On the detection of coherent structures in turbulent flows

ON THE DETECTION OF COHERENT

STRUCTURES IN TURBULENT FLOWS

J.M.G. Kunen

ON T H E DETECTION OF C O H E R E N T

S T R U C T U R E S IN T U R B U L E N T FLOWS

ON THE DETECTION OF COHERENT

STRUCTURES IN TURBULENT FLOWS

Ter verkrijging van de graad van doctor

in de technische wetenschappen aan de

Technische Hogeschool Delft, op gezag van

de Rector Magnificus, prof. ir. B.P.Th. Veltman

in het openbaar te verdedigen

ten overstaan van het College van Dekanen

op dinsdag 30 oktober 1984 te 14.00 uur

J O S E P H MATH IAS G E R A R D U S KUNEN

geboren te Ven ray

vliegtuigbouwkundig ingenieur

Proefschrift

door

Dit proefschrift is goedgekeurd door de promotor

PROF.DR. IR. G. O O M S

Aan mijn ouders

Aan Rosette

TABLE OF CONTENTS Quotes v i i Summary v i i i I INTRODUCTION 1 1.1 B r i e f r e v i e w of e x p e r i m e n t a l t u r b u l e n c e r e s e a r c h 2 1.2 S t r u c t u r e of wall-bounded t u r b u l e n c e 4 1.2.1 S t r u c t u r e o f the w a l l l a y e r 5 1.2.1.1 Flow v i s u a l i z a t i o n i n the w a l l l a y e r 5 1.2.1.2 Q u a n t i t a t i v e measurements i n the w a l l l a y e r 11 1.2.1.3 Comparison between methods of b u r s t d e t e c t i o n 16

1.2.2 S t r u c t u r e of the o u t e r l a y e r 16 1.2.2.1 Flow v i s u a l i z a t i o n i n the o u t e r l a y e r 16

1.2.2.2 Q u a n t i t a t i v e measurements i n the o u t e r l a y e r 18

1.2.3 S t r u c t u r e i n the Reynolds s t r e s s 20 1.2.4 Organized motion i n a t u r b u l e n t boundary l a y e r 23

1.3 S t r u c t u r e of f r e e t u r b u l e n c e 25 1.3.1 P l a n e m i x i n g l a y e r s 25 1.3.2 A x i s y m m e t r i c shear l a y e r s 28 1.4 P r e s e n t i n v e s t i g a t i o n 32 I I DESCRIPTION OF EXPERIMENTS 34 2.1 Boundary l a y e r 34 2.1.1 E x p e r i m e n t a l set-up 34 2.1.2 E x p e r i m e n t a l r e s u l t s 35 2.2 P i p e f l o w 37 2.2.1 E x p e r i m e n t a l s e t - u p 37 2.2.2 E x p e r i m e n t a l r e s u l t s 41 2.3 Channel f l o w 49 2.3.1 E x p e r i m e n t a l set-up 49 2.3.2 E x p e r i m e n t a l r e s u l t s 54 2.4 A x i s y m m e t r i c j e t f l o w 59 £.4.1 E x p e r i m e n t a l set-up 59 >.4.2 E x p e r i m e n t a l r e s u l t s 60

I I I DETECTION SCHEMES 65 3.1 Scheme of Ueda and H i n z e 65 3.1.1 D e s c r i p t i o n of the scheme 65 3.1.2 Test r e s u l t s 66 3.2 Scheme of B l a c k w e l d e r and K a p l a n 67 3.2.1 D e s c r i p t i o n of the scheme 67 3.2.2 Test r e s u l t s 70 3.2.3 F u r t h e r t e s t s 73 3.3 M o d i f i e d scheme of B l a c k w e l d e r and K a p l a n 83 3.3.1 D e s c r i p t i o n of the scheme 83 3.3.2 Test r e s u l t s 83 3.4 A u t o c o r r e l a t i o n method 89

IV HYDROGEN BUBBLE VISUALIZATION COMBINED WITH

LASER-DOPPLER ANEMOTRY 90 4.1 Observed f l o w s t r u c t u r e s 90 4.1.1 P l a n view 91 4.1.2 Side view 92 4.2 C h a r a c t e r i s t i c s i g n a l s of f l o w s t r u c t u r e s i n the w a l l l a y e r 94 4.2.1 Low-speed s t r e a k s 95 4.2.2 High-speed s t r e a k s 96 4.2.3 E d d i e s 96 4.2.4 Some i l l u s t r a t i o n s 97

4.3 Second quadrant d e t e c t i o n method 100 4.3.1 D e s c r i p t i o n and r e s u l t s 100 4.3.2 Comparison w i t h o t h e r v i s u a l i z a t i o n s t u d i e s 103

4.4 D e t e c t i o n s of B l a c k w e l d e r and Kaplan's method 105

V APPLICATION OF QUADRANT ANALYSIS TECHNIQUE TO JET

FLOW 107 5.1 Quadrant a n a l y s i s w i t h o u t h o l e 108

5.2 Quadrant a n a l y s i s w i t h h o l e 110

L i s t of symbols 118 References 122 Appendix A: D e s c r i p t i o n of a t u r b u l e n t boundary l a y e r 130 Appendix B: D e s c r i p t i o n of an a x i s y m m e t r i c j e t f l o w 132 Samenvatting 133 Acknowledgement 135 L e v e n s b e r i c h t 135

QUOTES

"Say t h a t a b l i n d man u s i n g a road bed sensor attempted t o f i n d out what a motor v e h i c l e looked l i k e . Happening t o use a road o n l y t r a v e l e d by a i r p o r t l i m o u s i n e s and m o t o r c y c l e s , he concludes t h a t the average v e h i c l e i s a compact car w i t h 2.4 wheels. He might l a t e r attempt t o c o n s t r u c t a t h e o r e t i c a l model of the mechanics of such a v e h i c l e , and may a t t a i n fame f o r a t e n t a t i v e model t h a t l o o k s l i k e a m o t o r c y c l e w i t h a s i d e c a r whose wheel i s o n l y i n con-t a c con-t w i con-t h con-the ground f o r con-t y p e r c e n con-t of con-the con-t i m e . "

M o l l o - C h r i s t e n s e n , E. [1971]

"Man, i r r e s p e c t i v e of whether he i s a t h e o l o g i a n or s c i e n t i s t , has a s t r o n g tendency t o see what he hopes t o see."

E i s e l e y , L. [1979]

"Turbulence r e s e a r c h e r s are v e r y much l i k e a r c h a e o l o g i s t s who seek the o r i g i n of man by e x t r a p o l a t i v e e v a l u a t i o n of b i t s and p i e c e s of f o s s i l i z e d remains; we t r y t o p i e c e t o g e t h e r e x p e r i m e n t a l obs e r v a t i o n obs and the 'remainobs' which our meaobsurement t e c h n i q u e obs a l -low us to o b t a i n w i t h the hope t h a t we can e s t a b i s h not o n l y the s i z e and shape of the t u r b u l e n c e 'beast', but i t s modes of growth, d e a t h , r e p r o d u c t i o n , and i n t e r a c t i o n s w i t h o t h e r ' b e a s t s ' . U n f o r -t u n a -t e l y , -the b i -t s and p i e c e s of i n f o r m a -t i o n we have f o r -t u r b u l e n -t boundary l a y e r s s t i l l l e a v e many h o l e s i n the m o r p h o l o g i c a l p u z z l e ; c o n s e q u e n t l y , c u r r e n t r e s e a r c h e r s s t i l l can't agree whether our 'beast' i s l a r g e or s m a l l , or whether we have more than one b e a s t , or i f ( l i k e the c a t e r p i l l a r / b u t t e r f l y ) we have a beast which passes through some metamorphosis."

SUMMARY

T h i s t h e s i s d e a l s w i t h the problem of d e t e c t i n g coherent s t r u c t u r e s i n t u r -b u l e n t f l o w s .

Some E u l e r i a n d e t e c t i o n methods were t e s t e d ; v i z . the method of Ueda and H i n z e , the method of B l a c k w e l d e r and K a p l a n and a m o d i f i e d v e r s i o n of B l a c k w e l d e r and K a p l a n ' s method. H e r e t o measurements were performed i n a t u r b u l e n t boundary l a y e r f l o w and a t u r b u l e n t p i p e f l o w . R e s u l t s show t h a t these methods are not o b j e c t i v e ; the mean time between s u c c e s s i v e d e t e c -t i o n s , -the d i s -t r i b u -t i o n of -time i n -t e r v a l s be-tween s u c c e s s i v e d e -t e c -t i o n s and the c o n d i t i o n a l l y averaged streamwise v e l o c i t y are v e r y dependent on the parameter v a l u e s used i n the methods. The d i s t r i b u t i o n of time i n t e r v a l s be-tween s u c c e s s i v e d e t e c t i o n s and the c o n t r i b u t i o n of d e t e c t i o n s t o the Reynolds s t r e s s a r e a l s o not i n agreement w i t h r e s u l t s of v i s u a l i z a t i o n s t u d i e s . T h e r e f o r e , t h e o n l y c o n c l u s i o n can be t h a t t h e s e E u l e r i a n d e t e c t i o n methods a r e not v e r y a p p r o p i a t e methods t o make measurements on coherent s t r u c t u r e s .

The a u t o c o r r e l a t i o n technique appears a l s o not t o be v e r y u s e f u l i n e s t a b -l i s h i n g p r o p e r t i e s of coherent s t r u c t u r e s , because t h i s technique can be ap-p l i e d o n l y ap-p a r t of the measuring time.

Flow v i s u a l i z a t i o n and E u l e r i a n measurement were combined i n an i n v e s t i g a -t i o n of a -t u r b u l e n -t wa-ter f l o w -t o compare v i s u a l and E u l e r i a n d e -t e c -t i o n on a one-to-one b a s i s . Hydrogen b u b b l e s were used t o v i s u a l i z e the f l o w . Only p a r t of the d e t e c t i o n s of B l a c k w e l d e r and Kaplan's method appears t o c o i n -c i d e w i t h v i s u a l d e t e -c t i o n s . E u l e r i a n d e t e -c t i o n s of the s o - -c a l l e d se-cond quadrant method, i n whicfi o n l y the c o n t r i b u t i o n s t o t h e Reynolds s t r e s s bel o n g i n g t o the second quadrant a r e c o n s i d e r e d , c o r r e bel a t e v e r y w e bel bel w i t h v i s u a l d e t e c t i o n s of e j e c t i o n s . A l s o b u r s t s a r e d e t e c t e d i n t h i s way, i f d e t e c -t i o n s w i -t h s m a l l -time i n -t e r v a l s a r e c o n s i d e r e d -t o be d e -t e c -t i o n s on -the same s t r u c t u r e s .

The quadrant a n a l y s i s t e c h n i q u e was a l s o a p p l i e d t o a t u r b u l e n t j e t . As t h i s t e c h n i q u e does not p r o v i d e i n f o r m a t i o n about o r i g i n and o r i e n t a t i o n of s t r u c t u r e s , i t i s o n l y s u c c e s s f u l i n d e t e c t i n g s t r u c t u r e s i n those p a r t s of a j e t f l o w where the i n f l u e n c e of the nearby boundary i s s u b s t a n t i a l ; v i z . the m i x i n g l a y e r r e g i o n and the o u t e r p a r t of the development r e g i o n .

Chapter I INTRODUCTION

I t i s g e n e r a l l y a c c e p t e d t h a t t h e time dependent N a v i e r - S t o k e s e q u a t i o n s d e s c r i b e t u r b u l e n c e .

So f a r i t has been i m p o s s i b l e t o s o l v e these e q u a t i o n s , because of the non-l i n e a r i t y of the e q u a t i o n s , the e s s e n t i a non-l non-l y t h r e e - d i m e n s i o n a non-l c h a r a c t e r o f t u r b u l e n c e and the wide range of s c a l e s t h a t c o n t r o l s t u r b u l e n c e .

Reynolds [1895] proposed the d e c o m p o s i t i o n of the v e l o c i t y components and the p r e s s u r e i n a mean and a f l u c t u a t i n g p a r t . S u b s t i t u t i o n i n t o the N a v i e r -Stokes e q u a t i o n s y i e l d s a f t e r t i m e - a v e r a g i n g a system of e q u a t i o n s almost i d e n t i c a l i n form t o t h e o r i g i n a l system. However, i n t h e new s e t of equa-t i o n s c o n v e c equa-t i v e s equa-t r e s s equa-terms a r i s e from a v e r a g i n g p r o d u c equa-t s of equa-the v e l o c i equa-t y f l u c t u a t i o n s - t h e s o - c a l l e d Reynolds s t r e s s e s . T h e r e f o r e , the s e t of equa-t i o n s i s noequa-t c l o s e d and an a d d i equa-t i o n a l e q u a equa-t i o n i s needed f o r equa-t h e r e l a equa-t i o n between t h e Reynolds s t r e s s e s and t h e mean v e l o c i t y f i e l d .

U n t i l r e c e n t l y much t u r b u l e n c e r e s e a r c h was c o n c e n t r a t e d on f i n d i n g t h e a d d i t i o n a l e q u a t i o n f o r s i m p l e f l o w c o n f i g u r a t i o n s hoping t h e e q u a t i o n c o u l d be m o d i f i e d so t h a t i t would h o l d f o r more complex f l o w c o n f i g u r a t i o n s . But u n t i l now i t has n o t been p o s s i b l e t o c o n s t r u c t a more g e n e r a l t u r b u l e n c e model t o say n o t h i n g of an u n i v e r s a l model.

I n the f o l l o w i n g s e c t i o n s f i r s t a b r i e f summary of e x p e r i m e n t a l t e c h n i -ques used t o i n v e s t i g a t e t u r b u l e n c e w i l l be g i v e n .

F u r t h e r , a r e v i e w of a new development i n t u r b u l e n c e r e s e a r c h - t h e coherent s t r u c t u r e s i n t u r b u l e n t f l o w s w i l l be p r e s e n t e d . T h i s r e v i e w w i l l be d i -v i d e d i n two p a r t s , one d e a l i n g w i t h wall-bounded t u r b u l e n t f l o w s and one w i t h f r e e t u r b u l e n t f l o w s . A more complete r e v i e w of coherent s t r u c t u r e s can be found i n t h e papers of W i l l m a r t h [1975] and C a n t w e l l [1981] - r e g a r d i n g wall-bounded t u r b u l e n c e - and of H u s s a i n [1983] - c o n c e r n i n g f r e e t u r b u l e n c e . I n the l a s t s e c t i o n t h e c o n t e n t s of t h i s t h e s i s w i l l be o u t l i n e d .

1.1 BRIEF REVIEW OF EXPERIMENTAL TURBULENCE RESEARCH

I n the 1920 's and e a r l y 1930's mean v e l o c i t y measurement was the most im-p o r t a n t e x im-p e r i m e n t a l method. Only im-p r e s s u r e measuring d e v i c e s ( im-p i t o t - t u b e , v e n t u r i - m e t e r ) and moving-part i n s t r u m e n t s (cup anemometer, vane anemometer) were o p e r a t i o n a l . Hot-wire anemometry s t i l l was i n development.

With these e x p e r i m e n t a l t o o l s i t was i m p o s s i b l e t o check the phenomenologi-c a l t h e o r i e s of those days.

These t h e o r i e s s t a r t e d from the i d e a t h a t t u r b u l e n c e was an e s s e n t i a l l y s t o -c h a s t i -c phenomenon:

A t u r b u l e n t f l o w f i e l d e x i s t s of a mean v e l o c i t y f i e l d and a randomly f l u c t u a t i n g f i e l d .

A l l s c a l e s s m a l l e r than the o v e r a l l dimensions of the f l o w are important f o r the t u r b u l e n t f l o w .

A well-known t h e o r y i s the m i x i n g - l e n g t h t h e o r y s e t up i n d e p e n d e n t l y by P r a n d t l [1925] and T a y l o r [1915, 1932]. I n t h i s t h e o r y Boussinesq's hypothe-s i hypothe-s of the eddy v i hypothe-s c o hypothe-s i t y i hypothe-s uhypothe-sed. I n analogy w i t h the e x p r e hypothe-s hypothe-s i o n f o r the m o l e c u l a r s t r e s s known from the k i n e t i c t h e o r y of gases B o u s s i n e s q [1877] assumed t h a t the Reynolds s t r e s s e s can be coupled to the mean f l o w f i e l d by means of an eddy v i s c o s i t y . The m i x i n g - l e n g t h t h e o r y s t a t e s t h a t t h i s eddy v i s c o s i t y i s e q u a l t o the product of a 'mixing' l e n g t h and a s u i t a b l e v e l o c i t y , a g a i n i n analogy w i t h the k i n e t i c t h e o r y of gases i n which the k i n e -m a t i c v i s c o s i t y i s e q u a l t o the product of the -mean f r e e path of the - mole-c u l e s and t h e i r r o o t - mean-square v e l o mole-c i t y .

( A l t h o u g h t h i s t h e o r y cannot be c o r r e c t i n a l l d e t a i l s , i t s t i l l proves to be most u s e f u l i n p r e d i c t i n g the d i s t r i b u t i o n of mean q u a n t i t i e s of t u r b u -l e n t f -l o w s i n t e c h n i c a -l a p p -l i c a t i o n s . )

In the 1940's and 1950's the h o t - w i r e t e c h n i q u e was developed so w e l l t h a t v a r i o u s components of the Reynolds s t r e s s and v a r i o u s r a t e terms o c c u r -r i n g i n the t u -r b u l e n c e - e n e -r g y e q u a t i o n c o u l d be measu-red.

These measurements r e s u l t e d i n a r e j e c t i o n of the phenomenological t h e o r i e s .

Because of the c o m p l e x i t y of inhomogeneous t u r b u l e n c e many r e s e a r c h e r s t u r n e d t h e i r a t t e n t i o n away t o the ' s i m p l e r ' but more academic homogeneous t u r b u l e n c e ( e . g . T a y l o r [1935]).

I t was n o t i c e d t h a t , i f the Reynolds number i s l a r g e enough, the energy-con-t a i n i n g s energy-con-t r u c energy-con-t u r e i n homogeneous and i s o energy-con-t r o p i c energy-con-t u r b u l e n c e shows s i m i l a r i energy-con-t y ( B a t c h e l o r & Townsend [1948 a & b ] ) and t h a t the s m a l l - s c a l e motion i s i n a s t a t e of l o c a l e q u i l i b r i u m (Kolmogorov [1941]).

H o t - w i r e measurements showed t h a t the o u t e r edges of t u r b u l e n t shear f l o w s -wakes (Townsend [1947]) and j e t s ( C o r r s i n [ 1 9 4 3 ] ) - are o n l y i n t e r m i t t e n t l y t u r b u l e n t . T h i s phenomenon was a l s o found i n the o u t e r p a r t of t u r b u l e n t boundary l a y e r s ( C o r r s i n & K i s t l e r [1954] and K l e b a n o f f [ 1 9 5 4 ] ) .

To study the i n t e r m i t t e n t n a t u r e of t u r b u l e n c e a new t e c h n i q u e was i n t r o -duced: s e l e c t i v e or c o n d i t i o n a l s a m p l i n g .

A new l i n e of approach was i n i t i a t e d by Favre [1946] who used an a n a l o g r e c o r d e r t o produce a t i m e d e l a y e d t u r b u l e n c e s i g n a l . By expanding t h i s t e c h -nique - r e c o r d i n g two s i g n a l s s i m u l t a n e o u s l y and r e p r o d u c i n g them u s i n g a moveable head on one c h a n n e l i t was p o s s i b l e to measure spacetime c o r r e l a -t i o n s of -t u r b u l e n -t f l u c -t u a -t i o n s ( F a v r e e-t a l . [1957, 1958]).

F o r the f i r s t time i n t u r b u l e n c e r e s e a r c h Townsend [1956] attempted t o draw a p i c t u r e of a t u r b u l e n t f l o w . He i n t r o d u c e d a double s t r u c t u r e to d e s c r i b e t u r b u l e n t shear f l o w :

T u r b u l e n t f l u i d i s moved by the c o n v e c t i v e a c t i o n of a system of l a r g e eddies whose dimensions are comparable to the w i d t h of the f l o w and the s m a l l - s c a l e e d d i e s aré r e s p o n s i b l e f o r the n e a r l y u n i f o r m d i s t r i b u t i o n of the t u r b u l e n c e i n t e n s i t y .

The development of a new technology - p r i m a r i l y of e l e c t r o n i c d e v i c e s and computers- guided the e x p e r i m e n t a l r e s e a r c h i n the 1960's and 1970's.

U s i n g v e r y f a s t s w i t c h i n g c i r c u i t r i e s f o r a n a l o g and d i g i t a l computation i t became p o s s i b l e to o b t a i n d e t a i l e d s t a t i s t i c a l i n f o r m a t i o n of the f l o w phe-nomena w i t h i n the t u r b u l e n t and n o n - t u r b u l e n t r e g i o n s of an i n t e r m i t t e n t l y t u r b u l e n t f l o w ( K a p l a n & L a u f e r [1969] and Kovasznay et a l . [ 1 9 7 0 ] ) .

Yeh and Cummins [1964] demonstrated t h a t a coherent l i g h t source a l a s e r -can be used to measure steady f l u i d v e l o c i t i e s by o b s e r v i n g the Doppler

s h i f t i n t h e frequency of l i g h t s c a t t e r e d from s m a l l p a r t i c l e s moving w i t h the f l u i d . The g r e a t advantage of t h i s measuring t e c h n i q u e over h o t - w i r e an-emometry i s t h a t the f l o w i s not d i s t u r b e d by a measuring probe.

From s p a t i a l - c o r r e l a t i o n s , averaged over l o n g time i n t e r v a l s , a p i c t u r e was deduced of the l a r g e - s c a l e motion i n t u r b u l e n c e , r e s u l t i n g i n a double-r o l l e double-r ladouble-rge-eddy s t double-r u c t u double-r e f o double-r a g e n e double-r a l sheadouble-r f l o w (Townsend [1970]) and a double-cone s t r u c t u r e f o r a wall-bounded shear f l o w (Townsend [ 1 9 7 6 ] ) .

But these approaches d i d not h e l p to answer t h e b a s i c q u e s t i o n about t h e g e n e r a t i o n and maintenance of t u r b u l e n c e .

New l i g h t on t h e t u r b u l e n c e problem was shed by two i m p o r t a n t o b s e r v a t i o n s ( K l i n e & R u n s t a d l e r [1959] and Brown & Roshko [ 1 9 7 4 ] ) .

I r o n i c a l l y these o b s e r v a t i o n s were not made w i t h s o p h i s t i c a t e d e l e c t r o n i c equipment, but v i s u a l l y w i t h r a t h e r s i m p l e o p t i c a l t e c h n i q u e s .

The essence of these o b s e r v a t i o n s was the d i s c o v e r y t h a t t u r b u l e n t shear f l o w s a r e not as c h a o t i c as p r e v i o u s l y had been assumed:

There i s some o r d e r i n t h e motion w i t h an o b s e r v a b l e c h a i n of events r e o c c u r r i n g randomly w i t h a s t a t i s t i c a l l y d e f i n a b l e mean p e r i o d .

T h i s c h a i n o f events ( l a r g e - s c a l e v o r t e x m o t i o n s ) dominates the t r a n s p o r t p r o p e r t i e s .

As a r e s u l t f l o w v i s u a l i z a t i o n (hydrogen b u b b l e s , dye, smoke) was and s t i l l i s i n the c e n t r e o f i n t e r e s t .

1.2 STRUCTURE OF WALL-BOUNDED TURBULENCE

I t i s d i f f i c u l t t o determine when a c t u a l l y the r e s e a r c h of o r g a n i z e d s t r u c t u r e i n t u r b u l e n c e s t a r t e d .

C r u c i a l moments a r e the d i s c o v e r y o f a r e l a t i v e l y sharp i n t e r f a c e between t u r b u l e n t and n o n - t u r b u l e n t f l u i d i n a j e t ( C o r r s i n [ 1 9 4 3 ] ) , t h e d i s c o v e r y of the t u r b u l e n t spots i n the t r a n s i t i o n s t a g e (Emmons [ 1 9 5 1 ] ) , the d i s c o v -e r y of t h -e c r -e a t i o n of a hors-esho-e v o r t -e x d u r i n g t r a n s i t i o n (W-esk-e &

P l a n k h o l t [1955]) and t h e d i s c o v e r y of the s t r e a k y b e h a v i o u r of the s u b l a y e r i n a t u r b u l e n t boundary l a y e r (Hama e t a l . [ 1 9 5 7 ] ) .

But beyond d i s p u t e the work of K l i n e and h i s c o l l e a g u e s a t S t a n f o r d U n i v e r -s i t y i -s t h e m a i n -s p r i n g behind t h e p r e -s e n t i n t e r e -s t i n o r g a n i z e d motion. In appendix A a d e s c r i p t i o n o f t h e v a r i o u s r e g i o n s i n a t u r b u l e n t bound-a r y l bound-a y e r i s g i v e n . 1.2.1 S t r u c t u r e of t h e w a l l l a y e r 1.2.1.1 Flow v i s u a l i z a t i o n i n the w a l l l a y e r

Twenty f i v e y e a r s ago, a t S t a n f o r d U n i v e r s i t y , improved f l o w v i s u a l i z a -t i o n me-thods were developed, u s i n g dye and hydrogen bubbles as markers o f a t u r b u l e n t boundary l a y e r a l o n g a f l a t p l a t e .

The e a r l y attempts ( K l i n e & R u n s t a d l e r [1959] and R u n s t a d l e r e t a l . [1963]) c o n f i r m e d t h e s t r e a k y s u b l a y e r * s t r u c t u r e o f a t u r b u l e n t boundary l a y e r as r e p o r t e d by Hama e t a l . [1957].

K l i n e ' s i n v e s t i g a t i o n s ( K l i n e e t a l . [1967]) showed t h a t w i t h i n a sub-l a y e r an a sub-l t e r n a t i n g a r r a y of h i g h - and sub-low-speed streamwise r e g i o n s , c a sub-l sub-l e d s t r e a k s , appeared a t random l o c a t i o n s and t i m e s . Some o f these s t r e a k s i n -t e r a c -t e d w i -t h -t h e o u -t e r f l o w . T h i s i n -t e r a c -t i n g p r o c e s s i s now c a l l e d a b u r s t . F i g . 1, from t y p i c a l s i d e views o f a dye s t r e a k as seen i n motion p i c t u r e s ( K l i n e e t a l . [ 1 9 6 7 ] ) , shows t h e b u r s t - p r o c e s s . The arrow f o l l o w s a dye p a r c e l .

The process s t a r t s w i t h t h e g r a d u a l o u t f l o w and l i f t u p ( f i g . 1 a) o f a low-speed s t r e a k . When t h e s t r e a k reaches y+ = 8 - 12, i t begins t o o s c i l l a t e

( f i g . 1 b ) .

[ y+ i s t h e c o - o r d i n a t e y p e r p e n d i c u l a r t o the w a l l made d i m e n s i o n l e s s w i t h

the w a l l f r i c t i o n v e l o c i t y (Uj- =

\/

/p

s t r e s s and p t h e d e n s i t y o f the f l o w ) and t h e k i n e m a t i c v i s c o s i t y v ( y+ = y uT/ v ) . ]

T h i s o s c i l l a t i o n a m p l i f i e s ( f i g . 1 c ) and t e r m i n a t e s i n a v e r y abrupt b r e a k -up ( f i g . 1 d ) , m o s t l y i n t h e r e g i o n 10 < y+< 30. A f t e r breakup the s t r e a k

i s c o n t o r t e d , s t r e t c h e d and e j e c t e d outwards a l o n g an i d e n t i f i a b l e t r a j e c

-The f l o w i n t h e r e g i o n v e r y near a smooth w a l l - u s u a l l y c a l l e d t h e v i s c o u s or l a m i n a r s u b l a y e r - i s not l a m i n a r as o b s e r v a t i o n s showed (Fage & Townsend [1932] and P o p o v i c h & Hummel [1967]). I n f a c t i n t h e s u b l a y e r t h e r e l a t i v e t u r b u l e n c e i n t e n s i t y i n streamwise d i r e c t i o n appears t o be h i g h e r than ev-erywhere e l s e i n the boundary l a y e r (Eckelmann [1974]).

F i g u r e 1: Dye s t r e a k breakup, i l l u s t r a t i o n as seen i n s i d e view. From K l i n e et a l . [1967].

t o r y ( f i g . 1 e ) . F i g . 2 shows the d i s t r i b u t i o n and the average t r a j e c t o r i e s of the c o n t o r t e d s t r e a k s . F l u i d from the low-speed s t r e a k can reach the o u t e r p a r t of the boundary l a y e r .

[6 i s the boundary l a y e r t h i c k n e s s . ]

K l i n e e t a l . deduced from v i s u a l data t h a t the average spanwise s t r e a k spac-i n g f o r a smooth w a l l was a p p r o x spac-i m a t e l y Az + = 100.

[ Xz + i s the n o n - d i m e n s i o n a l spanwise s t r e a k s p a c i n g ( Xz + = XzuT/ v ) . ]

A t S t a n f o r d U n i v e r s i t y Kim et a l . [1971] s t u d i e d the process of prod-u c t i o n and of Reynolds s t r e s s c o n t r i b prod-u t i o n s d prod-u r i n g b prod-u r s t i n g , prod-u s i n g the hydrogen bubble t e c h n i q u e . A n a l y z i n g motion p i c t u r e s they showed that v i r t u -a l l y -a l l of the net p r o d u c t i o n of t u r b u l e n c e - e n e r g y i n the r-ange

From t h i s v i s u a l i z a t i o n method o n l y v e l o c i t y i n f o r m a t i o n i n two d i r e c t i o n s i n the boundary l a y e r can be d e r i v e d . U s i n g a p l a t i n u m w i r e normal t o the w a l l the hydrogen bubbles e l u c i d a t e the motion i n a plane i n streamwise d i r e c t i o n normal t o the w a l l , a w i r e p l a c e d p a r a l l e l t o the w a l l g i v e s i n

-0 -05 1.-0 1.6 2.-0 Usee)

la)

F i g u r e 2: T r a j e c t o r i e s of e j e c t e d e d d i e s - f l a t p l a t e f l o w , dP/dx = 0, 6 = 2.15 i n . From K l i n e et a l . [1967].

0 < y+ < 100 o c c u r r e d d u r i n g b u r s t s . They expected t h a t t h i s would a l s o be

t r u e f o r y+ > 100.

From t h e i r motion p i c t u r e s Kim et a l . were a l s o a b l e t o o b t a i n i n s t a n t a n e o u s v e l o c i t y p r o f i l e s . A f t e r breakup t h e r e was a r e t u r n t o a more q u i e s c e n t f l o w which completed the b u r s t i n g c y c l e , c r e a t i n g such f l o w c o n d i t i o n s t h a t a new b u r s t c o u l d s t a r t .

At the same time C o r i n o and Brodkey [1969] a l s o s t u d i e d the i n n e r l a y e r of a t u r b u l e n t boundary l a y e r v i s u a l l y . They used high-speed motion p i c t u r e s of t r a j e c t o r i e s o f s m a l l p a r t i c l e s suspended i n a l i q u i d f l o w through a tube a t Reynolds numbers i n the range Rep = 20000 t o 50000 ( R ee = 900 t o 2250).

[Re^ i s the Reynolds number based on the diameter D of the tube (Rep = UgyD/v, where U& v i s the average f l o w v e l o c i t y i n the t u b e ) .

Reg i s the Reynolds number based on t h e momentum t h i c k n e s s 6 00

(Ree = Ua ye / v , where 9 i s d e f i n e d as 9 = jv/l^^ ( l - u V u ^ )dy, 0

w i t h R the r a d i u s of the tube, U the mean v e l o c i t y a t a p o s i t i o n y and U„ the mean v e l o c i t y a t the tube a x i s ) . ]

The depth of f i e l d of t h e i r photographs was of the o r d e r of 20\>/uT, so they

c o u l d see a s l i c e through the b u r s t i n g s t r u c t u r e . The camera was mounted on a t r a v e r s i n g mechanism so the b u r s t i n g phenomenon c o u l d be kept i n view as the b u r s t was swept downstream.

The o b s e r v a t i o n s of the b u r s t phenomena made by C o r i n o and Brodkey are i n agreement w i t h those r e p o r t e d by Kim et a l . [1971]. But the use of numerous t r a c e r p a r t i c l e s f o r f l o w v i s u a l i z a t i o n enabled C o r i n o and Brodkey t o i d e n -t i f y a d d i -t i o n a l f e a -t u r e s o f -the b u r s -t i n g p r o c e s s .

A c c o r d i n g t o C o r i n o and Brodkey the sequence of events b e f o r e and a f t e r cha-o t i c breakdcha-own d u r i n g the b u r s t i n g p r cha-o c e s s ( f i g . 3 ) , began w i t h the fcha-orma- forma-t i o n of a low-speed p a r c e l of f l u i d near forma-t h e w a l l i n forma-the r e g i o n 0 &lforma-t;_ y+ <_ 30

( f i g . 3 a ) . The v e l o c i t y of t h i s low-speed r e g i o n was o f t e n o n l y 50% of the l o c a l mean v e l o c i t y w i t h a v e r y s m a l l r a d i a l v e l o c i t y g r a d i e n t w i t h i n t h i s r e g i o n . The next phase which o c c u r r e d a f t e r d e c e l e r a t i o n was c a l l e d a c c e l e r -a t i o n ( f i g . 3 b ) . D u r i n g t h i s ph-ase -a much l -a r g e r h i g h speed p -a r c e l of f l u i d came i n t o view and began t o a c c e l e r a t e the low-speed f l u i d by ' i n t e r a c t i o n ' . R e p e a t e d l y the e n t e r i n g high-speed f l u i d was w i t h i n the f i e l d of view but at a d i f f e r e n t spanwise l o c a t i o n t o one s i d e o r the o t h e r of the lowspeed p a r -c e l of f l u i d ( f i g . 3 -c ) .

I f , i n the a c c e l e r a t i o n phase, the h i g h — and low-speed f l u i d met at the same spanwise s t a t i o n , the i n t e r a c t i o n was o f t e n immediate, the low-speed f l u i d above a p a r t i c u l a r y+ l o c a t i o n was a c c e l e r a t e d and a v e r y sharp i n t e r f a c e

-shear l a y e r - between the a c c e l e r a t e d and r e t a r d e d f l u i d was formed ( f i g . 3 d ) . The next phase i n t h e p r o c e s s was c a l l e d e j e c t i o n ( f i g . 3 e ) . D u r i n g e j e c t i o n an e r u p t i o n of low-speed f l u i d o c c u r r e d i m m e d i a t e l y or s h o r t a f t e r the s t a r t of the a c c e l e r a t i o n . Once e j e c t i o n s t a r t e d , the p r o c e s s p r o -ceeded r a p i d l y t o a f u l l y developed stage d u r i n g w h i c h e j e c t i o n of low-speed f l u i d p e r s i s t e d f o r v a r y i n g p e r i o d s of time and then g r a d u a l l y decayed. The l e n g t h s c a l e of e j e c t e d f l u i d p a r c e l s was s m a l l (7 < z+ < 20, 20 < x+ < 40)

and most of the e j e c t i o n s o r i g i n a t e d a t d i s t a n c e s from the w a l l i n the range 5 < y+ < 15. F r e q u e n t l y o t h e r e j e c t i o n s appeared a t a d j a c e n t downstream

pos-i t pos-i o n s of the f pos-i r s t l y observed e j e c t pos-i o n .

[ z+ i s the n o n - d i m e n s i o n a l spanwise c o - o r d i n a t e and x+ the n o n - d i m e n s i o n a l

streamwise c o - o r d i n a t e ( z+ = zu,./v , x+ = x i ^ / v ) . ]

When the e j e c t e d low-speed f l u i d encountered the i n t e r f a c e between h i g h - and low-speed f l u i d a v i o l e n t i n t e r a c t i o n o c c u r r e d w i t h i n t e n s e , abrupt and cha-o t i c mcha-ovements, r e s u l t i n g i n the c r e a t i cha-o n cha-of a r e l a t i v e l y l a r g e - s c a l e r e g i cha-o n

— 0.095 in » - |

F i g u r e 3: B u r s t phenomena a c c o r d i n g t o C o r i n o and Brodkey [1969].

of t u r b u l e n t motion. The e j e c t i o n o r b u r s t i n g phase ended w i t h the e n t r y from f u r t h e r upstream of f l u i d d i r e c t e d p r i m a r i l y i n the f l o w d i r e c t i o n w i t h a p p r o x i m a t e l y the mean v e l o c i t y p r o f i l e as v e l o c i t y d i s t r i b u t i o n ( f i g . 3 f ) . The e n t e r i n g high-speed f l u i d c a r r i e d away the r e t a r d e d f l u i d remaining from the e j e c t i o n p r o c e s s . T h i s phase was c a l l e d t h e sweep.

Both C o r i n o and Brodkey [1969] and Kim e t a l . [1971] agree t h a t the b u r s t i n g phenomena are important f o r t u r b u l e n c e - e n e r g y p r o d u c t i o n . C o r i n o and Brodkey e s t i m a t e d from a s m a l l sample of b u r s t i n g events t h a t 70% of the Reynolds s t r e s s , measured by L a u f e r [1954], was produced d u r i n g e j e c t i o n s .

Grass [1971] s t u d i e d the s t r u c t u r e of t u r b u l e n t boundary l a y e r s developed over smooth and rough s u r f a c e s . M o t i o n p i c t u r e s of hydrogen bubbles were used t o c a l c u l a t e i n s t a n t a n e o u s l o n g i t u d i n a l and v e r t i c a l v e l o c i t y p r o f i l e s . From t h e s e d i s t r i b u t i o n s the mean v e l o c i t y U, the f l u c t u a t i n g v e l o c i t i e s u and v and a l s o the c o n t r i b u t i o n s t o the Reynolds s t r e s s were computed.

[The d e c o m p o s i t i o n of Reynolds y i e l d s : U = U+u and V = V+v, where U i s t h e i n s t a n t a n e o u s v e l o c i t y i n streamwise d i r e c t i o n , 7J the time-averaged streamwise v e l o c i t y and u the f l u c t u a t i n g streamwise v e l o c i t y ; V, V and v are the c o r r e s p o n d i n g v e l o c i t i e s normal t o the w a l l . ]

C o n d i t i o n a l a v e r a g i n g i n d i c a t e d t h a t not o n l y the e j e c t i o n c o n t r i b u t e d t o the Reynolds s t r e s s but a l s o the sweep. However the e j e c t i o n events were im-p o r t a n t throughout the whole boundary l a y e r , w h i l e the sweeim-ps events aim-p- ap-peared t o be m a i n l y c o n f i n e d t o a r e g i o n c l o s e to the w a l l .

The r e s u l t s of the i n v e s t i g a t i o n of Grass [1971] agreed w e l l w i t h a l l t h a t has been r e p o r t e d above. However t h e r e i s some q u e s t i o n r e g a r d i n g the p r e c i s e r o l e of s u b l a y e r s t r e a k s i n the b u r s t i n g p r o c e s s . I n c o n t r a s t t o K l i n e et a l . [1967], C o r i n o and Brodkey [1969] c o n s i d e r e d the s u b l a y e r t o be e s s e n t i a l l y p a s s i v e i n the b u r s t i n g p r o c e s s . I n the paper of Grass t h e r e i s some s u p p o r t f o r the p a s s i v e r o l e because the same phenomena have been ob-served i r r e s p e c t i v e of boundary roughness c o n d i t i o n s .

Smith and Schwartz [1983] performed s i m u l t a n e o u s t o p and endview v i s u -a l i z -a t i o n s t u d i e s of the f l o w b e h -a v i o u r i n the n e -a r - w -a l l r e g i o n

(1 < y+ < 50) of t u r b u l e n t boundary l a y e r s f o r 1000 < Re» < 2200.

[For a boundary l a y e r Ref l i s based on the f r e e stream v e l o c i t y U„ and 8

( R ee = U^e/v, where 8 i s d e f i n e d as 6 = J U/U„( 1-U/UJdy). ] 0

U s i n g a twocamera, h i g h s p e e d v i d e o system they were a b l e to r e c o r d s i m u l t a n e o u s l y two d i f f e r e n t f i e l d s o f v i e w of a p l a n e p a r a l l e l t o the w a l l v i s u -a l i z e d w i t h hydrogen bubbles ( t o p - -and end-view: l o o k i n g i n norm-al -and up-stream d i r e c t i o n r e s p e c t i v e l y ) . T h i s v i s u a l study proved the e x i s t a n c e of r o t a t i n g , streamwise s t r u c t u r e s i n the i n n e r r e g i o n of t u r b u l e n t boundary l a y e r s f r e q u e n t l y a p p e a r i n g i n c o u n t e r r o t a t i n g p a i r s . Whenever c o u n t e r r o -t a -t i n g s -t r u c -t u r e s were v i s i b l e i n end-view, -they e v o l v e d e i -t h e r from or i n c o n j u n c t i o n w i t h a low-speed s t r e a k i n the c o r r e s p o n d i n g top-view.

Using the same e x p e r i m e n t a l arrangement as Smith and Schwartz, Smith and M e t z l e r [1983] s t u d i e d the c h a r a c t e r i s t i c s of low-speed s t r e a k s o c c u r r i n g i n the w a l l l a y e r of t u r b u l e n t boundary l a y e r s f o r 740 <_ Reg < 5830.

The s t r e a k s appeared t o have a tremendous p e r s i s t e n c e . I n the v i s c o u s subl a y e r the s t a t i s t i c s of n o n d i m e n s i o n a subl spanwise s t r e a k s p a c i n g was i n d e -pendent of the Reynolds number, h a v i n g an average v a l u e of 100. The s t r e a k s p a c i n g i n c r e a s e d w i t h i n c r e a s i n g d i s t a n c e from the w a l l owing to a merging and i n t e r m i t t e n c y process (apparent d i s a p p e a r e n c e and reappearence of s t r e a k s ) .

1.2.1.2 Q u a n t i t a t i v e measurements i n the w a l l l a y e r

The d e t e c t i o n problem i s perhaps the most d i f f i c u l t problem t h a t i s en-countered i n making q u a n t i t a t i v e measurements of b u r s t s , because the b u r s t near a w a l l i s immersed i n the background t u r b u l e n c e . Whether one uses a v i s u a l method or a measurement from a probe, or probes, t h e r e are two not u n r e l a t e d a s p e c t s of the problem of b u r s t d e t e c t i o n : what p r o p e r t y ( o r prop-e r t i prop-e s ) of thprop-e b u r s t s h o u l d bprop-e usprop-ed f o r d prop-e t prop-e c t i o n and how doprop-es onprop-e d prop-e c i d prop-e from the s e l e c t e d p r o p e r t y t h a t a b u r s t i s p r e s e n t . The l a t t e r i s s u e i s r e -a l l y -an i s s u e of d e t e c t i n g -a s i g n -a l (or s i g n -a l s ) i n n o i s e .

Gupta e t a l . [1971] have performed 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 to study the s t r e a k s w i t h a spanwise rake of ten h o t - w i r e s w i t h i n the s u b l a y e r . The l o n g - t i m e averaged two-point s p a t i a l c o r r e l a t i o n s of the streamwise ve-l o c i t y d i d not show the ' s t r e a k y ' n a t u r e of the v i s c o u s s u b ve-l a y e r ( f i g . 4 ) .

[Time averaged two-point s p a t i a l c o r r e l a t i o n Ru u( A z ) i s d e f i n e d as

R uu( Az) = u ( z ) u ( z + z ) / u ' ( z ) u ' (z+Az) , w i t h Az the spanwise s e p a r a t i o n and

u' the t u r b u l e n c e i n t e n s i t y i n streamwise d i r e c t i o n ( u ' = Y u2) - ]

But s h o r t - t i m e averaged c o r r e l a t i o n s showed the a l t e r n a t i n g h i g h - and low-speed s t r e a k s ( f i g . 5 ) . These s t r e a k s had a c h a r a c t e r i s t i c s p a c i n g of the o r d e r of lOOv/uj .

Kim et a l . [1971] have used the s h o r t - t i m e averaged a u t o c o r r e l a t i o n of the streamwise v e l o c i t y to measure the mean b u r s t p e r i o d . The measured pe-r i o d agpe-reed w i t h the v i s u a l d a t a f o pe-r the s m a l l sample s i z e c o n s i d e pe-r e d .

( a ) 25 50 4 2 * » 2 *

L

F i g u r e 4: Two-point spanwise l o n g - t i m e average c o r r e l a t i o n s of u f l u c t u a t i o n s , ( a ) Reg = 2200, y + = 3.4; (b) Reg = 3300, y + = 18.8; ( c ) R ee = 4700, y+ = 7.8; (d) Reg = 6500, y+ = 10.8. From Gupta e t a l . [1971]. li! F i g u r e 5: T y p i c a l s h o r t - t i m e average two-point c o r r e l a t i o n s of u f l u c t u a t i o n s . A v e r a g i n g over 0.375 ms, Reg = 3300, y+ = 5.4. From Gupta et a l . [1971].

B l a c k w e l d e r and K a p l a n [1972] employed a d e t e c t i o n scheme i n which the o c c u r r e n c e of a b u r s t was i n f e r r e d from a d i g i t a l p r o c e s s i n g scheme d e v i s e d by Kaplan and L a u f e r [1969]. U s i n g a s e r i e s of d i g i t i z e d v a l u e s of the us i g n a l the v a r i a n c e a t a c e r t a i n time waus computed over a us h o r t time i n t e r -v a l T,,, c e n t e r e d around the d i g i t i z e d -v a l u e of the u - s i g n a l c o r r e s p o n d i n g t o t h a t t i m e . A b u r s t was presumed to o c c u r i f the s h o r t time v a r i a n c e was g r e a t e r than a t h r e s h o l d l e v e l t h e t h r e s h o l d l e v e l e q u a l s a t h r e s h o l d p a r ameter k times the v a r i a n c e of the t o t a l d i g i t i z e d s i g n a l . Then the c a l c u l a t i o n was r e p e a t e d f o r the next d i g i t i z e d v a l u e of the u s i g n a l . T h i s d e t e c -t i o n scheme i s s e n s i -t i v e f o r l a r g e f l u c -t u a -t i o n s abou-t -the s h o r -t -time average of the s i g n a l .

B l a c k w e l d e r and K a p l a n [1976] r e p o r t e d t h a t t h e i r scheme i s not v e r y s e n s i -t i v e f o r -the s h o r -t a v e r a g i n g -time --they a d v i s e d -to use Tmur 2/ v = 10-, but

t h a t the scheme i s s e n s i t i v e f o r the t h r e s h o l d parameter k. However they s t a t e d t h a t the dependence on k does not a f f e c t the measured shape of the d e t e c t e d e v e n t s , because c o n d i t i o n a l l y averaged v e l o c i t y p r o f i l e s s c a l e w i t h the r o o t of the t h r e s h o l d v a l u e .

B l a c k w e l d e r and K a p l a n measured the i n s t a n t a n e o u s p r o f i l e s of the streamwise v e l o c i t y d u r i n g a b u r s t w i t h a r a k e of t e n h o t - w i r e s i n the w a l l r e g i o n . The u - s i g n a l a t y+ = 15 was used f o r d e t e c t i o n .

F i g . 6 shows the c o n d i t i o n a l l y sampled v e l o c i t y p r o f i l e s . These p r o f i l e s show the i n f l e c t i o n a l p o i n t near the w a l l j u s t b e f o r e d e t e c t i o n as i n d i c a t e d by the v i s u a l r e s u l t s of Kim e t a l . [1971] and C o r i n o and Brodkey [1969].

W i l l m a r t h and Lu [1972] used a d e t e c t i o n scheme based upon the v i s u a l ob-s e r v a t i o n t h a t f l u i d e j e c t i o n ob-s near the w a l l a r e preceeded by a r e g i o n of f l u i d w i t h low streamwise v e l o c i t y . A s i n g l e h o t - w i r e , a t y+ = 16.2, was

used f o r d e t e c t i o n . A b u r s t was deemed to o c c u r when the low-pass f i l t e r e d d e t e c t o r s i g n a l became lower than a t r i g g e r l e v e l . A g a i n t h e r e appeared t o be a dependency on t h i s l e v e l .

With t h i s scheme W i l l m a r t h and Lu and Lu and W i l l m a r t h [1973] s t u d i e d the i n s t a n t a n e o u s Reynolds s t r e s s near the w a l l . They found v e r y l a r g e v a l u e s d u r i n g the e j e c t i o n and sweep, as observed by C o r i n o and Brodkey [1969]. Lu and W i l l m a r t h measured a l s o the downstream c o n v e c t i o n of b u r s t s . The t r a

-j e c t o r y of the b u r s t s i n the x-y plane was i n agreement w i t h the r e s u l t s of K l i n e et a l . [1967] ( f i g . 2 ) .

F i g u r e 6: C o n d i t i o n a l l y sampled v e l o c i t y p r o f i l e s b e f o r e , T < 0, and a f t e r , T > 0, b u r s t d e t e c t i o n : ; mean v e l o c i t y p r o f i l e s :

R e6 = 2550. From B l a c k w e l d e r and K a p l a n [1972].

I n the f i r s t s t u d i e s of b u r s t s t h e p r o c e s s was c o n s i d e r e d t o be an essen t i a l wall-bounded phenomenon w i t h c h a r a c t e r i s t i c s c a l e s determined from t h e w a l l parameters uT and v. Rao e t a l . [1971] changed t h i s o p i n i o n . They

showed t h a t even i n t h e w a l l l a y e r over a f a i r l y wide range of Reynolds num bers (600 < R eQ < 9000) t h e mean b u r s t p e r i o d s c a l e d w i t h o u t e r (U„, <5 )

r a t h e r than w i t h i n n e r ( ux, 6) v a r i a b l e s . The mean d i m e n s i o n l e s s b u r s t

pe-r i o d was g i v e n by U„TB/ 6 = 5 ( f i g . 7 ) .

[Tg i s t h e mean b u r s t p e r i o d . ]

T h i s range has been extended by Narayanan and M a r v i n [1978] t o 600 < Ref t < 95000.

o w _a

1 02 O3 1 04 » - R t , t o5

F i g u r e 7: D i m e n s i o n l e s s mean b u r s t p e r i o d . From Rao e t a l . [1971].

u T

i B £

However Bandyopadhyay [1982] has d i s p r o v e d t h i s s c a l i n g . He showed t h a t t h e observed s c a t t e r i n measurements o f ILTg/cj i s not e n t i r e l y due t o t h e u n c e r -t a i n -t i e s of measuremen-t, bu-t -t h a -t -t h e s c a -t -t e r i s s y s -t e m a -t i c . So U^Tg/&l-t;$ i s not an u n i v e r s a l c o n s t a n t , but i t s v a l u e depends on the f l o w .

Ueda and H l n z e [1975] designed a d e t e c t i o n scheme based on t h e i n t e r m i t -t e n -t c h a r a c -t e r o f -the e j e c -t i o n and sweep p r o c e s s . They coun-ted -the b u r s -t r a t e u s i n g the h i g h - f r e q u e n c y band-pass s i g n a l of ( 3 u / 3 t )3. A c c o r d i n g t o Ueda and H i n z e a b u r s t o c c u r r e d when t h e a b s o l u t e v a l u e o f ( 3 u / 3 t )3 exceeded a g i v e n t h r e s h o l d v a l u e .

They measured t h a t t h e d i m e n s i o n l e s s mean b u r s t p e r i o d UraTg/6 was a p p r o x i -m a t e l y 5 f o r y+ 4 10, which v a l u e decreased t o 2.5 f o r y+ > 40 ( f i g . 8 ) .

1 10

xf

F i g u r e 8: D i s t r i b u t i o n of b u r s t p e r i o d Tg of band-pass s i g n a l . R e0: A, 1244; •, 4248. From Ueda and H i n z e [1975].

B l a c k w e l d e r and Eckelmann [1979] have made a r a t h e r d e t a i l e d s t u d y o f the s t r u c t u r e o f w a l l s t r e a k s u s i n g heated w a l l elements t o measure the s t r e a m -w i s e and span-wise v o r t i c i t y .

They i d e n t i f i e d t h e low-speed s t r e a k observed by K l i n e e t a l . [1967] as t h e a c c u m u l a t i o n r e g i o n between streamwise v o r t i c e s . They measured the stream-w i s e l e n g t h o f the v o r t i c e s t o be Xx + = 1000.

[The s u p e r s c r i p t + i n d i c a t e s t h a t t h e streamwise l e n g t h Xx of the v o r t i c e s i s made d i m e n s i o n l e s s w i t h uT and v ( Xx+ = XxuT/ v ) . ]

1.2.1.3 Comparison between methods of b u r s t d e t e c t i o n

O f f e n and K l i n e [1973] compared the b u r s t d e t e c t i o n schemes of B l a c k w e l d e r and K a p l a n [1972], W i l l m a r t h and Lu [1972] and t h r e e o t h e r schemes d e v i s e d by O f f e n and K l i n e , based upon the normal v e l o c i t y , the ve-l o c i t y - p r o f i ve-l e s ve-l o p e and the u v - s i g n a ve-l , w i t h t h e i r own v i s u a ve-l o b s e r v a t i o n s . They concluded t h a t

"none of the proposed d e t e c t i o n schemes c o r r e l a t e s v e r y w e l l w i t h the v i s u a l i n d i c a t i o n s of b u r s t i n g or w i t h any o t h e r scheme. Hence, t h e r e remain s e r i o u s q u e s t i o n s about what events a r e meas-ured by each t e c h n i q u e . D e s p i t e the poor c o r r e l a t i o n , the v a r i o u s schemes r a r e l y d e t e c t e j e c t i o n s t h a t do not pass the probe i n the p l a n e p a r a l l e l t o the w a l l , they agree w i t h each o t h e r t o a c e r -t a i n e x -t e n -t i n -t h e i r r e l a -t i o n s h i p -t o v i s u a l d a -t a , -they g e n e r a l l y produce c o n d i t i o n a l averages and v e l o c i t y s i g n a t u r e s which a r e s i m i l a r and agree q u a l i t a t i v e l y w i t h the expected r e s u l t s ( i . e . , streamwise v e l o c i t y d e f e c t , outward m o t i o n of the f l u i d , and Reyn o l d s s t r e s s e s g r e a t e r thaReyn the meaReyn), aReynd maReyny of them are as e f -f e c t i v e as the v i s u a l data at d e t e c t i n g p e r i o d s o-f h i g h uv."

1.2.2 S t r u c t u r e of the o u t e r l a y e r

1.2.2.1 Flow v i s u a l i z a t i o n i n the o u t e r l a y e r

Nychas e t a l . [1973], u s i n g the same f l o w v i s u a l i z a t i o n technique as C o r i n o and Brodkey [1969], s t u d i e d the o u t e r r e g i o n of a t u r b u l e n t boundary l a y e r .

They observed t h a t the s i n g l e most i m p o r t a n t event i n the o u t e r r e g i o n was a l a r g e - s c a l e m o t i o n , c a l l e d b u l g e , t h a t appeared as a t r a n s v e r s e v o r t e x t r a n s p o r t e d downstream w i t h a v e l o c i t y s l i g h t l y l e s s than the l o c a l mean. The observed l a r g e s c a l e motions appeared to be the r e s u l t of an i n s t a b i l i -t y - p r o d u c i n g i n -t e r a c -t i o n be-tween a c c e l e r a -t e d and d e c e l e r a -t e d f l u i d -t h a -t i s b e l i e v e d t o be c l o s e l y a s s o c i a t e d w i t h w a l l l a y e r e j e c t i o n s . The f l o w phe-nomena a s s o c i a t e d w i t h bulges extended a l l a c r o s s the boundary l a y e r and made s u b s t a n t i a l c o n t r i b u t i o n s t o the Reynolds s t r e s s .

F a l c o [1977] combined v i s u a l ( o i l d r o p p l e t s ) and h o t - w i r e o b s e r v a t i o n s . F a l c o found two types of l a r g e - s c a l e motion: one h a l f of the motions had a zone average streamwise v e l o c i t y l e s s than the l o c a l mean ( t y p e T l ) and one

I n the t u r b u l e n t boundary l a y e r F a l c o observed a r e p e t i t i v e f a m i l y of h i g h l y coherent motions, c a l l e d ' t y p i c a l e d d i e s ' . These eddies appeared a t the back of the l a r g e - s c a l e motions as s l i g h t l y f l a t t e n e d mushroom v o r t i c e s ( f i g . 9 ) .

6

.jj.^--^rl^--\r--^---^

! / * T , Jf T 2 / p T ,

V

^ 1

F i g u r e 9: A model of the f l o w i n the o u t e r r e g i o n of t u r b u l e n t boundary l a y e r s , showing the r e l a t i o n between t y p i c a l eddy s c a l e t o l a r g e - s c a l e motion s c a l e f o r moderate Reynolds numbers. From F a l c o [1977].

H o t - w i r e measurements showed t h a t the Reynolds number dependent t y p i c a l ed-d i e s proed-duce most of the Reynoled-ds s t r e s s i n the o u t e r h a l f of the l a y e r a t Reg = 1200. The l e n g t h s of the eddies s c a l e d on the i n n e r parameters and the frequency of o c c u r r e n c e of these e d d i e s s c a l e d on the o u t e r parameters, sug-g e s t i n sug-g t h a t t h e r e e x i s t s a r e l a t i o n between the s t r u c t u r e s i n the i n n e r and the o u t e r l a y e r .

Head and Bandyopadhyay [1981], u s i n g f l o w v i s u a l i z a t i o n (smoke) and h o t -w i r e measurements to study the z e r o - p r e s s u r e g r a d i e n t t u r b u l e n t boundary l a y e r over the Reynolds number range 500 < Re^ < 17500, o b t a i n e d a d i f f e r e n t p i c t u r e of the t u r b u l e n t boundary l a y e r .

At h i g h Reynolds numbers they observed many e l o n g a t e d h a i r p i n v o r t i c e s or v o r t e x p a i r s , o r i g i n a t i n g i n the w a l l r e g i o n and extended through a l a r g e p a r t of the boundary l a y e r t h i c k n e s s or beyond i t . For the most p a r t they are i n c l i n e d t o the w a l l a t a c h a r a c t e r i s t i c angle i n the range of 40° to 50°. Large s c a l e f e a t u r e s appear t o c o n s i s t m a i n l y of random a r r a y s of such h a i r p i n v o r t i c e s .

At low Reynolds numbers (which covers about t w o - t h i r d of the l i t e r a t u r e on t h i s s u b j e c t ) the h a i r p i n v o r t i c e s are much l e s s e l o n g a t e d and are b e t t e r d e s c r i b e d as horseshoe v o r t i c e s * or v o r t e x l o o p s . L a r g e - s c a l e f e a t u r e s now c o n s i s t s i m p l y of i s o l a t e d or a few i n t e r a c t i n g v o r t e x l o o p s .

Head and Bandyopadhyay suggest t h a t the t y p i c a l e d d i e s of F a l c o [1977] are i n f a c t the t i p s of the h a i r p i n v o r t i c e s .

1.2.2.2 Q u a n t i t a t i v e measurements i n the o u t e r l a y e r

I n v e s t i g a t i n g the o u t e r or i n t e r m i t t e n t r e g i o n of a t u r b u l e n t boundary l a y e r a s i m i l a r problem a r i s e s as i n d e t e c t i n g s t r u c t u r e s i n the w a l l l a y e r : what p r o p e r t y of the f l o w must be used t o d e c i d e i f the f l o w i s t u r b u l e n t or not.

The d e t e c t i o n scheme of Kovasznay et a l . [1970] was based on the presence of l a r g e - a m p l i t u d e f l u c t u a t i o n s of the d e r i v a t i v e 3u/3y, which i s one term i n the spanwise v o r t i c i t y component.

They observed t h a t v o r t i c i t y appeared t o e x h i b i t a d i s c o n t i n u i t y a c r o s s the t u r b u l e n c e i n t e r f a c e of the b u l g e , whereas the v e l o c i t y was c o n t i n u o u s . A c c o r d i n g t o Kovasznay et a l . the bulges i n the o u t e r f l o w are c o r r e l a t e d over 3 <5 i n the streamwise d i r e c t i o n and over § i n the spanwise d i r e c t i o n .

They suggested t h a t the b u r s t s observed by K l i n e e t a l . [1967] i n the n e a r -w a l l l a y e r are r e s p o n s i b l e f o r the bulges i n the o u t e r r e g i o n .

They a l s o r e p o r t e d t h a t t h e r e was a d i f f e r e n c e between the u p s t r e a m - f a c i n g (back) and the downstream-facing ( f r o n t ) p o r t i o n s of the bulges i n the o u t e r l a y e r . The back of the t u r b u l e n t n o n t u r b u l e n t i n t e r f a c e showed i n t e n s e t u r -b u l e n t a c t i v i t y * .

B l a c k w e l d e r and Kovasznay [1972] have r e p o r t e d measurements t h a t comple-ment t h e i r p r e v i o u s r e s u l t s (Kovasznay et a l . [ 1 9 7 0 ] ) , u s i n g the same exper i m e n t a l setup ( t u exper b u l e n t boundaexpery l a y e exper , Reg = 3000) and the same d e t e c -t i o n -t e c h n i q u e . They found -t h a -t i n -t e n s e f l u c -t u a -t i o n s of u and v i n -the w a l l r e g i o n remained s t r o n g l y c o r r e l a t e d out t o y/6 = 0.5, c o n f i r m i n g o t h e r ob-s e r v a t i o n ob-s t h a t the d i ob-s t u r b a n c e a ob-s ob-s o c i a t e d w i t h a b u r ob-s t extendob-s a c r o ob-s ob-s the e n t i r e boundary l a y e r .

B l a c k w e l d e r and Kovasznay e s t i m a t e d t h a t the l a r g e e d d i e s c o n t r i b u t e d as much as 80% t o the Reynolds s t r e s s i n the o u t e r l a y e r .

T h i s phenomenon i s not r e s t r i c t e d t o t u r b u l e n t boundary l a y e r s a l o n e . I n -tense t u r b u l e n t a c t i v i t y a l o n g u p s t r e a m - f a c i n g i n t e r f a c e s has has been found i n the t u r b u l e n t s l u g s and p u f f s i n p i p e f l o w (Wygnanski & Champagne [19731 and Wygnanski e t a l . [ 1 9 7 5 ] ) , i n the t u r b u l e n t spot (Wygnanski e t

Combining measured p o i n t averages of the streamwise and normal v e l o c i t i e s a t v a r i o u s l o c a t i o n s r e l a t i v e t o t h e d e t e c t o r probe they were a b l e t o c o n s t r u c t an average f l o w p a t t e r n w i t h i n and around a t u r b u l e n t bulge ( f i g - 10). T h i s p i c t u r e , showing a c i r c u l a t o r y f l o w w i t h i n the b u l g e , agrees w i t h F a l c o ' s o b s e r v a t i o n s [1977]. The o u t e r f l o w i s ' r i d i n g o v e r ' t h e t u r b u l e n t f l u i d w i t h i n the bulge h a v i n g an average v e l o c i t y Uc of 0.93U,,,.

scale IUI = 0 . 0 5 U «

F i g u r e 10: Composite v e l o c i t y d i s t r i b u t i o n i n the o u t e r r e g i o n . From B l a c k w e l d e r and Kovasznay [1972].

A n t o n i a [1972] used t h e f l u c t u a t i o n s o f the u v s i g n a l t o d e t e c t t u r b u -l e n c e i n the i n t e r m i t t e n t r e g i o n . I f ( 3 u v / 3 t )2 exceeds some a r b i t a r y t h r e s h

-o l d l e v e l , t u r b u l e n c e i s presumed t -o be p r e s e n t .

Except minor d i f f e r e n c e s r e g a r d i n g t h e shape o f the i n t e r f a c e and t h e p o i n t - a v e r a g e d streamwise v e l o c i t i e s A n t o n i a ' s r e s u l t s agree w i t h those of Kovasznay e t a l . [1970].

I n t h i s study A n t o n i a found t h a t t h e averaged Reynolds s t r e s s i n t h e bulges i s of t h e o r d e r o f h a l f t h e w a l l shear s t r e s s , s u p p o r t i n g t h e i d e a t h a t t h e s t r e n g t h of the l a r g e eddy motion i s c l o s e l y r e l a t e d t o the w a l l shear s t r e s s .

Hedley and K e f f e r [1974] performed i n v e s t i g a t i o n s s i m i l a r t o those of Kovasznay e t a l . [1970], but a t l a r g e s v a l u e s of Reg (Reg = 9700), u s i n g t h e

l a r g e a m p l i t u d e s o f [ ( 3 u / 3 t )2 + ( 3 v / 3 t )2] as d e t e c t o r .

I n g e n e r a l t h e i r r e s u l t s agree w i t h those of Kovasznay e t a l . Hedley and K e f f e r found t h a t the Reynolds s t r e s s s t r o n g l y i n c r e a s e d a c r o s s the back o f

Brown and Thomas [1977] c o r r e l a t e d t h e w a l l shear s t r e s s w i t h t h e stream-wise v e l o c i t y a c r o s s a t u r b u l e n t boundary l a y e r .

They found a l i n e of maximum c o r r e l a t i o n which l a y a t an a n g l e of 18° t o the w a l l i n downstream d i r e c t i o n . They a t t r i b u t e d t h i s l i n e t o some o r g a n i z e d s t r u c t u r e a t an o b l i q u e a n g l e t o the w a l l moving a l o n g t h e w a l l a t about 0.8UO,,. F o r they found evidence t h a t the l a r g e - s c a l e motion i n t h e o r g a n i z e d s t r u c t u r e produces a s l o w l y v a r y i n g component i n t h e w a l l shear s t r e s s and a l s o a h i g h f r e q u e n c y l a r g e a m p l i t u d e f l u c t u a t i o n o c c u r r i n g near the maximum i n the s l o w l y v a r y i n g w a l l shear s t r e s s . Brown and Thomas s t a t e d that t h e h i g h f r e q u e n c y p a r t i n the w a l l shear i s a s s o c i a t e d w i t h t h e b u r s t i n g phe-nomenon.

1.2.3 S t r u c t u r e i n t h e Reynolds s t r e s s

I n d e p e n d e n t l y W l l l m a r t h and Lu [1972] and W a l l a c e e t a l . [1972] developed a method of s o r t i n g the c o n t r i b u t i o n s t o t h e i n s t a n t a n e o u s Reynolds s t r e s s per u n i t d e n s i t y i n t o t h e f o u r quadrants of t h e u-v p l a n e . The reason f o r t h i s i s t o o b t a i n q u a n t i t a t i v e measurements o f t h e r e l a t i v e importance of the e j e c t i o n and sweep.

V i s u a l i n v e s t i g a t i o n s i n d i c a t e t h a t d u r i n g b u r s t s , t h e e j e c t i o n s h o u l d occur i n the second quadrant ( i n which u < 0 and v > 0) and t h a t t h e sweep s h o u l d occur i n the f o u r t h quadrant (u > 0, v < 0 ) . I n a d d i t i o n t o these major events t h e r e o c c u r i n t e r a c t i o n s between t h e s e two events which cause a nega-t i v e c o n nega-t r i b u nega-t i o n nega-t o nega-t h e Reynolds s nega-t r e s s . The f i r s nega-t quadrannega-t I s a s s o c i a nega-t e d w i t h a sweep b e i n g r e f l e c t e d back i n t h e o u t e r l a y e r (outward i n t e r a c t i o n : u > 0, v > 0) and t h e t h i r d quadrant w i t h an e j e c t i o n d e f l e c t e d back t o the w a l l ( i n w a r d i n t e r a c t i o n : u < 0, v < 0 ) . F i g . 11 shows the u-v p l a n e .

F i g . 12, from Brodkey e t a l . [1974] shows the d i f f e r e n t c o n t r i b u t i o n s of each quadrant t o t h e Reynolds s t r e s s . C l o s e t o the w a l l ( y+ < 15) t h e sweep

c o n t r i b u t e s most t o the Reynolds s t r e s s , whereas f o r t h e r e g i o n f u r t h e r away from t h e w a l l i t i s the e j e c t i o n t h a t i s most i m p o r t a n t f o r the Reynolds s t r e s s .

Lu and W i l l m a r t h [1973] extended t h e t e c h n i q u e of s o r t i n g uv c o n t r i b u t i o n s i n t o q u a d r a n t s . They i n t r o d u c e d a f u r t h e r c l a s s i f i c a t i o n of the uv c o n t r i b

-V u F i g u r e 11: The u-v p l a n e . F i g u r e 12: The s o r t e d Reynolds s t r e s s e s n o r m a l i z e d w i t h t h e l o c a l average Reynolds s t r e s s , (•, •, r e s u l t s of W i l l m a r t h and L u [1972]): , sweep,. , e j e c t i o n , , outward i n t e r a c t i o n , — , inward i n t e r a c t i o n . From Brodkey e t a l , [1974].

u t i o n s t o each quadrant depending upon the magnitude of the c o n t r i b u t i o n by drawing a ' h o l e ' i n t h e u-v plane ( f i g . 1 3 ) .

Now f i v e r e g i o n s can be d i s t i n g u i s h e d . The h o l e i s bounded by curves |uv| = Hu'v'.

[H i s c a l l e d the h o l e - s i z e .

v' i s the t u r b u l e n c e i n t e n s i t y i n normal d i r e c t i o n ( v ' =\vz).]

The f o u r quadrants e x c l u d i n g the h o l e a r e t h e o t h e r f o u r r e g i o n s . With t h i s h o l e t e c h n i q u e or quadrant a n a l y s i s t e c h n i q u e l a r g e c o n t r i b u t o r s t o uv r e l a

-V

l j l u v l = c o n s l a n t

~1

F i g u r e 13: S k e t c h of t h e h o l e i n the u-v p l a n e .

t i v e t o the l o c a l t u r b u l e n c e i n t e n s i t i e s u' and v' can be e x t r a c t e d l e a v i n g the s m a l l e r f l u c t u a t i n g u v ( t ) - s i g n a l i n t h e h o l e .

F i g . 14 i s a t y p i c a l r e s u l t of t h e h o l e - t e c h n i q u e . From t h i s f i g u r e i t can be deduced t h a t f o r most of t h e time the u v - s i g n a l i s s m a l l and t h a t i n a s h o r t time t h e e j e c t i o n and sweep events make s u b s t a n t i a l c o n t r i b u t i o n s to the Reynolds s t r e s s .

F i g u r e 14: F r a c t i o n a l c o n t r i b u t i o n s t o uv from d i f f e r e n t events at y/6 = 0.021. Quadrant 1: 0; quadrant 2: S; quadrant 3: SB; quadrant 4: N; h o l e : O. F r a c t i o n of time i n h o l e :

. From Lu and W i l l m a r t h [1973].

T a k i n g f o r i n s t a n c e a h o l e - s i z e of 1 i t f o l l o w s from f i g . 14 t h a t t h e h o l e c o n t r i b u t e s i n 80% o f t h e time o n l y 18% t o the Reynolds s t r e s s . The e j e c t i o n (72%) and the sweep (26%) account f o r t h e r e m a i n i n g p o s i t i v e Reynolds

s t r e s s , w h i l e the outward and inward i n t e r a c t i o n make s m a l l n e g a t i v e con-t r i b u con-t i o n s con-t o con-the Reynolds s con-t r e s s ( 4 % r e s p e c con-t i v e l y 1 0 % ) .

1.2.4 O r g a n i z e d motion i n a t u r b u l e n t boundary l a y e r

A l o t of models have been suggested to d e s c r i b e the behaviour of the w a l l and o u t e r l a y e r and the c o n n e c t i o n between these two r e g i o n s . I n t h i s con-t e x con-t o n l y con-the model of H i n z e [1975] i s d e s c r i b e d h a v i n g much i n common w i con-t h the models of O f f e n and K l i n e [1973] and of Smith [1983]. J o i n i n g f a c t s ob-t a i n e d from e x p e r i m e n ob-t a l i n v e s ob-t i g a ob-t i o n s H i n z e c o n s ob-t r u c ob-t e d ob-the f o l l o w i n g q u a l i t a t i v e d e s c r i p t i o n of the t u r b u l e n c e mechanism i n the w a l l l a y e r :

" I t i s s t r i k i n g t h a t , n o t w i t h s t a n d i n g the random n a t u r e o f the t u r b u l e n c e , a r e p e t i t i o n of s i m i l a r p r o c e s s e s may be d i s t i n -g u i s h e d , w i t h a d i s t i n c t and r e c o -g n i z a b l e avera-ge s p a c i n -g i n both spanwise and streamwise d i r e c t i o n s . I n time i t corresponds w i t h , on the average, some c y c l i c p r o c e s s , w i t h many f e a t u r e s s i m i l a r t o the l a m i n a r - t u r b u l e n t t r a n s i t i o n p r o c e s s . When t r y i n g t o g i v e a d e s c r i p t i o n of t h i s ' c y c l i c ' process i n the f u l l y developed t u r b u -l e n t f -l o w , i t i s i m m a t e r i a -l where the b e g i n n i n g of the ' c y c -l e ' i s f i x e d . Because of the s i m i l a r i t y mentioned w i t h the t r a n s i t i o n process we w i l l b e g i n the ' c y c l e ' w i t h the s i t u a t i o n where, owing t o a l a r g e - s c a l e d i s t u r b a n c e a l r e a d y p r e s e n t i n the o u t e r r e g i o n and o u t e r p a r t of w a l l r e g i o n , a horseshoeshaped v o r t e x i s b e g i n -n i -n g t o be formed l o c a l l y a t the w a l l . T h i s v o r t e x i s deformed by the f l o w i n t o a more and more e l o n g a t e d U-shaped l o o p i n stream-w i s e d i r e c t i o n . Because of s e l f - i n d u c t i o n processes the t i p of t h e loop moves away from the w a l l thereby coming i n t o r e g i o n s of e v e r - i n c r e a s i n g v e l o c i t i e s . Consequently the v o r t i c i t y i n c r e a s e s due t o s t r e t c h i n g p r o c e s s e s . A t the same time i t g i v e s r i s e t o an outward f l o w between the l e g s of the U-loop, w i t h a s t r o n g v-com-ponent near the t i p . Between the v o r t e x moving away from the w a l l and the w a l l a l o c a l d e c e l e r a t i o n of the f l u i d i s e f f e c t e d . T h i s p r o c e s s t r a n s p o r t s low-momentum f l u i d away from the the w a l l , thus p r o d u c i n g a p o s i t i v e and marked c o n t r i b u t i o n t o the Reynolds s t r e s s . Moreover, a t d i s t a n c e s y+ = 5 t o 30, an i n t e n s e h o r i z o n t a l

s h e a r - l a y e r i s formed, showing up i n the i n s t a n t a n e o u s U - v e l o c i t y as a dent w i t h i n f l e c t i o n p o i n t s . The r e s u l t a n t l o c a l i n f l e x i o n a l i n s t a b i l i t y and breakdown of the f l o w s u r r o u n d i n g t h e o r i g i n a l t i p

of the v o r t e x produces a t u r b u l e n c e b u r s t , s i m i l a r t o t h a t observed d u r i n g the l a m i n a r t u r b u l e n t t r a n s i t i o n p r o c e s s . The p r e s -sure waves a s s o c i a t e d w i t h the t u r b u l e n c e b u r s t a r e propagated throughout t h e whole boundary l a y e r . At t h e same time t h e b l o b of f l u i d of h i g h t u r b u l e n c e i n t e n s i t y produced d u r i n g t h e b u r s t i s convected downstream and moves f a r t h e r away from the w a l l , thereby i n c r e a s i n g i n s c a l e , amongst o t h e r s , by t u r b u l e n t d i f f u s i o n . S i n c e a t t h e same time high-momentum f l u i d i s e n t e r i n g from upstream, the above b l o b of f l u i d i s convected i n an a c c e l e r a t e d way o r swept i n downstream d i r e c t i o n . The above p r e s s u r e s waves may add to the movement of f l u i d towards t h e w a l l , r e s u l t i n g i n a sweepi n r u s h f l o w . The sweepi n r u s h process has a l r e a d y been preceded and sweepi n sweepi -t i a -t e d by a n e g a -t i v e v-componen-t downs-tream o f -the U-looped v o r -t e x b e f o r e i t s breakdown. The sweep-inrush f l o w makes a v e r y s m a l l an-g l e (5° t o 15°) w i t h t h e w a l l , w h i c h a t t h e w a l l a l s o i s observed as t h e e n t r y o f h i g h e r momentum f l u i d i n almost h o r i z o n t a l d i r e c -t i o n . Bo-th -t h e e j e c -t i o n b u r s -t p r o c e s s , as w e l l as -t h e sweep-inrush f l o w c o n t r i b u t e t o t h e s h e a r - s t r e s s , and c o n s e q u e n t l y a r e respon-s i b l e f o r t h e t u r b u l e n t p r o d u c t i o n , m a i n l y i n t h e r e g i o n y+ = 10 to 15 from t h e w a l l .

The h o r i z o n t a l movement d u r i n g the sweep-inrush p e r i o d w i l l be s t r o n g l y r e t a r d e d near t h e w a l l . I t may e v e n t u a l l y , i n c o n j u n c t i o n w i t h the a c t i o n of o v e r t a k i n g f a s t e r moving f l u i d a t a g r e a t e r d i s t a n c e from the w a l l develop i n t o a n o t h e r horseshoetype v o r -t e x . "

I n f i g . 15 an attempt i s made t o show t h e ' c y c l i c ' p r o c e s s d e s c r i b e d above. Of course t h i s model, showing o n l y the e j e c t i o n , i s h i g h l y i d e a l i z e d .

H i n z e and o t h e r s (Rao e t a l . [1971], Kovasznay e t a l . [1970], Nychas et a l . [1973]) c o n s i d e r t h e b u r s t process t o be a r e s u l t o f an i n s t a b i l i t y of the s u b l a y e r produced by the p r e s s u r e f i e l d a s s o c i a t e d w i t h the the l a r g e -s c a l e motion i n t h e o u t e r l a y e r .

A c c o r d i n g t o O f f e n and K l i n e [1973] t h e sweeping motions from the l o g a r i t h m i c r e g i o n impress on the w a l l l a y e r t h e temporary a d v e r s e p r e s s u r e g r a -d i e n t r e q u i r e -d t o cause the s t r e a k l i f t u p t h a t prece-des an e j e c t i o n . Smith

[1983] suggests t h a t d u r i n g b u r s t i n g n o t one but more (2 t o 5) h o r s e s h o e -shaped v o r t i c e s a r e formed c r e a t i n g a spanwise p r e s s u r e g r a d i e n t which