Meandering of small streams in Alluvium

1 6 .

MEANDERING OF SMALL STREAMS

IN ALLUVIUM

by

P e t e r A c k e r s and F.G. C h a r l t o n

M.Sc. (Eng.),A.G.G.I. B.Sc. (Eng.), M.I.C.E.,

M.I.C.E, M.I.Mun.E. M.I.W.E., M.A.S.C.E.,

Crown C o p y r i g h t

Report No. H y d r a u l i c s Research S t a t i o n

-rp^rp -77 W a l l i n g f o r d

B e r k s h i r e

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-SYNOPSIS

Investigations were made at the Hydraulics Research

Station of channels which achieved a meander pattern in

alluvium through natural processes at discharges between

0.2 and 3.2 cusecs.

These followed an earlier programme

in which the behaviour of straight channels was studied.

Discharge, sediment load, hydraulic gradient and channel

geometry were measured, and empirical correlations of the

stream geometry with discharge and sediment load were

deduced.

The movement of eroded bank material, the migration

of meanders and the effect of sediment load on meander length

were studied.

It emerged that channels with small

sediment loads remained straight and meandering occurred

naturally at higher sediment loads.

The ultimate pattern

was also shown to be influenced by the initial channel

condition.

Flow resistance and channel shape were compared

with a straight channel when about 60 percent of the

energy loss was found to be due to the non-prismatic boundary

of meandered channels.

At the threshold of meandering,

losses due to the development of shoals were found to be

25 percent of the total.

Dimensional analysis elucidated that no simple relation

between meander length and discharge is completely

satisfactory and none of the many empirical relations

between meander length and discharge has any special

significance.

A laboratory investigation of variable discharge

hydrographs and a study of field discharge data revealed

that the bank-full discharge or a flood with a recurrence

interval of about a year, whichever is the lesser,

CONTENTS

PAGE

INTRODUCTION ]_

D e f i n i t i o n s and t e r m i n o l o g y

SCOPE OF INVESTIGATION 7

RESEARCH FACILITIES 10

DESCRIPTION OF EXPERIMENTS 14

EXPERIMENTAL RESULTS 16

Development o f c h a n n e l 16

Development o f c h a n n e l v / i t h i n p r e v i o u s l y

formed w i d e r c h a n n e l 18

Geometry as f u n c t i o n o f d i s c h a r g e 19

I n t e r - r e l a t i o n s h i p o f c h a n n e l d i m e n s i o n s 23

I n f l u e n c e o f sediment charge on meander

geometry

Sediment movement and m i g r a t i o n o f

meanders

Flow r e s i s t a n c e and v a l l e y s l o p e 32

C r o s s - s e c t i o n a l shape and r e s i s t a n c e

compared w i t h a s t r a i g h t c h a n n e l 36

D i m e n s i o n a l a n a l y s i s o f meander geometry 4 3

The i n f l u e n c e o f a p e r i o d i c v a r i a t i o n i n 53

d i s c h a r g e

Comparison w i t h f i e l d d a t a 56

SUMflARY AND CONCLUSIONS 64

LIST OF SYMBOLS 7 I

REFERENCES

7 4

25

28

TABLES

1. D i m e n s i o n l e s s c o r r e l a t i o n . B e s t - f i t e q u a t i o n s .

m

2. Steady d i s c h a r g e e x p e r i m e n t s

, 3. V a r i a b l e d i s c h a r g e e x p e r i m e n t s .

M M

FIGURES

1. P l a n o f e x p e r i m e n t a l a r e a .

2. Grading c u r v e o f 0.15 mm sand.

3. V a r i a t i o n o f meander l e n g t h w i t h d i s c h a r g e .

4. R e l a t i o n between w a t e r s u r f a c e w i d t h , meander b r e a d t h

and d i s c h a r g e .

5. E f f e c t o f d i s c h a r g e on r a t i o s o f p l a n d i m e n s i o n s .

6. Comparison o f p l a n d i m e n s i o n s .

7. L i m i t i n g sediment l o a d s .

8. E x a m i n a t i o n o f e f f e c t o f c o n c e n t r a t i o n on meander l e n g t h .

9. Development o f meandering.

10. Development o f s h o a l s and meanders.

1 1 . F l u o r e s c e n t t r a c e r s t u d y o f movement o f eroded bank m a t e r i a l .

12. T y p i c a l v a r i a t i o n o f s l o p e w i t h t i m e .

13. R e s i s t a n c e a n a l y s i s

14. L i m i t i n g s l o p e s .

15. Area and h y d r a u l i c mean d e p t h .

16. Maximum d e p t h s a t bends and c r o s s - o v e r s .

17. C r o s s - s e c t i o n s o f s t r a i g h t and meandered c h a n n e l s .

18. D i m e n s i o n l e s s m e a n d e r - l e n g t h v e r s u s d i m e n s i o n l e s s

d i s c h a r g e : l a b o r a t o r y d a t a f r o m s e v e r a l s o u r c e s .

19. D i m e n s i o n l e s s c o r r e l a t i o n o f meander geometry:

l a b o r a t o r y d a t a f r o m s e v e r a l s o u r c e s .

20. V a r i a b l e f l o w h y d r o g r a p h s .

21. F i e l d and H.R.S. d a t a on meander l e n g t h p l o t t e d a g a i n s t

(a) b a n k - f u l l d i s c h a r g e (b) mean a n n u a l d i s c h a r g e

(c) mean o f month o f maximum d i s c h a r g e and (d)

mean annual f l o o d d i s c h a r g e .

22. D i m e n s i o n l e s s c o r r e l a t i o n o f meander geometry:

i n c o r p o r a t i o n o f f i e l d d a t a .

PLATES

1. G e n e r a l v i e w o f a r e a showing i n i t i a l s t r a i g h t c h a n n e l .

2. Channel w i t h v e r y low upstream sediment i n j e c t i o n r a t e

(Run 15, hour 145, low f l o w )

3. Channel w i t h s l i g h t l y i n a d e q u a t e u p s t r e a m sediment

i n j e c t i o n r a t e (Run 8, hour 312, low f l o w )

4(a) Channel showing w e l l d e v e l o p e d meanders a t low f l o w

(Run 12, hour 99 low f l o w )

4(b) Channel showing w e l l d e v e l o p e d meanders a t h i g h f l o w

(Run 12, hour 99, normal f l o w )

5. Channel w i t h h i g h upstream sediment i n j e c t i o n r a t e

showing b r a i d i n g . (Run 3, hour 236, low f l o w )

6(a) Channel w i t h no i n j e c t i o n o f sediment upstream showing

w e l l d e v e l o p e d s h o a l s a t 145 hours (Run 20/1, hour

14 5 low f l o w )

6(b) Channel w i t h no i n j e c t i o n o f sediment upstream showing

w e l l developed s h o a l s a t 362 hours and t h e maintenance

o f a s t r a i g h t c h a n n e l . (Run 20/1, hour 362, low f l o w )

7(a) Channel showing t h e development o f meanders a f t e r t h e

i n j e c t i o n o f s u f f i c i e n t sediment (Run 20/11 hour

559, low f l o w )

7(b) Channel showing i n c r e a s e i n meander b e l t w i d t h (Run

20/11, hour 794, low f l o w )

8(a) Channel w i t h adequate r a t e o f sediment i n j e c t i o n

upstream (Run 19, hour 4 52, low f l o w )

8(b) Channel w i d t h same d i s c h a r g e and sediment i n j e c t i o n

r a t e , showing change i n b e l t w i d t h due t o i n i t i a l

s l o p e (Run 2 1 , hour 480, low f l o w )

8(c) Channel showing i n c r e a s e i n b e l t w i d t h w i t h t i m e

(Run 2 1 , hour 651, low f l o w )

9. Channel w i t h s u f f i c i e n t sediment showing a change o f

phase (Run 7, hour 379, low f l o w )

10. Channel w i t h v a r i a b l e f l o w and low r a t e o f sediment

i n j e c t i o n upstream (Run 16, hour 360, low f l o w )

11. Channel w i t h v a r i a b l e f l o w and low r a t e o f sediment

i n j e c t i o n upstream (Run 17, hour 293, low f l o w )

12. Channel w i t h v a r i a b l e f l o w and adequate r a t e o f

MEANDERING OF SMALL STREAMS

IN ALLUVIUM

INTRODUCTION

N a t u r a l c h a n n e l s r a r e l y r e m a i n s t r a i g h t f o r

d i s t a n c e s g r e a t e r t h a n about t e n c h a n n e l w i d t h s , ( 3 0 ) , and

t h u s i t would appear t h a t a s t r a i g h t a l i g n m e n t i s u n u s u a l

under n a t u r a l c o n d i t i o n s i n e r o d i b l e m a t e r i a l . I n h e r e n t i n

t h e m a j o r i t y o f , i f n o t a l l , streams a r e f o r c e s w h i c h oppose

t h e maintenance o f a s t r a i g h t c h a n n e l and may cause a meander

or b r a i d e d p a t t e r n t o d e v e l o p .

A l t h o u g h meandering c h a n n e l s have been s t u d i e d i n b o t h

f i e l d and l a b o r a t o r y f o r many y e a r s and numerous h y p o t h e s e s

have been p u t f o r w a r d c o n c e r n i n g t h e i r c a u s a t i o n , t h e r e

e x i s t s t o d a y no g e n e r a l l y a c c e p t e d e x p l a n a t i o n f o r t h e i r

development. Werner (53) has summarised t h e e a r l y h i s t o r y

from Von Baer who i n 1858 suggested t h a t t h e r o t a t i o n o f t h e

e a r t h produced secondary c u r r e n t s w h i c h caused unequal bank

e r o s i o n and hence t h e development o f meanders. L o c a l d i s

-t u r b a n c e s due -t o v a r i a -t i o n s i n bank m a -t e r i a l , o b s -t r u c -t i o n s ,

t r i b u t a r y c o n f l u e n c e s e t c . , have a l s o been p u t f o r w a r d as

t h e cause o f meandering by many a u t h o r s , i n c l u d i n g Penck i n

1894, Davies i n 1903, Hedin i n 1904 and V u j e v i c i n 1906.

J e f f e r s o n (24) i n 1902 and S c h o k l i t s c h i n 1930 a t t r i b u t e d

t h e o r i g i n o f meanders t o e x c e s s i v e energy i n a s t r e a m , and

i n 1936 R u s s e l d i s c u s s e d t h e e f f e c t o f c h a n g i n g r i v e r s t a g e

as a p o s s i b l e c a u s e . The e x i s t e n c e o f s e c o n d a r y c u r r e n t s i n a s t r e a m has o f t e n b e e n s u g g e s t e d as t h e c a u s e o f m e a n d e r s , by Thomson i n i s y e ' ' ^ ^ ' , Hamburg i n 1 9 c 3 , de Geer i n 1 9 1 1 , S t a n l e y i n 1 8 8 1 , E x n e r i n 1919 and T a n n - r i n 1960. F u j i y o s h i i n 1950'-"-^^ p u t f o r w a r d an e x p l a n a t i o n b a s e d on t h e d e v e l o p m e n t o f c o n v e c t i o n c u r r e n t s , and S c h e i j e g g e r has s u g g e s t e d a t h e r m o d y n a m i c a n a l o g y . Werner'^^^ i n 1951 s u g g e s t e d t h a t a t r a n s v e r s e s e i c h e i n an i n i t i a l l y s t r a i g h t c h a n n e l c o u l d i n i t i a t e m e a n d e r i n g . The c o n c e p t o f t r a n s v e r s e o s c i l l a t i o n s was a l s o t h e b a s i s o f A n d e r s o n ' s ' ^ ' w o r k r e p o r t e d i n 19 67. A n o t h e r c o n c e p t t h a t has come t o t h e f o r e i n r e c e n t y e a r s r e c o g n i s e d t h e d e p e n d e n c e o f s t r e a m g e o m e t r y on s e d i m e n t t r a n s p o r t : C a l l a n d e r ' ^ ' , f o r e x a m p l e , has v e r y r e c e n t l y c o n s i d e r e d t h e s t a b i l i t y o f t h e r e s i s t a n c e and s e d i m e n t t r a n s p o r t f u n c t i o n . Schumm has s u g g e s t e d a dependence a l s o on t h e p e r c e n t a g e o f f i n e s e d i m e n t s i n t h e bed m a t e r i a l . I n s p i t e o f t h e v a r i o u s h y p o t h e s e s , h o w e v e r , t h e t r u e c a u s e i s s t i l l o b s c u r e . T h e r e e x i s t s no g e n e r a l l y a c c e p t e d means o f p r e d i c t i n g , u n d e r g i v e n c o n d i t i o n s o f f l u i d and s e d i m e n t f l u x , w h e t h e r meanders w i l l o c c u r , a l t h o u g h t h e r e i s c o n s i d e r a b l e e m p i r i c a l i n f o r m a t i o n w h i c h i s o f v a l u e i n p r e d i c t i n g a s p e c t s o f t h e g e o m e t r i c a l p a t t e r n w h i c h m i g h t r e s u l t . T h e r e r e m a i n c o n s i d e r a b l e d i f f e r e n c e s o f • p i n i o n a b o u t t h e t y p e s o f s t r e a m s w h i c h meander. W e r n e r , Jl example,'^^* , s t a t e s t h a t m e a n d e r i n g s t r e a m s a r e . . j t o r i o u s l y s h a l l o w and t h a t m e a n d e r i n g does n o t o c c u r i f t h e w a t e r d e p t h e x c e e d s a c e r t a i n v a l u e . He a l s o s t a t e s t h a t a c e r t a i n bed l o a d i s n e c e s s a r y t o i n i t i a t e i e a n d e r i n g and t h a t s u p e r f l u o u s s i l t c o n t e n t may p r e v e n t m e a n d e r i n g . Schumm''^^', on t h e o t h e r h a n d , b e l i e v e s t h a t r e l a t i v e l y w i d e s h a l l o w c h a n n e l s t e n d t o be s t r a i g h t w h e r e a s r e l a t i v e l y n a r r o w , deep c h a n n e l s t e n d t o meander, b u t he a l s o c o n c l u d e d t h a t s i l t c o n t e n t a f f e c t s t h e (41,43) g e o m e t r y L e o p o l d and W o l m a n a g r e e w i t h W e r n e r , s u g g e s t i n g t h a t i n c h a n n e l s deep i n r e l a t i o n t o w i d t h t h e v e l o c i t y i s n e a r l y c o n s t a n t w i t h d e p t h , h e n c e h e l i c a l c i r c u l a t i o n becomes n e g l i g i b l e and i n c u r v e d c h a n n e l s p o t e n t i a l f l o w a p p r o x i m a t e s . T h i s r e s u l t s i n a v a r i a t i o n o f d o w n s t r e a m v e l o c i t y i n v e r s e l y w i t h t h e r a d i u s o f t h e s t r e a m l i n e s ; t h e t h r e a d o f h i g h v e l o c i t y h u g s t h e c o n v e x b a n k a n d d o e s n o t c r o s s t h e c h a n n e l . Thus a m e c h a n i s m f o r t h e f o r m a t i o n o f s h o a l s i s a b s e n t . M a t t h e s ' ^ ^ ' , h o w e v e r , s t a t e s t h a t h e l i c o i d a l f l o w t a k e s p l a c e i n c h a n n e l s deep i n r e l a t i o n t o w i d t h and he b e l i e v e s t h a t m e a n d e r i n g c h a n n e l s a r e s h a l l o w and d e v o i d o f h e l i c o i d a l f l o w . T h e r e was no e v i d e n c e o f h e l i c o i d a l f l o w i n t h e M i s s i s s i p p i o r o t h e r r i v e r e x a m i n e d by h i m . B a g n o l d ' ^ ' has shown t h a t t h e r e s i s t a n c e t o f l o w i n a r i g i d c h a n n e l o f u n i f o r m c r o s s s e c t i o n f a l l s s h a r p l y t o a d e f i n e d minimum w i t h i n a n a r r o w r a n g e o f 2 < ^ < 3. I n a n a t u r a l l y o c c u r r i n g m e a n d e r i n g c h a n n e l t h e c r o s s s e c t i o n i s n o t u n i f o r m b u t i t has b e e n f o u n d b y L e o p o l d and Wolman t h a t t h e m a j o r i t y o f r i v e r c u r v e s h a v e a r a t i o o f c u r v a t u r e r a d i u s t o c h a n n e l w i d t h b e t w e e n 2 and 3. On t h e o t h e r h a n d , L e o p o l d e t a l ' ^ ^ ' h a v e c o n c l u d e d t h a t t h e r e i s no d o u b t t h a t b r a i d e d o r m e a n d e r i n g c h a n n e l s o f f e r l a r g e r r e s i s t a n c e t o f l o w t h a n o t h e r w i s e c o m p a r a b l e s t r a i g h t c h a n n e l s . T h i s i s s u p p o r t e d by B l e n c h and Q u r e s h y ' ^ ' who have s t a t e d t h a t m e a n d e r i n g c h a n n e l s o f l o w s i n u o s i t y r e q u i r e a b o u t 1.5 t i m e s t h e s l o p e o f c o m p a r a b l e s t r a i g h t c h a n n e l s and v e r y c o n v o l u t e d ones r e q u i r e a b o u t 2.5 t i m e s t h i s v a l u e . I n g l i s s u g g e s t e d t h a t t h e r e w e r e t w o c l a s s e s o f m e a n d e r i n g . I n w h a t he c a l l e d " p r i m a r y m e a n d e r i n g " t h e e x c e s s c h a r g e f r o m u p s t r e a m was s a i d t o c r o s s t o t h e c o n v e x b a n k , w h e r e a s i n s e c o n d a r y m e a n d e r i n g t h e e x c e s s c h a r g e , b e i n g d e v e l o p e d i n t h e meander embayment by b a n k e r o s i o n , w o u l d d e p o s i t as a s h o a l a l o n g t h e same b a n k . F r i e d k i n 3

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i n v e s t i g a t e d t h e movement o f m a t e r i a l e r o d e d f r o m t h e b a n k and c o n c l u d e d t h a t i t was d e p o s i t e d f u r t h e r d o w n s t r e a m o n t h e same s i d e o f t h e s t r e a m as t h a t f r o m w h i c h i t was e r o d e d , when

t h e b a n k s e r o d e d r a p i d l y , b u t t h a t when t h e b a n k s d i d n o t ^ e r o d e t h e s e d i m e n t c r o s s e d f r o m one b a n k t o t h e o t h e r . T h i s d e p o s i t i o n o f e r o d e d m a t e r i a l o n t h e same s i d e was c o n f i r m e d f by W h i t e . I t was s u g g e s t e d i n a p r e v i o u s p a p e r b y one o f t h e f (12) L p r e s e n t A u t h o r s t h a t t h e s e d i m e n t c h a r g e i s a n i m p o r t a n t f a c t o r i n t h e d e v e l o p m e n t and m a i n t e n a n c e o f a r e g u l a r s i n u o u s c h a n n e l . From t h e p r e v i o u s i n v e s t i g a t i o n o f t h e g e o m e t r y o f s t r a i g h t c h a n n e l s i t a p p e a r e d t h a t a l o w s e d i m e n t c o n t e n t i n h i b i t e d t h e p r o c e s s o f m e a n d e r i n g i n a n i n i t i a l l y s t r a i g h t c h a n n e l , b u t i t n e v e r t h e l e s s a p p e a r e d t h a t t h e mechanism l e a d i n g t o t h e d e v e l o p m e n t o f a meander p a t t e r n e x i s t e d i n t h e i n i t i a l l y s t r a i g h t c h a n n e l . B o t h F r i e d k i n a n d M a t t h e s ' ^ ^ ' b e l i e v e t h a t b a n k c u t t i n g and t h e t r a n s f e r o f s e d i m e n t t o a p o i n t o f d e p o s i t i o n o n a s h o a l a r e p r i n c i p a l r e q u i r e m e n t s i n t h e f o r m a t i o n o f m e a n d e r s . W h i l e a g r e e i n g w i t h t h e s e v e r y n e c e s s a r y s t a g e s i n t h e d e v e l o p m e n t o f m e a n d e r s , i t i s s u g g e s t e d t h a t t h e s e a r e e f f e c t s r a t h e r t h a n o r i g i n a l c a u s e s o f a s i n u s o i d a l component o f m o t i o n , and t h a t u n t i l a c e r t a i n amount o f s e d i m e n t i s i n movement i n s h o a l s o n a l t e r n a t e b a n k s

e r o s i o n o f embayments does n o t o c c u r . T h i s was d e m o n s t r a t e d i n t h i s s e r i e s o f i n v e s t i g a t i o n s b y t h e f o r m a t i o n o f

s h o a l s and d e e p s o n a l t e r n a t e s i d e s a l o n g a g e n e r a l l y s t r a i g h t c h a n n e l , f o l l o w e d b y t h e i r s t e a d y g r o w t h u n t i l , a l m o s t s i m u l t a n e o u s l y a l o n g t h e l e n g t h o f t h e c h a n n e l ,

bank e r o s i o n b e g a n and t h e meander l o o p s d e v e l o p e d . ^

L

I f b a n k e r o s i o n w e r e t h e i n i t i a l c a u s e o f r e g u l a r

m e a n d e r i n g t h e n an o b s t r u c t i o n i n a s t r a i g h t c h a n n e l c a u s i n g ^ e r o s i o n o f one bank w o u l d be e x p e c t e d t o p r o d u c e a p a t t e r n

o f r e g u l a r s i n u o u s c u r v e s . The s e c o n d a u t h o r i n e x p e r i m e n t s p some y e a r s ago w i t h o b s t r u c t i o n s and l o w s e d i m e n t d i s c h a r g e s

4 o b s e r v e d t h a t a s e r i e s o f c u r v e s o f g r a d u a l l y d i m i n i s h i n g a m p l i t u d e r e s u l t e d , s u g g e s t i n g a t e n d e n c y t o r e v e r t t o a s t r a i g h t c h a n n e l . I n a d d i t i o n , s u c h a s e r i e s o f e r o d e d embayments b e y o n d a n o b s t r u c t i o n d e v e l o p e d p r o g r e s s i v e l y d o w n s t r e a m and n o t s i m u l t a n e o u s l y a l o n g t h e l e n g t h o f c h a n n e l . Some o f t h e c o n f u s i o n w h i c h o c c u r s i n t h i s f i e l d may be due t o t h e l a c k o f a n y a g r e e d m e t h o d o f c l a s s i f y i n g m e a n d e r s . From t h e r e s u l t s o f t h e p r e s e n t and p r e v i o u s i n v e s t i g a t i o n s , t h e r e f o r e , i t w o u l d a p p e a r n e c e s s a r y t o d i f f e r e n t i a t e b e t w e e n : ( i ) c o n d i t i o n s w h i c h may l e a d t o t h e e r o s i o n o f a b a n k a t one o r more p o i n t s r e s u l t i n g i n a n i r r e g u l a r c h a n n e l f o r a l i m i t e d d i s t a n c e ( e . g . n o n - u n i f o r m i t y o f c h a n n e l b a n k , o b s t r u c t i o n , e t c . ) , and i i i ) c o n d i t i o n s n e c e s s a r y f o r t h e d e v e l o p m e n t and m a i n t e n a n c e o f a r e g u l a r s i n u o u s c h a n n e l i n a homogeneous a l l u v i u m . I t i s t h e s e c o n d c o n d i t i o n o n l y w h i c h i s c o n s i d e r e d i n t h i s r e p o r t . D e f i n i t i o n s a n d t e r m i n o l o g y N e a r l y a l l c h a n n e l s i n e r o d i b l e m a t e r i a l e x h i b i t some t e n d e n c y t o d e v e l o p c u r v e s , a n d a t t e m p t s h a v e b e e n made t o d e f i n e a m e a n d e r i n g c h a n n e l o n t h e b a s i s o f symmetry o f t h e meander l o o p s , d e g r e e o f s i n u o s i t y and so o n . However, due t o t h e e f f e c t o f t h e l a c k o f h o m o g e n i t y o f b e d and b a n k m a t e r i a l s o f n a t u r a l s t r e a m s , i r r e g u l a r p a t t e r n s f r e q u e n t l y o c c u r . Schumm''*^' c l a s s i f i e d c h a n n e l s i n t o f i v e g r o u p s : ( i ) t o r t u o u s , ( i i ) i r r e g u l a r ( i i i ) r e g u l a r ( i v ) t r a n s i t i o n a l a n d ( v ) s t r a i g h t . The e x p e r i m e n t a l l a b o r a t o r y c h a n n e l s e s t a b l i s h e d i n homogeneous, c o h e s i o n l e s s sand i n t h e p r e s e n t i n v e s t i g a t i o n h a v e b e e n g r o u p e d a s f o l l o w s : 5

(a) s t r a i g h t o r s l i g h t l y i r r e g u l a r c h a n n e l s ; (b) r e g u l a r s i n u o u s o r m e a n d e r i n g c h a n n e l s , a n d (c) b r a i d e d c h a n n e l s ( i . e . m u l t I - t h r e a d s y s t e m s d i v i d e d b y i s l a n d s o r s h a l l o w s ) . C h a n n e l w i d t h b i s t h e w i d t h o f a s t r a i g h t o r m e a n d e r i n g c h a n n e l , w h i c h i n t h e p r e s e n t c o n t e x t d e v e l o p s b y bank e r o s i o n f r o m a c h a n n e l i n i t i a l l y t o o n a r r o w . C r o s s - o v e r i s t h a t p a r t o f t h e m e a n d e r i n g c h a n n e l w h e r e t h e f l o w c r o s s e s f r o m one b a n k w h e r e t h e f l o w i s o f one sense ( c l o c k w i s e o r c o u n t e r - c l o c k w i s e ) t o t h e o t h e r bank w h e r e t h e s e n s e o f r o t a t i o n i s r e v e r s e d . F r e e b o a r d i s t h e h e i g h t b e t w e e n t h e w a t e r s u r f a c e a n d t h e t o p o f t h e c h a n n e l b a n k . Meander b e l t w i d t h B i s t h e w i d t h o f a b e l t b e t w e e n p a r a l l e l l i n e s w h i c h c o n t a i n t h e m e a n d e r i n g c h a n n e l . Meander l e n g t h X i s t h e d i s t a n c e m e a s u r e d a l o n g t h e a x i s o f t h e v a l l e y betv;een t w o c o r r e s p o n d i n g p o i n t s o n s u c c e s s i v e m e a n d e r s . A meander t h e r e f o r e c o n s i s t s o f t w o embayments o r l o o p s i n one o f w h i c h t h e f l o w i s c l o c k w i s e and i n t h e o t h e r c o u n t e r - c l o c k w i s e . S i n u o s i t y i s a measure o f t h e d e v i a t i o n o f a m e a n d e r i n g c h a n n e l f r o m a s t r a i g h t l i n e a n d i s t h e r a t i o o f t h e l e n g t h o f t h e t h a l w e g t o t h e s t r a i g h t l i n e d i s t a n c e a l o n g t h e a x i s o f t h e v a l l e y . The d e f i n i t i o n i s u s u a l l y r e s e r v e d f o r t h e m o r e s y m m e t r i c a l m e a n d e r i n g c h a n n e l s . • S t r a i g h t l i n e w a t e r s u r f a c e s l o p e and s t r a i g h t l i n e b e d s l o p e . i r e t h e a v e r a g e g r a d i e n t s o f t h e w a t e r s u r f a c e and t h e - • t r e a m b e d r e s p e c t i v e l y a l o n g a s t r a i g h t l i n e b e t w e e n t w o p o i n t s . They b o t h have t h e same v a l u e as t h e v a l l e y s l o p e i f I h e c h a n n e l i s n e i t h e r a g g r a d i n g n o r d e g r a d i n g . Thftlv.eg i s t h e l i n e f o l l o w e d by t h e d e e p e s t p a r t o f t h e l i i i i : - . w a t e r w a y o f a n o n - p r i s m a t i c c h a n n e l . ' i " . il.-jeg w a t e r s u r f a c e s l o p e i s t h e a v e r a g e g r a d i e n t o f t h e v.'riter s u r f a c e b e t w e e n t w o p o i n t s f o l l o w i n g t h e t h a l w e g , i . f j . t h e c u r v e d p a t h o f t h e deep w a t e r c h a n n e l . 6 T h r e s h o l d s e d i m e n t c h a r g e i s , i n t h e p r e s e n t c o n t e x t , t h e minimum s e d i m e n t t r a n s p o r t r a t e f o r a g i v e n s a n d and d i s c h a r g e n e c e s s a r y f o r t h e d e v e l o p m e n t o f m e a n d e r s . T o r t u o s i t y d e s c r i b e s t h e d e g r e e o f s i n u o s i t y o f a r i v e r c h a n n e l a n d i s m o s t f r e q u e n t l y u s e d f o r t h e c h a n n e l w i t h a l a r g e s i n u o s i t y , w i d e meander b e l t a n d t h e l e s s r e g u l a r meander p a t t e r n s o f n a t u r a l r i v e r s . V a l l e y s l o p e i s t h e s l o p e o f t h e s u r f a c e o f t h e sand i n t h e g e n e r a l d i r e c t i o n o f f l o w . SCOPE OF INVESTIGATION Much o f t h e w o r k a v a i l a b l e a t t h e moment o n m e a n d e r i n g s t r e a m s i s e i t h e r t h e a n a l y s i s o f n a t u r a l r i v e r s , whose d i s c h a r g e s r a n g e f r o m a f e w t e n s t o m i l l i o n s o f c u s e c s ( 1 3 , 2 1 , 3 1 , 43) o r t h e o b s e r v a t i o n o f v e r y s m a l l s t r e a m s i n l a b o r a t o r y f l u m e s ( 9 , 1 7 , 38 e t a l ) h a v i n g a d i s c h a r g e r a r e l y as l a r g e a s one c u s e c . The p r e s e n t l a b o r a t o r y e x p e r i m e n t s w e r e d e s i g n e d t o b r i d g e a p a r t o f t h e gap b e t w e e n t h e s e t w o f i e l d s o f i n v e s t i g a t i o n b y e s t a b l i s h i n g , i n e f f e c t , s m a l l n a t u r a l s t r e a m s i n a l a r g e a r e a o f sand u n d e r c l o s e l y c o n t r o l l e d c o n d i t i o n s . A p r e v i o u s s e r i e s o f e x p e r i m e n t s i n t h i s a r e a o f sand h a s a l r e a d y been r e p o r t e d u p o n ( 1 , 2 ) , and t h e r e s u l t s w i l l be r e f e r r e d t o a g a i n i n t h e p r e s e n t r e p o r t w h e r e a p p r o p r i a t e , a l t h o u g h t h e y r e l a t e d m o s t l y t o s t r a i g h t c h a n n e l s . A l s o , a l i m i t e d s e r i e s o f e x p e r i m e n t s was c o n d u c t e d i n a n

a d j a c e n t s t r i p o f c o a r s e r sand some y e a r s ago'^*^' . Of t h e many f a c t o r s t h a t may b e c o n s i d e r e d t o

i n f l u e n c e m e a n d e r s , t h e d i s c h a r g e a n d t h e i n i t i a l s e d i m e n t t r a n s p o r t r a t e w e r e e x p e r i m e n t a l l y v a r i a b l e i n t h e s e t e s t s ,

m a t e r i a l o f bed a n d b a n k s c o u l d n o t be v a r i e d c o n v e n i e n t l y b e c a u s e o f t h e v e r y l a r g e q u a n t i t i e s r e q u i r e d . The d e n s i t y and v i s c o s i t y o f t h e w a t e r v a r i e d w i t h s e a s o n a l t e m p e r a t u r e c h a n g e s , b u t w e r e n o t c o n t r o l l e d : a l l o w a n c e was made f o r t h e s e c h a n g e s i n a s s e s s i n g c e r t a i n o f t h e r e s u l t s . The v a l l e y s l o p e , o f some i n f l u e n c e i n t h e d e v e l o p m e n t o f m e a n d e r s , was v a r i a b l e w i t h i n c o n f i n e d l i m i t s , b u t t h e same v a l u e was u s e d a t t h e s t a r t o f m o s t o f t h e t e s t s .

The d i s c h a r g e was g e n e r a l l y m a i n t a i n e d c o n s t a n t , one o f t h e a i m s o f t h e i n v e s t i g a t i o n b e i n g t o d e t e r m i n e t h e r e l a t i o n b e t w e e n t h i s p a r a m e t e r and t h e r e s u l t a n t meander s h a p e , b u t some t e s t s w e r e made w i t h t h e d i s c h a r g e c o n t i n u o u s l y v a r i e d t h r o u g h o u t t o e s t a b l i s h t h e e f f e c t o f s u c h a c y c l i c a l d i s c h a r g e compared w i t h a s t e a d y f l o w . A f t e r a f i r s t r u n f o r f a m i l i a r i s a t i o n w i t h t h e e q u i p m e n t a s e r i e s o f s t e a d y d i s c h a r g e s o f 0.4, 0.7, 1.2 and 2.0 c u s e c s was u s e d , c o m b i n e d w i t h sand i n j e c t i o n r a t e s o f 100, 150, 300 a n d 600 m g / l i t r e ( e q u i v a l e n t t o p a r t s p e r m i l l i o n b y w e i g h t ) t o g i v e s i x t e e n t e s t s . T h r e e v a r i a b l e - d i s c h a r g e t e s t s w e r e a l s o made, e a c h h a v i n g a h y d r o g r a p h o f 8 h o u r p e r i o d and n e a r l y s i n e wave f o r m , t h e mean d i s c h a r g e b e i n g 0.7 c u s e c . I n t w o o f t h e v a r i a b l e d i s c h a r g e e x p e r i m e n t s t h i s was m o d u l a t e d f r o m 0.05 t o 1.9 5 t i m e s t h e mean, c o m b i n e d w i t h sand i n j e c t i o n r a t e s o f 150 and 300 m g / l i t r e i n t u r n . I n t h e t h i r d e x p e r i m e n t , a t 300 m g / l i t r e t h e f l o v z m o d u l a t i o n was f r o m 0.5 t o 1.5 o f t h e mean. I t i s t o be e x p e c t e d t h a t t h e i n i t i a l c o n d i t i o n s w i l l a f f e c t t h e s t a g e s o f d e v e l o p m e n t o f m e a n d e r i n g i n an i n i t i a l l y s t r a i g h t c h a n n e l i n a l l u v i u m . S e v e r a l i n i t i a l a n d o p e r a t i n g c o n d i t i o n s a r e p o s s i b l e a s f o l l o w s : (a) S e d i m e n t c h a r g e ( i ) b e l o w t h r e s h o l d f o r m e a n d e i r i n g ; ( i i ) a b o v e t h r e s h o l d . (b) I n i t i a l c h a n n e l w i d t h ( i ) l e s s t h a n d y n a m i c a l l y s t a b l e w i d t h o f a m e a n d e r e d c h a n n e l ; ( i i ) more t h a n t h i s b u t l e s s t h a n t h e meander b e l t w i d t h ; ( i i i ) more t h a n meander b e l t w i d t h . (c) V a l l e y s l o p e ( i ) i n i t i a l l y g r e a t e r t h a n t h e s t r a i g h t - l i n e w a t e r s u r f a c e s l o p e f o r a s t a b l e m e a n d e r e d s t r e a m a n d m a i n t a i n e d c o n s t a n t ; ( i i ) a s a b o v e b u t v a r i e d t h r o u g h o u t t h e r u n b y b a n k l e v e l a d j u s t m e n t t o m a i n t a i n a c o n s t a n t f r e e b o a r d , i . e . v a l l e y s l o p e a d j u s t e d t o r e m a i n p a r a l l e l t o s t r a i g h t l i n e w a t e r s u r f a c e s l o p e ; ( i i i ) i n i t i a l l y l e s s t h a n t h e s t r a i g h t l i n e w a t e r s u r f a c e s l o p e f o r a s t a b l e m e a n d e r e d s t r e a m and m a i n t a i n e d c o n s t a n t ; ( i v ) as above b u t v a r i e d t h r o u g h o u t t h e r u n t o m a i n t a i n a c o n s t a n t f r e e b o a r d . A c o m p r e h e n s i v e c o v e r a g e o f t h e a b o v e i n i t i a l and o p e r a t i n g c o n d i t i o n s w o u l d r e q u i r e t w e n t y f o u r d i f f e r e n t t e s t s f o r e v e r y c h o s e n d i s c h a r g e a n d t h e s e r i e s w o u l d c l e a r l y be u n r e a s o n a b l y p r o l o n g e d . T h u s , i n t h e i n v e s t i g a t i o n s d e s c r i b e d i n t h i s p a p e r o n l y f o u r o f t h e p o s s i b l e c o m b i n a t i o n s o f c o n d i t i o n s w e r e u s e d f o r t h e v a r i o u s d i s c h a r g e s , as f o l l o w s : (a) ( b ) ( c ) S e d i m e n t c h a r g e I n i t i a l w i d t h V a l l e y s l o p e C o n d i t i o n A i i i v C o n d i t i o n B i i i i v C o n d i t i o n C i i i i ü C o n d i t i o n D i i i i i ü I n e a c h c a s e b o t h t h e d e v e l o p m e n t a n d t h e f i n a l c h a n n e l p a t t e r n w e r e d i f f e r e n t . Under c o n d i t i o n A t h e c h a n n e l 9

r e m a i n e d s t r a i g h t aJ, t l i o u g l i i t i n c r e a s e d i t s w i d t h and s h o a l s d e v e l o p e d on a l t e r n a t e c i t i e s . Under C o n d i t i o n B a meander p a t t e r n d e v e l o p e d as t h e bank l e v e l s w e r e a d j u s t e d t h r o u g h o u t t o m a i n t a i n a c o n s t a n t f r e e b o a r d . When t h e v a l l e y s l o p e was k e p t c o n s t a n t as i n C o n d i t i o n C, t h e w a t e r s o o n o v e r t o p p e d t h e b a n k s i n t h e u p p e r r e a c h e s as t h e g r a d i e n t i n c r e a s e d and a v;ide b r a i ' d e d c h a n n e l r e s u l t e d . I n t h e l a s t c a s e , t h e s t r e a m d e v e l o p e d a meander p a t t e r n w i t h i n t h e s i n u o u s c h a n n e l p r e v i o u s l y f o r m e d by a l a r g e r d i s c h a r g e b u t as t h e meander m i g r a t e d and i n c r e a s e d i t s s l o p e i t c u t t h r o u g h t h e p r e v i o u s l y f o r m e d s h o a l s and d e v e l o p e d a w i d e b r a i d e d p a t t e r n . RESEARCH F A C I L I T I E S

The m a i n s e r i e s o f e x p e r i m e n t s was made a t t h e H y d r a u l i c s R e s e a r c h S t a t i o n o f t h e M i n i s t r y o f T e c h n o l o g y a t W a l l i n g f o r d o v e r a p e r i o d o f a b o u t two y e a r s . An o p e n - a i r a r e a 300 f t l o n g by 34 f t w i d e f i l l e d w i t h u n i f o r m l y g r a d e d sand was u s e d , t h i s b e i n g i n f a c t one o f t h r e e s e c t i o n s o f t h e e x p e r i m e n t a l a r e a . P l a t e 1 and F i g . 1 g i v e a g e n e r a l p i c t u r e . W a t e r s u p p l y was by s h a l l o w w e l l f r o m t h e l o c a l g r o u n d w a t e r , s t o r e d b e l o w sand s u r f a c e l e v e l i n a r e s e r v o i r t a n k o f a b o u t 16 000 cu f t c a p a c i t y a t one end o f t h e a r e a . A 5 c u s e c c a p a c i t y h o r i z o n t a l a x i a l f l o w pump moved w a t e r f r o m t h i s s t o r a g e t a n k t h r o u g h a 15 i n p i p e t o t h e head o f t h e sand s t r i p , where i t was d i s c h a r g e d i n t o an e x p a n s i o n chamber w i t h l o w v e l o c i t y . The d i s c h a r g e t o t h e s t r e a m was c o n t r o l l e d f i r s t l y by a l t e r i n g pump d e l i v e r y and s e c o n d l y by means o f a b r o a d - c r e s t e d w e i r d i s c h a r g i n g f r o m t h e e x p a n s i o n chamber. A s t r e a m l i n e d s p l i t t e r b l o c k c o u l d be 10 moved a c r o s s t h e w e i r c r e s t , d i v i d i n g t h e f l o w i n t o t h e r e q u i r e d f r a c t i o n w h i c h p a s s e d t o t h e e x p e r i m e n t a l c h a n n e l , t h e r e m a i n d e r o f t h e n e a r - c o n s t a n t pump d e l i v e r y b e i n g t a k e n i n a b y - p a s s c h a n n e l d i r e c t l y b a c k t o t h e s t o r a g e sump. F o r t h e m a j o r i t y o f t h e t e s t s a t s t e a d y d i s c h a r g e , a c o n v e n i e n t b r e a d t h was s e l e c t e d and t h e h e a d o v e r t h e w e i r a d j u s t e d t o g i v e t h e r e q u i r e d f l o w . F o r t h e t e s t s w i t h c o n t i n u o u s l y v a r i a b l e d i s c h a r g e , a n e l e c t r i c d r i v e was p r o v i d e d w h i c h t r a v e r s e d t h e f l o w s p l i t t e r a c r o s s t h e w e i r c r e s t u n d e r t h e c o n t r o l o f a cam r e p r e s e n t i n g t h e h y d r o g r a p h s h a p e , so v a r y i n g t h e b r e a d t h o f w e i r d e l i v e r i n g f l o w t o t h e t e s t c h a n n e l w h i l e t h e h e a d r e m a i n e d c o n s t a n t .

The sand i n w h i c h t h e e x p e r i m e n t s t o o k p l a c e 4- was f o u n d by s i e v e a n a l y s i s t o h a v e a m e d i a n g r a i n d i a m e t e r o f 0.15 mm, W i t h 90 p e r c e n t l y i n g b e t w e e n 0.1 and 0.23 mm d i a m e t e r , see F i g . 2. Samples w e r e t a k e n f r o m s e v e r a l l o c a t i o n s e a r l y i n t h e p e r i o d o f e x p e r i m e n t s t o c o n f i r m t h i s c l o s e g r a d i n g , and a t i n t e r v a l s d u r i n g t h e e x p e r i m e n t a l p e r i o d t o e n s u r e t h a t no s o r t i n g e f f e c t was p r e s e n t as t h e sand was r e - w o r k e d . The sand bed was Ik f t d e e p , u n d e r l a i n by 2 f t o f c o a r s e r s a n d c o n t a i n i n g g r o u n d d r a i n s t o p r e v e n t w a t e r l o g g i n g ; b e l o w t h i s t h e e x i s t i n g sub s o i l had b e e n c o m p a c t e d by sheep's f o o t r o l l e r s . The g r o u n d d r a i n f l o w was c o n t i n u o u s l y m e t e r e d o v e r a V - n o t c h w e i r b a c k i n t o t h e m a i n s u p p l y w e l l , b u t some o v e r a l l l o s s o f w a t e r f r o m t h e sand a r e a i n t o t h e u n d e r l y i n g g r o u n d w a t e r was s u s p e c t e d . Hence t h e o u t l e t d i s c h a r g e f r o m t h e e x p e r i m e n t a l sand s t r i p was n o t n e c e s s a r i l y t h e d i f f e r e n c e b e t w e e n t h e m e t e r e d i n f l o w and g r o u n d w a t e r r e t u r n . A s h a r p c r e s t e d r e c t a n g u l a r w e i r ( o f m u l t i - u n i t d e s i g n i n o r d e r t o o b t a i n t h e n e c e s s a r y head r e q u i r e m e n t s o f B.S. + The same sand as u s e d i n t h e e x p e r i m e n t s o f r e f . 1 , b u t a f t e r s i e v i n g t o remove i s o l a t e d g r a v e l p a r t i c l e s and e l u t r i a t i o n t o e l i m i n a t e a l m o s t e n t i r e l y p a r t i c l e s b e l o w 0.06 mm.

3680: P t 4A: 1965) was p r o v i d e d t o m e a s u r e o u t f l o w a t t h e l o w e r end o f t h e sand s t r i p . I m m e d i a t e l y u p s t r e a m o f t h i s w e i r was a l a r g e s e t t l i n g b a s i n w h i c h e f f e c t i v e l y r e m o v e d t r a n s p o r t e d sand f r o m t h e w a t e r b e f o r e i t was r e t u r n e d o v e r t h e s h a r p c r e s t e d w e i r t o t h e m a i n pump f o r r e - c i r c u l a t i o n . The s e t t l i n g b a s i n was p r e c e d e d b y a t i l t i n g t a i l g a t e f o r c o n t r o l o f w a t e r s u r f a c e l e v e l a t t h e s t r e a m o u t l e t .

A sand i n j e c t o r was p r o v i d e d a t t h e u p s t r e a m end o f t h e a r e a , f e e d i n g d r y s a n d t h e same as t h a t o f t h e b e d a n d b a n k s , by f r e e f a l l i n t o a l i n e d s e c t i o n o f c h a n n e l i m m e d i a t e l y d o w n s t r e a m o f t h e v a r i a b l e - b r e a d t h w e i r a t t h e i n l e t . T h i s e n s u r e d good m i x i n g o f t h e d r y s a n d w i t h t h e f l o w . The i n j e c t o r was a c o m m e r c i a l s c r e w - f e e d m a c h i n e , w h i c h c o u l d p r o v i d e any c h o s e n r a t e o f sand i n j e c t i o n b y a c o m b i n a t i o n o f v a r i a b l e h y d r a u l i c g e a r b o x and a r a n g e o f f e e d s c r e w p i t c h e s and d i a m e t e r s . D u r i n g t e s t s w i t h v a r i a b l e d i s c h a r g e t h e i n j e c t o r g e a r b o x was l i n k e d t o t h e f l o w s p l i t t e r c o n t r o l i n s u c h a way as t o m a i n t a i n a c h o s e n c o n s t a n t p r o p o r t i o n o f sand i n t h e v a r y i n g w a t e r d i s c h a r g e .

The amount o f sand i n t r a n s p o r t a t t h e d o w n s t r e a m end o f t h e s t r e a m was e s t i m a t e d b y p a s s i n g t h e e n t i r e f l o w o f w a t e r and a s s o c i a t e d s e d i m e n t t h r o u g h a t r o u g h o f 6 i n s q u a r e s e c t i o n e x t e n d i n g a c r o s s t h e w h o l e w i d t h o f t h e s e t t l i n g b a s i n , j u s t b e y o n d t h e t i l t i n g t a i l - g a t e . The t r o u g h was d e s i g n e d t o g i v e a good r o l l e r a c t i o n w i t h i n i t , and had m u l t i p l e w i t h d r a w a l t a p p i n g s i n t o a common m a n i f o l d w h i c h

was c o n n e c t e d t o a s m a l l c e n t r i f u g a l pump. I n t h i s way a

l a r g e r e p r e s e n t a t i v e s a m p l e o f t h e w a t e r - s a n d c o m p l e x c o u l d be t a k e n i n t o a s e t t l i n g t a n k o f known c a p a c i t y , a n d hence t h e c o n c e n t r a t i o n c o u l d be o b t a i n e d a f t e r s e t t l i n g a n d •weighing. I n p r a c t i c e , t h e w i t h d r a w a l t a p p i n g s commanding i n a c t i v e p a r t s o f t h e s t r e a m c r o s s s e c t i o n w e r e t e m p o r a r i l y c l o s e d o f f , a n d t h e p u m p i n g speed t h r o u g h t h e t a p p i n g s i n use was a d j u s t e d t o m a t c h t h e f l o w v e l o c i t y i n t h e t r o u g h i n an a t t e m p t t o t a k e a n u n d i s t u r b e d s a m p l e . W a t e r s u r f a c e l e v e l s w e r e m e a s u r e d a t n i n e p o i n t s an a v e r a g e d i s t a n c e o f 30 f t a p a r t b y a s e r i e s o f p i t o t -s t a t i c p r o b e -s c a r r i e d o n beam-s -s p a n n i n g t h e c h a n n e l . Each was c o n n e c t e d b y s i p h o n t u b e t o a s t i l l i n g p o t p r o v i d e d w i t h a v e r n i e r h o o k gauge r e a d i n g t o 0 . 0 0 1 f t . As t h e s e o p e n - a i r e x p e r i m e n t s w e r e c o n t i n u e d t h r o u g h o u t t w o w i n t e r s , m e t h y l a l c o h o l was a d d e d t o t h e w a t e r i n t h e s t i l l i n g p o t s as an " a n t i - f r e e z e " ; t h e r e s u l t a n t d e n s i t y c h a n g e o f t h e l i q u i d c o l u m n was c a l c u l a t e d t o b e w i t h i n t h e a c c u r a c y o f m e a s u r e m e n t . C r o s s s e c t i o n s o f t h e c h a n n e l s , w h e t h e r d u r i n g a t e s t o r when d r a i n e d a t c o m p l e t i o n , w e r e u s u a l l y t a k e n w i t h a s i m p l e beam and p r o b e . T h i s was q u i c k e r t o s e t up a t a n y p o i n t o f t h e e x t e n s i v e s a n d a r e a t h a n t h e a u t o m a t i c bed p l o t t i n g d e v i c e a v a i l a b l e , t h o u g h s u c h a n i n s t r u m e n t w o u l d h a v e b e e n s u i t a b l e i f a l a r g e number o f p l o t s a t one s e c t i o n h a d b e e n n e e d e d . V e r t i c a l p h o t o g r a p h s w e r e t a k e n d u r i n g t h e t e s t s ( P l a t e s 2-12 b y m o u n t i n g a camera o n t h e s p e c i a l l y l e n g t h e n e d boom o f a m o b i l e c r a n e , t h e camera s h u t t e r t h e n b e i n g r e l e a s e d b y a n e l e c t r i c s o l e n o i d f r o m t h e g r o u n d . T h r e e e x p o s u r e s c o v e r e d t h e w h o l e l e n g t h o f a c h a n n e l , a n d when s l i g h t l y e n l a r g e d p r o d u c e d o v e r l a p s o f a s c a l e a b o u t 1 i n t o 10 f t . By u s i n g some g r o u n d c o n t r o l i n t h e f o r m o f o b j e c t s o f known p o s i t i o n , many r e s u l t s w e r e o b t a i n e d f r o m t h e s e p h o t o g r a p h s b y s c a l i n g . 13

DESCRIPTION OF EXPERIMENTS Each e x p e r i m e n t was s t a r t e d b y p r e p a r i n g a s t r a i g h t c h a n n e l down t h e c e n t r e o f t h e s a n d s t r i p f r o m t h e r e s t r i c t e d s e c t i o n u n d e r t h e sand i n j e c t o r t o t h e t i l t i n g t a i l - w e i r . T h i s i n i t i a l c h a n n e l was o f t r a p e z o i d a l c r o s s - s e c t i o n s u f f i c i e n t t o r u n f u l l a t t h e s t a r t o f t h e t e s t . D e p e n d i n g o n t h e d i s c h a r g e t o b e u s e d i t s d e p t h v a r i e d b e t w e e n 5 a n d 6h i n a n d i t s t o p w i d t h b e t w e e n 1 f t 8 i n a n d 4 f t 6 i n ( s i d e s l o p e s 45°). A l l o w i n g f o r a f r e e b o a r d o f a b o u t 0.75 i n t h e i n i t i a l w i d t h / d e p t h r a t i o o f t h e c h a n n e l v a r i e d f r o m 4.7 f o r t h e s m a l l e s t d i s c h a r g e c h a n n e l s t o 9.4 f o r t h e l a r g e s t . The b e d a n d f l o o d p l a i n f l a n k s o f t h e c h a n n e l w e r e c a r e f u l l y a d j u s t e d b y s u r v e y o r ' s l e v e l t o a c o n s t a n t s l o p e , u s u a l l y 0.0020 e x c e p t f o r t h e f i n a l t e s t when t h e i n i t i a l v a l l e y s l o p e was 0.0026.

The f l o w was s t a r t e d s l o w l y , e n t e r i n g f r o m t h e head o f t h e c h a n n e l ( i t was n o t p o s s i b l e t o b a c k f l o o d t h e a r e a ) on an a x i a l l i n e , a n d n o t a r t i f i c i a l l y i n c l i n e d a g a i n s t e i t h e r b a n k . As soon a s t h e f u l l r e q u i r e d d i s c h a r g e h a d been o b t a i n e d , t h e w a t e r s u r f a c e s l o p e was a d j u s t e d b y means o f t h e t i l t i n g t a i l g a t e t o be p a r a l l e l w i t h t h e i n i t i a l b e d g r a d i e n t , u s u a l l y 0.002. A f t e r t h i s , no a d j u s t m e n t was made t o t h e t a i l w a t e r c o n t r o l d u r i n g a t e s t and t h e c h a n n e l g r a d i e n t was f r e e t o v a r y . Sand i n j e c t i o n was s t a r t e d when t h e d i s c h a r g e was a t i t s r e q u i r e d v a l u e , a n d t h e e x p e r i m e n t t h e n r a n c o n t i n u o u s l y f o r a p e r i o d , v a r y i n g b e t w e e n a b o u t 5 a n d 35 d a y s i n t h e d i f f e r e n t t e s t s , u n t i l i t was j u d g e d t h a t a s t a b l e c h a n n e l p a t t e r n had f o r m e d i n a t l e a s t p a r t o f t h e l e n g t h o f t h e s t r e a m . T h i s was n o t a l w a y s a r e g u l a r meander p a t t e r n , b u t s u c h s t r a i g h t o r b r a i d e d c h a n n e l s as d e v e l o p e d w e r e h i g h l y i n f o r m a t i v e i n t h e m s e l v e s . As t h e c h a n n e l w i d e n e d o r meandered d u r i n g a t e s t a t c o n s t a n t f r e e b o a r d , sand was moved o n t h e f l o o d p l a i n as n e c e s s a r y t o e n s u r e a u n i f o r m b a n k h e i g h t w i t h 14 r e s p e c t t o w a t e r s u r f a c e l e v e l , i n o r d e r n o t t o i n t r o d u c e v a r i a t i o n s i n t h e amount o f sand a v a i l a b l e f o r t r a n s p o r t when b a n k c u t t i n g t o o k p l a c e . O b s e r v a t i o n s w e r e t a k e n t w i c e e a c h d a y o f i n l e t a n d o u t l e t d i s c h a r g e , w a t e r s u r f a c e l e v e l s a t t h e n i n e m e a s u r i n g p o i n t s , sand i n j e c t i o n r a t e a n d w a t e r t e m p e r a t u r e . Sand t r a n s p o r t r a t e a t o u t l e t was o f n e c e s s i t y m e a s u r e d r a t h e r l e s s f r e q u e n t l y , due t o t h e t i m e n e e d e d t o o b t a i n and p r o c e s s l a r g e numbers o f s a m p l e s . P h o t o g r a p h s w e r e t a k e n f r o m t h e m o b i l e c r a n e a n d c r o s s - s e c t i o n s s u r v e y e d a t r e p r e s e n t a t i v e s t a g e s o f d e v e l o p m e n t o f t h e c h a n n e l s , as f r e q u e n t l y as d a i l y i n t h e l a t e r t e s t s . F o r m o s t o f t h e p h o t o g r a p h s t h e f l o w was t e m p o r a r i l y r e d u c e d t o a b o u t one t h i r d o f t h e c h o s e n v a l u e , a n d a d y e i n j e c t e d a t t h e head o f t h e c h a n n e l i n o r d e r t o show t h e s h o a l p a t t e r n c l e a r l y . A t t h e c o n c l u s i o n o f e a c h e x p e r i m e n t t h e c h a n n e l was d r a i n e d , a n d meander l e n g t h a n d b r e a d t h a n d t h a l w e g l e n g t h w e r e m e a s u r e d , t o g e t h e r w i t h f i n a l c r o s s - s e c t i o n s and r i p p l e p r o f i l e s . I n t h e s u b s e q u e n t a n a l y s i s , a c c o u n t was t a k e n o f t h e r e d u c t i o n i n d i s c h a r g e a l o n g t h e c h a n n e l s d u e t o e x f i l t r a t i o n . F o r w a n t o f a b e t t e r b a s i s , a l i n e a r r a t e o f l o s s b e t w e e n i n l e t and o u t l e t was assumed; t h e r e s u l t a n t f l o w a t t h e c e n t r e p o i n t o f c o m p a r t m e n t s n e a r t h e c e n t r e and t o w a r d s t h e d o w n s t r e a m end o f t h e c h a n n e l was t h e n c a l c u l a t e d . The e x a c t l o c a t i o n o f t h e c o m p a r t m e n t s v a r i e d f r o m t e s t t o t e s t , a n d was c h o s e n b y i n s p e c t i o n t o i n c l u d e o n l y s t a b l e c h a n n e l f o r m s . By t h i s means t w o r e s u l t s c o u l d u s u a l l y be o b t a i n e d f o r t h e r e l a t i o n s b e t w e e n d i s c h a r g e a n d o t h e r d e p e n d e n t v a r i a b l e s i n any one t e s t o f a g i v e n n o m i n a l d i s c h a r g e . 15

EXPERIMENTAL RESULTS D e v e l o p m e n t o f c h a n n e l I m m e d i a t e l y a f t e r t h e i n t r o d u c t i o n o f w a t e r and s e d i m e n t a t t h e u p s t r e a m end o f t h e p r e p a r e d t r a p e z o i d a l c h a n n e l , t h e bed d e v e l o p e d r i p p l e s w h i c h w e r e s y m m e t r i c a l a b o u t a l o n g i t u d i n a l l i n e . A f t e r a p e r i o d o f b e t w e e n a b o u t 6 h o u r s f o r t h e h i g h e r d i s c h a r g e s a n d a b o u t 24 h o u r s f o r t h e l o w e r v a l u e s , t h e s y m m e t r y d e t e r i o r a t e d and s h o a l s b e g a n t o f o r m n e a r t h e s i d e s o f t h e c h a n n e l a l o n g i t s l e n g t h . These w e r e a t f a i r l y r e g u l a r i n t e r v a l s , t h e s h o a l s f o r m i n g on a l t e r n a t e s i d e s o f t h e c h a n n e l w i t h d e e p s n e a r t h e o p p o s i t e b a n k . The s h o a l s c o n t i n u e d t o i n c r e a s e i n l e n g t h and h e i g h t w h i l e t h e y m i g r a t e d f a i r l y r a p i d l y d o w n s t r e a m , i n c r e a s i n g t h e i r p i t c h as t h e c h a n n e l became w i d e r t h r o u g h g e n e r a l bank e r o s i o n e v e n t h o u g h i t r e m a i n e d s t r a i g h t . Then, a l m o s t s i m u l t a n e o u s l y a l o n g t h e c h a n n e l , embayments w e r e e r o d e d i n t h e b a n k s o p p o s i t e e a c h s h o a l . These e x p a n d e d , p r o d u c i n g a s i n u o u s c h a n n e l p a t t e r n i n p l a n , and a l s o m i g r a t e d d o w n s t r e a m , a l t h o u g h more s l o w l y t h a n t h e s h o a l s had d o n e . The p i t c h o f t h e s e f e a t u r e s t h e n r e m a i n e d c o n s t a n t , o r t e n d e d t o d e c r e a s e s l i g h t l y . A t t h e u p s t r e a m end o f t h e i n i t i a l l y s t r a i g h t c h a n n e l t h e p a t t e r n o f d e v e l o p m e n t d i f f e r e d somewhat. A s h o a l f o r m e d i n t h e c e n t r e o f t h e c h a n n e l n e a r t h e i n l e t , and s c o u r o c c u r r e d on b o t h s i d e s . The s h o a l i n c r e a s e d i n l e n g t h , w i d t h and h e i g h t as t h e c h a n n e l w i d e n e d , u n t i l t h e b a n k s on b o t h s i d e s o f t h e c h a n n e l became m a r k e d l y c o n c a v e . The r e s u l t i n g b u l b - l i k e shape a t t h e e n t r y t o t h e c h a n n e l was a f a m i l i a r f e a t u r e i n a l m o s t e v e r y t e s t o f t h e s e r i e s ; (see P l a t e 1 2 ) . I t expanded f a i r l y e v e n l y , b u t f l o w was d i s p o s e d t o c o n c e n t r a t e more t o one s i d e o r t h e o t h e r w h e r e more m a r k e d b a n k e r o s i o n w o u l d o c c u r . The d e p o s i t i o n o f s e d i m e n t t o f o r m t h e c e n t r a l s h o a l a t t h e i n l e t and t h e f l a n k i n g s h o a l s a l o n g t h e l e n g t h o f t h e 16 c h a n n e l u s u a l l y b e g a n a l m o s t s i m u l t a n e o u s l y . j I n t h e l a t e r s t a g e s o f d e v e l o p m e n t o f t h e c e n t r a l s h o a l , when f l o w t e n d e d t o c o n c e n t r a t e t o w a r d s one s i d e , t h e

J p r e d o m i n a n t s t r e a m was o b s e r v e d t o change f r o m one s i d e t o t h e o t h e r o n more t h a n one o c c a s i o n w i t h o u t a p p a r e n t l y

1 s e r i o u s l y a f f e c t i n g t h e d o w n s t r e a m p a t t e r n o f e r o s i o n p o i n t s . T h i s may h a v e b e e n due p e r h a p s t o t h e d i s t a n c e b e t w e e n t h e 1 " b u l b " and t h e f i r s t e r o s i o n p o i n t w h i c h was a b o u t t w i c e

t h e d i s t a n c e b e t w e e n e r o s i o n p o i n t s d o w n s t r e a m , i . e . e q u a l t o ^ a b o u t one meander l e n g t h . The p r e d o m i n a t i n g f l o w f r o m t h e ^ b u l b d i d n o t a t t a c k t h e o p p o s i t e b a n k d o w n s t r e a m ; i t s c o u r e d t h e bed n e a r t h e c e n t r e b u t s l i g h t l y t o w a r d s t h e J o p p o s i t e b a n k . The c u r r e n t t h e n swung b a c k a g a i n t o e r o d e t h e b a n k f u r t h e r d o w n s t r e a m , f r o m w h i c h p o i n t o n w a r d s i e r o s i o n o c c u r r e d a t i n t e r v a l s on a l t e r n a t e s i d e s . The -I f a i l u r e o f t h e m a i n c u r r e n t e m e r g i n g f r o m t h e b u l b t o 1 a t t a c k t h e o p p o s i t e b a n k was presumed t o be due t o t h e

e f f e c t o f t h e s t r e a m f r o m t h e o p p o s i t e s i d e o f t h e b u l b . S u f f i c i e n t d i s t u r b a n c e was p r o d u c e d t o c a u s e bed s c o u r a t ^ t h e i r j u n c t i o n , b u t t h e s t r o n g e r f l o w was d e f l e c t e d t o ^ an a n g l e i n s u f f i c i e n t t o c a u s e b a n k e r o s i o n . ^ W i t h v a r i a b l e f l o w , t h e s e q u e n c e o f s t a g e s l e a d i n g up t o t h e f o r m a t i o n o f a s i n u o u s c h a n n e l was s i m i l a r t o J t h o s e f o r a c h a n n e l w i t h a s t e a d y d i s c h a r g e e x c e p t f o r two m a i n d i f f e r e n c e s : ^ ( i ) t h e c h a n n e l w i t h a v a r i a b l e f l o w t o o k l o n g e r t o _ d e v e l o p meanders t h a n one w i t h a s t e a d y d i s c h a r g e J e q u a l t o t h e mean o f t h e v a r i a b l e f l o w , and t h e same s e d i m e n t i n j e c t i o n r a t e , and j ( i i ) t h e p a t t e r n o f t h e f i n a l c h a n n e l was s i m i l a r t o t h a t o f c h a n n e l s c o n v e y i n g a s t e a d y d i s c h a r g e J g r e a t e r t h a n t h e mean v a l u e o f t h e v a r i a b l e f l o w . The s l o w e r r a t e o f d e v e l o p m e n t o f t h e c h a n n e l * c o n v e y i n g t h e v a r i a b l e f l o w may be due t o t h e s c o u r i n g o f

]

17

t h e s h a l l o w c r o s s - o v e r p o i n t s a t l o w f l o w and t h e d e p o s i t i o n o f sand i n t h e deep p o o l s . T h u s , as t h e d i s c h a r g e i n c r e a s e s , w o r k has t o be done t o s c o u r t h e p o o l s b e f o r e a n y f u r t h e r d e v e l o p m e n t o f t h e s i n u o u s p a t t e r n c a n o c c u r . One s p e c i a l t e s t was c o n d u c t e d t o e x a m i n e t h e i n f l u e n c e o f an i n c r e a s e i n s e d i m e n t i n j e c t i o n r a t e o n t h e d e v e l o p m e n t o f t h e c h a n n e l . T h i s was t e s t 2 0 , i n w h i c h i n i t i a l l y no s e d i m e n t was added a t t h e u p s t r e a m end and m e a n d e r s d i d n o t d e v e l o p . L a t e r , when s e d i m e n t was i n t r o d u c e d , t h e c h a n n e l p r o g r e s s e d f r o m a s h o a l e d p a t t e r n t o f u l l m e a n d e r i n g . The i m p l i c a t i o n s o f t h i s e x p e r i m e n t a r e d i s c u s s e d l a t e r . D e v e l o p m e n t o f c h a n n e l w i t h i n p r e v i o u s l y f o r m e d w i d e r c h a n n e l A c h a n n e l Was a l l o w e d t o d e v e l o p as d e s c r i b e d a b o v e u s i n g a d i s c h a r g e o f 2.0 c u s e c s and a s e d i m e n t i n j e c t i o n r a t e o f 600 mg p e r l i t r e . The c h a n n e l g r a d u a l l y i n c r e a s e d i n w i d t h b u t r e m a i n e d s t r a i g h t f o r 20 h o u r s , b u t b y 28 h o u r s a f t e r t h e s t a r t o f t h e t e s t embayments had been e r o d e d a t i n t e r v a l s a l o n g t h e c h a n n e l . These g r a d u a l l y g r e w l a r g e r u n t i l b y a b o u t 15 h o u r s l a t e r a m a r k e d s i n u o u s c h a n n e l p a t t e r n had d e v e l o p e d w i t h a wave l e n g t h o f a b o u t 52 f e e t i n t h e u p p e r r e a c h e s . The o p e r a t i n g f l o w was t h e n r e d u c e d t o 0.5 c u s e c w i t h a s e d i m e n t c h a r g e o f 300 mg p e r l i t r e . Under t h e s e c o n d i t i o n s t h e w a t e r s u r f a c e was b e l o w t h e t o p o f t h e s h o a l s f o r m e d p r e v i o u s l y a n d t h e c h a n n e l f o l l o w e d a s i n u o u s c o u r s e . A b o u t t h r e e d a y s l a t e r t h e w a t e r s u r f a c e s l o p e had i n c r e a s e d and a c h a n n e l had b e e n c u t t h r o u g h t h e m o s t u p s t r e a m o f t h e o r i g i n a l s h o a l s a n d t h e s t r e a m was a d o p t i n g a s i n u o u s p a t h a l o n g t h e o r i g i n a l t h a l w e g w i t h a meander l e n g t h o f a b o u t 27 f e e t . From t h i s s t a g e o n w a r d s t h e s i n u o u s p a t t e r n d e v e l o p e d . When some o f t h e o r i g i n a l s h o a l s w e r e c u t t h r o u g h , b e i n g o n t h e e r o d i n g b a n k , an i s l a n d d e v e l o p e d i n t h e m i d d l e o f t h e c h a n n e l . On e a c h s i d e o f t h e i s l a n d 18 w h e r e t h e d i s c h a r g e was a b o u t h a l f t h e t o t a l f l o w i n t h e c h a n n e l t h e r e was e v i d e n c e o f t h e d e v e l o p m e n t o f a s e c o n d a r y s i n u o u s p a t t e r n w i t h a w a v e l e n g t h o f t h e o r d e r o f a b o u t 20 f e e t . F i n a l l y t h e c h a n n e l d e v e l o p e d a b r a i d e d p a t t e r n a s more o f t h e o r i g i n a l s h o a l s w e r e c u t a n d s m a l l i s l a n d s w e r e f o r m e d w i t h i n t h e w i d e c h a n n e l f o r m e d b y t h e 2.0 c u s e c f l o w . The f i r s t p a r t o f t h e t e s t f o l l o w e d t h e u s u a l p a t t e r n o f d e v e l o p m e n t o f a c h a n n e l w i t h a s e d i m e n t c h a r g e i n e x c e s s o f t h e t h r e s h o l d v a l u e , i n i t i a l c h a n n e l a n d v a l l e y s l o p e s l e s s t h a n t h e f i n a l s t r a i g h t l i n e w a t e r s l o p e , a n i n i t i a l c h a n n e l w i d t h w h i c h was t o o n a r r o w and a c o n s t a n t f r e e b o a r d . The s e c o n d p a r t o f t h e t e s t f o l l o w e d t h e p a t t e r n f o r a c h a n n e l w i t h a s e d i m e n t c h a r g e i n e x c e s s o f t h e t h r e s h o l d v a l u e , i n i t i a l c h a n n e l and v a l l e y s l o p e s l e s s t h a n t h e s t r a i g h t l i n e w a t e r s u r f a c e s l o p e , a c o n s t a n t v a l l e y s l o p e ( n o t c o n s t a n t f r e e b o a r d ) a n d an i n i t i a l c h a n n e l w i d t h i n t e r m e d i a t e b e t w e e n t h e w i d t h w h i c h w o u l d d e v e l o p u n d e r c o n s t a n t f r e e b o a r d f r o m a c h a n n e l i n i t i a l l y t o o n a r r o w and t h e w i d t h o f t h e meander b e l t w h i c h w o u l d d e v e l o p u n d e r t h e same c i r c u m s t a n c e s . Thus t h e f l o w was a b l e t o a t t a c k t h e c h a n n e l b a n k s c a u s i n g embayments and a s i n u o u s p a t t e r n b u t as t h e w a t e r s u r f a c e s l o p e i n c r e a s e d and t h e s h o a l s w e r e e r o d e d t h e w h o l e v a l l e y was f l o o d e d and a b r a i d e d c h a n n e l d e v e l o p e d . Geometry as f u n c t i o n o f d i s c h a r g e I n t u i t i v e l y , ' i t i s a n t i c i p a t e d t h a t t h e g e o m e t r i c a l d i m e n s i o n s o f a m e a n d e r e d c h a n n e l may be d e p e n d e n t o n : ( i ) t h e d i s c h a r g e , and i t s v a r i a t i o n w i t h t i m e i f u n s t e a d y ; ( i i ) t h e s l o p e o f t h e v a l l e y c o n t a i n i n g t h e s t r e a m ; ( i i i ) t h e r a t e o f s e d i m e n t t r a n s p o r t ( i v ) t h e r e s i s t a n c e o f t h e b e d and b a n k s t o movement, w h i c h i n t u r n i s d e p e n d e n t on 19

g r a i n s i z e , s p e c i f i c g r a v i t y and c o h e s i v e s t r e n g t h ; (v) t h e v i s c o s i t y and d e n s i t y o f t h e l i q u i d . However, t h e s l o p e o f t h e s t r e a m and t h e r a t e o f s e d i m e n t t r a n s p o r t a r e n o t i n d e p e n d e n t v a r i a b l e s . I t was c l e a r f r o m p r e v i o u s e x p e r i m e n t s , and c o n f i r m e d i n t h e new e x p e r i m e n t s , t h a t l o c a l s l o p e s and r a t e s o f s e d i m e n t t r a n s p o r t a r e i n t e r d e p e n d e n t . I f , f o r e x a m p l e , t h e c h a n n e l s l o p e i s l e s s t h a n t h a t r e q u i r e d t o c a r r y f o r w a r d t h e i n j e c t e d s e d i m e n t l o a d u n d e r t h e p a r t i c u l a r c o n d i t i o n s o f f l o w and s t r e a m g e o m e t r y , a g g r a d a t i o n w i l l o c c u r a t t h e head o f t h e s t r e a m . T h e r e b y t h e s l o p e i n c r e a s e s , u n t i l i t i s a d e q u a t e , w i t h t h e d i s c h a r g e and g e o m e t r y o b t a i n i n g , t o c o n v e y t h e f u l l i n j e c t e d c h a r g e . The s l o p e o f t h e c h a n n e l t h e r e f o r e c a n n o t be c o n t r o l l e d i n t h i s t y p e o f e x p e r i m e n t : i t i s s e l f - a d j u s t i n g o n c e t h e o p e r a t i n g c o n d i t i o n s a r e d e t e r m i n e d . P r e v i o u s w o r k , i n b o t h f i e l d and l a b o r a t o r y , has i n d i c a t e d t h a t t h e meander l e n g t h i s s t r o n g l y d e p e n d e n t on d i s c h a r g e , and h e n c e t h i s w i l l be e x a m i n e d f i r s t . The e q u a t i o n s u g g e s t e d by I n g l i s i n 1938 i s w e l l known: A = a Q (1) w h e r e a i s o f t h e o r d e r o f 25 t o 30 ( i n f t . sec u n i t s ) , when Q i s t h e maximum d i s c h a r g e , o r o f t h e o r d e r o f 3 6 when Q i s t h e d o m i n a n t d i s c h a r g e . The r e s u l t s o f t h e p r e s e n t e x p e r i m e n t s a r e shown on F i g . 3, i n t e r m s o f d i s c h a r g e a g a i n s t meander l e n g t h . U s i n g t h e m e t h o d o f l e a s t s q u a r e s , t h e e q u a t i o n b e s t f i t t i n g t h e r e s u l t s a t a m e d i a n g r a i n s i z e o f 0.15 imn and w i t h d i s c h a r g e s r a n g i n g f r o m 0.238 t o 2.74 c u s e c s i s : X = 37.8 Q°-506 (2) The c o r r e l a t i o n c o e f f i c i e n t i s 0.958 and t h e s t a n d a r d e r r o r i s 0.0426 l o g u n i t s . T h i s e q u a t i o n a g r e e s c l o s e l y w i t h t h e f o r m o f e q u a t i o n 1 g i v e n a b o v e , and c o n f i r m s a s t r o n g 20

c o r r e l a t i o n b e t w e e n meander l e n g t h and d i s c h a r g e . Some o f t h e e a r l y t e s t s w e r e a f f e c t e d by a l g a l g r o w t h on t h e b a n k s o r by o t h e r d i f f i c u l t i e s w h i c h p r e v e n t e d f u l l meander d e v e l o p m e n t . These r u n s a r e shown by a d i f f e r e n t s y m b o l i n F i g . 3. E x c l u d i n g t h e s e d o u b t f u l r e s u l t s t h e e q u a t i o n becomes X = 38.0 Q ° - ^ " (3) I t i s a l s o p o s s i b l e t h a t a t l o w d i s c h a r g e t h e l o s s o f f l o w t h r o u g h e x f i l t r a t i o n has a g r e a t e r e f f e c t o n t h e c h a n n e l p a t t e r n b e c a u s e i t was p r o p o r t i o n a t e l y h i g h e r . A f u r t h e r c o r r e l a t i o n was t h e r e f o r e made e x c l u d i n g a l l r u n s w i t h d i s c h a r g e s l e s s t h a n 0.4 c u s e c . T h i s y i e l d e d X = 38.0 Q°-^54 I t i s o n l y by e x a m i n i n g d a t a c o v e r i n g a w i d e r d i s c h a r g e r a n g e t h a t t h e u n c e r t a i n t y i n t h e v a l u e o f e x p o n e n t o f Q can be r e s o l v e d , and t h i s p o i n t w i l l be r e t u r n e d t o l a t e r . The v a l u e o f t h e e x p o n e n t i s o f some s i g n i f i c a n c e , as i n R e f . 1 an e x p o n e n t o f 0.42 i n t h e w i d t h e q u a t i o n was d e d u c e d f r o m s t r a i g h t c h a n n e l d a t a o b t a i n e d a t W a l l i n g f o r d , compared w i t h t h e u s u a l l y a c c e p t e d r e g i m e f i g u r e o f 0.50. F i g . 4a shows t h e r e l a t i o n b e t w e e n c h a n n e l w i d t h and d i s c h a r g e f o r t h e p r e s e n t r e s u l t s t o g e t h e r w i t h t h e p o i n t s o b t a i n e d f o r t h e i n v e s t i g a t i o n s on s t r a i g h t c h a n n e l s (1) u n d e r t a k e n p r e v i o u s l y a t W a l l i n g f o r d u s i n g t h e same s a n d . I t w i l l be s e e n t h a t i n a l l c a s e s t h e w i d t h o f t h e meandered c h a n n e l s i s g r e a t e r t h a n t h a t o f t h e s t r a i g h t c h a n n e l s a t t h e same d i s c h a r g e . The b e s t - f i t e q u a t i o n t o t h e s t r a i g h t c h a n n e l d a t a was: b = 3.6 Q°-^2 and i t a p p e a r s f r o m F i g . 4a t h a t t h e f r e e l y - d e v e l o p e d meandered c h a n n e l s had w i d t h s , a l m o s t w i t h o u t e x c e p t i o n , o f a t l e a s t t w i c e t h e w i d t h o f a s t r a i g h t c h a n n e l f o r t h e same d i s c h a r g e . The r e l a t i o n s h i p : 2 1

b = 7.2 Q°-42 f o r m s a l o w e r l i m i t t o t h e w i d t h d a t a f o r m e a n d e r i n g c h a n n e l s . S t r e a m s t h a t r e m a i n e d s t r a i g h t b u t had p r o m i n e n t a l t e r n a t e s h o a l s l a y i n t h e b a n d :

^ ^

T h e r e has b e e n d i v e r s i t y o f o p i n i o n a b o u t t h e w i d t h t o d e p t h r a t i o o f m e a n d e r i n g c h a n n e l s . From t h e s e i n v e s t i g a t i o n s , i t i s a p p a r e n t t h a t i t i s o n l y s t r e a m s o f l o w s e d i m e n t c h a r g e t h a t r e m a i n s t r a i g h t ; s t r e a m s t h a t d e v e l o p m e a n d e r s a r e d e p e n d e n t on a h i g h e r s e d i m e n t c h a r g e , and a l s o h a v e a g r e a t e r w i d t h t o d e p t h r a t i o . On t h e o t h e r h a n d , b a n k e r o s i o n w i l l p r e s u m a b l y o n l y o c c u r when c h a n n e l s a r e n o t e x c e s s i v e l y w i d e , and t h u s t h e r e may be a n u p p e r l i m i t t o t h e w i d t h o f t h e c h a n n e l w h i c h w i l l meander i n t h i s f a s h i o n . T u r n i n g n e x t t o t h e e f f e c t o f d i s c h a r g e on t h e w i d t h o f t h e meander b e l t . F i g . 4b shows c o n s i d e r a b l e s c a t t e r , f a r g r e a t e r t h a n t h a t i n F i g . 3, w h e r e meander l e n g t h i s s i m i l a r l y p l o t t e d . T h i s i s n o t u n e x p e c t e d , as i t a p p e a r e d f r o m t h e p a t t e r n o f d e v e l o p m e n t t h a t t h e u l t i m a t e s t a b l e wave l e n g t h m i g h t be a c h i e v e d b e f o r e t h e w i d t h o f t h e meander b e l t had r e a c h e d a maximum. G i v e n more t i m e

-i n some t e s t s a t l e a s t - w -i d e r meander b e l t s m -i g h t h a v e r e s u l t e d , b u t e v e n more i m p o r t a n t i s t h e f a c t t h a t t h e b e l t w i d t h may d e p e n d a p p r e c i a b l y on f a c t o r s o t h e r t h a n d i s c h a r g e . T h i s w i l l be r e f e r r e d t o a g a i n l a t e r i n t h i s r e p o r t . From a l e a s t s q u a r e s a n a l y s i s o f t h e d a t a f r o m t h e same t e s t s u s e d f o r t h e d e r i v a t i o n o f e q u a t i o n (3) t h e r e g r e s s i o n o f meander b e l t w i d t h o n d i s c h a r g e i s : e = 18.50 Q°-505 The c o r r e l a t i o n c o e f f i c i e n t i s 0.838 and t h e s t a n d a r d e r r o r i s 0.082 l o g u n i t s . 22 The meander l e n g t h b e i n g s t r o n g l y d e p e n d e n t o n d i s c h a r g e and t h e b e l t - w i d t h and c h a n n e l w i d t h a l s o b e i n g d e p e n d e n t on d i s c h a r g e ( a m o n g s t o t h e r f a c t o r s ) , i t may be i n s t r u c t i v e t o c o n s i d e r how t h e r a t i o s b e t w e e n t h e s e t h r e e l i n e a r m e a s u r e m e n t s v a r y w i t h d i s c h a r g e . F i g . 5 shows t h e r a t i o s X/b, B/b, and A/3: s c a t t e r i s a p p r e c i a b l e i n e a c h c a s e . The b e s t - f i t e q u a t i o n s , a g a i n u s i n g d a t a f r o m t h e same t e s t s u s e d i n t h e d e r i v a t i o n o f e q u a t i o n ( 3 ) , a r e : A = 4.47 (9) b I = 2.17 Q°-^3S (10) b ^ = 2.06 Q-°-°^^ (11) p The c o r r e l a t i o n c o e f f i c i e n t s a r e 0.399, 0.461 and 0.136 r e s p e c t i v e l y . The s t a n d a r d e r r o r s a r e 0.085, 0.090, and 0.070 i n l o g u n i t s r e s p e c t i v e l y . T h u s , a l t h o u g h t h e r a t i o o f meander l e n g t h t o b e l t w i d t h i s n o t v e r y d e p e n d e n t o n d i s c h a r g e , t h e t w o g e o m e t r i c r a t i o s i n v o l v i n g c h a n n e l w i d t h show a v a r i a t i o n w i t h d i s c h a r g e i n t h e p r e s e n t r a n g e o f e x p e r i m e n t s , t h o u g h t h i s i s o f d o u b t f u l s i g n i f i c a n c e . I n t e r - r e l a t i o n s h i p o f c h a n n e l d i m e n s i o n s 'When p l o t t i n g meander l e n g t h a g a i n s t d i s c h a r g e t h e s c a t t e r i s s m a l l p r o v i d e d t h a t , as i n t h e s e t e s t s , a s i n g l e g r a d e o f m a t e r i a l i s u s e d . I f t h e d i f f e r e n t g r a d e s o f m a t e r i a l o c c u r r i n g i n n a t u r e some s l i g h t l y c o h e s i v e , a r e c o n s i d e r e d h o w e v e r , i t i s t o be e x p e c t e d t h a t s c a t t e r w o u l d o c c u r b e c a u s e o f d i f f e r i n g m o b i l i t y o f bed s e d i m e n t s and e r o d i b i l i t y o f b a n k s . A f u r t h e r f a c t o r t h a t has i n f l u e n c e d p r e v i o u s a u t h o r s i n a n a l y s i n g p r o t o t y p e d a t a i s t h a t b a n k - f u l l c h a n n e l w i d t h s and meander l e n g t h s a r e m e a s u r a b l e e v e n i f somewhat i l l - d e f i n e d , w h e r e a s t h e d i s c h a r g e t h a t g e n e r a t e d t h e p a t t e r n may be d i f f i c u l t t o