and p e r p e n d i c u l a r t o t h e w i n d d i r e c t i o n . T h e i r F i g u r e 1 i n d i c a t e s t h a t t h e r a t i o S (k ) t o S ( k ) , ° w v uu where k^ i s t h e wave number component i n t h e d i r e c t i o n o f t h e v component, i s about 1.4: t h e c o n d i t i o n o f i s o t r o p y r e q u i r e s t h a t S (k) = S (k ) = S (k ) . ' fj -1 u u w v w w w However, s i n c e t h e measurements o f t h e two h o r i z o n t a l components were s e p a r a t e d b o t h i n spac e and t i m e , t h i s r e s u l t r e j e c t s t h e p o s s i b i l i t y o f l o c a l i s o t r o p y o n l y i f t h e t u r b u l e n t f i e l d was b o t h s t a t i o n a r y and homogeneous o v e r t h e r e l e v a n t i n t e r v a l s o f t i m e and s p a c e . S h e i h (1969) u s i n g a i r b o r n e x - w i r e s o b t a i n e d v a l u e s o f [S (k)]/[S ( k ) ] r a n g i n g f r o m 0.8 t o 2.4 f o r v a r i o u s wave ww uu numbers between 1 and 4000 m A l t h o u g h t h i s range o f v a l u e s o f [S ( k ) ] / [ S ( k ) ] i n c l u d e s t h e v a l u e (4/3) i n d i c a t i v e o f i s o t r o p y , t h e s c a t t e r WW uu i s t o o l a r g e t o a l l o w the c o n c l u s i o n t h a t t h e f l o w was l o c a l l y i s o t r o p i c . A p p a r e n t l y , c o n c l u s i v e e v i d e n c e f o r t h e e x i s t e n c e o f i s o t r o p y i n a t m o s p h e r i c t u r b u l e n c e i s s t i l l l a c k i n g . However, s i n c e t h e s e p a r a t e v e l o c i t y components a l w a y s e x h i b i t a -5/3 power law i n t h e i r s p e c t r a , t h e s p e c t r a l d e n s i t y i n t h i s r e g i o n can be us e d t o e s t i m a t e t h e d i s s i p a t i o n u s i n g t h e t e c h n i q u e f i r s t s u g g e s t e d by Obukhov (1951) and t h e i d e a s f o r m u l a t e d by K o l m o g o r o f f (1941) b u t r e l a t e d t o s p e c t r a 35 i n L U U J CD o tn (*1 CM i n in C3 0.0 U P W I N D s i 6 4 z ai 4 4 2 "oTT 1.0 ^ 1.5 1 2.5 -I FIGURE 15. '4/3' TEST FOR ISOTROPY 36 rather than, s t r u c t u r e functions: or s (k) =K« £ 2 / 3 k" 5' 3 t 3 - 2 ' 1 -) xx * = ^ K ' " 3 / 2 ^ x x ^ J 3 7 2 (3.2.2.) where K' i s the Kolmogoroff one dimensional wave number constant. In the past the published values of K' were i n the neighbourhood of 0.48 (Grant et a l , 1962; Pond et a l , 1963). More recent measurements i n d i c a t e that i t may be somewhat higher: perhaps as high as 0.57. However, as there i s yet no agreement as to what the revised value should be, the value (K' = 0.48) w i l l be used here. I f i t i s assumed that production ( u 2 |^ ) and d i s s i p a t i o n £ of turbulent k i n e t i c energy are nearly equal near the surface and that "6 u ^ U * ,.. . (Lumley and Panofsky, 1964, p.107), where K. = 0.4, von Karman's constantj then the f r i c t i o n v e l o c i t y u^ and hence the drag c o e f f i c i e n t 2 2 = u A/U may be estimated from n-spectrum of the downwind component nS (n) : uu u 2 = 3.85 # ) 2 / 3 nS (n) (1 + 5 Z / L ) " 2 / 3 (3-2.3.) x V uu Table 4 shows u* and ( C D ) 2 0 c o m v u t e d f r o m (3.2.3.) and from d i r e c t measurements of u'w1 (Section 3.2.5) f o r the lowest l e v e l of f l i g h t s 1 to 6. With the exception of f l i g h t // 1, the values of ( C ^ ) c o m p u t e d by the eddy -3 , , , ,„-3 c o r r e l a t i o n technique (u'w') l i e between 1.4 x 10 and 1.6 x 10 . To determine the approximate values of C.̂  at Z = 5 m the wind p r o f i l e i s assumed to be logarithmic and the surface roughness length i s taken to be _3 0.05 mm or equivalently (Cp)^ = 1.2 x 10 . Thus the values of (Cp)^ f o r RUN m U20 DOPPLER RADAR from -u'w' m/s (cm/s) cm/s [ CD ]20 xlO" Z/L (cm/s)' from nS (n) uu u. cm/s [ CD ]20 xlO" 1/6 2/9 3/6 4/5 5/2 6/2 20 18 18 18 26 29 4.0 6.0 8.6 8.3 8.0 9.4 497 500 1140 990 1040 1150 22.3 22.4 34.0 31.0 32.0 34.0 3.1 1.4 1.5 1.4 1.6 1.3 -0.28 -0.30 -0.034 -0.10 -0.094 -0.093 1240 2140 2600 1520 35.3 46.3 51.0 39.0 1.7 3.2 4.1 1.7 TABLE 4 DRAG COEFFICIENTS 38 f l i g h t s 1 t o 6 l i e between 1.7 x 10 and 2.Q x 10 . S i n c e t h e s e v a l u e s depend on t h e a c c u r a c y o f t h e w i n d s p e e d e s t i m a t e s , w h i c h a r e o b t a i n e d w i t h t h e a i r b o r n e D o p p l e r r a d a r , t h e y may be i n e r r o r by 50% o f t h e v a l u e s q u o t e d . However t h e y a r e w i t h i n t h e range o f v a l u e s o f ( C p ) ^ o b t a i n e d o v e r t h e w a t e r by s e v e r a l i n v e s t i g a t o r s and summarized by S m i t h ( 1 9 6 7 ) . The v a l u e s o f (C Q ^ Q r r o m (3.2.3.) a r e , on a v e r a g e , 85% l a r g e r than t h o s e computed by t h e eddy c o r r e l a t i o n t e c h n i q u e . W e i l e r and B u r l i n g (1967) and M i y a k e e t a l (19 70a) o b t a i n e d s i m i l a r r e s u l t s f r o m n e a r s u r f a c e o v e r w a t e r measurements: i n t h e c a s e o f t h e f o r m e r an o v e r e s t i m a t e o f 40% was o b t a i n e d w h i l e i n t h e l a t t e r t h e o v e r e s t i m a t e was 25%. B o t h W e i l e r and B u r l i n g (1967) and M i y a k e e t a l (1970) s u g g e s t p o s s i b l e r e a s o n s f o r t h i s d i s c r e p a n c y . However, i t a p pears t h a t i n t h e s e d a t a t h e a s s u m p t i o n t h a t s h e a r p r o d u c t i o n e q u a l s d i s s i p a t i o n may be t h e p r i m a r y r e a s o n f o r t h e o v e r e s t i m a t e s ( s e e S e c t i o n 3.4). Many w o r k e r s ( s e e , f o r example, Lumley and P a n o f s k y , 1964) have f o u n d t h a t t h e s t a n d a r d d e v i a t i o n <J^ o f 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 v e l o c i t y component i s p r o p o r t i o n a l t o t h e f r i c t i o n v e l o c i t y ; t h e r a t i o ^ / u ^ i s u s u a l l y f o u n d t o be about 2.5. I n t h e s e d a t a t h e k - s p e c t r a o f 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 v e l o c i t y component a r e q u i t e f l a t a t l a r g e s c a l e s ; t h e r e f o r e t h e v a l u e o f ^"u i s v e r y s e n s i t i v e t o t h e c h o i c e o f t h e low wave number l i m i t . I n t h i s s t u d y a low wave number l i m i t i s s e l e c t e d f o r each r u n s u c h t h a t more t h a n 9 0 % o f t h e v a r i a n c e o f t h e f l u c t u a t i o n s o f t h e v e r t i c a l v e l o c i t y component i s a t l a r g e r wave numbers; t h i s l i m i t i s u s e d f o r a l l t h e s p e c t r a and c o s p e c t r a o f t h a t r u n . F i g u r e 16 d i s p l a y s t h e r a t i o ^ u / u A ; w i t h a few e x c e p t i o n s the p o i n t s l i e between 1.8 and 2.8 and appear n o t t o be h e i g h t dependent. The v a l u e s o f ^*u/u. a r e a l s o l i s t e d i n T a b l e 3 and A p p e n d i x D. 39 CQ U J CD O in rn' in cV a rv ' in in 0.0 1.0 UPWIND 34 1 3 5 2 3 4 2.0 3.0 4 . 0 FIGURE 16. C T / u ^ V S . Z 40. 3.2.3 Temperature Measurements of temperature f l u c t u a t i o n s over water often reveal s p e c t r a l d i s t r i b u t i o n s not unlike those of the l o n g i t u d i n a l v e l o c i t y com- ponent (e.g. Miyake et a l , 1970C). But the temperature k-spectra of Figure 17 are quite unlike the l o n g i t u d i n a l v e l o c i t y k-spectra of Figure 14. There are two d i s t i n c t peaks i n almost a l l the temperature k-spectra analysed and, as w i l l be shown i n Section 3.5, these peaks are d i f f e r e n t i n o r i g i n . The behaviour of the high frequency peak i s much the c l e a r e r , which i s not s u r p r i s i n g i n view of the low r e l i a b i l i t y of the s p e c t r a l estimates at large s c a l e s . The wavelength of the high wave number peak shows a steady increase with height, but the amplitude decreases at f i r s t up to 150 m; i t then appears to increase between 150 m and 500 m (Figure 17 and 18), but with only two us e f u l runs at 500 m no d e f i n i t e pattern can be e s t a b l i s h e d . In general the behaviour of the low frequency peak i s e r r a t i c both with regard to i t s amplitude and wave length. However the importance of i t s c o n t r i b u t i o n to the t o t a l variance increases s t e a d i l y with height (Figure 17). Although there are no previous comparable temperature measurements, i t i s i n t e r e s t i n g and us e f u l to search f o r a convenient d e s c r i p t i o n of the height dependence of these k-spectra. Figure 19 shows a cl e a r dependence of of the high frequency hump on height. In f a c t the dependence as Z^*7"* i s the same as that of the v e r t i c a l v e l o c i t y peak. This i s not s u r p r i s i n g , s i n c e , i n a convective s i t u a t i o n temperature f l u c t u a t i o n s are maintained by the ac t i o n of the v e r t i c a l v e l o c i t y on the temperature g r a d i - ent, i t i s reasonable to suppose that temperature should scale with height i n much the same way as v e r t i c a l v e l o c i t y does. For convenience i n further d i s c u s s i o n , i t i s of use to state e x p l i c i t l y the dependence of L on Z: 41 FIGURE 17. TEMPERATURE SPECTRA (UPWIND) 42 01 U J U J CD CD O in rn' a in a rv' in tn o ' 0.0 T E M P E R A T U R E T f UPWIND 0.1 ~ I — 0.2 0.3 0.4 A/oise 1 0.5 S T R N D R R D D E V I A T I O N ( M K S ) FIGURE 18. CT, VS. Z (UPWIND) 43 T E M P E R A T U R E T ' U P W I N D / / / 1 g / (S)A/OISJ= / / / / / / / / / 6 / D 1 1 1 T 1 — 1 1.0 1.5 2.0 2.5 3.0 3.5 L 0 G 1 0 ( L M I N M E T R E S ) ' FIGURE 19. ( L ^ V S ' Z ( U P W I N D ) 44 = 1 3 (^/^Q)^* 7^ metres w h i c h r e p r e s e n t s the l i n e shown i n F i g u r e 19. The s t a n d a r d d e v i a t i o n 0*-̂, ( F i g u r e 18) d e c r e a s e s by about 40% f r o m 18 m t o 150 m, t h e n i n c r e a s e s a t much t h e same r a t e . Thus t h e r e i s a minimum o f t e m p e r a t u r e v a r i a n c e a t about 150 m e t r e s . T h i s c o n c l u s i o n depends on f l i g h t s 1 and 6 ( F i g u r e 18) o n l y , and t h e r e f o r e v i n u s t be r e g a r d e d as t e n t a t i v e . How- e v e r t h e t i m e s e r i e s o f F i g u r e 20 s u p p o r t t h i s i d e a t o some e x t e n t . FIGURE 20. TEMPERATURE TRACES (UPWIND) 46 3.2.4. Humidity The k-spectra of Figure 21, corrected by the intake tube t r a n s f e r func- t i o n , d i s p l a y a -2/3 power law at high frequencies. They are much more l i k e the l o n g i t u d i n a l v e l o c i t y k-spectra, than are the temperature k-spectra, even to the extent of 'obeying , : the -̂ 2/3 law at anomalously low wave numbers. A l i k e as they are i n s p e c t r a l shape, humidity and the l o n g i t u d i n a l v e l o c i t y component are quite d i f f e r e n t i n the dependence of t h e i r variances on height. ^Tu, decreases continuously with increasing height, whereas 0"a decreases and then increases again (Figure 22) i n the same manner as CT T , although here too the argument rests on only three points. The greater s c a t t e r of the points of Figure 22, compared to Figure 18, r e f l e c t s the r e l a t i v e l y strong depend- ence of vT^on the sampling length.. However, the minimum of the variances of both temperature and humidity between 50 m and 500 m i s very i n t e r e s t i n g and bears f u r t h e r i n v e s t i g a t i o n . This matter w i l l be discussed f u r t h e r i n the Section(3.4) dealing with the temperature-humidity c o r r e l a t i o n . The humidity traces at 18 m, 150 m and 500 m are displayed i n Figure 23 f o r f l i g h t s 1 and 3. I t i s evident that the traces at 150 m are the l e a s t energetic; t h i s observation i s also r e f l e c t e d i n the k-spectra of Figure 21. Unlike the temperature k- spectrum, k S ^ k ) (Figure 21) appears to r e t a i n i t s shape at a l l l e v e l s , at l e a s t i n the wave number range k = .002 m ^ to k = 1 m ^. FIGURE 21. HUMIDITY SPECTRA (UPWIND) HUMIDITY Q UPWIND Z 3 1 6 1 2* 5 6 2 4 '3 » 48 1 1 — i r 1 0.0 0.1 0.2 0.3 0.4 0.5 S T A N D A R D D E V I A T I O N ( M K S ) FIGURE 22... CT VS.- Z (UPWIND)  50 3.2.5. Momentum F l u x The momentum f l u x can be s e p a r a t e d i n t o two p a r t s : t h e component i n the d i r e c t i o n o f t h e s u r f a c e w i n d (x d i r e c t i o n ) TT = - / O u V and t h e component i n t h e y d i r e c t i o n f = -/^v'w' . H e r e , as t h r o u g h o u t t h i s t h e s i s , t h e f i g u r e s a r e p r e s e n t e d i n k i n e m a t i c t e r m s , i . e . t h e d e n s i t y / O , w h i c h i s assumed c o n s t a n t , i s o m i t t e d . S i n c e t h e r e was no e v i d e n c e o f r o t a t i o n o f t h e mean w i n d v e c t o r w i t h h e i g h t ( F i g u r e 6 ) , o n l y t h e momentum component i n t h e d i r e c t i o n o f t h e s u r f a c e w i n d w i l l be c o n s i d e r e d . I n F i g u r e 24 t h e i n s t a n t a n e o u s p r o d u c t u'w' i s d i s p l a y e d . I n a l l c a s e s b u t one ( r u n #1/7) t h e t r a c e has t h e c o r r e c t s i g n ; i . e . a n e g a t i v e v a l u e means p o s i t i v e momentum d i r e c t e d downwards. Run # 1/7 was a downwind r u n , and so t h e measured u v e l o c i t y i n t h e c o o r d i n a t e s y s t e m f i x e d t o t h e a i r c r a f t was a n t i - p a r a l l e l w i t h t h e w i n d d i r e c t i o n . F i g u r e 25 shows t h e h e i g h t dependence o f t h e momentum f l u x k - c o s p e c t r a f o r f l i g h t #3, and t h e i n t e g r a l under t h e s e c u r v e s (-u'w' = u^ ) i s d i s p l a y e d f o r a l l s i x f l i g h t s on l i n e a r axes i n F i g u r e 26. I t must be remembered t h a t i n t he a n a l y s i s t r e n d s a r e removed f r o m b o t h v e l o c i t y components and t h e l o w e r c u t - o f f o f t h e s e c o s p e c t r a i s d e c i d e d by t h e shape o f t h e v e r t i c a l v e l o c i t y k - s p e c t r a and j u s t i f i e d on t h e b a s i s o f i t s w e l l e s t a b l i s h e d shape n e a r t h e s u r f a c e . However, i t may be t h a t away f r o m t h e boundary the v e r t i c a l v e l o c i t y c o n t a i n s e n e r g y a t s c a l e s l a r g e r t h a n t h o s e c o n s i d e r e d h e r e , and t h a t an a p p r e c i a b l e amount o f t h e momentum f l u x i s c a r r i e d by t h e s e l a r g e s c a l e s . Whether t h i s i s so o r n o t cann o t be f u l l y examined w i t h t h e d a t a p r e s e n t e d h e r e , b u t t h e r a p i d d e c r e a s e o f t h e s t r e s s ( F i g u r e s 25 and 26) i s c o n s i s t e n t w i t h the r e l a t i v e c o n s t a n c y o f w i n d d i r e c t i o n and speed w i t h h e i g h t (see F i g u r e 6) o n l y i f o t h e r terms i n t h e mean e q u a t i o n s o f m o t i o n were comparable t o t h e v e r t i c a l s t r e s s g r a d i e n t . F o r i n s t a n c e , t o FIGURE 24. MOMENTUM TRACES (UPWIND) 52 / " N -.4-18 500 0 -ool 0 •<> I 0-1 M>1 OS- •3 \ -9 , \ \ A - N • ~r 0 • ooi 0 • 0 I O-l FIGURE 25. MOMENTUM COSPECTRA (UPWIND) F l i g h t // 3. 5 3 600 500- H 400 C O L U L U 300 H 200 H 100 H 6 5 S - U'W UPWIND 0.0 0.05 0.1 0.15 0.2 0.25 V A R I A N C E ( M K S ) F I G U R E 2 6 . ul ...VS. Z 54 b a l a n c e t h e s t r e s s g r a d i e n t a t s a y , 50 m: the mean w i n d s p e e d w o u l d have t o d e c r e a s e a t t h e r a t e o f 2 m/sec/hour o r i n c r e a s e towards t h e e a s t by 4 cm/sec/km ; on t h e o t h e r hand, e i t h e r a z o n a l p r e s s u r e g r a d i e n t o f 10 yU. b a r s / k m o r t e m p e r a t u r e g r a d i e n t o f 0.2C°/km w o u l d a l o n e be adequate t o c o u n t e r b a l a n c e t h e o b s e r v e d s t r e s s g r a d i e n t a t 50 m. A l t h o u g h i t i s p o s s i b l e t h a t . i n any one c a s e t h e s e terms were o f t h e c o r r e c t s i z e and -2 2 s i g n t o b a l a n c e t h e s t r e s s g r a d i e n t ( = 1 0 dynes/cm /m) , i t i s e x t r e m e l y u n l i k e l y t h a t t h i s u n u s u a l c o i n c i d e n c e o c c u r r e d d u r i n g t h e f i v e d a ytime f l i g h t s and t h e s i n g l e f l i g h t a t n i g h t . Hence, i t seems l i k e l y t h a t a t 50 m and above some o f t h e momentum f l u x was c a r r i e d by s c a l e s l a r g e r t h a n 20 km. B o t h t h e momentum k - c o s p e c t r a and t h e a s s o c i a t e d s p e c t r a l c o r r e l a t i o n -1 12 c o e f f i c i e n t s r (k) = S ( k ) . [S (k) . S (k) ] ' a r e d i s p l a y e d uw uw uu ww v J i n s e m i - l o g a r i t h m i c c o o r d i n a t e s a g a i n s t t h e wave number k i n F i g u r e 25. and t h e o v e r a l l c o r r e l a t i o n c o e f f i c i e n t - r =-u'w' . [ CT . ] i s p l o t t e d uw u w a g a i n s t Z f o r a l l t h e f l i g h t s i n F i g u r e 27. • The k - c o s p e c t r a ( F i g u r e 25) a t 18 m a r e l i k e t h o s e o b t a i n e d under s i m i l a r c o n d i t i o n s i n t h e s u r f a c e l a y e r , and t h e v a l u e (0.4) o f t h e a v e r a g e o f 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 s - r a t t h i s l e v e l ( F i g u r e 27) i s a l s o uw t y p i c a l o f t h e s u r f a c e l a y e r . However, w i t h i n c r e a s i n g h e i g h t d e c r e a s e s r a p i d l y , e s p e c i a l l y i t s c o n t r i b u t i o n f r o m t h e s m a l l e r e d d i e s (see F i g u r e 2 5 ) . I n o t h e r w o r d s , as s u c c e s s i v e l y l a r g e r e d d i e s become l e s s a n i s o t r o p i c ( s e e F i g u r e s 8 and 14) t h e y l o s e t h e i r a b i l i t y t o t r a n s p o r t momentum. P r e v i o u s w o r k e r s have remarked on t h e i n t e r m i t t e n c y o f t h e i n s t a n t a n e o u s momentum t r a n s f e r , and have c o n c l u d e d t h a t most o f t h e momentum t r a n s f e r n e a r t h e s u r f a c e t a k e s p l a c e i n s h o r t i n t e n s e b u r s t s s e p a r a t e d by l o n g q u i e t a r e a s . F i g u r e 24 does n o t a g r e e w i t h t h i s o b s e r v a t i o n a t low l e v e l s ; a l t h o u g h t h e r e a r e a r e a s o f u n u s u a l l y h i g h i n t e n s i t y , t h e y cannot be s a i d t o dominate t h e o v e r a l l t r a n s f e r . H i g h e r up, however, t h e p r o d u c t does become 55 C O U J L U CD o a in cu" a rvi" in LTW UPWIND 2 14 6 g SB §3 T r~ 1 - 0 . 3 -0.1 0.1 0.3 0.5 0.7 C O R R E L A T I O N C O E F F I C I E N T FIGURE 27. - r VS.Z uw. 56 spotty (see run // 1/7 of Figure 24). I t seems reasonable that t h i s e f f e c t could be due to the action of convection; i n which case the momentum f l u x and density f l u x should become more s i m i l a r i n appearance with inc r e a s i n g height. The two components of the density f l u x w'T' and w'Q' are p l o t t e d i n Figures 30 and 33 on scales such that equal ordinate steps of both w'T' and w'Q' contribute about equally to w'/O' ; p o s i t i v e values of w'T' imply downward f l u x of a i r molecules, but p o s i t i v e values of w'Q' imply upward f l u x of water molecules. From these figures (see, for example, runs 1/7 and 1/12) i t seems that the momentum fl u x i s c a r r i e d by the la r g e r scales associated with the moisture flux rather than by those res- ponsible for the transport of sensible heat. Figure 28 i n d i c a t e s that the momentum carrying eddies tend to be la r g e r with height at l e a s t up to a height of about 150 m. The i n i t i a l increase of r e f l e c t s the tendency for the energy peak of kS (k) to s h i f t to l a r g e r scales with height; the p o s s i b l y less r a p i d increase of l ^ a t great- er height may be i n d i c a t i v e of the e f f e c t s of buoyancy. That i s to say: l i g h t e r a i r r i s i n g i n a v e l o c i t y shear probably contributes more to the momentum f l u x than heavier r i s i n g a i r since i t w i l l on average r i s e higher and f a s t e r ; with the r e s u l t that the momentum f l u x i s enhanced at scales where buoyancy i s important. These scales tend not to be height dependent. The n a t u r a l logarithmic bandwidth B (Figure 29) does not appear to be p a r t i c u l a r l y height dependent. 57 CO LU L U CD o tn pi' a oi' i n rvi' o n i " in in o ' 2 .0 - i r w UPWIND 4 2 s 3 1 2 .5 3 .0 3 .5 1— 4 .0 1 4 .5 L 0 G 1 0 ( L M I N M E T R E S ) F I G U R E 2 8 . 58 CO U J L U o in a CO' i n rvi" a ru" m m 0.0 - I T UPWIND 1 3 S 42 S , «3 a * s 2.0 4.0 8.0 10.0 B N A T . L O G . " B A N D W I D T H FIGURE 29. B V S . Z uw 3.2.6 Heat F l u x ~ 7 F Here t h e d i s c u s s i o n i s h a n d l e d i n terms o f w T = H A Q C r p where F T T i s t h e h e a t f l u x , C t h e s p e c i f i c h e a t a t c o n s t a n t p r e s s u r e H p of t h e a i r and f ° i t s d e n s i t y . The most s t r i k i n g f e a t u r e o f t h e s e t r a c e s ( F i g u r e 30) i s t h e p r e - p o n d erence o f s m a l l s c a l e e nergy a t t h e l o w e s t leve3_s; w h i c h i s n o t s u r p r i s i n g i n v i e w o f t h e c h a r a c t e r o f t h e t e m p e r a t u r e t r a c e ( F i g u r e 2 0 ) . L i k e momentum, t h e r e i s a g e n e r a l d e c r e a s e o f i n t e n s i t y w i t h h e i g h t , and a tendency towards s p o t t i n e s s . L i k e t e m p e r a t u r e , t h e h e a t f l u x a c q u i r e s renewed s t r e n g t h a t t h e h i g h e s t l e v e l i n t h e l a r g e s c a l e s i z e s , b u t t h e h e a t f l u x a t t h e s e s c a l e s i s g e n e r a l l y d i r e c t e d downwards. I t seems, t h e n , t h a t t he h i g h e r a l t i t u d e s o u r c e o f l a r g e s c a l e t e m p e r a t u r e f l u c t u a t i o n s i s o f t e n a s s o c i a t e d w i t h a n e g a t i v e h e a t f l u x . Some peaks o f F i g u r e 30 have been d e s i g n a t e d 'U' o r 'D\ d e p e n d i n g on w h e t h e r t h e v e r t i c a l v e l o c i t y was upward o r downward; i t a p p ears t h a t , a l t h o u g h t h e u p d r a f t s c a r r y p o s i t i v e h e a t f l u x , t h e d o w n d r a f t s may be a s s o c i a t e d w i t h f l u x o f e i t h e r s i g n . Lumley and P a n o f s k y (1964) r e p o r t e d t h a t i n s p e c t i o n o f some t e m p e r a t u r e r e c o r d s o f E.K. Webb's ( u n p u b l i s h e d ) r e v e a l e d t h a t r i s i n g a i r t e n d e d t o c o i n c i d e w i t h e n e r g e t i c t e m p e r a t u r e f l u c t u a t i o n s and s u b s i d i n g a i r w i t h a smooth t e m p e r a t u r e t r a c e - t h e s m a l l s c a l e v e r t i c a l v e l o c i t y b e i n g e q u a l l y e n e r g e t i c t h r o u g h o u t . T h i s phenomenon i s f r e q u e n t l y o b s e r v e d under c o n v e c t i v e c o n d i t i o n s ; f o r example K a t z ( 1 9 7 0 ) , i n w h i c h i t i s shown t h a t t h e h u m i d i t y t r a c e behaves i n a s i m i l a r f a s h i o n . C l o s e i n s p e c t i o n o f F i g u r e s 9, 20 and 23, however, i n d i c a t e s t h a t l a r g e s c a l e u p d r a f t s and d o w n d r a f t s a r e about e q u a l l y endowed w i t h s m a l l e r s c a l e 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 and h u m i d i t y . The f a c t t h a t t h e u p d r a f t s a r e a s s o c i a t e d  w i t h ai.more e n e r g e t i c w'T' p r o d u c t (.Figure 30) i n d i c a t e s t h a t t h e s m a l l s c a l e s o f v e r t i c a l v e l o c i t y t e n d t o be c o h e r e n t w i t h s m a l l s c a l e t e m p e r a t u r e f l u c t - u a t i o n s i n t h e u p d r a f t s b u t n o t i n t h e d o w n d r a f t s . The k - c o s p e c t r a and c o r r e l a t i o n c o e f f i c i e n t s o f F i g u r e 31 r e v e a l some i n t e r e s t i n g f e a t u r e s o f t h e h e a t f l u x and i t s h e i g h t dependence d u r i n g t h e e x p e r i m e n t . I t a p p e a r s t h a t t h e t o t a l s e n s i b l e h e a t f l u x i s c o m p r i s e d o f a b a l a n c e between t h e l a r g e s c a l e n e g a t i v e f l u x and a comparable p o s i t i v e p o r t i o n c a r r i e d by much s m a l l e r e d d i e s . The t r a n s i t i o n eddy s i z e between th e f l u x e s o f o p p o s i t e s i g n does n o t seem t o be v e r y h e i g h t dependent b u t a p p e a r s a t s m a l l e r s c a l e s i n t h e h i g h e r w i n d s p e e d c a s e . C o s p e c t r a o f temp- e r a t u r e and v e r t i c a l v e l o c i t y have been computed i n t h e p a s t ; o f t e n i n t h e s u r f a c e l a y e r o v e r l a n d and w a t e r ( e . g . P a n o f s k y and M a r e s , 1968; M i y a k e e t a l 1970c ; M i y a k e and McBean, 1 9 7 0 ) ; and i n f r e q u e n t l y i n t h e p l a n e t a r y b o undary l a y e r o v e r l a n d ( K u k h a r e t s and Tsvang, 1969). G u r v i c h and Tsvang ( r e p o r t e d by M o n i n , 1962) and R o b i n s o n (1959) p r e s e n t e d d a t a w h i c h s u g g e s t e d t h a t t h e h e a t f l u x n e a r t h e s u r f a c e i s a s s o c i a t e d w i t h s l i g h t l y l a r g e r e d d i e s t h a n i s t h e momentum f l u x ; whereas t h o s e o f P a n o f s k y and Mares (1968) and M i y a k e , S t e w a r t and B u r l i n g (1970) show no d i f f e r e n c e w h i l e d a t a d e s c r i b e d by M i y a k e and McBean (1970) i n d i c a t e t h e r e v e r s e . G e n e r a l l y , i t i s f o u n d t h a t t h e c o s p e c t r a o f t h e h e a t and momentum f l u x e s a r e q u i t e s i m i l a r . Thus, t h e o u t - s t a n d i n g d i s s i m i l a r i t y o f t h e k - c o s p e c t r a o f F i g u r e s 25 and 31 s u g g e s t s an i m p o r t a n t d i f f e r e n c e i n t h e s t r u c t u r e o f t h e a t m o s p h e r i c boundary l a y e r from t h a t p r e v i o u s l y o b s e r v e d . However, t h e a i r b o r n e measurements o f K u k h a r e t s and T svang (1969) p r o v i d e an i n t e r e s t i n g c o m p a r i s o n . I n t h e i r F i g u r e 3 t h e n o n - n o r m a l i z e d h e a t f l u x n - c o s p e c t r a a r e d i s p l a y e d i n t h e same f a s h i o n as F i g u r e 31; t h e i r k - c o s p e c t r a h a ve a s i n g l e peak n e a r k = 0.008m ^ and e x t e n d o v e r t h e wave number range 0.001 < k < 0 . 1 m The Bomex k - c o s p e c t r a have FIGURE 31. HEAT FLUX COSPECTRA (UPWIND) 63 two d i s t i n c t peaks o f o p p o s i t e s i g n . Both. the. R u s s i a n k - c o s p e c t r a and t h e p o s i t i v e hump o f t h e Bomex k - c o s p e c t r a show a t e n d e n c y t o d e c r e a s e i n a m p l i t u d e w i t h i n c r e a s i n g h e i g h t . F u r t h e r m o r e , K u k h a r e t s and Tsvang remark t h a t a t a l t i t u d e s > 500 m t h e k - c o s p e c t r a o f t e n d e v e l o p a n e g a t i v e hump a t l a r g e s c a l e s . They s p e c u l a t e t h a t t h i s may be caused by a mechanism p r o p o s e d by V u l ' f s o n ( 1 9 6 1 ) , i n w h i c h t h e downward h e a t f l u x a t l a r g e s c a l e s i s due t o d i s p l a c e d c o l d e r a i r masses w h i c h descend s l o w l y around t h e s m a l l e r b l o b s o f r i s i n g warm a i r . T h i s mechanism r e q u i r e s the p r e s e n c e o f a l a y e r o f a i r a b o v e . i n w h i c h t h e p o t e n t i a l t e m p e r a t u r e g r a d i e n t i s n e g a t i v e . The h e i g h t dependence o f t h e s e n s i b l e h e a t f l u x i s d i s p l a y e d i n F i g u r e 32. I t i s s e e n t h a t t h e r e i s a g e n e r a l t e n d e n c y f o r t h e f l u x t o d e c r e a s e w i t h i n c r e a s i n g a l t i t u d e . The av e r a g e v a l u e o f t h e h e a t f l u x n e a r t h e s u r f a c e i s 2 about 1.0 mW/cm ( s e e F i g u r e 32 and T a b l e 3 ) . I n summary: t h e t o t a l s e n s i b l e h e a t f l u x , d u r i n g t h e s e a i r c r a f t o b s e r v - a t i o n s i n Bomex, i s due t o a l a r g e s c a l e n e g a t i v e c o n t r i b u t i o n and a s m a l l e r 2 s c a l e p o s i t i v e c o n t r i b u t i o n . A t t h e s u r f a c e t h e h e a t f l u x i s about 1.0 mW/cm on a v e r a g e , b u t w i t h i n c r e a s i n g a l t i t u d e t h e n e g a t i v e c o n t r i b u t i o n due t o l a r g e s c a l e s i n c r e a s e s i n i m p o r t a n c e and c o n s e q u e n t l y t h e h e a t f l u x i s r e d u c e d . The s y s t e m a t i c a p p e a r a n c e o f t h e n e g a t i v e 'hump' i n t h e k - c o s p e c t r a has n o t p r e v i o u s l y been n o t i c e d a t su c h low a l t i t u d e s . B o t h the wave number and t h e a m p l i t u d e o f th e p o s i t i v e k - c o s p e c t r a J p e a k d e c r e a s e w i t h i n c r e a s i n g h e i g h t . The e f f e c t o f i n c r e a s i n g w i n d s p e e d appears t o be s i m p l y t o s h i f t t h e k - c o s p e c t r a b o d i l y t o h i g h e r wave numbers, and the c o s p e c t r a l t r a n s i t i o n f r o m n e g a t i v e t o p o s i t i v e does h o t seem t o be v e r y s e n s i t i v e t o a l t i t u d e . 64 CD L U IT) ru* U J C3 ru" 4 2 o i n 5 1 3 a 4 i n -0.02 -0.01 -0.0 0.OJ 0.02 Q.03 w'T' i n [m/sec].C° SENSIBLE HEAT FLUX i n mw/cm2 - T — O "4- —i— 4- KINETIC ENERGY PRODUCTION i n cm2 sec 3 FIGURE 32. HEAT FLUX VS. Z (UPWIND) 65 3.2.7 M o i s t u r e F l u x w'Q1, w h i c h when m u l t i p l i e d by /° L y i e l d s t h e f l u x o f l a t e n t h e a t , i s now c o n s i d e r e d . (L i s t h e l a t e n t h e a t o f v a p o t i r i z a t i o n o f w a t e r ) . The s i m i l a r i t y o f t h e s e t r a c e s ( F i g u r e 33) w i t h t h o s e o f momentum f l u x ( F i g u r e 24) i s s t r i k i n g , as i s t h e c o n t r a s t w i t h t h e h e a t f l u x t r a c e s ( F i g u r e 3 0 ) . W'T' and W'Q' become s p o t t y w i t h i n c r e a s i n g h e i g h t ; b u t , w h i l e t h e h e a t f l u x changes s i g n f r e q u e n t l y , t h e m o i s t u r e f l u x i s p o s i t i v e n e a r l y e v e r y w h e r e . Here a g a i n t h e d i r e c t i o n o f t h e v e r t i c a l v e l o c i t y a t some peaks o f W'Q' i s i n d i c a t e d , and i t i s se e n t h a t t h e u p d r a f t s t e n d t o p r o d u c e s l i g h t l y more i n t e n s e m o i s t u r e f l u x e s t h a n t h e d o w n d r a f t s , a l t h o u g h , as i n t h e c a s e o f t e m p e r a t u r e , t h e m o i s t u r e f l u c t u a t i o n s a r e no more e n e r g e t i c i n t h e u p d r a f t s t h a n i n t h e s u b s i d e n c e a r e a s . A c o m p a r i s o n o f F i g u r e s 25 and 34 r e v e a l s t h e s i m i l a r i t y o f t h e f l u x e s o f momentum and m o i s t u r e a t low l e v e l s , t h e main d i f f e r e n c e b e i n g t h e r e l a t i v e l y l a r g e r e n e r g y i n t h e m o i s t u r e f l u x a t wave numbers i n e x c e s s o f 0.1 m ^. B o t h k - c o s p e c t r a become n a r r o w e r and s h i f t t o l o w e r f r e q u e n c i e s w i t h h e i g h t , b u t w h i l e t h e momentum t r a n s f e r d i m i n i s h e s r a p i d l y t h e m o i s t u r e f l u x does n o t . As m e n t i o n e d b e f o r e , i t has o f t e n been n o t i c e d t h a t under w e a k l y c o n v e c t i v e c o n d i t i o n s , t h e momentum and s e n s i b l e h e a t f l u x a r e v e r y s i m i l a r . However, i n s u c h cases t h e boundary l a y e r c o n v e c t i v e p r o c e s s i s dominated by t e m p e r a t u r e v a r i a t i o n s ; whereas o v e r t h e t r o p i c a l ocean t h e m o i s t u r e f l u c t u a t i o n s c o n t r i b u t e a t l e a s t as much t o t h e buoyancy as do t h o s e o f t e m p e r a t u r e . I t seems t h a t t h e h u m i d i t y f l u c t u a t i o n s a r e more c l o s e l y c o r r e l a t e d w i t h t h e v e r t i c a l v e l o c i t y and r e t a i n t h e i r c o r r e l a t i o n a t l a r g e r h e i g h t s t h a n t h e t e m p e r a t u r e f l u c t u a t i o n s . N o n e t h e l e s s , s i n c e t h e boundary l a y e r between h e i g h t s o f 50 m and 500 m d u r i n g t h i s e x p e r i m e n t was c h a r a c t e r - FIGURE 33. MOISTURE FLUX TRACES (UPWIND) <* 67 •S i •2.5 J / / X - - - A > -r \ \ O'OPl o ' O l o. / A 5 J FIGURE 34. MOISTURE FLUX COSPECTRA (UPWIND) Flight # 3. 68 i z e d by a v e r y s m a l l g r a d i e n t o f p o t e n t i a l v i r t u a l t e m p e r a t u r e ( s e e F i g u r e 5 ) , most l a r g e s c a l e u p d r a f t s w e r e b o t h ; warm and wet ( F i g u r e s 9, 20 and 2 3 ) . I t i s t h e r e f o r e a p p r o p r i a t e t o adopt B a l l ' s (1960) c o i n a g e , and t o r e f e r t o s u c h u p d r a f t s as warm ' m o i s t a l s ' . The l a r g e s c a l e s u b s i d e n c e z o n e s , on t h e o t h e r hand, a r e g e n e r a l l y d r i e r b u t n o t n e c e s s a r i l y c o l d e r t h a n t h e a v e r a g e . S i n c e t h e d e n s i t y f l u c t u a t i o n s due t o t e m p e r a t u r e a r e about as l a r g e as t h o s e due t o m o i s t u r e , t h e s i m i l a r i t y o f m o i s t u r e and momentum f l u x e s and t h e d i s s i m i l - a r i t y o f h e a t and momentum f l u x e s must be a t t r i b u t e d t o t h e more e f f i c i e n t momentum t r a n s f e r p r o p e r t i e s o f t h e l a r g e s c a l e s a s s o c i a t e d w i t h t h e f l u c t u - a t i o n s o f h u m i d i t y r e l a t i v e t o t h o s e a s s o c i a t e d w i t h t e m p e r a t u r e v a r i a t i o n s . From t h i s i t can be i n f e r r e d t h a t under u n s t a b l e c o n d i t i o n s the s i m i l a r i t y o f t h e mass and momentum t r a n s f e r depends on t h e s p e c t r a l d i s t r i b u t i o n o f buoyancy v a r i a t i o n s . T h at i s , i f t h e most e n e r g e t i c s c a l e s i z e s o f t h e buoyancy v a r i a t i o n s a r e t h o s e c a p a b l e o f t h e most e f f i c i e n t t r a n s f e r of momentum t h e f l u x e s o f mass and momentum w i l l have s i m i l a r s p e c t r a l d i s t r i b - u t i o n s ; o t h e r w i s e t h e peak o f t h e k - c o s p e c t r u m o f t h e momentum f l u x w i l l be s h i f t e d , r e l a t i v e t o t h a t o f t h e mass f l u x , towards t h e s c a l e s i z e s w h i c h t r a n s p o r t momentum most e f f i c i e n t l y . 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^ C k ) and - r^ C k ) ( F i g u r e s 25 and 34) a r e q u i t e s i m i l a r a t low l e v e l s , and t h e i r o v e r a l l v a l u e s ( F i g u r e s 27 and 36) d i m i n i s h w i t h i n c r e a s i n g a l t i t u d e : v e r y r a p i d l y a t f i r s t and t h e n more s l o w l y ; r ^ d e c r e a s e s q u i t e s l o w l y from a s u r f a c e v a l u e o f about 0.4 t o a b o ut 0.3 on h i g h . The r e d u c t i o n o f r ^ w i t h h e i g h t , even though t h e e f f e c t s o f c o n v e c t i o n become more pr o n o u n c e d , as t h e m e c h a n i c a l t u r b u l e n c e d i m i n i s h e s , i s p r o b a b l y due t o t h e c o u n t e r e f f e c t s - o f t e m p e r a t u r e f l u c t u a t i o n s and t h o s e o f h u m i d i t y t o c o n t r o l t h e buoyancy ( s e e S e c t i o n 3.5). The h e i g h t dependence o f t h e l a t e n t h e a t f l u x i s d i s p l a y e d i n F i g u r e 37. 69 if) L U L U CD o in tn" a in oi" o n i ' in in 1 . 5 2.0 W P Q UPWIND a i z 6 a 3.0 3 . 5 4.0 L 0 G 1 0 i l I N M E T R E S ) FIGURE 35. CLj,)^ VS. Z (UPHIND) UPWIND 6 3» « 1 Z 3 s 8  S 3 £ - * I 6 1 i « 1 1 C O R R E L A T I O N C O E F F I C I E N T FIGURE 3 6 . VS. Z (UPWIND) 71 cn U J i — UJ IT) a o3" 3 6 4 z ̂  j o .—; CD O 4 LO _1 __ , _ , , 0.02 0.04 0.06 0.08 w'Q' i n [m/sec].[gm/kgm] 0.1 —I— 10 — i — 20 - 1 — 30 LATENT HEAT FLUX i n mW/cm —i— 4 — i — 2 KINETIC ENERGY PRODUCTION in cm2 sec 3 FIGURE 37. MOISTURE FLUX VS. Z (UPWIND) 72 2 The f l u x decreases from an average value near the surface of about 12 mW/cm 2 to a minimum of about 8 mW/cm at an a l t i t u d e of about 150 m; above t h i s l e v e l there appears to be a general increase i n the l a t e n t heat f l u x ; but th i s tendency may have been more c l e a r l y revealed had there been data from at l e a s t one more l e v e l between 150 m and 500 m. 73 3.3 Comparison o f c r o s s w i n d measurements w i t h , measurements; along' the w i n d 3.3.1 I n t r o d u c t i o n One o f t h e i m p o r t a n t f e a t u r e s o f t h e s e a i r b o r n e t u r b u l e n c e measurements i s t h e d i f f e r e n c e o b t a i n e d f r o m f l i g h t p a t h s a l o n g and p e r p e n d i c u l a r t o t h e w i n d . The f l i g h t s ( 1 , 2, 3 and 4) w h i c h were f l o w n i n a r e c t a n g u l a r p a t t e r n ( f l i g h t p a t t e r n 1; see F i g u r e 4) were d e s i g n e d t o i n v e s t i g a t e t h i s d i f f e r e n c e . However, i n o r d e r t h a t t h e a i r c r a f t r e m a i n i n t h e v i c i n i t y o f t h e s u r f a c e p l a t f o r m , w h i c h w o u l d l a t e r a c t as a 'ground t r u t h ' s t a t i o n , t h e c r o s s w i n d f l i g h t s were much s h o r t e r t h a n t h e upwind cases d i s c u s s e d . T h i s l i m i t a t i o n p r o v e d t o be n o t v e r y s e r i o u s b e c a u s e t h e l a r g e s t s c a l e s i z e s were somewhat s m a l l e r a c r o s s t h a n a l o n g t h e w i n d . I n t h i s s e c t i o n many o f t h e r e s u l t s o f measurements i n t h e w i n d d i r e c t i o n ( S e c t i o n 3.2) a r e compared and c o n t r a s t e d x ^ i t h t h e i r c r o s s - w i n d c o u n t e r p a r t s and v a r i o u s i n f e r e n c e s a r e drawn from t h e i r s i m i l a r i t i e s and d i f f e r e n c e s . 74 3.3.2 V e r t i c a l V e l o c i t y The t r a c e s o f v e r t i c a l v e l o c i t y - measured in. flights a l o n g CFigure 9) and p e r p e n d i c u l a r t o ( F i g u r e 38) t h e w i n d p r e s e n t some i n t e r e s t i n g c o n t r a s t s , t h e most s t r i k i n g o f w h i c h i s t h e i n c r e a s e d r e g u l a r i t y and s h a r p n e s s o f t h e l a r g e s c a l e u p d r a f t s s a m p l e d a t 150 m and 500 m i n c r o s s w i n d f l i g h t o v e r t h o s e d i s c u s s e d p r e v i o u s l y . R a dar p h o t o g r a p h s o f low l e v e l c l e a r - a i r c o n v e c t i o n , i n w h i c h t h e c o n v e c t i v e c e l l s a r e a l i g n e d i n rows a n a l o g o u s t o c l o u d s t r e e t s b u t an o r d e r o f m a gnitude s m a l l e r i n h o r i z o n t a l s c a l e , i n d i c a t e t h a t t h e c o n v e c t i v e a r e a s a r e g e n e r a l l y c i r c u l a r i n h o r i z o n t a l c r o s s - s e c t i o n and v a r y i n d i a m e t e r by about a f a c t o r 3 between t h e s m a l l e s t and l a r g e s t ( K o n r a d , 1970). A c r o s s - w i n d t r a v e r s e t h r o u g h s u c h a b u o y a n t f i e l d w o u l d e n c o u n t e r u p d r a f t s o f v a r i o u s d u r a t i o n s . C r o s s w i n d runs # 1 / 8 a t 150 m and # 1/11 a t 500 m p r o v i d e e s t i m a t e s o f t h e a v e r a g e c r o s s w i n d w i d t h and s e p a r a t i o n o f t h e u p d r a f t s as a p p r o x i m a t e l y 500 m and 800 m r e s p e c t i v e l y . Windwise t r a v e r s e s on t h e o t h e r hand, may e n c o u n t e r many, few o r no u p d r a f t s , a c c o r d i n g as t h e f l i g h t p a t h i s d i r e c t l y t h r o u g h , on t h e edge o f , o r f a r f r o m an a l i g n e d c o n v e c t i v e s t r i p . The c h a r a c t e r o f # 1/7 ( F i g u r e 9) s u g g e s t s t h a t i t may have b e e n d i r e c t l y t h r o u g h a c o n v e c t i v e s t r i p . A s s uming, f o r t h e moment, t h a t t h i s i s t h e c a s e , i t i s a s i m p l e m a t t e r t o deduce f r o m r u n # 1/7 t h a t t h e w i d t h and s e p a r a t i o n o f t h e s e u p d r a f t s i n t h e w i n d d i r e c t i o n a r e a p p r o x i m a t e l y 500 m and 800 m r e s p e c t i v e l y . T h e r e i s a p r o n o u n c e d d i f f e r e n c e between t h e appearance o f t h e u p d r a f t s o f r u n # 1/7 and t h o s e o f # 1/11; t h e d i f f e r e n c e i m p l i e s t h a t t h e t r a n s i t i o n between and u p d r a f t and s u b s i d e n c e i s s h a r p e r on t h e c r o s s w i n d s i d e s o f an u p d r a f t t h a n on i t s downwind o r upwind s i d e s . The k - s p e c t r a o f t h e v e r t i c a l v e l o c i t y component a r e d i s p l a y e d i n F i g u r e 39 ( c r o s s w i n d t r a v e r s e s ) and i n F i g u r e 8 ( a l o n g w i n d t r a v e r s e s ) . 500 M #1/11 SECONDS I SECONDS FIGURE 38. VERTICAL VELOCITY TRACES (CROSSWIND) 76 FIGURE 39. VERTICAL VELOCITY SPECTRA (CROSSWIND) 77 E v i d e n t l y t h e shape o f t h e k - s p e c t r a a r e q u i t e s i m i l a r ; t h e main d i f f e r e n c e b e i n g t h a t t h e k - s p e c t r a o f t h e a l o n g w i n d measurements ( F i g u r e 8) a r e s l i g h t l y b r o a d e r t h a n t h o s e measured a c r o s s t h e w i n d . The k - s p e c t r a l peak o c c u r s a t about t h e same wave l e n g t h i n b o t h a l o n g w i n d ( F i g u r e 8) and c r o s s w i n d ( F i g u r e 39). measurements, and i n c r e a s e s w i t h i n c r e a s i n g a l t i t u d e i n much t h e same manner i n b o t h c a s e s . P r i e s t l y (1959) has f o u n d t h a t i n c o n v e c t i v e s i t u a t i o n s o v e r l a n d t h e s c a l e o f v e r t i c a l v e l o c i t y f l u c t u a t i o n s i s s m a l l e r a c r o s s t h a n a l o n g t h e w i n d . He a t t r i b u t e s t h i s e f f e c t t o t h e s t r e t c h i n g o f plumes' i n t h e d i r e c t i o n o f t h e w i n d s h e a r and t o t h e m e r g i n g o f t h e s t r e t c h e d plumes i n t h a t d i r e c t i o n . P e r h a p s t h e r e a s o n f o r t h e absence o f t h i s e f f e c t h e r e i s t h a t o v e r w a t e r w i t h s u c h u n i f o r m s u r f a c e t e m p e r a t u r e s t h e c o n v e c t i v e a r e a s a r e n o t t i e d t o t h e s u r f a c e , whereas o v e r l a n d t h e y f r e q u e n t l y a r e . The a p p e a r - ance o f t h e t i m e t r a c e s ( F i g u r e s 9 and 38) s u g g e s t s t h a t t h e plumes do n o t d e v e l o p u n t i l h e i g h t s o f 50 m o r more, where t h e w i n d s h e a r i s f a r t o o weak t o p r o d u c e any a p p r e c i a b l e plume e l o n g a t i o n . One o f t h e s t r i k i n g f e a t u r e s o f F i g u r e 8 was t h e enormous d i s p a r i t y o f t h e n o r m a l i z e d k - s p e c t r a a t .150 m between f l i g h t s 1 and 3 when th e k - s p e c t r a a t o t h e r l e v e l s were q u i t e c o m p a r a b l e . The e f f e c t i s n o t n e a r l y s o p r o n ounced i n F i g u r e 39 and t h i s s u g g e s t s t h a t t h e t u r b u l e n t f i e l d e i t h e r c o n t a i n s i m p o r t a n t i n h o m o g e n e i t i e s o f s e v e r a l k i l o m e t e r s i n e x t e n t o r i s s u f f i c i e n t l y w e l l o r g a n i z e d t h a t t h e measured s t a t i s t i c s depend on t h e c h o i c e o f f l i g h t p a t h . The l a t t e r p o s s i b i l i t y i s t h e more p a l a t a b l e s i n c e i t i s d i f f i c u l t t o i m a g i n e a mechanism c a p a b l e o f p r o d u c i n g i m p o r t a n t v e r t i c a l v e l o c i t y d i f f e r e n c e s o f s u c h l a r g e e x t e n t a t t h e s e a l t i t u d e s . 78 3.3.3 H o r i z o n t a l V e l o c i t y Measurements o v e r l a n d (Lumley and P a n o f s k y , 1964) r e v e a l a g r e a t d e a l o f low f r e q u e n c y energy i n the s p e c t r u m o f l a t e r a l v e l o c i t y u n d e r u n s t a b l e c o n d i t i o n s ; w h i l e t h e i n s h o r e o v e r w a t e r measurements o f M i y a k e , S t e w a r t and B u r l i n g (19 70) r e v e a l a l a t e r a l v e l o c i t y s p e c t r u m h a v i n g c o n s i d e r a b l y more low f r e q u e n c y e n e r g y t h a n t h a t o f t h e v e r t i c a l v e l o c i t y b u t s l i g h t l y l e s s t h a n t h e l o n g i t u d i n a l v e l o c i t y s p e c t r u m . A c o m p a r i s o n o f F i g u r e s 8, 14 and 40 i n d i c a t e s t h a t t h e l a t e r a l v e l o c i t y f l u c t u a t i o n s c o n t a i n l e s s l a r g e s c a l e e nergy t h a n t h o s e o f t h e l o n g i t u d i n a l v e l o c i t y component and more t h a n t h o s e o f t h e v e r t i c a l ; l y i n g , i n f a c t , c l o s e t o the median o f t h e s e two. T h i s i s what one w o u l d e x p e c t a s , h a v i n g t o e x t r a c t i t s energy f r o m t h e mean f l o w , t h e l a t e r a l v e l o c i t y component i s l i k e l y t o be l e s s e n e r g e t i c a t l a r g e s c a l e s t h a n t h e component i n t h e d i r e c t i o n o f the mean f l o w i t s e l f ; on t h e o t h e r hand, n o t b e i n g d i r e c t l y r e s t r i c t e d by t h e p r e s e n c e o f b o u n d a r y , t h e l a t e r a l v e l o c i t y component's l a r g e s c a l e f l u c t u a t i o n s d e v e l o p more e a s i l y t h a n t h o s e o f t h e v e r t i c a l v e l o c i t y . P e r h a p s t o p o g r a p h i c f e a t u r e s were i n s t r u m e n t a l i n i n c r e a s i n g t h e l a r g e s c a l e l a t e r a l v e l o c i t y f l u c t u a t i o n s i n t h e i n s h o r e and o v e r l a n d measurements. C e r t a i n l y t h e c o n s t a n c y o f d i r e c t i o n o f t h e t r a d e w i n d s o f f Barbados w o u l d n o t o b t a i n o v e r o r n e a r a l a n d mass. I t i s i n t e r e s t i n g t o n o t e t h a t t h e wave l e n g t h o f t h e k - s p e c t r a l p eak ( F i g u r e 40) does n o t v a r y a p p r e c i a b l y w i t h h e i g h t . T h i s u n d e r l i n e s t h e u n i m p o r t a n c e o f t h e boundary i n l i m i t i n g t h e s c a l e s i z e s o f t h e l a t e r a l v e l o c i t y component. 79 FIGURE 40. LATERAL VELOCITY SPECTRA The s t a n d a r d d e v i a t i o n s o f the t e m p e r a t u r e f l u c t u a t i o n s 0*T and t h o s e o f h u m i d i t y 0"̂  a r e p l o t t e d v e r s u s l o g ^ Z i n F i g u r e s 41 and 42 r e s p e c t i v e l y . H e r e , as i n the c o r r e s p o n d i n g f i g u r e s i n the s e c t i o n on measurements i n t h e w i n d d i r e c t i o n ( F i g u r e s 18 and 2 2 ) , i t seems t h a t b o t h t h e t e m p e r a t u r e and h u m i d i t y f l u c t u a t i o n s a r e l e a s t e n e r g e t i c a t some a l t i t u d e between 50 m and 500 m. I n t h e d a t a g a t h e r e d a l o n g t h e w i n d ( S e c t i o n 3.2) t h e peak o f k S T T ( k ) ( F i g u r e 19) d i s p l a y e d a s y s t e m a t i c s h i f t t o l o w e r wave numbers w i t h i n c r e a s i n g a l t i t u d e : the peak o f k S ^ ^ ( k ) d i d n o t . I n c o n t r a s t the c r o s s w i n d measurements show no s y s t e m a t i c h e i g h t dependence o f t h e wave l e n g t h o f the peak o f kS^,^,(k), b u t they do i n d i c a t e ( F i g u r e 43) t h a t t h e r e i s a d e f i n i t e s h i f t o f the wave l e n g t h o f t h e peak o f k S ^ ( k ) t o l a r g e r s c a l e s w i t h i n c r e a s i n g a l t i t u d e . L^. =? 185 (^/-^Q)^ ' ̂  metres r e p r e s e n t i n g t h e l i n e shown i n F i g u r e 43. 3.3.5 Heat F l u x One o f t h e s t r i k i n g f e a t u r e s o f t h e k - c o s p e c t r a o f t h e h e a t f l u x measured a l o n g t h e w i n d ( F i g u r e 31) was t h e i r d o u b l e peak: upward f l u x a t s m a l l s c a l e s and downward f l u x a t l a r g e s c a l e s . I n t h e k - c o s p e c t r a measured a c r o s s t h e w i n d ( F i g u r e 44) t h i s d u a l i t y i s e v i d e n t i n t h e r u n s a t 150 m, b u t the n e g a t i v e peak i s a b s e n t o r much r e d u c e d i n a m p l i t u d e a t t h e o t h e r l e v e l s . T E M P E R A T U R E T ' CROSSWIND 1 4 » i 1 — 1 1— — i 1 0.0 0.1 0.2 0.3 0.4 0.5 S T A N D A R D D E V I A T I O N ( M K S ) FIGURE 41. 0" VS.'Z (CROSSWIND) HUMIDITY Q CROSSWIND a t i I r i i 0.0 0.1 0.2 0.3 0.4 0.5 STANDARD DEVIATION ( M K S ) F I G U R E 4 2 . 0* V S . Z (CROS SWIND) HUMIDITY Q CROSSWIND / 0-4-5 ' 2 / / r i 3 Z1 4 I / / / I f / / / i I 4 » / « / / r — 1 — — — ~ r — 1 1 2.0 2.5 3.0 3.5 4.0 4 . ! LOG 1 0 f l _ M IN METRES) FIGURE.43. (L^) VS. Z (CROSSWIND) 84 FIGURE 44. HEAT FLUX COSPECTRA (CROSSWIND) 85 3.3.6 M o i s t u r e F l u x The t r a c e s o f F i g u r e s 33 and 45 a r e q u i t e s i m i l a r i n g e n e r a l c h a r a c t e r , e x c e p t t h a t t h e b u r s t s o f p o s i t i v e m o i s t u r e f l u x have s h a r p e r s i d e s i n the c r o s s w i n d sample. The same p a t t e r n was n o t i c e d i n t h e v e r t i c a l v e l o c i t y t r a c e s ( F i g u r e s 9 and 3 8 ) , and i t i s n o t d i f f i c u l t t o see t h a t t h e e f f e c t o f a mechanism t e n d i n g t o a l i g n c o n v e c t i v e c e l l s i n one d i r e c t i o n , w h i l e i m p o s i n g no r e s t r i c t i o n s on t h e i r s p a c i n g s i n the o t h e r , w o u l d be t o s h a r p e n t h e t r a n s i t i o n f r o m u p d r a f t t o d o w n d r a f t a c r o s s the a l i g n m e n t d i r e c t i o n . A c o m p a r i s o n o f F i g u r e s 35 and 46 r e v e a l s t h a t t h e wave l e n g t h o f the peak o f kS _ ( k ) i s c o n s i d e r a b l y more h e i g h t dependent i n the wQ measurements a c r o s s t h e w i n d ( F i g u r e 46) t h a n i n t h o s e o b t a i n e d f r o m t r a v e r s e s i n the w i n d d i r e c t i o n ( F i g u r e 3 5 ) . The l i n e drawn on F i g u r e 46, as a c o n v e n i e n t r e p r e s e n t a t i o n o f the b e h a v i o u r o f v e r s u s h e i g h t , can be e x p r e s s e d a s : 1^ 4= 80 ( Z / 1 0 ) ° * 7 metres 86 1 #3/11 500 M #1/11 1.0 (M/SEC)(GM/KGM) O.O 1 20.0 40.0 SECONDS n U U 0.0 ' 20.0 40.0 60.0 SECONDS #3/8 150 M #V8 1.0 20.0 40.0 'GC SECONDS U 0..0 20.0 40.0 ^0. SECONDS #3/5 18 M #1/5 20.0 40.0 SECONDS 20.0 40.0 SECONDS FIGURE 45. MOISTURE FLUX TRACES (CROSSWIND) L O G . n ( Z I N M E T R E S ) o t/1 n pd o to co S3 o cn m ~?3 rn a.5 tn o In • • in 1.0 _ L _ 1.5 2.0 2.5 3.0 o s O TO a cn a 3.5 E D oo 88 3.4 The T u r b u l e n t K i n e t i c E n e r gy Budget • 3.4.1 I n t r o d u c t i o n The t u r b u l e n t k i n e t i c e n e r g y budget o f h o r i z o n t a l l y homogeneous t u r b u - l e n c e w i t h a mean w i n d s h e a r i n t h e v e r t i c a l ( f r o m Lumley and P a n o f s k y , 1964, p. 120) m o d i f i e d f o r t h e e f f e c t o f m o i s t c o n v e c t i o n can be g i v e n b y : I f + f - - u • + 0.61., ?5>T - * f f - I (3.4.1) The measurements made d u r i n g t h i s e x p e r i m e n t do n o t p r o v i d e e s t i m a t e s o f e v e r y t e r m i n t h e k i n e t i c e n e r g y b u d g e t . Some o f the terms a re measured d i r e c t l y ; o t h e r s a r e i n f e r r e d f r o m t h e d a t a c o u p l e d w i t h c e r t a i n p r e v i o u s l y o b t a i n e d r e l a t i o n s ; y e t o t h e r s , w h i c h a r e g e n e r a l l y b e l i e v e d t o be s m a l l , a r e i g n o r e d . The s e c o n d t e r m on t h e l e f t hand s i d e o f E q u a t i o n 3.4.1 i s t h e r a t e o f d i s s i p a t i o n o f t h e k i n e t i c e n e r g y £ . I t i s e s t i m a t e d f r o m t h e s p e c t r a l d e n s i t y o f t h e l o n g i t u d i n a l v e l o c i t y component a t h i g h wave numbers as d i s c u s s e d i n S e c t i o n 3.2.2. S i n c e t h e mean w i n d g r a d i e n t c a n n o t be a c c u r a t e l y d e t e r m i n e d f r o m t h e a i r c r a f t ' s D o p p l e r r a d a r measurements, t h e f i r s t two terms on t h e r i g h t hand s i d e o f 3.4.-1 a r e n o t d i r e c t l y a c c e s s i b l e . The s e c o n d o f t h e s e - v'w' i s n e g l e c t e d on t h e grounds t h a t a t l o w l e v e l s where t h e r e may be an a p p r e c i a b l e w i n d g r a d i e n t v'w' i s n e g l i g i b l e . The f i r s t p r o d u c t i o n t e r m - u'w' j r y i s e s t i m a t e d b y u A /j^Z, a r e l a t i o n w h i c h , s t r i c t l y s p e a k i n g , i s o n l y v a l i d under n e u t r a l c o n d i t i o n s The t e r m (g/=) w'T' i s t h e b u o y a n t p r o d u c t i o n due t o t h e s e n s i b l e h e a t - v'w' I f + (g/-) w'T 89 f l u x , w h i l e 0.61 g w'Q' i s t h e m o i s t u r e f l u x ' s c o n t r i b u t i o n t o the b u o y a n t p r o d u c t i o n . B o t h o f t h e s e a r e d i r e c t l y measured. The t e r m - 1__ ^ w' p' .. has, r e c e n t l y been c a r e f u l l y measured o v e r w a t e r ( E l l i o t t , 1970) and found t o be about 10% o f t h e s h e a r p r o d u c t i o n t e r m a t l e v e l s between 1 m and 4 m. E l l i o t t a l s o measured t h e energy d i v e r g e n c e t e r m + Vw]_e_. H i s r e s u l t s i n d i c a t e t h a t a t t h o s e l e v e l s t h e d i v e r g e n c e and i z p r e s s u r e terras have about t h e same magnitudes arid o p p o s i t e s i g n s . A t t h e l e v e l s b e i n g c o n s i d e r e d h e r e i t i s p r o b a b l e t h a t t h e s e terms a r e more i m p o r t a n t e i t h e r j o i n t l y o r s i n g l y . However, as t h e a i r c r a f t measurements cann o t p r o v i d e any d i r e c t e s t i m a t e o f them i t i s c o n v e n i e n t t o t r e a t them, t o g e t h e r w i t h any o t h e r terms o m i t t e d t h r o u g h t h e i n i t i a l a s s u m p t i o n s , as a c o l l e c t i v e r e s i d u a l t e r m , D. A t some d i s t a n c e f r o m l a n d w i t h a s t e a d y w i n d b l o w i n g o v e r e f f e c t i v e l y i n f i n i t e f e t c h , i f t h e t u r b u l e n t f i e l d i s r e a s o n a b l y h o r i z o n t a l l y homogeneous, t h e l o c a l r a t e o f change o f e n e r g y may be n e g l e c t e d . G e n e r a l l y u n d e r t h e s e c o n d i t i o n s i t i s two o r d e r s o f magnitude l e s s t h a n t h e p r o d u c t i o n and d i s s i p a t i o n terms (Lumley and P a n o f s k y , 1964). I n t h i s s e c t i o n t h e t u r b u l e n t k i n e t i c e nergy b u d g e t i s i n v e s t i g a t e d i n two ways: 1) The h e i g h t dependence o f each term f o r a l l t h e f l i g h t s a n a l y s e d ( S e c t i o n 3.4.2); 2) The b u d g e t f o r f l i g h t s 1 and 3 t a k e n s e p a r a t e l y ( S e c t i o n 3.4.3). 90 3.4.2 H e i g h t dependence o f terms i n K i n e t i c E n e r gy Budget ' u..3 3.4.2.1 M e c h a n i c a l p r o d u c t i o n e s t i m a t e d b y 'ytz F i g u r e 47 i l l u s t r a t e s t h e r a p i d d e c r e a s e o f s h e a r p r o d u c t i o n w i t h i n c r e a s i n g a l t i t u d e . T h i s a r i s e s from two f a c t o r s : t h e measured s t r e s s ( S e c t i o n 3.2.5) d e c r e a s e s w i t h h e i g h t ; and t h e w i n d g r a d i e n t , i n f e r r e d f r o m \ t h e r a t i o o f f r i c t i o n v e l o c i t y t o a l t i t u d e , r a p i d l y d e c r e a s e s . E v i d e n t l y t h e i m p o r t a n c e o f m e c h a n i c a l p r o d u c t i o n i s r e s t r i c t e d t o t h e f i r s t 100 metres o n l y . The v a r i o u s terms o f e q u a t i o n (.3.4.1) a r e t a b u l a t e d i n A p p e n d i x D. 3.4.2.2 Buoyancy P r o d u c t i o n ^g/V ^ Y 7 " and 0.61 g w'Q' The buoyancy p r o d u c t i o n terms a r e summarized f o r a l l t h e f l i g h t s i n F i g u r e s 32 and 37, i n w h i c h t h e t h i r d s c a l e on t h e a b s c i s s a i s i n k i n e m a t i c 2 -3 u n i t s o f energy p r o d u c t i o n (cm s e c ) . A t t h e l o w e s t l e v e l t h e s e terms a r e , i n most c a s e s , an o r d e r o f magnitude s m a l l e r t h a n t h e s h e a r p r o d u c t i o n t e r m , b u t w h i l e t h e l a t t e r d e c r e a s e s r a p i d l y w i t h h e i g h t t h e b uoyancy p r o d u c t i o n terms change l i t t l e . Thus a t h i g h e r l e v e l s (above 100 m) most o f the k i n e t i c e n e r g y i s p r o d u c e d by t h e a c t i o n o f buoyancy. A t i n t e r m e d i a t e and h i g h e r l e v e l s t h e o v e r a l l h e a t f l u x may be n e g a t i v e , b u t i n t h e s e c a s e s the buoyancy p r o d u c t i o n due t o t h e m o i s t u r e f l u x exceeds t h e n e g a t i v e c o n t r i b u t i o n due t o t h e h e a t f l u x . Thus t h e t o t a l buoyancy p r o d u c t i o n was everywhere p o s i t i v e between 18 m and 500 m d u r i n g t h i s e x p e r i m e n t . 3.4.2.3 D i s s i p a t i o n F i g u r e 48 i l l u s t r a t e s t h e dependence o f t h e r a t e o f d i s s i p a t i o n on h e i g h t . A p p a r e n t l y t h e r a t e o f d e c r e a s e o f £ i s v e r y much more r a p i d a t l o w l e v e l s t h a n a t t h e h i g h e r l e v e l s . F i g u r e 48 a l s o i n d i c a t e s t h a t t h e r e d u c t i o n o f € between t h e 18 m l e v e l and t h e 50 m l e v e l i s l e s s p r o n o u n c e d i n t h e 'low' w i n d speed f l i g h t s t h a n i t i s i n t h e o t h e r s . T h i s b e h a v i o u r a t T U R B U L E N T K . £ . . . B U D G E T MECHRNICRL PRODUCTION UPWIND " T 20 -20 AO 60 PRODUCTION OF KINETIC ENERGY in cm2 sec 3 FIGURE 47. MECHANICAL PRODUCTION VS. Z cn U J cr. \— U J CD ED in TURBULENT K..E.. BUDGET DISSIFRJI UPWIND in ni" in in » — -40 -20 fe 3 »5 3 T 0 T 20 40 2 -3 DISSIPATION i n cm sec FIGURE 48. DISSIPATION VS. Z 93 lew l e v e l s r e f l e c t s t h a t o f t h e s h e a r p r o d u c t i o n t e r m ( F i g u r e 47); i . e . where k i n e t i c e n e r g y i s b e i n g p r o d u c e d by- s h e a r t u r b u l e n c e i t i s a l s o b e i n g d i s s i p a t e d . The q u e s t i o n o f w h e t h e r o r n o t a l l t h e s h e a r p r o d u c e d e n e r g y i s d i s s i p a t e d l o c a l l y w i l l be ap p r o a c h e d t h r o u g h t h e magnitude and h e i g h t dependence o f t h e r e s i d u a l t e r m D. 3.4.2.4 The r e s i d u a l term: D = - b'Z (w'e + T w'p') There i s some c o n c e p t u a l d i f f i c u l t y i n d i s c u s s i n g t h i s t e r m w i t h o u t knowing w h e t h e r i t i s dominated b y t h e d i v e r g e n c e o f energy ( + ^ T % ) o r by 0 L t h e w o r k i n g o f t h e p r e s s u r e f o r c e s . I t i s e v i d e n t however ( F i g u r e 49) t h a t i t i s c o n s i d e r a b l y l a r g e r a t l o w l e v e l s t h a n a t h i g h , and i t i s g e n e r a l l y p o s i t i v e b e l o w t h e 150 m l e v e l . T h i s means e i t h e r t h a t e n e r g y i s b e i n g e x p o r t e d upwards t o be d i s s i p a t e d a t l e v e l s above t h e l a y e r o f i n t e n s e s h e a r p r o d u c t i o n o r t h a t t h e r a t e o f w o r k i n g o f t h e p r e s s u r e f o r c e s d e c r e a s e s r a p i d l y w i t h h e i g h t . I n any c a s e i t appears t h a t s h e a r p r o d u c t i o n i s n o t b a l a n c e d l o c a l l y b y v i s c o u s d i s s i p a t i o n . 94 L U U J CD O m a p i " in ru in i n T U R B U L E N T K . E . B U D G E T ~ t ~ -20 RESIDUAL, D 3 *. I. 3 6 20 40 60 2 -3 IMPORT OF KINETIC ENERGY i n cm sec FIGURE 49. DIVERGENCE VS. Z 95 3.4,3 The b u d g e t f o r f l i g h t s 1 and 3 The f i v e terms d i s c u s s e d i n t h e p r e v i o u s s e c t i o n a r e p l o t t e d v e r s u s h e i g h t i n F i g u r e 50 ( f l i g h t // 1) and F i g u r e 51 ( f l i g h t // 3 ) . The h e i g h t dependence o f t h e s e p a r a t e terms h a v i n g j u s t been t r e a t e d a t some l e n g t h , t h e r e l e v a n c e o f t h e s e f i g u r e s l i e s i n t h e i r i l l u s t r a t i o n o f t h e r e l a t i v e i m p o r t a n c e o f t h e f i v e terms f o r a p a r t i c u l a r f l i g h t . A t low l e v e l s t h e b a l a n c e i s e s s e n t i a l l y between s h e a r p r o d u c t i o n . d i s s i p a t i o n and t h e r e s i d u a l t e r m ; a t h i g h e r l e v e l s t h e s h e a r p r o d u c t i o n t e r m i s n e g l i g i b l e and t h e f o u r o t h e r terms a r e comparable i n m a g n i t u d e . I t seems t h e n t h a t t h e s u r f a c e l a y e r s h e a r g e n e r a t e d t u r b u l e n c e i s n o t c o m p l e t e l y d i s s i p a t e d l o c a l l y , b u t some o f i t r i s e x p o r t e d t o h i g h e r l e v e l s and d i s s i p a t e d w i t h r e d u c e d i n t e n s i t y u n t i l , a t about 200 m i n t h e s e d a t a , t h e p r o c e s s i s v i r t u a l l y c o m p l e t e . I f t h e v a l u e o f the K o l m o g o r o f f c o n s t a n t i s 0.55 r a t h e r t h a n t h e v a l u e u s e d (K = 0.48), the n t h e d i s s i p a t i o n e s t i m a t e s o b t a i n e d h e r e a r e 18% too l a r g e . A r e d u c t i o n o f 18% i n £" w i l l d e c r e a s e b u t n o t remove t h e d i f f e r e n c e between d i s s i p a t i o n and s h e a r p r o d u c t i o n . I t appears t h a t t h e o v e r e s t i m a t e o f the d r a g c o e f f i c i e n t o b t a i n e d f r o m t h e e s t i m a t e d d i s s i p a t i o n ( S e c t i o n 3.2.2 and T a b l e 4) may be due, i n p a r t , t o t h e a s s u m p t i o n t h a t e n e r g y i s p r o d u c e d and d i s s i p a t e d a t t h e same r a t e . 96 CO LU c r U J s in cn" in ru" a ru' i n in T U R B U L E N T K . E . B U D G E T -20 FLIGHT NO. 1 UPWIND —r 20 40 60 2 - 3 PRODUCTION, DISSIPATION OR IMPORT in cm sec FIGURE 50. KINETIC ENERGY BUDGET FOR FLIGHT .# 1 97 TURBULENT K . E . BUDGET FLIGHT NO. 3 UPWIND - 2 0 ' 2 - 3 PRODUCTION, DISSIPATION OR IMPORT i n cm sec FIGURE 51, KINETIC ENERGY BUDGET FOR FLIGHT j/ 3 98 3.5 The Temperature-Humidity Correspondence One of the most s t r i k i n g aspects'.of the. data presented was the d i s s i m i l a r i t y of the cospectral shapes of the fluxes of heat and water- vapour. I t may be/ that the correspondence between f l u c t u a t i o n s of temp- erature and humidity w i l l throw some l i g h t on the matter. The instantaneous product of the f l u c t u a t i o n s of temperature and humidity i s displayed i n Figures 52 and 53. From an energetic and p o s i t i v e (at a l l but the l a r g e s t scales) value near the surface, the T'Q' product decreases to a small and intermittent value at intermediate l e v e l s . When i t reappears strongly again i t does so at r e l a t i v e large scale s i z e s , and i t may be e i t h e r p o s i t i v e or negative. I t i s of i n t e r e s t , here, to examine the sig n of the c o r r e l a t i o n i n the d i f f e r e n t areas depicted i n Figures 52 and 53. For t h i s purpose the more pronounced updrafts and downdrafts have been, as before, designated 'U' and 'D'. In general i t seems that the updrafts are associated with a p o s i t i v e temperature-humidity c o r r e l a t i o n while the c o r r e l a t i o n i s usually negative i n the downdrafts. __The time s e r i e s of Figure 52 and 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 ^ of Figure 54 are very s i m i l a r to the corresponding W'T' time s e r i e s (Figure 30) and c o r r e l a t i o n c o e f f i c i e n t s (Figure 31). In Figure 54 i t i s seen that temperature and humidity are p o s i t i v e l y c orrelated at the small scale s i z e s and negatively c o r r e l a t e d at the large s c a l e s i z e s . This observation i s consistent with the observation that the updrafts carry a p o s i t i v e value of r ^ and the downdrafts, a negative value; i . e . the updrafts, containing a i r from close to the surface, are w e l l endowed with the small s c a l e f l u c t u a t i o n s generated by shear turbulence; the downdrafts, on the other hand, consist of a i r whose v e l o c i t y f l u c t u a t i o n s are c h a r a c t e r i s t i c of the l a r g e r ' s c a l e s associated with buoyancy. F l i g h t s 1 and 3 (Figure 54) show no d e f i n i t e height FIGURE 52. T'Q' (t) (UPWIND) VO FIGURE 53. T'Q* (t) (CROSSWIND) 9 101 FIGURE 54. r T n ( k ) (UPWIND) 102 dependence o f t h e wave length,. L a s s o c i a t e d w i t h , t h e change o f s i g n o f r ^ O O T iQ f r o m n e g a t i v e t o p o s i t i v e v a l u e s . Whereas t h e c o r r e s p o n d i n g L v a l u e s f r o m c r o s s w i n d t r a v e r s e s ( F i g u r e 55) i n d i c a t e t h a t L d e c r e a s e s w i t h i n c r e a s i n g "r a l t i t u d e . To c l a r i f y t h i s p o i n t t h e v a l u e s o f L f o r a l l t h e f l i g h t s a r e "r p l o t t e d v e r s u s h e i g h t i n F i g u r e 56 (upwind) and F i g u r e 57 ( c r o s s w i n d ) . I n t h e upwind c a s e L + shows no d e f i n i t e h e i g h t dependence ( t h e v a l u e i n d i c a t e d by 'F' was o b t a i n e d f r o m F l i p d u r i n g f l i g h t 4 ) . The c r o s s w i n d c a s e , on t h e o t h e r hand, behaves i n t h e same way above 150 m b u t i s b o t h a l t i t u d e and w i n d speed dependent b e l o w t h a t h e i g h t . I n g e n e r a l t h e l o w w i n d s p e e d cas e i s t h e more h e i g h t dependent; i n b o t h c a s e s L d e c r e a s e s w i t h h e i g h t . T e m p e r a t u r e p r o f i l e s o b t a i n e d f r o m F l i p showed t h a t t h e n e a r s u r f a c e l a y e r was u n s t a b l e w i t h r e g a r d t o t h e t e m p e r a t u r e g r a d i e n t ; and t h e h u m i d i t y g r a d i e n t i s , o f c o u r s e , n e g a t i v e . T h e r e f o r e b l o b s o f r i s i n g a i r n e a r t h e s u r f a c e a r e warmer and m o i s t e r t h a n t h e i r s u r r o u n d i n g s . A t h i g h e r l e v e l s (500 m) t h e t i m e domain t r a c e s c l e a r l y r e v e a l a l a r g e s c a l e n e g a t i v e t e m p e r a t u r e - h u m i d i t y c o r r e l a t i o n , w h i c h , as we have s e e n , i s due t o d e s c e n d i n g a i r w h i c h i s r e l a t i v e l y warm ( r i s n e g a t i v e , F i g u r e 31) and d r y W X ( r y q i s p o s i t i v e , F i g u r e 3 4 ) . As t h e warm, d r y a i r descends i t mixes w i t h a s c e n d i n g warm m o i s t a i r . Somewhere between t h e s u r f a c e and 500 m t h i s m i x i n g p r o c e s s i s most c o m p l e t e and t h e i n s t a n t a n e o u s T'Q' p r o d u c t i s a minimum ( s e e t h e 150 m l e v e l i n F i g u r e s 52 and 5 3 ) . T h e r e i s no c o r r e s p o n d i n g minimum i n 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 ^ ( k ) a t t h e 150 m l e v e l . T h i s i m p l i e s t h a t t h e a m p l i t u d e s o f t h e 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 o r h u m i d i t y o r b o t h a r e s m a l l e s t a t t h i s l e v e l . Such, minima i n ^ v T ^ G O and 0*Q(Z) have a l r e a d y b e e n n o t i c e d ( S e c t i o n s 3.2.3 and 3.2.4) b u t , due t o t h e . p a u c i t y o f d a t a p o i n t s a t t h e 500 m l e v e l , t h e e v i d e n c e was n o t o v e r w h e l m i n g . The p r o d u c t o f t e m p e r a t u r e and h u m i d i t y i s , o f c o u r s e , d o u b l y s e n s i t i v e t o s u c h  T Q C O R R E L A T I O N C O E F F I C I E N T > 0.0 U P W I N D AB 2 # 25 2 a r r i 1 1 0.0 L.O 2.0 3.0 4.0 5. L 0 G 1 0 + I N M E T R E S ) FIGURE 56. CLJ^. VS. Z (UPWIND) + 11} 105 in in rvi" o in in a TQ CORRELATION COEFFICIENT > 0.0 CROSSWIND 4 1 4 a 1 _ j — I 1 j 1 0.0 1.0 2.0 3.0 4.0 5.0 L 0 G 1 0 ( ! _ • ' , I N M E T R E S ) FIGURE 57. ( L + ) ^ VS. Z (CROSSWIND) 106 minima i n t h e a m p l i t u d e s o f t h e fl u c . t u a t i . o n s o f b o t h T' and Q' ; t h e t r a c e s o f F i g u r e s 52 and 53 e x h i b i t t h i s c l e a r l y Csee a l s o F i g u r e 58}. The minimum i n t h e a m p l i t u d e o f t h e T'Q' p r o d u c t b u t n o t i n t h e v a l u e o f r T Q ^ ^ a t t* i e m ^- e v e^ s u g g e s t s t h a t , d u r i n g t h e m i x i n g p r o c e s s , p a r c e l s o f a i r r e t a i n t h e i r m o i s t u r e and t e m p e r a t u r e s i g n a t u r e s . T h i s , o f c o u r s e , i s the e x p e c t e d r e s u l t , s i n c e t h e o p p o s i t e r e s u l t w o u l d i m p l y t h a t t h e m o l e c u l a r d i f f u s i v i t y o f e i t h e r w a t e r - v a p o u r ' o r h e a t i s comparable t o i t s eddy d i f f u s i v i t y . 107 FIGURE 58. CROSS-SPECTRA OF T' AND Q' (UPWIND) 108 3.6 D i s c u s s i o n of a p o s s i b l e p a t t e r n o f c o n v e c t i v e o r g a n i z a t i o n I n t h e l a s t s e c t i o n i t was shown t h a t a number o f c u r i o u s r e s u l t s , s u c h as t h e minima o f ^ T ' ^ ( Z ) and <0"Q(Z), were c l a r i f i e d somewhat by an examin- a t i o n o f t h e t e m p e r a t u r e - h u m i d i t y c o r r e s p o n d e n c e . However some o f t h e r e s u l t s o f t h e measurements a l o n g t h e w i n d ( S e c t i o n 3.2) and o f t h e c o m p a r i - s o n o f them w i t h measurements a c r o s s t h e w i n d ( S e c t i o n 3.3) i n d i c a t e d t h a t t h e r e were d i f f e r e n c e s between the. measurements made i n t h e w i n d d i r e c t i o n and t h o s e made i n t h e c r o s s w i n d d i r e c t i o n . T h i s i m p l i e s t h a t t h e t u r b u l e n t f i e l d was o r g a n i z e d t o some d e g r e e . I n o r d e r t o t i e t o g e t h e r t h e o b s e r v a t i o n s w h i c h have no r e a d y e x p l a n a t i o n a p a r t i c u l a r p a t t e r n o f c o n v e c t i v e o r g a n i z a t i o n i s s u g g e s t e d . B e f o r e d e s c r i b i n g t h e p a t t e r n i t may be u s e f u l t o summarize t h e o b s e r v a t i o n s d i s c u s s e d b e f o r e , w h i c h p e r t a i n d i r e c t l y t o t h e q u e s t i o n o f c o n v e c t i v e o r g a n - i z a t i o n : a) A t e v e r y l e v e l and i n b o t h f l i g h t d i r e c t i o n s t h e p r o d u c t s W'T'and T'Q' a r e much a l i k e . One p a r t i c u l a r l y i m p o r t a n t a s p e c t o f t h e i r b e h a v i o u r i s the o c c u r r e n c e o f a l a r g e s c a l e n e g a t i v e k - c o s p e c t r a l peak i n a l l cases a l o n g t h e w i n d , b u t n o t i n runs a t 18 m a c r o s s t h e w i n d . b) A l t h o u g h t h e wave l e n g t h a t w h i c h r^, f i r s t becomes p o s i t i v e L + i s i n s e n s i t i v e t o h e i g h t a l o n g t h e w i n d , i t i s n o t a c r o s s t h e w i n d , e x c e p t above 150 m. A c r o s s t h e w i n d t h e low w i n d s p e e d c a s e s a r e a s s o c i a t e d w i t h L + v a l u e s l a r g e r and more h e i g h t dependent t h a n t h e h i g h w i n d s p e e d c a s e s i n s u c h a way t h a t t h e L v a l u e s d e c r e a s e and c o n v e r g e t o a common v a l u e a t and above 150 m. c) The wave l e n g t h o f t h e k - s p e c t r a l peak, o f h u m i d i t y f l u c t u a t i o n s and t h e m o i s t u r e f l u x d i s p l a y no d e f i n i t e h e i g h t dependence i n t h e w i n d d i r e c t i o n , b u t do so a c r o s s t h e w i n d : t h e wave l e n g t h o f t h e k - s p e c t r a l peak o f t h e m o i s t u r e f l u x i n c r e a s e s w i t h h e i g h t l i k e t h a t o f t h e v e r t i c a l v e l o c i t y , b u t more 109 q u i c k l y t h a n t h a t o f t h e h u m i d i t y f l u c t u a t i o n s . I f i t i s assumed t h a t above 50Q. m, b u t s t i l l some d i s t a n c e b e n e a t h c l o u d b a s e , t h e a i r i s q u i t e d r y and t h e t e m p e r a t u r e g r a d i e n t i s v e r y s l i g h t l y s t a b l e ( R o l l , 1965, p . 2 9 2 ) , t h e n a warm m o i s t a l r i s i n g t o t h i s l e v e l w i l l d i s p l a c e d r y a i r , w h i c h d e s c e n d i n g w i l l be s l i g h t l y warmer t h a n i t s s u r r o u n d i n g s . I f i t i s f u r t h e r s u p p o s e d t h a t t h e s u b s i d e n c e i s n o t e v e n l y d i s t r i b u t e d a r o u n d t h e u p d r a f t b u t t e n d s t o be more prono.unced on i t s upwind and downwind s i d e s , t h e n , u s i n g t h e e s t i m a t e d u p d r a f t d i m e n s i o n s o b t a i n e d f r o m t h e t r a c e s o f v e r t i c a l v e l o c i t y ( S e c t i o n 3.3.2), a p o s s i b l e p a t t e r n o f c o n v e c t i v e o r g a n - i z a t i o n emerges. F i g u r e 59 d e p i c t s t h i s p a t t e r n by means o f i s o t a c h s o f v e r t i c a l v e l o c i t y . The d i r e c t i o n s o f t h e l a r g e s c a l e f l u x e s o f s e n s i b l e h e a t and m o i s t u r e a r e i n d i c a t e d i n t h e u p d r a f t s and subsidence, z o n e s , as i s t h e s i g n o f t e m p e r a t u r e - h u m i d i t y c o r r e l a t i o n a t l a r g e s c a l e s . I n t h e a l o n g w i n d s u b s i d e n c e a r e a s t h e d o w n d r a f t s a r e s t r o n g enough t o i m p r e s s on t h e f u l l y t u r b u l e n t r e g i o n b e l o w t h e n e g a t i v e t e m p e r a t u r e - h u m i d i t y c o r r e l a t i o n ; however, i n t h e c r o s s w i n d s u b s i d e n c e a r e a s the d o w n d r a f t s a r e f r e q u e n t l y too weak t o i n f l u e n c e t h e t u r b u l e n c e much b e l o w t h e c o n v e c t i v e l a y e r . As a r e s u l t ; a l o n g w i n d r u n s a l t e r n a t e l y e n c o u n t e r r e g i o n s o f p o s i t i v e h e a t and m o i s t u r e f l u x e s and r ( u p d r a f t s ) and r e g i o n s o f p o s i t i v e m o i s t u r e f l u x and n e g a t i v e h e a t f l u x and r ^ ( d o w n d r a f t s ) . The c r o s s w i n d r u n s , on t h e o t h e r hand, show b a s i c a l l y t h e same p a t t e r n i n t h e c o n v e c t i v e l a y e r , b u t o f t e n f a i l t o e n c o u n t e r r e g i o n s o f n e g a t i v e h e a t f l u x and r^, i n t h e t u r b u l e n t l a y e r . I n t h e w i n d d i r e c t i o n t h e f a c t t h a t t h e wave l e n g t h o f s i g n change o f r ^ i s i n v a r i a n t s u g g e s t s t h a t t h e d e s c e n d i n g warm, d r y a i r a l w a y s s u c c e e d s i i i s e e p i n g down, i n t o t h e t u r b u l e n t s u r f a c e l a y e r . Whereas i n t h e c r o s s w i n d d i r e c t i o n t h e s u c c e s s o f t h e weaker d o w n d r a f t s i n a f f e c t i n g t h e t u r b u l e n t 2 -m goo - 600- ISOTACHS - ARBITRARY UNITS w < 0 w = 0 - w >- 0 4o0 ZOO- o - J e Plan view of suggested convective f i e l d ; showing isotachs of large scale v e r t i c a l v e l o c i t y and the sign of the c o r r e l a t i o n s of w with T and with Q and of T with Q. The p r o f i l e s of p o t e n t i a l temperature and s p e c i f i c humidity are also shown. FIGURE 59. A POSSIBLE PATTERN OF CONVECTIVE ORGANIZATION I l l l a y e r i s less frequent, and, of course, the fewer the penetrations the longer the measured wave length of r ^ ^ s i g n change. Thus, from Figure 57, i t may be t e n t a t i v e l y concluded that i n c r e a s i n g the wind speed increases the e f f e c t i v e n e s s of the downdrafts i n impressing a negative r value on the turbulent l a y e r . Although t h i s i s a paradoxical r e s u l t , as increased turbulence would be expected to reduce the e f f e c t s of convection on the turbulence, i t can be explained i n terms of the observed increase of organization of the convection w i t h wind speed (e.g. Woodcock, 1942). The height dependence of the wave length of the k - s p e c t r a l peak of the humidity f l u c t u a t i o n s and the moisture f l u x i s quite pronounced across the wind but not i n the wind d i r e c t i o n . This can be a t t r i b u t e d to the r e l a t i v e i n t e n s i t y of the moisture fluxes i n the various downdrafts; i . e . i n the downdrafts between successive updrafts along the wind the moisture f l u x i s as strong as i t i s i n the updrafts, whereas i n the downdrafts separating updrafts across the wind d i r e c t i o n i t i s not. Thus, i n runs along the wind, the k-cospectrum of moisture f l u x and the humidity k-spectrum are quite f l a t , making the determination of a peak wave length rather uncertain. Whereas the weaker f l u x encountered i n crosswind downdrafts serves to reduce the s p e c t r a l values at large scales and hence produce a k - s p e c t r a l peak whose wave length i s r e l a t e d to the s i z e and spacing of the large updrafts. The convective pattern postulated above was used to explain a number of curious features of the data presented. I t i s not suggested t h i s pattern i s t y p i c a l of the trade wind zone or even that i t d i d occur during t h i s e x peri- ment; but i t i s suggested that some s i m i l a r pattern could have been associated with a turbulent f i e l d of the kind described herein. 112 CHAPTER 4 SUMMARY OF CONCLUSIONS The purpose of t h i s study was the experimental i n v e s t i g a t i o n of the turbulent atmospheric boundary layer i n the a t l a n t i c trade wind zone. The data were c o l l e c t e d on f i v e consecutive days using a l i g h t a i r c r a f t which was instrumented to measure the fluctuations of temperature, humidity and two components of a i r v e l o c i t y ; the v e r t i c a l component and the component i n the d i r e c t i o n of the a i r c r a f t ' s v e l o c i t y r e l a t i v e to the a i r . During each of the s i x f l i g h t s data were c o l l e c t e d at s e v e r a l a l t i t u d e s between 18 m and 500 m. Spectra of and cross-spectra between the f l u c t u a t i o n s of the four measured parameters (w', u', T' and Q') were computed. The following i s a summary of the r e s u l t s obtained. The fluxes of momentum, heat and moisture The fluxes of moisture and momentum have s i m i l a r single-peaked k- c o s p e c t r a l d i s t r i b u t i o n s below 50 m and the most predominant of the scales responsible f o r the transfers have about the same wave length i n both fluxes at a l l a l t i t u d e s . These wave lengths seem to show a general increase with height i n both cases, but there i s a great deal of s c a t t e r . The s i m i l a r i t y of these fluxes i s also evident from the time domain traces of t h e i r instantaneous values. By contrast, the k-cospectra of the sensible heat f l u x often contain two peaks of opposite s i g n . The p o s i t i v e peak i s at smaller scales than are the peaks of the other flu x e s , while the negative peak occurs at 113 l a r g e r s c a l e s . A p p a r e n t l y buoyancy i n f l u e n c e s t he c o s p e c t r a l d i s t r i b u t i o n o f th e momentum f l u x , b u t , a l t h o u g h 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 and h u m i d i t y p r o d u c e d e n s i t y v a r i a t i o n s w h i c h a r e c o m p a r a b l e , t h e momentum f l u x a p p e ars t o have a g r e a t e r a f f i n i t y f o r t h e r e l a t i v e l y l a r g e s c a l e s o f t h e h u m i d i t y v a r i a t i o n s compared t o t h o s e o f t e m p e r a t u r e . I t i s s u g g e s t e d t h a t t h e momentum f l u x s e e k s the 'path o f l e a s t r e s i s t a n c e ' ; i . e . i f t h e d e n s i t y f l u c t u a t i o n s a r e a s s o c i a t e d w i t h t h e s c a l e s w h i c h t r a n s p o r t momentum most e f f i c i e n t l y , t h e n t h e f l u x e s o f mass and momentum w i l l h a v e s i m i l a r c o s p e c t r a l d i s t r i b u t i o n s ; o t h e r w i s e t h e peak o f t h e k - c o s p e c t r u m o f t h e momentum f l u x w i l l be s h i f t e d , r e l a t i v e t o t h a t o f t h e mass f l u x , towards t h e s c a l e s i z e s w h i c h t r a n s p o r t momentum most e f f i c i e n t l y . 2 The l a t e n t h e a t f l u x measured a t 18 m was 12 mW/cm on a v e r a g e , 2 w h i l e t h e a v e r a g e s e n s i b l e h e a t f l u x a t t h a t l e v e l was o n l y 1.0 mW/cm , i . e . l e s s t h a n 10% o f t h e t o t a l t u r b u l e n t h e a t t r a n s f e r . B o t h f l u x e s d e c r e a s e d w i t h h e i g h t between 18 m and 100 m, b u t , w h i l e t h e s e n s i b l e h e a t f l u x showed a weak tend e n c y t o c o n t i n u e t h i s t r e n d , t h e m o i s t u r e f l u x i n c r e a s e d s l i g h t l y a g a i n about 150 m. I n some ca s e s t h e h e a t f l u x was z e r o o r even n e g a t i v e (downward f l u x ) above 100 m; whereas t h e minimum 2 m o i s t u r e f l u x , a v e r a g e d a t any l e v e l , was about 8 mW/cm ( a t t h e 150 m l e v e l ) . The 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 , h u m i d i t y and t h e v e r t i c a l and l o n g i t u d i n a l v e l o c i t y components The s p e c t r a o f t e m p e r a t u r e , h u m i d i t y and e a c h o f t h e v e l o c i t y components i n v a r i a b l y d i s p l a y e d a -5/3 s l o p e a t h i g h wave numbers. However, c o n s i d e r a t i o n 114 o f t h e a v a i l a b l e e v i d e n c e i n d i c a t e d t h a t t h e flow, was n o t l o c a l l y i s o t r o p i c . The v a l u e o f t h e d r a g c o e f f i c i e n t e s t i m a t e d f r o m nS Cn) was ° uu -3 (2,68 + 1.03) x 10 ; t h e l i m i t s g i v e n a r e one s t a n d a r d d e v i a t i o n on e i t h e r s i d e o f t h e mean. T h i s method o v e r e s t i m a t e d t h e d r a g c o e f f i c i e n t computed by _3 t h e 'eddy c o r r e l a t i o n t e c h n i q u e ' (1.45 + 0.08) x 10 by about 85%. The d r a g c o e f f i c i e n t s g i v e n were e s t i m a t e d f o r 4 runs o f mean w i n d s p e e d between 7 m/sec and 10 m/sec. There a p p e a r e d t o be no d e f i n i t e h e i g h t dependence o f t h e v a r i a n c e o f v e r t i c a l v e l o c i t y ; on t h e o t h e r hand, t h e v a r i a n c e o f t h e l o n g i t u d i n a l v e l o c i t y component showed a g e n e r a l d e c r e a s e w i t h , h e i g h t , b u t t h e r a t i o o f t h e s t a n d a r d d e v i a t i o n o f t h i s component t o t h e f r i c t i o n v e l o c i t y was more o r l e s s i n d e p e n d e n t o f h e i g h t ; w i t h some s c a t t e r t h e mean v a l u e o f t h i s r a t i o was about 2.3. The v a r i a n c e s o f t h e f l u c t u a t i o n s o f b o t h t e m p e r a t u r e and h u m i d i t y d e c r e a s e d by about 40% w i t h h e i g h t up t o about 100 m and i n c r e a s e d by r o u g h l y t h e same amount between 100 m and 500 m. The wave l e n g t h s o f t h e s c a l e s c o n t a i n i n g t h e most e n e r g y showed a d i f f e r e n t h e i g h t dependence f o r each p a r a m e t e r ; t h o s e o f t h e v e r t i c a l v e l o c i t y component i n c r e a s e d as Z^*^"* a p p r o x i m a t e l y , and t h e r e was no e s s e n t i a l d i f f e r e n c e between measurements a c r o s s and a l o n g t h e w i n d ; t h o s e o f t h e h o r i z o n t a l v e l o c i t y component were n o t h e i g h t dependent f o r e i t h e r t h e a l o n g w i n d o r t h e c r o s s w i n d component; t h o s e o f t h e t e m p e r a t u r e f l u c t u a t i o n s i n c r e a s e d as Z®'^~* i n t h e w i n d d i r e c t i o n , b u t were n o t c o n s i s t e n t l y h e i g h t dependent a c r o s s t h e w i n d ; t h o s e o f t h e f l u c t u a t i o n s o f h u m i d i t y were n o t . 45 h e i g h t dependent a l o n g t h e w i n d , b u t i n c r e a s e d about as Z" a c r o s s t h e w i n d . Throughout t h e l a y e r between 18 m and 500 m t h e s p e c t r a o f t h e f l u c t - u a t i o n s o f h u m i d i t y and t h o s e o f t h e h o r i z o n t a l v e l o c i t y component were v e r y s i m i l a r i n shape i n t h e measurements made a l o n g t h e w i n d . The s p e c t r a o f t h e l a t e r a l v e l o c i t y component c o n t a i n e d more low f r e q u e n c y energy t h a n t h o s e o f t h e v e r t i c a l v e l o c i t y - component b u t l e s s t h a n t h o s e o f t h e l o n g i t - u d i n a l v e l o c i t y component. The s p e c t r a o f t h e t e m p e r a t u r e f l u c t u a t i o n s were u n i q u e : a t l o w l e v e l s t h e s m a l l s c a l e s ( t h o s e h a v i n g wave numbers l a r g e r t h a n t h a t o f t h e peak o f t h e v e r t i c a l v e l o c i t y k - spectrum) c o n t a i n e d most o f t h e e n e r g y ; h i g h e r up a low f r e q u e n c y peak app e a r e d and, i n g e n e r a l , grew w i t h h e i g h t , so t h a t a t i n t e r m e d i a t e l e v e l s ( a b o u t 50 m t o 150 m) t h e two peaks were about e q u a l and a t t h e t o p l e v e l (500 m) t h e low f r e q u e n c y peak was t h e l a r g e r . The k i n e t i c e n e r g y budget The buoyancy p r o d u c t i o n terms were d i r e c t l y measured; t h e d i s s i p a t i o n was i n f e r r e d f r o m t h e s p e c t r a l e n e r g y d e n s i t y i n t h e '-2/3 r e g i o n ' o f t h e k - s p e c t r u m o f t h e l o n g i t u d i n a l v e l o c i t y component; s h e a r p r o d u c t i o n was e s t i m a t e d u s i n g t h e measured f r i c t i o n v e l o c i t y and an assumed l o g a r i t h m i c w i n d p r o f i l e ; t h e o t h e r terms o f t h e e n e r g y b u d g e t were lumped t o g e t h e r as a ' r e s i d u a l ' term. A t t h e l o w e r l e v e l s (18 m and 50 m) t h e b a l a n c e was between s h e a r p r o d u c t i o n , d i s s i p a t i o n and t h e r e s i d u a l t e r m ; a t h i g h e r l e v e l s t h e s h e a r p r o d u c t i o n t e r m was n e g l i g i b l e and the buoyancy terms were comparable t o t h e d i s s i p a t i o n and r e s i d u a l t e r m s . I t was c o n c l u d e d t h a t t h e k i n e t i c e n e r g y g e n e r a t e d by the v e l o c i t y s h e a r n e a r t h e s u r f a c e i s p r o b a b l y n o t a l l d i s s i p a t e d l o c a l l y . C o n v e c t i v e o r g a n i z a t i o n Measurements made d u r i n g f l i g h t s i n t h e w i n d d i r e c t i o n o f t h e 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 and h u m i d i t y a t a l l l e v e l s y i e l d e d a p o s i t i v e c o r r e l a t i o n between them a t s m a l l s c a l e s and a n e g a t i v e one a t l a r g e ( i n e x c e s s o f 100 m) s c a l e s . I t was s u g g e s t e d t h a t t h i s i s due t o a p o s i t i v e 116 gradient of p o t e n t i a l temperature and a negative s p e c i f i c humidity gradient above the highest (500 m) l e v e l . Measurements made across the wind, on the other hand, i n d i c a t e d a s i m i l a r pattern except at the lowest l e v e l , where a negative temperature-humidity c o r r e l a t i o n c o e f f i c i e n t occurred only at the la r g e s t scales i n v e s t i g a t e d . The c o r r e l a t i o n c o e f f i c i e n t between v e r t i c a l v e l o c i t y and temperature behaved i n a s i m i l a r fashion. I t was speculated that there may have been a c e r t a i n amount of organ- i z a t i o n of the convective elements. The a v a i l a b l e evidence suggested that the convective c e l l s tended to l i n e up i n the d i r e c t i o n of the mean wind, which, as f a r as could be determined from the Doppler radar measurements, did not change d i r e c t i o n appreciably between 18 m and 500 m. 117 L I S T OF REFERENCES B a l l , F.K. ( 1 9 6 0 ) . . C o n t r o l o f i n v e r s i o n h e i g h t b y s u r f a c e h e a t i n g . Q u a r t . J . Roy. M e t e o r o l . S o c . , 8 6 , p.483. Blackman, R.B. and J.W. Tukey ( 1 9 5 8 ) . The Measurement o f Power S p e c t r a . Dover, New Y o r k . BOMEX P r o j e c t O f f i c e , ( 1 9 6 9 ) . Bomex b u l l e t i n No. 3. U.S. Dept. o f Commerce, E n v i r o n . S c i . S e r v i c e s Admin., R o c k v i l l e , Md. B u n k e r , A.F., ( 1 9 5 5 ) . T u r b u l e n c e and S h e a r i n g S t r e s s e s Measured Over t h e N o r t h A t l a n t i c by an A i r p l a n e A c c e l e r a t i o n T e c h n i q u e , J. M e t e o r . 12_, 445. B u n k e r , A.F., ( 1 9 5 7 ) . A i r c r a f t (PBY-6A) F l u c t u a t i o n and F l u x D a t a - Woods H o l e O c e a n o g r a p h i c I n s t i t u t i o n , Sec. 5.3 i n E x p l o r i n g t h e Atmosphere's F i r s t M i l e , (H. L e t t a u and B. D a v i d s o n , eds.) Pergamon P r e s s , London and New Y o r k . B u n k e r , A.F., ( 1 9 6 0 ) . Heat and Water Vapor F l u x e s i n A i r F l o w i n g Southward Over t h e W e s t e r n N o r t h A t l a n t i c Ocean, J. M e t e o r . , JL7, 52. D a s c h e r , A.J., ( 1 9 6 6 ) . NCAR A i r c r a f t R e s e a r c h I n s t r u m e n t a t i o n System ( A R I S ) . I n t e r n a l r e p o r t , F a c i l i t i e s D i v i s i o n , N a t i o n a l C e n t r e f o r A t m o s p h e r i c R e s e a r c h , B o u l d e r , C o l o r a d o . D a v i d s o n , B., ( 1 9 6 8 ) . The Barbados O c e a n o g r a p h i c and M e t e o r o l o g i c a l E x p e r i - ment, B u l l . Amer. M e t e o r o l . S o c , 49, 928-934. D u t t o n , J.A. and D.H. Lenschow, ( 1 9 6 2 ) . An a i r b o r n e m e a s u r i n g s y s t e m f o r m i c r o m e t e o r o l o g i c a l s t u d i e s , A n n u a l R e p o r t , C o n t r a c t No. DA-36-039-SC- 80282, Dept. o f M e t e o r . , U n i v . o f W i s . , M a d i s o n , Wis. E l l i o t t , J.A., ( 1 9 7 0 ) . M i c r o s c a l e p r e s s u r e f l u c t u a t i o n s measured w i t h i n t h e l o w e r a t m o s p h e r i c boundary l a y e r . Ph.D. D i s s e r t a t i o n , U n i v e r s i t y of B r i t i s h C o l u m b i a . G a r r e t t , J.F., ( 1 9 7 0 ) . F i e l d o b s e r v a t i o n s o f f r e q u e n c y domain s t a t i s t i c s and n o n l i n e a r e f f e c t s i n w i n d - g e n e r a t e d ocean waves. Ph.D. D i s s e r t a t i o n , U n i v e r s i t y o f B r i t i s h C o l u m b i a . G r a n t , H.L., R.W." S t e w a r t and A. M o i l l i e t , ( 1 9 6 2 ) . T u r b u l e n c e s p e c t r a from a t i d a l c h a n n e l . J. F l u i d Mech., 12-, P t . 2, p.241. H i n z e , .J/0.-, ( 1 9 5 9 ) . T u r b u l e n c e . M c G r a w - H i l l , New Y o r k . K a t z , I . , ( 1 9 7 0 ) . A c o m p a r i s o n of remote and i n - s i t u measurement i n c o n v e c t i o n . To be p r e s e n t e d a t t h e 1 4 t h Weather Radar C o n f e r e n c e , Tucson, A r i z o n a i n November. \ 118 Kolmogorov, A.N., ( 1 9 4 1 ) . The l o c a l s t r u c t u r e o f t u r b u l e n c e i n i n c o m p r e s s i b l e v i s c o u s f l u i d f o r v e r y l a r g e R e y n o l d s numbers. D o k l a d y ANSSSR, _30_, p.301. K o n r a d , T.G., ( 1 9 7 0 ) . The dynamics o f t h e c o n v e c t i v e p r o c e s s i n t h e c l e a r a i r as s e e n by r a d a r . To be p r e s e n t e d a t t h e 1 4 t h Weather Radar C o n f e r e n c e , T u c s o n , A r i z o n a i n November. K u e t t n e r , J .P., and J . H o l l a n d , ( 1 9 6 9 ) . The BOMEX P r o j e c t , B u l l . Amer. M e t e o r o l . Soc., 50, 394-402. K u k h a r e t s , V.P., and L.R. T s v a n g , ( 1 9 6 9 ) . S p e c t r a o f t h e t u r b u l e n t h e a t f l u x i n t he a t m o s p h e r i c boundary l a y e r . I z v . , A t m o s p h e r i c and O c e a n i c P h y s i c s , V o l . 5, No. 11, 1969, pp. 1132-1142, t r a n s l a t e d by A l l e n B. Kaufman. K u p r o v , B.M. and L.R. Tsvang, ( 1 9 6 5 ) . D i r e c t measurements o f t h e t u r b u l e n t h e a t f l u x f r o m an a i r c r a f t , B u l l . ( I z v . ) Acad. S c i . USSR, A t m o s p h e r i c and O c e a n i c P h y s i c s , 1, No. 6. Lappe, U.O., B. D a v i d s o n and C.B. N o t e s s , ( 1 9 5 9 ) . A n a l y s i s o f a t m o s p h e r i c t u r b u l e n c e s p e c t r a o b t a i n e d f r o m c o n c u r r e n t a i r p l a n e and t o w e r measure- ments. I n s t . A e r o . S c i . Rep., No. 59-44. Lumley, J . L . and H.A. P a n o f s k y , ( 1 9 6 4 ) . The S t r u c t u r e o f A t m o s p h e r i c T u r b u l e n c e . I n t e r s c i e n c e P u b l i s h e r s , New Y o r k . McBean, G.A., ( 1 9 7 0 ) . 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. D i s s e r t a t i o n , U n i v e r s i t y o f B r i t i s h C o l u m b i a . M i y a k e , M., M. D o n e l a n , G. McBean, C. P a u l s o n , F. B a d g l e y , and E. L e a v i t t , ( 1 9 7 0 a ) . C o m p a r i s o n o f t u r b u l e n t f l u x e s o v e r w a t e r d e t e r m i n e d by p r o f i l e and eddy c o r r e l a t i o n t e c h n i q u e s , Q u a r t . J . Roy. M e t e o r . S o c , 96, pp. 132-137. M i y a k e , M., M. D o n e l a n , and Y. M i t s u t a , ( 1 9 7 0 ) . A i r b o r n e measurement of t u r b u l e n t f l u x e s , J . Geophys. R e s e a r c h , 75_, No. 24, pp. 4506-4518 M i y a k e , M., R.W. S t e w a r t , and R.W. B u r l i n g , ( 1 9 7 0 c ) . S p e c t r a and c o s p e c t r a o f t u r b u l e n c e o v e r w a t e r , Q u a r t . J . Roy. M e t e o r . S o c , £ 6 , pp. 138-143. M i y a k e , M., and G. McBean, ( 1 9 7 0 ) . On t h e measurement o f h u m i d i t y t r a n s p o r t o v e r l a n d , Boundary L a y e r M e t e o r o l o g y , . 1, pp. 88-101. M o n i n , A.S., ( 1 9 6 2 ) . E m p i r i c a l d a t a on t u r b u l e n c e i n t h e s u r f a c e l a y e r o f t h e atmosphere. J . Geophys. R e s e a r c h , 6_7, p.3103. M o n i n , A.S., and A.M. Obukhov, ( 1 9 5 4 ) . B a s i c r e g u l a r i t y i n t u r b u l e n t m i x i n g i n t h e s u r f a c e l a y e r o f t h e atmosphere. Trudy Geophys. I n s t . ANSSSR, No. 24, p.163. Myrup, L.O., ( 1 9 6 5 ) . The S t r u c t u r e o f T h e r m a l C o n v e c t i o n i n t h e Lower Atmos- p h e r e Under C o n d i t i o n s o f L i g h t Winds and S t r o n g S u r f a c e H e a t i n g . Ph.D. T h e s i s , U n i v . o f C a l . a t Los A n g e l e s , Los A n g e l e s , C a l . Obukhov, A.M., ( 1 9 5 1 ) . I n v e s t i g a t i o n s o f t h e m i c r o s t r u c t u r e o f t h e w i n d i n • t h e atmosphere n e a r t h e s u r f a c e . I z v . , ANSSSR Geophys. S e r . , No. 3, p. 49. 119 P a n o f s k y , H.A. , and E. M a r e s , ( 1 9 6 8 ) . R ecent measurements o f c o s p e c t r a o f h e a t - f l u x and s t r e s s . Q u a r t . J . Roy. M e t e o r o l . S o c , 9_4, 402, p.581. Payne, F.R., and J.L. Lumley, ( 1 9 6 6 ) . 1-D s p e c t r a d e r i v e d f r o m an a i r b o r n e h o t - w i r e anemometer. Q u a r t . J . Roy. M e t e o r o l . Soc., 92, 393, p.397. Pond, S., R.W. S t e w a r t and R.W. B u r l i n g , ( 1 9 6 3 ) . T u r b u l e n c e s p e c t r a i n w i n d o v e r waves. J . Atmosph. S c i . , 20, p.319. P r i e s t l e y , C.H.B., ( 1 9 5 9 ) . T u r b u l e n t t r a n s f e r i n t h e l o w e r atmosphere. U n i v e r s i t y o f C h i c a g o P r e s s , C h i c a g o . R o b i n s o n , G.D., ( 1 9 5 9 ) . V e r t i c a l m o t i o n and t h e t r a n s f e r o f h e a t and momentum n e a r t h e ground. Advances i n G e o p h y s i c s , 6_, p. 259. R o l l , H.U., ( 1 9 6 5 ) . P h y s i c s o f t h e M a r i n e Atmosphere. Academic P r e s s , New Y o r k . R u d n i c k , P., ( 1 9 6 4 ) . F L I P : an o c e a n o g r a p h i c buoy. S c i e n c e , 146, pp. 1268-1273. S h e i h , C., ( 1 9 6 9 ) . A i r b o r n e h o t - w i r e measurements o f t h e s m a l l - s c a l e s t r u c t u r e o f a t m o s p h e r i c t u r b u l e n c e . Ph.D. D i s s e r t a t i o n , P e n n s y l v a n i a S t a t e U n i v e r s i t y . S m i t h , S., ( 1 9 6 7 ) . T h r u s t anemometer measurements o f w i n d - v e l o c i t y s p e c t r a and o f R e y n o l d s s t r e s s o v e r a t i d a l i n l e t . J . Mar. Res., 25_ ( 3 ) . pp. 239-262. T a y l o r , G.I., (1954) The D i s p e r s i o n o f M a t t e r i n T u r b u l e n t Flow Through a P i p e . P r o c . Roy. Soc. S e r i e s A, V o l . c c x x i i i , pp. 446-468 T e l f o r d , J.W., and J . Warner, ( 1 9 6 2 ) . On t h e measurement from an a i r c r a f t o f buoyancy and v e r t i c a l a i r v e l o c i t y i n c l o u d . J . Atmos. S c i . , 19, pp. 415- 423. von M i s e s , R. , ( 1 9 4 5 ) . Theory o f F l i g h t . 629 pp., Dover P u b l i c a t i o n s I n c . , New Y o r k . V u l ' f s o n , N . I . , ( 1 9 6 1 ) . A Study o f C o n v e c t i v e M o t i o n s i n a F r e e Atmosphere, Acad. S c i . USSR P u b l i s h i n g House. W e i l e r , H.S., and R.W. B u r l i n g , ( 1 9 6 7 ) . D i r e c t measurements of s t r e s s ^ a n d s p e c t r a o f t u r b u l e n c e i n t h e boundary l a y e r o v e r t h e s e a . J . Atmos. S c i . , 24-, (6) pp. 653-664. Woodcock, A.H. , ( 1 9 4 2 ) . S o a r i n g o v e r t h e open s e a . S c i . M o n t h l y , 55_, pp.226- 232. 120 APPENDIX A THE INSTRUMENTS A.1 I n t r o d u c t i o n The i n s t r u m e n t a t i o n and method o f c o r r e c t i o n f o r t h e a i r c r a f t ' s m o t i o n a r e d e s c r i b e d by M i y a k e e t a l (1970b). However, t h e i r c o n c e r n was l a r g e l y w i t h the d e t e r m i n a t i o n o f t h e v e l o c i t y components and t h e momentum f l u x . Inasmuch as s e v e r a l o f t h e r e s u l t s o f t h i s t h e s i s h i n g e on t h e measurement o f the f l u x e s o f s e n s i b l e and l a t e n t h e a t , i t i s a d v i s a b l e t o a t t e m p t t o a s s e s s t h e a c c u r a c y , r e s o l u t i o n and f r e q u e n c y r e s p o n s e o f t h e t e m p e r a t u r e and h u m i d i t y s e n s o r s . A.2 The t e m p e r a t u r e s e n s o r T h i s d e v i c e , c o n s t r u c t e d i n t h i s l a b o r a t o r y , c o n s i s t e d o f a t h e r m i s t o r b e a d i n a DC Wheats tone b r i d g e . The p r i m a r y b a s i s f o r c h o i c e o f b e a d was i t s s m a l l t h e r m a l l a g ; V i c t o r y E n g i n e e r i n g Company's t h e r m i - s t o r model 41 A 401C was f o u n d t o be q u i t e s u i t a b l e . I t has a n o m i n a l d i a m e t e r o f YL1 /*• and r e s i s t a n c e and r e s i s t a n c e change p e r C° a t 25 degrees c e n t i g r a d e o f 10 and 360 TU r e s p e c t i v e l y . The p r o b e c u r r e n t o f 5^A amps was s e l e c t e d by w i n d t u n n e l t e s t i n g t o e n s u r e adequate s e n s i t i v i t y t o t e m p e r a t u r e and i n s i g n i f i c a n t r e s p o n s e t o v e l o c i t y f l u c t u a t i o n s (the'anemometer e f f e c t ' ) . The c u r r e n t was p r o v i d e d by an a l k a l i n e b a t t e r y (9.7 v o l t s ) and l i m i t e d by f i x e d b r i d g e arms o f 2.2 M-fi-so t h a t f o r t e m p e r a t u r e f l u c t u - a t i o n s o f 6 C° t h e p r o b e c u r r e n t v a r i e d l e s s t h a n 0.01%. Mean temper- a t u r e o f f s e t was a c h i e v e d by means of a t e n t u r n p o t e n t i o m e t e r i n t h e f o u r t h b r i d g e arm. The b r i d g e o u t p u t was b u f f e r e d by a h i g h impedence u n i t y g a i n s t a g e ( v o l t a g e f o l l o w e r ) and t h e n a m p l i f i e d i n two s t a g e s , 121 t h e s e c o n d o f w h i c h was a d j u s t a b l e t o g i v e an o v e r a l l s e n s i t i v i t y o f e i t h e r 1.4 o r 3.2 C°/volt a p p r o x i m a t e l y . The n o i s e l e v e l was about 0.5 mv, w h i c h i s e q u i v a l e n t t o a s i g n a l l e v e l o f about 0.001 C°. The t h e r m i s t o r was c a l i b r a t e d i n the l a b o r a t o r y ; a l s o t h e ' i n s i t u ' r e s i s t a n c e v e r s u s t e m p e r a t u r e r e s p o n s e was d e t e r m i n e d by comparing t h e t r a c e s o f t h e t h e r m i s t o r and a s t a n d a r d a i r b o r n e therm- ometer d u r i n g a s o u n d i n g ; b o t h ' c a l i b r a t i o n s p r o d u c e d e s s e n t i a l l y the same r e s u l t . A l t h o u g h the mean r e s p o n s e i s non l i n e a r , t h e d e v i c e i s e s s e n t i a l l y l i n e a r f o r s m a l l ( < 3 C°) f l u c t u a t i o n s . The r e s p o n s e o f t h e i n s t r u m e n t was measured d i r e c t l y i n t h r e e ways: two i n t h e w i n d t u n n e l and one i n t h e f i e l d . The f i r s t w i n d t u n n e l method was t o s u p e r i m p o s e a s t e p v o l t a g e d e c r e a s e on the b r i d g e v o l t a g e and r e c o r d t h e c o o l i n g r e s p o n s e on c h a r t p a p e r ; the t i m e c o n s t a n t was deduced from t h e e x p o n e n t i a l decay t r a c e . I n t h e s e c o n d method t h e t h e r m i s t o r and a t h i n w i r e r e s i s t a n c e thermometer ( r e s p o n s e f l a t t o 20 kHz) were p l a c e d i n t h e wake o f a h e a t e d s o l d e r i n g i r o n ; t h e c u t - o f f o f a low p a s s RC f i l t e r i n the o u t p u t o f t h e r e s i s t a n c e thermometer was a d j u s t e d u n t i l the o u t p u t s o f b o t h i n s t r u m e n t s p r o d u c e d t h e most s i m i l a r c h a r t r e c o r d s . B o t h t e s t s i n d i c a t e d a c u t - o f f f r e q u e n c y (-3 db p o i n t ) n e a r 30 Hz. The f i e l d t e s t r e l i e s on a c o m p a r i s o n o f a measured t e m p e r a t u r e s p e c t r u m w i t h i t s w e l l e s t a b l i s h e d f o r m i n t h e i n e r t i a l s u b-range ( F i g u r e 60) w h i c h i s known t o e x t e n d w e l l beyond 30 Hz. I f t h e f r e q u e n c y r e s p o n s e i n f e r r e d from t h e w i n d t u n n e l t e s t s i s used t o c o r r e c t t h e measured s p e c t r u m , t h e r e s u l t , shown i n F i g u r e 6 0 , l e n d s c r e d e n c e t o t h e r e p r e s e n t a t i o n o f t h e t h e r m i s t o r ' s r e s p o n s e as s i m i l a r t o t h a t o f a s i m p l e low pass f i l t e r w i t h a f r e q u e n c y c u t - o f f o f 30 Hz. 122 FIGURE 60. THE FREQUENCY RESPONSE OF THE THERMISTOR There a r e two f u r t h e r p roblems a s s o c i a t e d w i t h t h e use on a i r c r a f t o f an exposed, s l i g h t l y h e a t e d s e n s o r f o r t h e measurement o f t e m p e r a t u r e : one i s f r i c t i o n a l - c o m p r e s s i o n a l h e a t i n g and t h e o t h e r i s t h e 'anemometer e f f e c t ' . F o r t u n a t e l y t h e s e a c t i n o p p o s i t i o n ; an i n c r e a s e i n a i r speed i n c r e a s e s t h e f r i c t i o n a l - c o m p r e s s i o n a l h e a t i n g and a t t h e same t i m e r e d u c e s t h e s e l f h e a t i n g by i m p r o v i n g t h e v e n t i l a t i o n ; thus t h i s c i r c u m - s t a n c e can be employed i n t h e d e s i g n t o make an exposed b e a d thermometer q u i t e i n d i f f e r e n t t o v e l o c i t y f l u c t u a t i o n s . However i n t h i s case the ap p r o a c h t a k e n was a c a u t i o u s one: t h e anemometer e f f e c t was made n e g l i - g i b l e w i t h t h e i n t e n t i o n o f c o r r e c t i n g f o r t h e f r i c t i o n a l - c o m p r e s s i o n a l h e a t i n g i n t h e a n a l y s i s i f t h i s p r o v e d n e c e s s a r y . I t i s o f i n t e r e s t t o examine t h e i m p o r t a n c e o f t h e s e two e f f e c t s . The w i d e l y used h o t - w i r e anemometer e q u a t i o n s ( H i n z e , 1959, p. 78) p r o v i d e an e s t i m a t e o f 6.6 x 10 ^ C° f o r t h e s e l f h e a t i n g a t t h e a i r c r a f t ' s p e e d (70 m/sec), and i n d i c a t e t h a t t h e a p p a r e n t t e m p e r a t u r e s e n s i t i v i t y t o v e l o c i t y changes i s o n l y -4.5 x 10 ^ C° (m/sec) and i s p r o p o r t i o n a l t o t h e s q u a r e o f t h e p r o b e c u r r e n t . E v i d e n t l y t h e l a t t e r e f f e c t i s n e g l i g i b l e , and t h e i n - f l i g h t e x c e s s t e m p e r a t u r e i s t h e r e f o r e due t o f r i c t i o n a l - c o m p r e s s i o n a l h e a t i n g . A t l i g h t a i r c r a f t s p e e d s , as a rough a p p r o x i m a t i o n , t h e a c t u a l s e n s o r o v e r h e a t T^, due t o f r i c t i o n a l - c o m p r e s s i o n a l h e a t i n g , i s assumed t o be p r o p o r t i o n a l t o t h e s q u a r e o f t h e a i r speed. S i n c e T^ was o b s e r v e d t o be 1.9 C° a t 70 m/sec, t h e c o n s t a n t o f p r o p o r t i o n a l i t y i s -4 o -2 3.9 x 10 C (m/sec) . Thus t h e t e m p e r a t u r e s e n s i t i v i t y t o v e l o c i t y —2 ~ 1 changes i s 5.4 x 10 C (m/sec) a t the same a i r c r a f t s p e e d . O b v i o u s l y the v e l o c i t y c o n t a m i n a t i o n due t o f r i c t i o n a l - c o m p r e s s i o n a l h e a t i n g i s n o t n e g l i g i b l e , and, w i t h t y p i c a l maximum v e l o c i t y changes o f 124 2m/sec occurring with, temperature f l u c t u a t i o n s of about 1C , i t reduces the equivalent s i g n a l to noise r a t i o to ten (20 db). Although i t i s a r e l a t i v e l y simple matter to remove the e f f e c t of f r i c t i o n a l - c o m p r e s s i o n a l heating i n the d i g i t a l a n a l y s i s , i t was regarded as unnecessary. I t i s i n t e r e s t i n g to note that, merely by increasing the probe current one hundred-fold, the two v e l o c i t y e f f e c t s would counter- balance each other and, of course, the bridge s e n s i t i v i t y wo\ild increase with the-probe current. Such an increase of the probe current would produce an overheat of 6.6 C°. A.3 The humidiometer The Lyman-Alpha humidiometer used i n this experiment i s described by Miyake et a l (1970b). As stated by them the primary f a c t o r which l i m i t e d the response to small scale humidity f l u c t u a t i o n s was the mixing of a i r i n the i n l e t tubing and instrument housing. Because of the 'S' bend i n the tygon i n l e t tube, i t i s d i f f i c u l t to determine t h e o r e t i c a l l y the exact t r a n s f e r function of the a i r passage. However Taylor (1954) has shown that i n turbulent flow i n a s t r a i g h t pipe the impulse response of the pipe i s gaussian. In terms of the s p e c t r a l amplitude t r a n s f e r 2 function H. N = e ^ B n ^ , where B was estimated to be about 0.01. (n; However, t h i s t r a n s f e r function produces a cut-of f which i s f a r sharper than that observed. I t i s presumed that the many sharp bends i n the tube aire the cause of t h i s . I t was found, by comparison of the measured spectra with the expected -2/3 slope, that the t r a n s f e r function of the tube could be reasonably w e l l represented by: H T(n) = [ 1 - An J [ o ] An ^ 1 An ^ 1 125 Where the value of A represents the degree of turbulent d i f f u s i o n over the length of the tube and depends on the flow rate through i t . Turbu- lent d i f f u s i o n , therefore, acts to smooth,rapid changes i n moisture content symmetrically i n both d i r e c t i o n s along the axis of the tube with respect to the frame of reference moving with the mean flow. Thus, there i s i d e a l l y no phase s h i f t associated with the amplitude reduction. In Figure 61 a measured humidity spectrum nS ^(n) and a corrected spectrum are displayed. The value of A (0.023) was selected from a l l the spectra so that the t r a n s f e r function would be s i g n i f i c a n t l y d i f f e r e n t from unity at the point where the measured spectrum f a l l s beneath the -2/3 l i n e . I t i s seen that the corrected spectrum follows the commonly observed -2/3 law i n the same region as the downwind v e l o c i t y component (Figure 14) lending credence to the postulated approximate i n l e t tube t r a n s f e r function. As with the other turbulence sensors., the p r a c t i c e of ' i n s i t u ' c a l i b r a t i o n was observed whenever p o s s i b l e . In this case the standard of comparison was the spectrum obtained from a laboratory c a l i b r a t e d Bendix Dew Point Hygrometer. Neither the c a l i b r a t i o n s of these two instruments nor the r e l a t i o n between them i s l i n e a r , but for small excursions about a mean value the e f f e c t of n o n - l i n e a r i t y i s unimportant. Dr. S. Pond of Qvegon State U n i v e r s i t y has computed spectra, from a record obtained by the Lyman Alpha Humidiometer, using f i r s t a c a l i b r a t i o n constant and then the actual logarithmic dependence of the detector current on the moisture content: he reports (personal communication) that there i s no s i g n i f i c a n t d i f f e r e n c e for f l u c t u a t i o n s of one or two gm/Kgm about a mean value ten times as great. Consequently no attempt has been made to l i n e a r i z e the humidiometer records used herein. The n o n - l i n e a r i t y of the 126 0- I 1 0 too //z. n FIGURE 61. THE FREQUENCY RESPONSE OF THE HUMIDIOMETER 127 dew point hygrometer arises i n i t s thermistor detection c i r c u i t ; however, from the c a l i b r a t i o n curve i t i s evident that the n o n - l i n e a r i t y i s not i n excess of 2% for 10% deviations from the mean value. Hence the appropriate slope of the c a l i b r a t i o n curve was used to c a l i b r a t e the spectrum of Figure 61, but the curve i t s e l f was used i n the computation of the soundings of Figure 5. The s p e c t r a l comparison y i e l d s the humidiometer c a l i b r a t i o n i n terms of dew point f l u c t u a t i o n s . From the Clausius-Clapeyron equation the following approximate r e l a t i o n s between the average (overbar) and f l u c t u a t i n g (primed) parts of the dew point and the s p e c i f i c humidity are obtained (see McBean, 1970): \273 + Id } Where P i s the atmospheric pressure i n m i l l i b a r s . Q i s the s p e c i f i c humidity i n Kgm/Kgm. Td i s the dew point i n ^C. The humidiometer was mounted i n the cabin and vented by means of an impact tube on the top of the fuselage (see Miyake et a l , 1970 b), In the d i g i t a l analysis the time delay due to the l o n g i t u d i n a l separation of the humidiometer from the other turbulence sensors was removed by advancing the humidiometer record by the appropriate number of samples. In Q P 0.622 Q T 19.9 128 APPENDIX B DATA PROCESSING B . l Introduction A l l the spectra and time s e r i e s presented herein were computed from the o r i g i n a l analogue recorded data. Spectra for a few runs were computed from the data recorded d i g i t a l l y merely to check the c a l i b r a t i o n of the analogue tape recorder and subsequent conversion to d i g i t a l format. In the following sections of this Appendix the method of s e l e c t i o n of data segments i s described, and the d i g i t i z a t i o n and sub-r.-. sequent machine processing i s o u t l i n e d . B.2 S e l e c t i o n of data segments F i r s t the channels to be d i g i t i z e d were reproduced on a s i x pen chart recorder and examined for noise, dropout and changes of zero b i a s . Each data segment, or run, was s e l e c t e d between successive turns ( r o l l angle) and/or to avoid a l l of these d i s c o n t i n u i t i e s i n the data. In some cases, when bursts of noise i n the temperature record were the only b l o t s on an otherwise e x c e l l e n t run, the run was used anyway and the r e s u l t s i n v o l v i n g temperature f l u c t u a t i o n s were rejected. I f the temperature record i s applied to the input of an audio a m p l i f i e r with speaker, the bursts of noise are recognised as radio pick-up from the Queen A i r ' s UHF trans- m i t t e r (1230 M Hz). In f a c t the p i l o t ' s voice i s about as c l e a r as i t would be from a cheap portable radio. Evidently the thermistor probe and supports acted as an antenna, and the n o n - l i n e a r i t y of the thermistor i t s e l f p a r t i a l l y r e c t i f i e d the c a r r i e r , thereby demodulating i t . The p i t c h angle record also played an important part i n the s e l e c t i o n of the s t a r t of each run. During the 90 degree turns the c e n t r i f u g a l 129 f o r c e on t h e g y r o s c o p e ' s b a i l r i n g s i n t r o d u c e d a s p u r i o u s p i t c h a n g l e d e v i a t i o n o f about 1.5 d e g r e e s . Once l e v e l f l i g h t was resumed t h e g y r o s c o p e e r e c t e d i t s e l f a t a r a t e , p r o p o r t i o n a l t o g s i n Q' ( s e e M i y a k e e t a l , 19 70b). Thus a s p u r i o u s e x p o n e n t i a l decay was imposed on the r e c o r d e d p i t c h a n g l e a t t h e b e g i n n i n g o f e v e r y r u n . S i n c e i n t h e a n a l y s i s l i n e a r t r e n d s a r e r e j e c t e d , the p r o c e d u r e used was t o omit t h a t p a r t o f the f i r s t h a l f o f e a c h r u n i n w h i c h the p i t c h a n g l e ' s t r a c e d e v i a t e d a p p r e c i a b l y f r o m a s t r a i g h t l i n e drawn t h r o u g h i t s t r a c e i n the s e c o n d h a l f . B.3 M achine p r o c e s s i n g Once t h e r u n s were s e l e c t e d t h e a n a l o g u e d a t a was q u a n t i z e d and w r i t t e n on d i g i t a l t a p e . F i g u r e 62 i l l u s t r a t e s t h i s i n b l o c k d i a g r a m f o r m and a l s o o u t l i n e s t h e s u b s e q u e n t p r o c e s s i n g s t e p s . The a n a l o g u e t o d i g i t a l c o n v e r t or ( d e s i g n e d and b u i l t i n t h i s l a b o r a t o r y ) a c c e p t s s i g n a l l e v e l s between - 5 . 1 2 v o l t s and q u a n t i z e s them i n 10 m i l l i v o l t s s t e p s . To r e d u c e t h e q u a n t i z a t i o n n o i s e e f f e c t some c h a n n e l s were p r e - a m p l i f i e d . A l l the c h a n n e l s were low p a s s f i l t e r e d w i t h matched l i n e a r p hase s h i f t f i l t e r s h a v i n g a h i g h f r e q u e n c y r o l l - o f f o f 40 db/decade above t h e 3 db p o i n t a t 160 Hz and phase s h i f t o f 0.45°/Hz up t o 240 Hz. A l i n e a r phase s h i f t i s e q u i v a l e n t t o a t i m e d e l a y , and so t h e wave forms a r e d i s t o r t e d o n l y i n r e g a r d t o t h e a m p l i t u d e s o f t h e h i g h f r e q u e n c y components, w h i c h a r e r e s t o r e d l a t e r i n t h e program, 'SIMPLOT'. The p u r p o s e o f the f i l t e r s i s , o f c o u r s e , t o r e d u c e a l i a s i n g , a n d t h e s a m p l i n g f r e q u e n c y o f t h e A-D c o n v e r t o r was s e t a t 320 Hz i . e . a t .: t w i c e the N y q u i s t f r e q u e n c y . A l t h o u g h t h i s means an a t t e n u a t i o n o f o n l y 3 db a t t h e N y q u i s t f r e q u e n c y (160 H z ) , i t i s adequate b e c a u s e the 130 TAPE EEC. , A-D CONV. a GAIN FILTERS C.D.C. 8092 PROGRAM 'FLINOP* CARDS AVERAGES I ANI PROGRAM 'D-A PLOT' ^3- V TIME SERIES SPECTRAL PLOTS TAPE PROGRAM 'FLINOP' CARDS AVERAGES AND TRENDS PROGRAM 'FTOR* CARDS SPECTRAL JSJTJMAXES- PROGRAM 'SIMPLOT' NORMALISED SPECTRA MOMENTS AND DISTRIBUTIONS -gg, ( COEFF. TAPE V PROGRAM 'SCOR' SPECTRA FIGURE 62. BLOCK DIAGRAM OF MACHINE PROCESSING STEPS 131 s p e c t r a o f t u r b u l e n c e f a l l o f f r a p i d l y w i t h , i n c r e a s i n g f r e q u e n c y i n t h i s r e g i o n . Thus, 320 t i m e s p e r s e c o n d the c o n v e r t o r c o m p l e t e d one ' c r o s s c h a n n e l sweep' o f a l l t e n c h a n n e l s , w a i t i n g o n l y 45 m i c r o - s e c o n d s between a d j a c e n t c h a n n e l s o r 405 m i c r o - s e c o n d s between f i r s t and l a s t c h a n n e l s . A l l t h e d a t a was d i g i t i z e d w i t h the a n a l o g u e t a p e r e c o r d e r p l a y i n g b a c k a t e i g h t times the r e c o r d i n g s p e e d , and some of i t was d i g i t i z e d a s e c o n d t i m e a t r e a l p l a y b a c k s p e e d ; i . e . t h e r e a l t i m e s a m p l i n g f r e q u e n c i e s were 40 Hz and 320 Hz r e s p e c t i v e l y . Thus, the l o n g e s t r e a l t i m e i n t e r v a l between s a m p l i n g two c h a n n e l s i s 3.3 m i l l i s e c o n d s c o r r e s - p o n d i n g t o a s p a c e l a g o f 23 cm. A c a r e f u l c a l i b r a t i o n o f t h e t a p e r e c o r d e r , a m p l i f i e r s , f i l t e r s and A-D c o n v e r t o r was p e r f o r m e d b o t h b e f o r e and a f t e r each d i g i t i z i o n s e s s i o n . A C o n t r o l D a t a C o r p o r a t i o n Computer (CDC 8902, see F i g u r e 62) w r i t e s t h e s e q u e n t i a l l y s a m p l e d d a t a on d i g i t a l t a p e , w h i c h can t h e n be h a n d l e d by the IBM 360 s y s t e m a t U.B.C. B e f o r e p r o c e e d i n g w i t h the p r o c e s s i n g o f a d i g i t a l t a p e i t was p r u d e n t t o a s c e r t a i n w h e t h e r o r n o t t h e d i g i t - i z a t i o n p r o c e s s was s u c c e s s f u l . T h i s was done by the program, 'TAPE VERIFY', w r i t t e n by R. W i l s o n o f t h i s I n s t i t u t e , i n t h e f o r m o f 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 , s e c o n d , t h i r d and f o u r t h moments. The l o w e s t f r e q u e n c y e s t i m a t e o b t a i n a b l e f r o m a s e c t i o n o f d a t a o f l e n g t h N A t s e c o n d s i s a t 1/N A t Hz. Thus, i f t h e d a t a c o n t a i n s an a p p r e c i a b l e t r e n d t h e e n e r g y a s s o c i a t e d w i t h the t r e n d w i l l a p p e a r i n t h e low f r e q u e n c y e s t i m a t e s ( s e e Blackman and Tukey, 1959). I n v i e w o f t h e g y r o s c o p e ' s l i m i t a t i o n s and t h e f a c t t h a t t h e a c c e l e r a t i o n s i g n a l s h a ve t o be i n t e g r a t e d , i t i s h a r d l y r e a s o n a b l e t o 132 e x p e c t t h e c o r r e c t e d v e l o c i t i e s t o be d e v o i d o f t r e n d even i f t h e a c t u a l v e l o c i t y components w e r e . F u r t h e r m o r e , due t o a i r c r a f t range l i m i t a t i o n s , l o n g f l i g h t s a t any l e v e l h ad t o be s a c r i f i c e d i n f a v o u r o f m u l t i - l e v e l s a m p l i n g ; w i t h the r e s u l t t h a t t h e s h o r t c r o s s w i n d f l i g h t s , a t h i g h a l t i t u d e s i n p a r t i c u l a r , r e f l e c t t h e p r e s e n c e o f energy a t s c a l e s l a r g e r t h a n the t o t a l sample l e n g t h . I t was t h e r e f o r e d e c i d e d t h a t t h e most c o n s i s t e n t a p p r o a c h w o u l d be t o remove t h e averages and t r e n d s f r o m a l l t h e c h a n n e l s b o t h b e f o r e computing t h e c o r r e c t e d v e l o c i t y components and b e f o r e d e t e r m i n i n g t h e f o u r i e r c o e f f i c i e n t s o f t h e s e components. Thus, t h e a u t h o r u n d e r t o o k t o w r i t e a program, 'FLINOP' w h i c h c o u l d be c o n t r o l l e d t o compute and remove a v e r a g e s and l i n e a r t r e n d s ( i n s u c c e s s i v e p a s s e s ) , p e r f o r m a l l o f the o p e r a t i o n s r e q u i r e d f o r c o r r e c t i o n o f a i r c r a f t m o t i o n , m u l t i p l y t i m e s e r i e s t o g e t h e r p o i n t by p o i n t and d e l a y o r advance any s i g n a l w i t h r e s p e c t t o t h e o t h e r s . These l a s t two were r e q u i r e d t o p r o d u c e t i m e s e r i e s o f i n s t a n t a n e o u s f l u x e s and t o advance t h e h u m i d i o - m e t e r s i g n a l by d/VAt samples r e s p e c t i v e l y , where d i s t h e downstream d i s t a n c e o f t h e h u m i d i o m e t e r f r o m t h e n o s e , A t i s the i n t e r v a l between samples and V i s t h e a v e r a g e a i r s p e e d o f t h e a i r c r a f t . The i n t e - g r a t i o n was done i n s t a i r c a s e f a s h i o n and the d i f f e r e n t i a t i o n by f i n i t e d i f f e r e n c e s a f t e r f i r s t c o m p u t i n g a n " e q u a l l y w e i g h t e d r u n n i n g mean o v e r a s e l e c t a b l e number o f s a m p l e s . The t a p e w r i t t e n by the s e c o n d pass t h r o u g h 'FLINOP ' i s r e p r o d u c e d on a Calcomp d i g i t a l p l o t t e r i n t h e fo r m o f t i m e s e r i e s -using t h e program 'D-A' PLOT 1, w r i t t e n by R. W i l s o n . These t i m e s e r i e s a r e d i s p l a y e d i n many o f the f i g u r e s i n t h i s t h e s i s . The f r e q u e n c y domain i s e n t e r e d by means o f t h e programme, ' FTOR' u s i n g t h e f a s t f o u r i e r t r a n s f o r m a l g o r i t h m , PK FORT 5DA 3465. The tape 133 o f f o u r i e r c o e f f i c i e n t s w h i c h i t p r o d u c e s i s a c c e p t e d by t h e programme, 'SCOR' w h i c h p r o d u c e s 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 , coherence and p h a s e s . B o t h o f t h e s e programmes were w r i t t e n by J . G a r r e t t o f t h i s I n s t i t u t e and a r e d e s c r i b e d i n h i s Ph.D t h e s i s ( G a r r e t t , 1970). However, b e c a u s e t h e r e i s some d i v e r g e n c e o f n o m e n c l a t u r e i n t h e l i t e r a t u r e , t h e forms f o r t h e 'spectrum', 'coherence' and ' c o r r e l a t i o n c o e f f i c i e n t ' , w h i c h a r e u s e d h e r e a r e e x p l a i n e d : -i C C Spectrum: S (n) i s d e f i n e d s o t h a t : x = IS ( n ) d n = nS ( n ) d ( l n n) x x j xx I xx r u K • r \ f 5 , 2 (n) + Q 2 ( n ) \ 1/2 Coherence: coh (n) = f xy xy 1 X y » S (n) S (n) xx yy C o r r e l a t i o n c o e f f i c i e n t : r (n) = S (n) _2Y_ Ys (n).S ( n ) ) 1 / 2 V x x yy / Where S (n) and Q (n) a r e the c o - s p e c t r u m and q u a d - s p e c t r u m r e s p e c t -xy xy r n i v e l y . The a v e r a g e c o r r e l a t i o n c o e f f i c i e n t : r = x'y' xy J C T x . C y I n 'FTOR' each r u n was d i v i d e d i n t o f o u r o r more b l o c k s , and t h e c o e f f i c i e n t s computed f o r each b l o c k . T h i s a l l o w e d t h e programme, 1SCOR' t o compute the mean s p e c t r a l e s t i m a t e a t each f r e q u e n c y , i t s s t a n d a r d d e v i a t i o n CT (n) among the b l o c k s and i t s t r e n d t h r o u g h o u t the r u n . The l a t t e r two p r o v i d e an i n d i c a t i o n o f t h e s t a t i o n a r i t y o f t h e p r o c e s s . The b l o c k l e n g t h was g e n e r a l l y 1024 s a m p l e s , b u t was r e d u c e d t o 512 f o r a few o f t h e v e r y s h o r t r u n s . S i n c e t h e sequence o f b l o c k a v e r a g e s o f x ( t ) i s i t s e l f a t i m e . 1 3 4 ( • , , s e r i e s i n which the o r i g i n a l data has been box-car averaged and sampled at i n t e r v a l s of ( N A t ) / K seconds (K i s the number of b l o c k s ) , a few K s p e c t r a l estimates (^ i n number) can be obtained using the f a s t f o u r i e r transform a l g o r i t h m . G. McBean of t h i s I n s t i t u t e has extended 'SCOR' to do t h i s (McBean, 1970). These 'low frequency' estimates a l s o appear on the s p e c t r a , but, s i n c e there i s only one estimate a v a i l a b l e , at each frequency, no observations of t h e i r variances are a v a i l a b l e . I t i s worth n o t i n g t h a t these low frequency estimates contain so few degrees of freedom that only consistency i n t h e i r values should be taken as a p o s s i b l e i n d i c a t i o n of the s p e c t r a l shape. The f i n a l stage of machine processing i s the programme 'SIMPLOT' w r i t t e n by G. McBean of t h i s I n s t i t u t e . 'SIMPLOT' accepts the s p e c t r a l estimates from 'SCOR', c o r r e c t s f o r the a t t e n u a t i o n of the f i l t e r s used i n the d i g i t i z a t i o n process and the path averaging of the s o n i c anemometer, obtains the cumulative i n t e g r a l under the s p e c t r a as a f u n c t i o n of decreasing frequency, and p l o t s (on a calcomp p l o t t e r ) s p e c t r a and co-spectra on s e l e c t a b l e axes. 135 APPENDIX C COMPARISON OF SIMULTANEOUS MEASUREMENTS FROM FL I P AND THE AIRCRAFT C.1 I n t r o d u c t i o n D u r i n g BOMEX the Queen A i r made s e v e r a l f l i g h t s a r o u n d t h e s p e c i a l - i z e d R e s e a r c h s h i p ' F L I P ' ( f l o a t i n g i n s t r u m e n t p l a t f o r m , R u d n i c k , 1964), f r o m w h i c h i n s t r u m e n t a t i o n s i m i l a r t o t h a t on the a i r c r a f t was used t o measure t h e v e r t i c a l t u r b u l e n t f l u x e s . One o f t h e s e f l i g h t s i s p r e s e n t e d h e r e i n an a t t e m p t t o e s t a b l i s h the v a l i d i t y o f t h e a i r b o r n e f l u x measurements. Inasmuch as F L I P i s s u b j e c t t o w i n d and wave i n d u c e d m o t i o n and s i n c e i t i s known t o d i s t o r t t h e mean f l o w , r e s u l t s from i t s use a r e a l s o s u b j e c t t o doubt. However, s i n c e t h e l i k e l i h o o d o f t h e s e two v e r y d i f f e r e n t p l a t f o r m s y i e l d i n g t h e same b u t e r r o n e o u s r e s u l t i s s m a l l , agreement o f t h e r e s u l t s w i l l be t a k e n as s h o w i n g t h a t measure- ments from b o t h p l a t f o r m s a r e e s s e n t i a l l y c o r r e c t . C.2 D a t a o u t l i n e T a b l e 5 p r o v i d e s a b r i e f o u t l i n e o f t h e d a t a s e c t i o n s t o be compared. The d u r a t i o n o f the d a t a r u n f r o m F L I P was 45 m i n u t e s , d u r i n g w h i c h the mean w i n d was about 8.5 m/sec; w h i l e t h e upwind and downwind runs each y i e l d e d 4 m i n u t e s o f u s a b l e d a t a . T h e r e f o r e , a t t h e same h e i g h t t h e up- w i n d and downwind f l i g h t s c o v e r e d about t h e same s c a l e s i z e s as t h e FLIP d a t a . F u r t h e r m o r e , t h e d a t a g a t h e r e d from F L I P s t r a d d l e s t h e a i r - c r a f t d a t a i n t i m e . Hence, w i t h i n t h e range o f v a l i d i t y o f T a y l o r ' s h y p o t h e s i s , t h i s c o m p a r i s o n i s o v e r a p p r o x i m a t e l y t h e same s c a l e s ; p r o v i d e d , o f c o u r s e , t h a t c o n d i t i o n s a r e homogeneous w i t h i n about 50 km o f F L I P . PLATFORM RUN LOCAL TIME HEIGHT OF INSTRUMENTS DIRECTION OF FLIGHT SYMBOL FLIP B-55/1 START 15.05 END 15.50 30 m AIRCRAFT 4/3 15.33 15.37 15 m DOWNWIND AIRCRAFT 4/5 15.43 15.47 18m UPWIND ON TABLE 5 THE DATA. USED.IN THE FLIP / AIRCRAFT COMPARISON 137 C.3 S p e c t r a and c o s p e c t r a The a n a l y s i s o f t h e F L I P d a t a p r e s e n t e d some i n t e r e s t i n g p r o b l e m s , the s o l u t i o n o f w h i c h a r e due i n t h e main t o t h e e f f o r t s o f G. McBean o f t h i s I n s t i t u t e , who p r o c e s s e d the F L I P d a t a d i s c u s s e d h e r e i n . The a b s c i s s a o f F i g u r e s 63 , 64. and 65 i s the n a t u r a l f r e q u e n c y f (=nZ/^). T h i s s i m i l a r i t y c o o r d i n a t e was used i n o r d e r t o be a b l e t o compare the s p e c t r a by d i r e c t s u p e r i m p o s i t i o n . The v a l u e s o f V were 70 m/sec i n the c a s e o f t h e a i r c r a f t and 8.5 m/sec i n t h e case o f F L I P ; and t h e i n s t r u m e n t s were mounted 30 m above the s u r f a c e on F L I P when t h e Queen A i r f l e w by a t an a l t i t u d e o f 18 m. The i n s t r u m e n t s on t h e two p l a t f o r m s were i n d e p e n d e n t l y c a l i b r a t e d , and s o t h e o r d i n a t e s o f F i g u r e s 63, 64 and 65 a r e n o t n o r m a l i z e d . I t i s s e e n t h a t t h e n - s p e c t r a o f v e r t i c a l ( F i g u r e 6 3 ) , h o r i z o n t a l ( F i g u r e 64) v e l o c i t y f l u c t u a t i o n s and t h e momentum n - c o s p e c t r a ( F i g u r e 65) a r e v e r y s i m i l a r i n a m p l i t u d e and shape i n a l l t h r e e cases p r e s e n t e d : two a i r b o r n e measurements i n t h e v i c i n i t y o f F l i p and t h e c o n c u r r e n t F l i p measurements. I n a l l t h r e e f i g u r e s t h e F l i p n - s p e c t r a d i s p l a y a 'bump' a t f = 0.2, w h i c h i s n o t i n the a i r c r a f t n - s p e c t r a . T h i s 'bump' c o i n c i d e s w i t h t h e peak of t h e measured w a t e r wave s p e c t r u m , and i s due t o wave i n d u c e d m o t i o n of F l i p . I t seems t h a t , a p a r t f r o m t h e wave i n d u c e d bump i n t h e F l i p s p e c t r a and some s c a t t e r o f t h e low f r e q u e n c y p o i n t s , t h e agreement i s e x c e l l e n t between t h e measurements made from F l i p and t h o s e made from t h e a i r c r a f t . Thus, i n v i e w o f t h e e x c e l l e n t c o r r e s p o n d e n c e o f r e s u l t s from t h e s e two -•so d i f f e r e n t p l a t f o r m s , t h e r e cannot be much doubt o f t h e v a l i d i t y o f t h e c o n c l u s i o n t h a t t h e Queen A i r , e q u i p p e d as i t was, i s an a c c e p t a b l e • o e 0 • p/- x o • F l i p , Z = 30 m * Aircraft, Z = 15 m o Aircraft, Z = 18 m 1 . 001 fO n z / v FIGURE 63. COMPARISON OF w' SPECTRA FROM THE AIRCRAFT AND FLIP W CO 0 oo* 0 o F l i p , Z = 30 m X Aircraft, Z = 15 m . o Aircraft, Z = 18 m — T ; ; r r- 1 » » OOf -0/ -I f 1 0 7 1 Z / V FIGURE 64. COMPARISON OF u SPECTRA FROM THE AIRCRAFT AND FLIP J 1 f?' 'OOl >000H o X «*<» 0 QX o © F l i p , Z x Aircraft, Z o Aircraft, Z 30 ro 15 m 18 m i 001 -f— '01 10 72 Z ' / V FIGURE 65. COMPARISON OF THE MOMENTUM COSPECTRA FROM THE AIRCRAFT AND FLIP H 1 O 141 platform for the measurement of turbulence near the surface. APPENDIX D STATISTICS RUN ^ z x • cm/s cm/s c° gm/kgm dynes cm 2 mW/cm̂  mW/cm2 1/6 1/3 1/7 1/12 30.8 31.0 47.3 33.8 52.2 37.8 38.5 42.9 .105 .071 .063 .155 .291 .188 .223 .499 .643 .306 .579 .079 .77 .75 -.11 -1.22 10.30 9.49 15.65 19.60 2/8 2/7 2/4 2/10 33.5 30.3 33.5 34.2 56.9 43.8 46.0 68.5 .128 .096 .074 .411 .225 .246 .171 .508 .985 .347 .212 1.09 2.47 .34 -.21 1.13 13.19 8.97 7.10 21.61 3/6 3/3 3/9 3/12 40.2 41.5 31.5 42.0 74.6 59.5 56.6 44.4 .117 .093 .066 .527 .302 .252 .184 .198 1.47 .921 .789 .504 -.05 .64 .51. 17.14 7.68 8.10 9.27 4/5 37.7 73.5 ,105 .255 1.28 .85 12.31 4/2 31.5 74.8 .073 .192 .478 .31 6.80 4/8 37.8 42.2 .069 .152 .401 -.48 4.54 4/9 24.3 45.9 .230 .226 .297 .13 3.56 5/2 37.0 76.6 .092 .277 1.34 .18 13/93 5/4 37.8 66.3 .093 .288 .905 .04 11.99 5/6 34.9 42.1 .071 .190 .375 -.07 7.78 5/8 34.9 36.7 .072 .152 .556 .52 8.42 6/2 39.7 66.4 .091 .245 1.49 .10 6/4 33.5 38.1 .102 .251 .272 -.12 6/6 40.2 39.2 .221 .649 .014 .39 TABLE 6 - VARIANCES 144 ZKgw'/D' _Zj _Zj + Z/ = -ZXgw'T' , ZH0.61 g w'Q' ; — 3 L L T L 3 3 2 RUN ** Z n w'T' - Z / L w'Q' - Z/Ln - Z / L * I Q m (m/s)2 (m/s)C° (J?) (IS? ) s kgm 1/6 U 20 .049 7 .0059 . .14 .0318 .14 .28 1/3 u 43 .0237 .0058 .89 .0293 .83 1.72 1/7 D 150 .0448 - . 00083 - . 1 7 .0483 1.9 1.73 1/12 U 500 .0061 - . 0094 -130 . .0605 150. 20. •2/8 D 18 .0762 .019 .21 .0407 .085 .30 2/7 U 46 .0268 .0026 .35 .0277 .69 1.04 2/4 U 150 .0164 - .0016 - 1 . 5 .0219 3.8 2 .3 2/10 D 460 .0842 .0087 2.1 .0667 3.0 5 .1 3/6 U 18 .114 - .00042 - . 0 2 5 .0529 .059 .034 3 /3 U 49 .0712 .0049 .16 .0237 .15 .31 3/9 U 150 .061 .0039 .51 .0250 .61 1.12 3/12 U 500 .0391 .0286 4 .4 4 .4 4 /5 U 18 .099 .0065 .048 .038 .053 .10 4 /2 U 52 .037 .0024 .23 .021 .37 .60 4 /8 . • U 150 .031 - .0037 - 1 . 3 .014 .94 - . 3 6 4/9 D 490 .023 .001 1.8 .011 3.7 5.5 U 26 .104 .0014 .014 .043 .08 .094 U 49 .070 .00034 .011 .037 .23 .24 u 88 .029 - .00052 - . 1 2 .024 1.0 .88 u 140 .043 .0040 .81 .026 .98 1.79 6 /2 U 29 .115 .00077 .007 .048 .086 .093 6/4 u 98 .021 - .0009 - . 3 8 .026 2 i00 1.62 6/6 u 480 .0011 .0030 520. .035 1100. 1620. U = Upwind, D = Downwind TABLE 7 - STABILITY RUN u* -Q* O'u/u* -̂ Q/Q, cm/s c° gm/kgm 1/6 22.3 .066 .357 1.38 2.34 1.59 .82 1/3 15.4 .094 .476 2.01 2.45 .76 .39 1/7 21.2 -.010 .570 2.33 1.82 -6.30 .39 1/12 7.8 -.301 1.939 4.33 5.50 -.51 .26 2/8 27.6 .172 .369 1.21 2.06 .74 .61 2/7 16.4 .040 .422 1.85 2.67 2.40 .58 2/4 12.8 -.031 .428 2.62 3.59 -2.39 .40 2/10 29.0 .075 .575 • 1.18 2.36 5.48 .88 3/6 33.8 -.003 .391 1.19 2.21 -39.0 .77 3/3. 26.7 .046 .222 1.55 2.23 2.02 1.14 3/9 24.̂ 7 .039 .253 1.28 2.29 1.69 .73 3/12 19.8 — .361 2.12 2.24 —— .55 4/5 31.5 .052 .302 1.20 2.33 2.02 .84 4/2 19.2 .031 .273 1.64 3.90 2.35 .70 4/8 17.6 -.053 .199 2.15 2.40 -1.30 .76 4/9 15.2- .016 .191 1.60 3.02 14.38 1.18 5/2 "' 32.2 .011 .334 1.15 2.37 8.36 .83 5/4 26.5 .003 .349 1.43 2.50 31.00 .83 576 17.0 -.008 .353 2.05 2.'48 -8.88 .54 5/8 20*8 .048 . .313 1.68 1.76 1.50 .49 6/2 33.9 .006 .354 1.17 1.96 15.17 .69 6/4 14.5 -.016 .448 2.31 2.63 -6.38 .56 6/6 3.3 .227 2.65 12.18 11.88 .97 .24 TABLE 8 - SIMILARITY RATIOS 146 RUN X Z g w'T' T •0.61g w'Q' D m cm cm cm cm cm 1/6 1/3 1/7 1/12 20 43 150 500 13.86 2.12 1.59 0.02 1.93 1.90 -0.27 -3.07 1.90 1.75 2.89 3.62 10.81 7.78 3.81 1.86 -6.88 2.01 -0.40 1.29 2/8 2/7 2/4 2/10 18 46 150 460 29.20 2.40 0.35 1.33 6.21 0.85 -0.52 2.84 2.44 1.66 1.31 3.99 18.23 6.41 3.54 5.86 -19.62 1.50 2.40 -2.30 3/6 3/3 3/9 3/12 18 49 150 500 53.63 9.71 2.51 0.39 -0.14 1.60 1.28 3.17 1.42 1.50 1.71 51.58 27.30 4.66 5.95 -5.08 14.57 -0.63 3.85 4/5 4/2 4/8 4/9 18 52 150 490 43.41 3.40 0.91 0.18 2.13 0.78 -1.21 0.33 2.27 1.26 0.84 0.66 68.39 19.73 5.87 3.30 20.58 14.29 5.33 2.13 5/2 5/4 5/6 5/8 26 49 88 140 32.10 9.49 1.40 1.61 0.46 0.11 -0.17 1.31 2.57 2.21 1.44 1.56 69.02 21.96 6.97 7.69 33.89 10.25 4.30 3.21 6/2 6/4 6/6 29 98 480 33.58 0.78 0.00 0.25 -0.29 0.98 2.87 1.56 2.09 28.76 4.25 2.56 -7.94 2.20 -0.51 TABLE 9 - THE KINETIC ENERGY BUDGET

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