M A N U A L
OFODIFLOCS
MAST-G6S COASTAL STRUCTURES
I
Co-sponsored by
Commission of the European Communities, Directorate General XII.
, TU Delft
M.R.A. van GentMANUAL
OF
ODIFLOCS
RESEARCH VERSION 1.3
M.R.A. VAN GENT NOVEMBER 1 9 9 2
TU Delft
COASTAL
STRUCTURES
tit-TV Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
CONTENTS
1 . Introduction. 3 2 . Manual of the P.C.-program O D I F L O C S . 5
2.1 G e n e r a l . 5 2 . 2 T h e i n p u t . 6 2 . 3 T h e o u t p u t . 1 4 2 . 3 . 1 C o n t e n t s o f RUN ??.INP. 1 4 2 . 3 . 2 C o n t e n t s of RUN_??.HIS. 15 2 . 3 . 3 C o n t e n t s of RUN ??.SNP. 1 6 2 . 3 . 4 C o n t e n t s o f R U N _ ? ? . M A X . 17 2 . 3 . 5 F r o m o u t p u t files t o g r a p h s . 18 3 . S u m m a r y . 2 0 A ckno wledgemen ts 2 1 References 2 2 APPENDICES Equations 2 4 Figures 2 5 Papers T h e m o d e l l i n g of w a v e a c t i o n o n and in c o a s t a l s t r u c t u r e s . A p p l i c a t i o n s of a n u m e r i c a l m o d e l f o r w a v e a c t i o n o n p o r o u s s t r u c t u r e s . 2
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S1. Introduction.
In t h e E u r o p e a n M A S T - G 6 S p r o g r a m , n u m e r i c a l m o d e l s h a v e b e e n d e v e l o p e d f o r t h e d e s c r i p t i o n o f w a v e m o t i o n o n and in c o a s t a l s t r u c t u r e s . T h i s m e a n s t h a t t h e e x t e r n a l f l o w had t o be c o u p l e d t o t h e i n t e r n a l f l o w . T h e m o d e l O D I F L O C S d e v e l o p e d at D e l f t U n i v e r s i t y o f T e c h n o l o g y , is s u c h a c o u p l e d m o d e l . It is based o n a o n e - d i m e n s i o n a l d e s c r i p t i o n o f t h e f l o w ( w h i c h d o e s n o t m e a n t h a t it c a n n o t give a t w o - d i m e n s i o n a l i m p r e s s i o n o f t h e f l o w ) . It m e a n s t h a t t h e m o d e l uses s o m e s i m p l i f i c a t i o n s t h a t m a k e t h e results of t h e m o d e l d e v i a t e f r o m reality b u t in s u c h a w a y t h a t t h e results d o n o t d e v i a t e t o o m u c h and w i l l give a rather g o o d i m p r e s s i o n o f t h e m o v e m e n t o f t h e w a t e r o n and in a c o a s t a l s t r u c t u r e . D e s c r i b i n g t h e w a v e a c t i o n o n and in c o a s t a l s t r u c t u r e s c a n lead t o a p r e d i c t i o n o f f o r c e s o n e l e m e n t s o f t h o s e s t r u c t u r e s . For p e r m e a b l e s t r u c t u r e s several a s p e c t s c o n c e r n i n g t h e i n t e r a c t i o n b e t w e e n t h e e x t e r n a l f l o w and t h e internal f l o w h a v e t o be d e s c r i b e d a c c u r a t e l y in order t o p r e d i c t f o r i n s t a n c e v e l o c i t i e s a n d r u n - u p levels. T h o s e a s p e c t s are i m p l e m e n t e d in t h e m o d e l . In f i r s t i n s t a n c e , t h e m o d e l c a n be used t o p r e d i c t s e v e r a l h y d r a u l i c p r o p e r t i e s . For t h e p r e d i c t i o n o f f o r c e s , f u r t h e r v e r i f i c a t i o n is r e q u i r e d . T h e c o m p u t e r p r o g r a m ODIFLOCS w h i c h runs on a P.C., d e s c r i b e s t h e w a v e m o t i o n o n a n d in several t y p e s o f s t r u c t u r e s . T h i s s t r u c t u r e c a n be an i m p e r m e a b l e or a p e r m e a b l e s t r u c t u r e . For i n s t a n c e d i k e s , b r e a k w a t e r s a n d s u b m e r g e d s t r u c t u r e s c a n be dealt w i t h . T h e p r o g r a m t a k e s v a r i o u s p h e n o m e n a into a c c o u n t s u c h as r e f l e c t i o n , p e r m e a b i l i t y , i n f i l t r a t i o n , d e s o r p t i o n , o v e r t o p p i n g , v a r y i n g r o u g h n e s s a l o n g t h e s l o p e , linear and non-linear p o r o u s f r i c t i o n (Darcy- a n d t u r b u l e n t f r i c t i o n ) , a d d e d m a s s , internal s e t - u p and t h e d i s c o n n e c t i o n o f t h e free s u r f a c e and t h e p h r e a t i c s u r f a c e . A s e n s i t i v i t y a n a l y s i s , a v e r i f i c a t i o n and s e v e r a l a p p l i c a t i o n s of t h e m o d e l have been d o n e . Especially c o n v e n t i o n a l - a n d b e r m b r e a k w a t e r s have been s t u d i e d . T h e s e n s i t i v i t y analysis s h o w s t h e i n f l u e n c e o f several p a r a m e t e r s o n t h e v e l o c i t i e s . A n u m b e r o f m e a s u r e m e n t s have been used f o r v e r i f i c a t i o n o f t h e m o d e l . S a t i s f a c t o r y r e s u l t s w e r e o b t a i n e d w i t h t h e m o d e l l i n g o f r u n - u p , s u r f a c e e l e v a t i o n s and v e l o c i t i e s . T h e p h e n o m e n o n internal s e t - u p is s i m u l a t e d . T h e m o d e l gives a p r e d i c t i o n o f t h e p e r m e a b i l i t y c o e f f i c i e n t P a p p e a r i n g in t h e s t a b i l i t y f o r m u l a e of V a n der Meer as w e l l .TU Delft
M A N U A L O F T H E P . C . - P R O G R A M O D I F L O C S T h e t h e o r e t i c a l b a c k g r o u n d is d e s c r i b e d in V a n G e n t ( 1 9 9 2 - b ) . In t h e a p p e n d i c e s , t w o papers c o n c e r n i n g t h e m o d e l O D I F L O C S give a s h o r t d e s c r i p t i o n of t h e m o d e l and d e s c r i b e f u r t h e r r e s e a r c h w i t h t h e m o d e l . T h e m o d e l is still in a so called r e s e a r c h s t a g e w h i c h m e a n s t h a t f o r t h e use of t h e m o d e l in a p a r t i c u l a r case o n e has t o v e r i f y w h e t h e r s a t i s f a c t o r y v e r i f i c a t i o n has been d o n e f o r t h e c o n d i t i o n s , o n e w a n t s t o use t h e m o d e l f o r . If t h i s is n o t t h e c a s e , f u r t h e r v e r i f i c a t i o n is n e c e s s a r y b e f o r e one c a n s a y t h a t t h e m o d e l is able t o p r e d i c t t h e required p a r a m e t e r . In a n y c a s e , t h e a u t h o r , t h e U n i v e r s i t y and o t h e r p e o p l e i n v o l v e d , do n o t t a k e any r e s p o n s i b i l i t y f o r t h e results o f t h i s p r o g r a m . It is n o t a l l o w e d t o use t h i s m o d e l f o r c o m m e r c i a l p u r p o s e s . 4TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
2. Manual of the P. C.-model ODIFLOCS.
2.1 General.
T h e m o d e l O D I F L O C S (One D i m e n s i o n a l F l o w o n and in C o a s t a l S t r u c t u r e s ) c o m p u t e s t h e w a v e m o t i o n o n and in a c o a s t a l s t r u c t u r e u s i n g l o n g w a v e e q u a t i o n s . T h e m a t h e m a t i c a l d e s c r i p t i o n and t h e m o s t i m p o r t a n t a s p e c t s o f t h e m o d e l l i n g have been d i s c u s s e d in t h e papers in t h e a p p e n d i c e s o f t h i s m a n u a l . T h e earlier p u b l i c a t i o n V a n Gent ( 1 9 9 2 - b ) gives an e v e n m o r e d e t a i l e d d e s c r i p t i o n .
T h i s r e s e a r c h v e r s i o n 1.3 o f t h e P . C . - m o d e l O D I F L O C S c a n o n l y deal w i t h regular w a v e s . T h e w a v e s are c o m p u t e d w i t h t h e S t o k e s s e c o n d - o r d e r t h e o r y or t h e C n o i d a l w a v e t h e o r y , d e p e n d i n g on t h e Ursell n u m b e r . T h e d e s c r i p t i o n o f t h e e x t e r n a l f l o w is based on w o r k by K o b a y a s h i et a l . ( 1 9 8 7 ) . T h i s d e s c r i p t i o n o f t h e e x t e r n a l f l o w is a d a p t e d in order t o c o u p l e t h e m o d e l t o a p o r o u s f l o w m o d e l . T h e t r e a t m e n t o f t h e b o u n d a r y p o i n t at t h e slope is also a d a p t e d b e c a u s e it w a s f o u n d t h a t instabilities w e r e o f t e n due t o t h e t r e a t m e n t of t h i s b o u n d a r y . N o w , instabilities d o n o t o c c u r if t h e c o m b i n a t i o n o f v a l u e s of several i n p u t p a r a m e t e r s (A, A x and A t ) d o e s n o t d i f f e r t o o m u c h f r o m r e c o m m e n d e d v a l u e s . A f i n i t e d i f f e r e n c e m e t h o d ( L a x - W e n d r o f f ) is used f o r t h e n u m e r i c a l s o l u t i o n of t h e l o n g w a v e e q u a t i o n s , b o t h for t h e internal f l o w and t h e e x t e r n a l f l o w . T h e grid s p a c e is c o n s t a n t . T h e t i m e - s t e p is c o n s t a n t as w e l l . T h e p r o g r a m is w r i t t e n in T u r b o P a s c a l . It r u n s o n a P.C. T h e use o f a c o m p u t e r f a s t e r t h a n a 3 8 6 w i t h a c o - p r o c e s s o r and w i t h a c o l o u r s c r e e n is r e c o m m e n d e d t o s h o r t e n t h e c o m p u t a t i o n t i m e a n d t o m a k e use o f t h e c o l o u r e d i n p u t - and o u t p u t s c r e e n s . T h e p r o g r a m c a n b e t t e r be c o p i e d t o a hard d i s k t o speed up t h e c o m p u t a t i o n p r o c e s s . Files w i l l be w r i t t e n t o t h e s a m e d i r e c t o r y as t h e d i r e c t o r y w h e r e t h e p r o g r a m is l o c a t e d . T h e p r o g r a m w i l l s t a r t by t y p i n g ODIFLOCS and t h e n pressing ENTER.
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
2.2 The input.
T h e p r o g r a m s t a r t s b y t y p i n g O D I F L O C S if y o u are in t h e s a m e d i r e c t o r y as t h e p r o g r a m itself (files O D I F L O C S . E X E a n d O D I F L O C S . O V R ) . First, t h e s c r e e n as s h o w n in t h e f i g u r e b e l o w w i l l a p p e a r . A f t e r p r e s s i n g ENTER, r e f e r e n c e s w i l l be g i v e n . A f t e r a g a i n p r e s s i n g ENTER, t h e s c r e e n gives i n f o r m a t i o n c o n c e r n i n g t h e o u t p u t files t h a t w i l l be c r e a t e d . T h e main i n p u t s c r e e n w i l l appear a f t e r p r e s s i n g ENTER a g a i n .
•DiFLDES
P R O G R A M NAME O D I F L O C S O n e D I n e n s i o n a l F L D u o n a n d i n C o a s t a l S t r u c t u r e s . by : n . R . n . U A N G E N T D E L F T U N I U E R S I T V O F T E C H N O L O G V F U N C T I ON T h i s p r o a r a n c o n p u t e s t h e u a u e n o t i o n o n a n d i n a c o a s t a l s t r u c t u r e u s i n g l o n g u a u e e q u a t i o n s . T h e a u t h o r a n d U n i v e r s i t y d o n o t t a k e a n y r e s p o n s i b i l i t y f o r t h e u s e a n d t h e r e s u l t s o f t h i s p r o g r a n . I t i s p r o h i b i t e d t o u s e t h i s p r o g r a n f o r c o t - m e r e i a l p u r p o s e s . V E R S I O N : 1 . 3 ( N o v e n b e r 1 9 9 2 > P R E S S E N T E R T O C O N T I N U E T i t l e s c r e e n o f t h e P . C . - m o d e l . T h e m a i n i n p u t s c r e e n c o n t a i n s i n f o r m a t i o n as s h o w n b e l o w . T h e k e y F1 gives h e l p - i n f o r m a t i o n c o n c e r n i n g t h e data t h a t has t o be filled in a t y o u r c u r r e n t p o s i t i o n . T h e k e y F2 gives i n f o r m a t i o n c o n c e r n i n g t h e k e y s t h a t have a f u n c t i o n in t h i s i n p u t s c r e e n .TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
Input O D I F L O C S - d a t a
Data
N o . o f run (for f i l e n a m e s ) Read f r o m file " R U N ??.INP"
[ 0 . . 9 9 ] N o I Y e s
F 1 : HELP
F 2 : KEY F U N C T I O N S
Structure and Incident W a v e
N o . o f Slope S e c t i o n s N o . o f Core S e c t i o n s S W L (m) H (m) T (s) I n c l u d e Porous f l o w m o d e l l i n g ? Num. Computation Delta (m) D x (m) Dt (s) L e n g t h o f c o m p . (s) O v e r t o p p i n g a l l o w e d ? Data Output N o . of p o i n t s o f t i m e ( S n a p s h o t s ) N o . o f slope p o i n t s (Time-histories) [ 1 . . 8 ] [ 0 . . 5 ] [ > 0 ] [ 0 . . S W L / 2 ] [ > 0 ] N o | Y e s [ O . O O O L . D x ] [ 0 . 0 0 0 1 . . 1 ] [ 0 . 0 0 0 1 . . 0 . 1 ] [ > 0 ] N o ! Y e s [ 0 . . 1 0 ] [ 0 . . 5 ] SELECT F 1 0 SELECT F 1 0 SELECT F 1 0 SELECT F 1 0 SELECT F 1 0 SELECT F 1 0 Each i n p u t line f r o m t h i s i n p u t s c r e e n w i l l n o w be d i s c u s s e d s e p a r a t e l y . Y o u c a n edit in e a c h i n p u t line. Y o u can also m o v e t o o t h e r lines by using t h e up a n d d o w n a r r o w s . W i t h t h e ESC key y o u can t e r m i n a t e t h e p r o g r a m .
I n p u t data c o n c e r n i n g i n p u t and o u t p u t f i l e s :
(1) T h e o u t p u t files c o n t a i n a n u m b e r . T h e o u t p u t files w i l l be called r u n _ [ n u m b e r ] . [ e x t e n s i o n ] . For e x a m p l e , if t h e n u m b e r 12 is c h o s e n t h e f o l l o w i n g data files w i l l be m a d e : r u n _ 1 2 . i n p , r u n _ 1 2 . h i s , r u n _ 1 2 . s n p , r u n _ 1 2 . m a x and r u n _ 1 2 . f l m . V a l u e s b e t w e e n 0 a n d 9 9 c a n be p r e s c r i b e d .
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
(2) I n p u t d a t a f r o m an earlier c o m p u t a t i o n c a n be used (and a d a p t e d ) . C h o o s e YES (-*) if y o u w a n t t o use t h i s o p t i o n . Prescribe t h e n u m b e r o f t h e i n p u t file f r o m t h e earlier c o m p u t a t i o n w i t h f i l e n a m e r u n _ [ n u m b e r ] . i n p . T h e d a t a f r o m t h e i n p u t file w i l l be filled in if t h e i n p u t file e x i s t s in t h e c u r r e n t d i r e c t o r y . T h e data c a n be e d i t e d a f t e r w a r d s . For i n s t a n c e , if t h e v a l u e 1 2 is c h o s e n , t h e i n p u t d a t a f r o m t h e file r u n _ 1 2 . i n p w i l l be red a n d t h e c u r r e n t v a l u e s in t h e i n p u t m e n u w i l l be replaced in case t h e file r u n _ 1 2 . i n p e x i s t s . V a l u e s b e t w e e n 0 and 9 9 c a n be p r e s c r i b e d .
Data c o n c e r n i n g t h e s t r u c t u r e and t h e i n c i d e n t w a v e :
(3) T h e slope o f t h e s t r u c t u r e has t o be p r e s c r i b e d u s i n g a n u m b e r o f slope s e c t i o n s . For e a c h slope s e c t i o n , t h e f r i c t i o n c o e f f i c i e n t f, t h e t a n g e n t o f t h e angle o f t h e slope s e c t i o n w i t h t h e h o r i z o n t a l a x i s , a n d t h e h o r i z o n t a l w i d t h B of t h e slope s e c t i o n , have t o be p r e s c r i b e d . First, p r e s c r i b e t h e t o t a l n u m b e r o f slope s e c t i o n s . A f t e r s e l e c t i n g F 1 0 , t h e d a t a f o r e a c h slope s e c t i o n c a n be filled i n . Y o u can leave t h e s u b - m e n u a g a i n by s e l e c t i n g F 1 0 . For t h e t a n g e n t o f t h e angle also n e g a t i v e v a l u e s c a n be c h o s e n as l o n g as t h e level o f t h e slope s t a y s a b o v e t h e level o f t h e t o e o f t h e s t r u c t u r e . T h e v a l u e zero c a n not be u s e d . For v a l u e s of t h e f r i c t i o n c o e f f i c i e n t f, t h e f o r m u l a o f M a d s e n and W h i t e can o f t e n be u s e d : ( w V0 5/ rl \0-7 ƒ = 0.29 — — - — \dgj ( , / ? c o t a ; w h e r e d : s t o n e d i a m e t e r . ds : d e p t h in f r o n t of t h e s t r u c t u r e . R : r u n - u p level f o r w h i c h t h e w a v e h e i g h t c a n be an a p p r o x i m a t i o n . c o t a : f o r a b e r m b r e a k w a t e r , t h e m o s t g e n t l e s l o p i n g part o f t h e slope can be u s e d . (4) A n i m p e r m e a b l e c o r e c a n be i m p l e m e n t e d . If y o u w a n t a h o m o g e n e o u s s t r u c t u r e , j u s t prescribe zero core s e c t i o n s . If y o u w a n t t o i m p l e m e n t an i m p e r m e a b l e c o r e , t h i s core has to s t a y inside t h e b o u n d a r y o f t h e s t r u c t u r e w h i c h is d e s c r i b e d w i t h t h e slope s e c t i o n s in t h e p r e v i o u s i n p u t line. For
ik*
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S e a c h c o r e s e c t i o n , t h e t a n g e n t of t h e angle o f t h e c o r e s e c t i o n w i t h t h e h o r i z o n t a l axis has t o be p r e s c r i b e d , as w e l l as t h e h o r i z o n t a l w i d t h B o f t h e c o r e s e c t i o n . First, p r e s c r i b e t h e t o t a l n u m b e r o f c o r e s e c t i o n s . A f t e r s e l e c t i n g F 1 0 , t h e data f o r e a c h c o r e s e c t i o n c a n be filled i n . Y o u c a n leave t h e s u b - m e n u again by s e l e c t i n g F 1 0 .In case o n e w a n t s t o c o m p u t e a s t r u c t u r e w i t h m o r e t h a n o n e layer, f o r i n s t a n c e a layer o n a c o r e , o n e has t o c h o o s e b e t w e e n t w o o p t i o n s . If t h e c o r e has a p p r o x i m a t e l y t h e s a m e p e r m e a b i l i t y as t h e o u t e r layer, t h e t w o c a n be t a k e n t o g e t h e r and t h e s t r u c t u r e w i l l be d e a l t w i t h as a h o m o g e n e o u s s t r u c t u r e . If t h e core is a l m o s t i m p e r m e a b l e , o n e can use an i m p e r m e a b l e c o r e . In o t h e r cases in w h i c h t h e s t r u c t u r e can n o t be s c h e m a t i z e d u s i n g o n l y o n e p e r m e a b l e layer w i t h or w i t h o u t an i m p e r m e a b l e layer, t h e m o d e l c a n n o t deal w i t h t h a t t y p e o f s t r u c t u r e .
(5) T h e still w a t e r level S W L has t o be p r e s c r i b e d . T h i s is t h e w a t e r d e p t h at t h e t o e o f t h e s t r u c t u r e . Since o v e r t o p p i n g c a n be c o m p u t e d , a v a l u e larger t h a n t h e t o p of t h e s t r u c t u r e c a n be p r e s c r i b e d in c a s e f o r OVERTOPPING AL L O W E D , m e n t i o n e d a f e w input lines b e l o w , t h e o p t i o n YES is c h o s e n . (6) T h e h e i g h t o f t h e i n c i d e n t w a v e at t h e s e a w a r d b o u n d a r y has t o be
p r e s c r i b e d . T h i s is a regular w a v e h e i g h t . T h e m o d e l c a n n o t c o m p u t e irregular w a v e s .
(7) T h e w a v e period o f t h e i n c i d e n t w a v e at t h e s e a w a r d b o u n d a r y has t o be p r e s c r i b e d . This is a regular w a v e p e r i o d . T h e m o d e l c a n not c o m p u t e irregular w a v e s .
(8) T h e m o d e l c a n be used f o r an i m p e r m e a b l e s t r u c t u r e by c h o o s i n g NO («-) f o r t h i s o p t i o n . For a p e r m e a b l e s t r u c t u r e , m o r e i n p u t d a t a has t o be p r e s c r i b e d . C h o o s e YES (-»), and t h e n s e l e c t F 1 0 . First, t h e p h r e a t i c level at t h e b o u n d a r y at t h e l a n d w a r d side has t o be g i v e n . In m o s t c a s e s , f o r t h i s v a l u e , t h e Still W a t e r Level o u t s i d e t h e s t r u c t u r e is used h e r e . A f t e r s e l e c t i n g F 1 0 , v a r i o u s p r o p e r t i e s o f t h e p o r o u s p a r t have t o be g i v e n . All p r o p e r t i e s are c o n s t a n t f o r t h e hole p o r o u s m e d i u m . For wm a x, a and /?, r e c o m m e n d e d
v a l u e s w i l l be g i v e n j u s t b e f o r e t h e c o m p u t a t i o n s t a r t s if t h e y d i f f e r f r o m e x i s t i n g k n o w l e d g e c o n c e r n i n g t h e s e v a l u e s .
T h e data f o r t h e p o r o u s m e d i u m , t o be filled in in t h e s u b - m e n u are:
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S n [ 0 . 1 . . 0 . 9 ] T h e p o r o s i t y . de q [ 0 . 0 0 1 . . 1 0 ] T h e e q u i v a l e n t d i a m e t e r o f t h e p a r t i c l e s has t o be p r e s c r i b e d (see t h e e q u a t i o n s f o r c, a n d c2 b e l o w ) . wm a x T h e m a x i m u m v e r t i c a l v e l o c i t y at t h e p h r e a t i c s u r f a c e has t o be p r e s c r i b e d . In case t h i s v a l u e s d i f f e r s f r o m t h e v a l u e b e l o w , i ci 1 \w \ = - + 2 c2 2 \J c, 2 4 ( ) + -C2 C2 a r e c o m m e n d e d v a l u e , w h i c h c a n be i g n o r e d , w i l l be g i v e n b e f o r e t h e c o m p u t a t i o n s t a r t s . For t h e F o r c h h e i m e r c o e f f i c i e n t s c, a n d c2, t h e f o l l o w i n g f o r m u l a e are u s e d : c, = a ^ — ^ — with a = ƒ ( Re , KC ) 1 3 J 2 n 3 g dz c2 = p — , with p = ƒ ( Re , KC ) n3 8 d w h e r e Re : R e y n o l d s n u m b e r . KC : K e u l e g a n - C a r p e n t e r n u m b e r .a This p a r a m e t e r is part of t h e linear F o r c h h e i m e r t e r m
w i t h c o e f f i c i e n t cv A l t h o u g h t h i s v a l u e v a r i e s , d e p e n d i n g o n t h e R e y n o l d s n u m b e r a n d t h e K e u l e g a n -C a r p e n t e r n u m b e r , a c o n s t a n t v a l u e has t o be p r e s c r i b e d . In c a s e t h i s v a l u e d i f f e r s t o o m u c h f r o m t h e r e c o m m e n d e d v a l u e , t h e r e c o m m e n d e d v a l u e , w h i c h c a n be i g n o r e d , w i l l be g i v e n b e f o r e t h e c o m p u t a t i o n s t a r t s . /? This p a r a m e t e r is part o f t h e n o n - l i n e a r F o r c h h e i m e r t e r m w i t h c o e f f i c i e n t c2. A l t h o u g h t h i s v a l u e v a r i e s , d e p e n d i n g on t h e R e y n o l d s n u m b e r a n d t h e K e u l e g a n
-i t
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M A N U A L OF THE P . C . - P R O G R A M O D I F L O C S C a r p e n t e r n u m b e r , a c o n s t a n t v a l u e has t o be p r e s c r i b e d . In case t h i s v a l u e d i f f e r s t o o m u c h f r o m t h e r e c o m m e n d e d v a l u e , t h e r e c o m m e n d e d v a l u e , w h i c h c a n be i g n o r e d , will be g i v e n b e f o r e t h e c o m p u t a t i o n s t a r t s . cA [-1 . . 1 0 ] T h i s c o e f f i c i e n t t o t a k e t h e p h e n o m e n o n " A d d e d M a s s " i n t o a c c o u n t has t o be t a k e n c o n s t a n t . In case t h e v a l u e 0 is c h o s e n t h e p h e n o m e n o n is n o t t a k e n into a c c o u n t . If n o t , t h e p h e n o m e n o n is d e a l t w i t h as d e s c r i b e d in t h e set o f e q u a t i o n s for t h e p o r o u s m o d e l . c, [ 0 . . 1 0 ] T h i s c o n s t a n t a l l o w s t h e user t o p r e s c r i b e a d i f f e r e n t v a l u e f o r the i n f i l t r a t i o n . T h e v a l u e 1 gives t h e r e c o m m e n d e d v a l u e . T h e r e c o m m e n d e d v a l u e c a n be m u l t i p l i e d w i t h c,. cF [ > 1 ] This c o n s t a n t a l l o w s t h e user t o p r e s c r i b e a d i f f e r e n t v a l u e f o r t h e m a x i m u m v a l u e of q ( f l o w b e t w e e n t h e m o d e l s ) . T h e v a l u e 1 gives t h e r e c o m m e n d e d v a l u e . T h i s v a l u e can be m u l t i p l i e d w i t h cF. Data c o n c e r n i n g t h e n u m e r i c a l c o m p u t a t i o n :(9) A v a l u e f o r A has t o be g i v e n . A slope p o i n t w i t h a w a t e r d e p t h smaller t h e n A is set d r y d u r i n g t h e c o m p u t a t i o n . T h i s v a l u e s h o u l d be smaller t h e n A x . A f t e r s e l e c t i n g F 1 0 , values f o r Ai c a n be p r e s c r i b e d . T h e s e v a l u e s h a v e no i n f l u e n c e o n t h e c o m p u t a t i o n itself. T h e y are o n l y used f o r t h e c o m p u t a t i o n of r u n - u p levels. Each v a l u e of A| c o r r e s p o n d s w i t h a w a t e r d e p t h at w h i c h t h e slope is s u p p o s e d t o be dry for t h e r u n - u p levels c o m p u t e d w i t h t h a t particular v a l u e o f A^ Y o u can leave t h e s u b - m e n u a g a i n by s e l e c t i n g F 1 0 . (10) A c o n s t a n t grid s p a c e , d e f i n e d by A x has t o be p r e s c r i b e d . T o o small v a l u e s c a n c a u s e t o o m a n y data p o i n t s . If t h e c h o s e n v a l u e d i f f e r s f r o m t h e r e c o m m e n d e d v a l u e , a w a r n i n g w i l l be g i v e n j u s t b e f o r e t h e c o m p u t a t i o n s t a r t s . T h e r e c o m m e n d e d v a l u e f o r A x is: Ax = lOO*tan0 11
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S w h e r e f o r 8 t h e m a x i m u m angle is c h o s e n . (11) A c o n s t a n t t i m e - s t e p , d e f i n e d by A t has t o be p r e s c r i b e d . If t h e c h o s e n v a l u e d i f f e r s f r o m t h e r e c o m m e n d e d v a l u e , a w a r n i n g w i l l be g i v e n j u s t b e f o r e t h e c o m p u t a t i o n s t a r t s . A n i n d i c a t i o n f o r t h e v a l u e o f A t c a n be g i v e n b y : (12) T h e l e n g t h o f t h e c o m p u t a t i o n has t o be g i v e n . T h i s s h o u l d be larger t h a n t h r e e t i m e s t h e w a v e period b e c a u s e a f t e r t h a t , a m o r e or less p e r i o d i c s i t u a t i o n is a c h i e v e d . (13) T h e o p t i o n w h e t h e r o v e r t o p p i n g is a l l o w e d has t o be a n s w e r e d . In case o v e r t o p p i n g is a l l o w e d (-»), a m e s s a g e w i l l appear o n t h e s c r e e n d u r i n g t h e c o m p u t a t i o n , g i v i n g t h e p o i n t of t i m e at w h i c h t h e last o v e r t o p p i n g o c c u r r e d . In case o v e r t o p p i n g is n o t a l l o w e d («-), t h e c o m p u t a t i o n s t o p s in case o v e r t o p p i n g o c c u r s . Data c o n c e r n i n g t h e o u t p u t : (14) Several o u t p u t p a r a m e t e r s c a n be s t o r e d at a c e r t a i n m o m e n t o f t i m e . First, t h e t o t a l n u m b e r o f p o i n t s o f t i m e has t o be g i v e n . A f t e r s e l e c t i n g F 1 0 , t h e p o i n t s o f t i m e have t o be g i v e n . Y o u c a n leave t h e s u b - m e n u a g a i n by s e l e c t i n g F 1 0 . ( 1 5 ) Several o u t p u t p a r a m e t e r s at a p a r t i c u l a r c r o s s s e c t i o n c a n be s t o r e d as a f u n c t i o n o f t i m e . A f t e r s e l e c t i n g F 1 0 , t h e p o s i t i o n s o f t h e c r o s s s e c t i o n s , relative t o t h e t o e o f t h e s t r u c t u r e , have t o be g i v e n . A f t e r s e l e c t i n g F 1 0 a g a i n , t h e f r e q u e n c y of t i m e - s t e p s t h a t have t o be s a v e d can be p r e s c r i b e d . For i n s t a n c e , if f o r t h i s v a l u e 4 is t a k e n , data w i l l be s a v e d a f t e r 4 A t ; 8 A t ; 1 2 A t , e t c . Y o u c a n r e t u r n t o t h e m a i n m e n u by s e l e c t i n g F 1 0 a g a i n .A f t e r p r e s c r i b i n g t h e i n p u t d a t a , o n e has t o m o v e t o t h e last i n p u t line ( w i t h t h e a r r o w - k e y s or w i t h t h e P a g e D o w n - k e y ) . A f t e r p r e s s i n g ENTER t h e p r o g r a m
p r o c e e d s w i t h c h e c k i n g o f t h e i n p u t v a l u e s . In case c h e c k i n g o f t h e i n p u t v a l u e s gives a n e g a t i v e result, t h e p r o g r a m gives error m e s s a g e s a f t e r w h i c h t h e c u r s o r
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
is placed t o t h e i n p u t v a l u e t h a t gives t h e error. W h e n all i n p u t p a r a m e t e r s are p r e s c r i b e d c o r r e c t l y , t h e p r o g r a m gives s o m e w a r n i n g s , w h i c h c a n be i g n o r e d , in case s o m e v a l u e s d i f f e r t o o m u c h f r o m r e c o m m e n d e d v a l u e s . A f t e r t h i s , t h e p r o g r a m p r o c e e d s w i t h t h e c o m p u t a t i o n s . T h e f r e e s u r f a c e , t h e p h r e a t i c s u r f a c e (in c a s e p o r o u s f l o w m o d e l l i n g is i n c l u d e d ) , t h e s t r u c t u r e t o g e t h e r w i t h c u r r e n t t i m e , are d i s p l a y e d o n t h e s c r e e n w h i l e t h e p r o g r a m is r u n n i n g . T h e s c r e e n w i l l be u p d a t e d e v e r y 1 0 t i m e - s t e p s . T h e p r o g r a m c a n be t e r m i n a t e d by p r e s s i n g t h e E S C - k e y . 13
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M A N U A L O F T H E P . C . - P R O G R A M O D I F L O C S2.3 The output.
2.3.1 Contents of RUNJ7.INP. T h e o u t p u t file RUN_??.INP w h e r e i n ?? is t h e n u m b e r o f t h e r u n , c o n t a i n s t h e i n p u t p a r a m e t e r s . T h i s file c a n be u s e d f o r a f o l l o w i n g c o m p u t a t i o n . T h e file l o o k s l i k e : Breakwaterdata : Number of Slope-Sections : 7 Slopesection Length 0 . 1 8 5 0 0 . 6 1 0 0 0 . 5 4 0 0 0 . 3 3 5 0 0 . 4 0 5 0 0 . 3 0 0 0 0 . 1 0 0 0Tan of Angle Frictioncoeff.
2 3 4 5 6 7 0 . 0 0 5 0 0 . 8 1 8 0 0 . 2 3 1 5 0 . 2 6 8 7 0 . 3 8 2 7 0 . 6 6 6 7 0 . 0 0 5 0 0 . 1 5 0 0 0 . 1 5 0 0 0 . 1 5 0 0 0 . 1 5 0 0 0 . 1 5 0 0 0 . 1 5 0 0 0 . 1 5 0 0 Number of Core 3 Coresection Sections : Length 1.0000 1.4500 0 . 2 0 0 0 Tan of Angle 2 3 0 . 0 0 2 5 0 . 6 6 6 7 0 . 0 0 2 5 Wave data : Wavetheory : Stokes B 1 : 0 . 1 0 0 0 B2 : 0 . 0 1 3 9 Waveheight Waveperiod Still Water Level 0 . 2 0 0 0 1.5000 0 . 7 9 0 0 Include Porous Flow modelling ?
Wavelength 3 . 2 0 9 3
Ursell 4 . 1 7 8 0
Yes
Internal waterlevel at landward boundary : 0 . 7 9 0 0
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M A N U A L O F T H E P . C . - P R O G R A M O D I F L O C S Porosity 0 . 4 0 0 0 D-Eq 0 . 0 3 4 0 Wmax 0 . 1 0 0 6 A l p h a ( c l ) 5 0 0 7 . 0 0 0 0 Beta(c2) 2 . 6 3 7 7 cA 0.0 cl 1.0 cF 1.0 Numerical computation :Dx (m) Dt (s) Final Time Labda Delta (m) SMax 0 . 0 1 2 5 0 . 0 0 1 4 6 . 0 0 0 0 . 1 5 6 6 0 . 0 0 5 0 198 Number of Delta Visual :
2 0 . 0 1 0 0 0 . 0 1 5 0 A l l o w Overtopping ? Yes Number of Snapshots : ( A t T = .. s ) 10 4 . 6 5 0 0 4 . 8 0 0 0 4 . 9 5 0 0 5 . 1 0 0 0 5 . 2 5 0 0 5 . 4 0 0 0 5 . 5 5 0 0 5 . 7 0 0 0 5 . 8 5 0 0 6 . 0 0 0 0 Number of Slopepoints : ( A t X = .. m ) 5 0 . 8 2 5 0 0 . 9 0 0 0 0 . 9 9 0 0 1.1000 1.2375 Frequency of timesteps saved for Timehistories :
4
2.3.2 Contents of RUN ??.HIS.
T h e o u t p u t file RUN_??.HIS w h e r e i n ?? is t h e n u m b e r o f t h e r u n , c o n t a i n s t h e t i m e h i s t o r i e s . S e v e r a l p a r a m e t e r s are s a v e d , i n c l u d i n g t h e w a t e r d e p t h a n d v e l o c i t i e s at t h e s e l e c t e d c r o s s s e c t i o n s . T h e file l o o k s like: T i m e n i ( x = 0) n r ( x = 0) u(x = 0) h [ 0 . 8 2 5 ] u [ 0 . 8 2 5 ] hP[0.825] uP[0.825] h[ 0 . 9 0 0 ] 0 . 0 0 0 0 0 . 0 0 0 6 0 . 0 0 0 0 0 . 0 0 0 0 0 . 2 8 3 2 0 . 0 0 0 0 0 . 5 0 4 8 0 . 0 0 0 0 0 . 2 6 5 8 0 . 0 0 5 6 - 0 . 0 0 1 9 - 0 . 0 0 0 0 - 0 . 0 0 6 8 0 . 2 8 3 2 - 0 . 0 0 0 1 0 . 5 0 4 8 0 . 0 0 0 0 0 . 2 6 5 8 0 . 0 1 1 2 - 0 . 0 0 4 4 - 0 . 0 0 0 0 - 0 . 0 1 5 5 0.2831 - 0 . 0 0 0 2 0 . 5 0 4 8 - 0 . 0 0 0 0 0 . 2 6 5 8
Runup(rJO) Runup J1 Runup 62 Frontvel. Q-in sum 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 - 0 . 0 0 0 0 - 0 . 0 0 0 1 - 0 . 0 0 0 1 0 . 0 0 0 0 - 0 . 0 1 3 7 - 0 . 0 0 0 0 - 0 . 0 0 0 2 - 0 . 0 0 0 1 0 . 0 0 0 1 - 0 . 0 3 8 0
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
T h e data in t h i s file are : T i m e : Point o f t i m e . O i ( x = 0 ) : S u r f a c e e l e v a t i o n of t h e i n c i d e n t w a v e . n r ( x = 0 ) : S u r f a c e e l e v a t i o n o f t h e r e f l e c t e d w a v e . T h e r e f l e c t i o n c o e f f i c i e n t is d e f i n e d by r = f ï r ( x = 0 ) / n i ( x = 0 ) . u ( x = 0 ) : V e l o c i t y at t h e s e a w a r d b o u n d a r y . h [ 0 . 8 2 5 ] : W a t e r - d e p t h at t h e selected c r o s s s e c t i o n , x = 0 . 8 2 5 m . u [ 0 . 8 2 5 ] : D e p t h - a v e r a g e d v e l o c i t y o u t s i d e t h e s t r u c t u r e at x = 0 . 8 2 5 m . h P [ 0 . 8 2 5 ] : T h i c k n e s s o f t h e p o r o u s layer at t h e s e l e c t e d c r o s s s e c t i o n s , x = 0 . 8 2 5 m . u P [ 0 . 8 2 5 ] : D e p t h - a v e r a g e d filter v e l o c i t y inside t h e s t r u c t u r e at x = 0 . 8 2 5 m . h[ 0 . 9 0 0 ] : T h e s a m e data f o r o t h e r c r o s s s e c t i o n s . R u n u p ( £ 0 ) : R u n - u p level c o m p u t e d w i t h A . R u n u p ó"] : Run-up level c o m p u t e d w i t h Av R u n u p 62: R u n - u p level c o m p u t e d w i t h A2. F r o n t v e l . : F r o n t v e l o c i t y ; a v e r a g e of t h e v e l o c i t i e s c o m p u t e d at t h e t h r e e m o s t u p w a r d w e t grid p o i n t s . Q-in s u m : T o t a l o f w a t e r v o l u m e s t h a t f l o w into t h e s t r u c t u r e r e g a r d e d f r o m a c e r t a i n m o m e n t of t i m e . T h e m a x i m u m v a l u e is t h e t o t a l v o l u m e t h a t f l o w s into t h e s t r u c t u r e d u r i n g t h e last w a v e c y c l e . T h i s v a l u e is d e r i v e d f r o m o n l y regarding t h e w a t e r t h a t f l o w s i n t o t h e s t r u c t u r e . A t t h e s a m e t i m e w a t e r c a n f l o w o u t o f t h e s t r u c t u r e at a n o t h e r p o s i t i o n . T h e v a l u e is n o t an a v e r a g e v a l u e . T h e m a x i m u m v a l u e in t h i s c o l u m n c a n be used but has t o be m o r e or less c o n s t a n t f o r e a c h w a v e c y c l e . If t h e m a x i m u m v a l u e f o r a c e r t a i n w a v e c y c l e is n o t m o r e or less t h e s a m e as t h e m a x i m u m f r o m t h e w a v e c y c l e b e f o r e , m o r e w a v e c y c l e s have to be c o m p u t e d . U s i n g t h i s p a r a m e t e r , a p r e d i c t i o n of t h e P e r m e a b i l i t y c o e f f i c i e n t P, c a n be m a d e . 2.3.3 Contents of RUN ??.SNP. T h e o u t p u t file RUN_??.SNP w h e r e i n ?? is t h e n u m b e r o f t h e r u n , c o n t a i n s t h e t i m e h i s t o r i e s . A t t h e s e l e c t e d points o f t i m e , t h e b o t t o m e l e v a t i o n , t h e w a t e r d e p t h a n d t h e v e l o c i t i e s are s a v e d . T h e file looks like:
4 *
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S T = 4 . 6 5 0 0 sP = 117 s i = 1 1 3 s C 1 = 1 6 4 i x zO zO + h u Core + hP uP q qlnfil 1 0 . 0 1 5 0 0 . 0 0 0 1 0 . 7 4 5 7 - 0 . 2 2 0 8 0 . 0 0 0 1 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 2 0 . 0 3 0 0 0 . 0 0 0 2 0 . 7 4 7 5 - 0 . 2 1 5 1 0 . 0 0 0 2 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 3 0 . 0 4 5 0 0 . 0 0 0 2 0 . 7 4 9 4 - 0 . 2 0 9 4 0 . 0 0 0 2 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 T = 4 . 8 0 0 0 sP = 116 s 1 = 1 1 8 s C 1 = 1 6 4 i x zO zO + h u Core + hP uP q qlnfil 1 0 . 0 1 5 0 0 . 0 0 0 1 0 . 7 1 9 7 - 0 . 3 2 7 2 0 . 0 0 0 1 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 2 0 . 0 3 0 0 0 . 0 0 0 2 0 . 7 2 0 4 - 0 . 3 2 4 7 0 . 0 0 0 2 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 3 0 . 0 4 5 0 0 . 0 0 0 2 0 . 7 2 1 1 - 0 . 3 2 2 3 0 . 0 0 0 2 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0For e a c h s e l e c t e d p o i n t o f t i m e , s e v e r a l data are s t o r e d . T h e f i r s t c o l u m n is t h e n u m b e r o f t h e grid p o i n t , relative t o t h e t o e o f t h e s t r u c t u r e , is p r i n t e d . T h e s e c o n d c o l u m n is t h e h o r i z o n t a l d i s t a n c e (in m) f r o m t h e t o e . T h e t h i r d (zO) is t h e e l e v a t i o n of t h e slope o f t h e s t r u c t u r e . T h e f o u r t h (zO + h) is t h e s u r f a c e e l e v a t i o n relative t o t h e h o r i z o n t a l a x i s . T h e f i f t h (u) is t h e d e p t h - a v e r a g e d v e l o c i t y at t h a t p o i n t . T h e s i x t h c o l u m n (Core + hP) is t h e p h r e a t i c l e v e l , relative t o t h e h o r i z o n t a l a x i s . T h e s e v e n t h (uP) is t h e d e p t h - a v e r a g e d filter v e l o c i t y at t h a t p o s i t i o n . T h e e i g h t h c o l u m n (q) is t h e i n t e r a c t i v e f l o w b e t w e e n t h e e x t e r n a l and t h e i n t e r n a l f l o w ( m / s ) . T h e last c o l u m n (qlnfil) is t h e i n f i l t r a t i o n f l o w t h r o u g h t h e partially s a t u r a t e d zone ( m / s ) .
2.3.4 Contents of RUN ??. MAX.
T h e o u t p u t file R U N _ ? ? . M A X w h e r e i n ?? is t h e n u m b e r o f t h e r u n , c o n t a i n s m a x i m u m v a l u e s of several p r o p e r t i e s (at e a c h grid p o i n t ) t h a t are r e a c h e d d u r i n g t h e last w a v e c y c l e . T h e file looks like:
x-points zO 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 1 5 0 0 . 0 0 0 1 0 . 0 3 0 0 0 . 0 0 0 2 UMax UMin 0 . 4 8 0 0 - 0 . 3 4 7 2 0 . 4 7 9 5 - 0 . 3 4 7 8 0 . 4 7 8 9 - 0 . 3 4 8 3 UPMax UPMin 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 n - m a x n - m i n 0 . 8 7 9 3 0 . 8 7 9 3 0 . 8 7 9 5 0 . 8 7 9 5 0 . 8 7 9 7 0 . 8 7 9 7 17
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S T h e f i r s t c o l u m n c o n t a i n s t h e h o r i z o n t a l d i s t a n c e f r o m t h e t o e o f t h e s t r u c t u r e . T h e s e c o n d c o l u m n c o n t a i n s t h e e l e v a t i o n o f t h e s l o p e o f t h e s t r u c t u r e . T h e t h i r d c o l u m n ( U M a x ) c o n t a i n s t h e m a x i m u m d e p t h - a v e r a g e d v e l o c i t y in t h e d i r e c t i o n t o w a r d s t h e s t r u c t u r e , t h a t w a s r e a c h e d d u r i n g t h e last w a v e c y c l e at t h a t p a r t i c u l a r p o s i t i o n . T h e f o u r t h c o l u m n is t h e m a x i m u m in t h e o p p o s i t e d i r e c t i o n ( a w a y f r o m t h e s t r u c t u r e ) . The f i f t h and t h e s i x t h c o l u m n s c o n t a i n t h e s a m e kind o f i n f o r m a t i o n f o r t h e d e p t h - a v e r a g e d filter v e l o c i t i e s . T h e last t w o c o l u m n s ( D - m a x and n - m i n ) c o n t a i n t h e m a x i m u m - and t h e m i n i m u m s u r f a c e e l e v a t i o n s r e a c h e d d u r i n g t h e last w a v e c y c l e .2.3.5 From output files to graphs.
T h e o u t p u t files c a n easily be i m p o r t e d in S p r e a d s h e e t p r o g r a m s in o r d e r t o m a k e g r a p h s . For i n s t a n c e t h e p r o g r a m s S Y M P H O N Y a n d Q U A T T R O can be u s e d . F o r S Y M P H O N Y c h o o s e [ F 9 ] - [ F I L E ] - [ I M P O R T ] - [ S T R U C T U R E D ] - [ f i l e n a m e ] t o i m p o r t t h e o u t p u t f i l e . G r a p h s c a n be made a f t e r s e l e c t i n g [ F 1 0 ] - [ G R A P H ] - [ [ 1 STS E T T I N G STS ] [ T Y P E : X Y ] [ R A N G E : s e i e c t x and o t h e r d a t a r a n g e s ] ] [ [ 2 N D STS E T T I N G STS ] -[TITLES-prescribe t i t l e s ] ] . [PREVIEW] s h o w s t h e g r a p h . W i t h [ I M A G E S A V E ] y o u c a n s a v e t h e g r a p h . T h e g r a p h c a n be r e t r i e v e d in f o r i n s t a n c e WORDPERFECT w i t h [ A L T + F 9 ] - [ 1 - F I G U R E ] - [ 1 - C R E A T E ] - [ 1 - f i l e n a m e ] . T h e p r o g r a m O D I D E M O c a n be used t o s h o w o u t p u t o n t h e s c r e e n as w e l l . It gives a d e m o f i l m w i t h t h e s u r f a c e e l e v a t i o n and v e l o c i t y a r r o w s . T h e m o d e l O D I F L O C S gives o n l y d e p t h - a v e r a g e d v e l o c i t i e s . T h e v e l o c i t y a r r o w s are d e r i v e d w i t h a kind o f i n t e r p r e t a t i o n of t h e results as d e s c r i b e d in t h e f i r s t paper o f t h e A p p e n d i x . S o m e e x a m p l e s for a b e r m b r e a k w a t e r and a s u b m e r g e d s t r u c t u r e are s h o w n in t h e A p p e n d i x F i g u r e s . T h e p r o g r a m O D I D E M O d o e s n o t s t o r e a n y d a t a . T h e p r o g r a m s t a r t s by t y p i n g O D I D E M O and p r e s s i n g ENTER. T h e i n p u t s c r e e n w i l l be s h o w n a f t e r p r e s s i n g ENTER. Five i n p u t data have t o be g i v e n :
(1) T h e n u m b e r o f t h e run w i t h t h e d a t a . T h e file R U N _ [ n u m b e r ] . F L M has t o e x i s t . If t h e p r o g r a m O D I F L O C S did not y e t c a l c u l a t e t h i s RUN or if t h e file R U N _ [ n u m b e r ] . F L M does n o t e x i s t s in t h e c u r r e n t d i r e c t o r y , t h e p r o g r a m w i l l be t e r m i n a t e d a f t e r c o m p l e t i n g t h e i n p u t m e n u .
(2) T h e f r e q u e n c y o f t h e t i m e - s t e p s t h a t has t o be s h o w n o n t h e s c r e e n has t o p r e s c r i b e d . T h e file R U N _ [ n u m b e r ] . F L M c o n t a i n s data f o r c e r t a i n p o i n t s o f t i m e w i t h a c o n s t a n t t i m e - s t e p i n - b e t w e e n . T h i s t i m e - s t e p c a n be m u l t i p l i e d
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w i t h t h e v a l u e in t h i s i n p u t line. For i n s t a n c e if t h e v a l u e 4 is c h o s e n and t h e file R U N _ [ n u m b e r ] . F L M c o n t a i n s d a t a w i t h a t i m e - s t e p A t = 0 . 1 s, d a t a w i l l be s h o w n o n t h e s c r e e n e v e r y 0 . 4 s.
(3) Data f r o m all grid p o i n t is s t o r e d in t h e d a t a f i l e . T h e d i s t a n c e b e t w e e n t h e v e l o c i t y a r r o w s m a y be t o o small if all grid p o i n t s are s h o w n o n t h e s c r e e n . One c a n p r e s c r i b e t h e f r e q u e n c y of t h e grid p o i n t s t h a t w i l l s h o w a v e l o c i t y a r r o w . If f o r i n s t a n c e 5 is c h o s e n , v e l o c i t y a r r o w s w i l l be s h o w n w i t h a d i s t a n c e 5 A x i n - b e t w e e n w h e r e A x is t h e s p a c e - s t e p f r o m t h e o r i g i n a l c o m p u t a t i o n w i t h O D I F L O C S . (4) T h e size o f t h e v e l o c i t y a r r o w s ( f r o m t h e e x t e r n a l f l o w ) c a n be s c a l e d . T h e r e f o r e , a scale f a c t o r c a n be g i v e n . If y o u w a n t larger a r r o w s , p r e s c r i b e a larger scale f a c t o r . (5) T h e size of t h e v e l o c i t y a r r o w s ( f r o m t h e internal f l o w ) c a n be s c a l e d . T h e r e f o r e , a scale f a c t o r c a n be g i v e n . If y o u w a n t larger a r r o w s , p r e s c r i b e a larger scale f a c t o r . N o r m a l l y t h e c a l c u l a t e d v e l o c i t i e s are smaller inside t h e s t r u c t u r e . T h e r e f o r e it c a n be u s e f u l t o p r e s c r i b e a larger scale f a c t o r t h a n for t h e v e l o c i t y a r r o w s inside t h e s t r u c t u r e .
If y o u are p o s i t i o n e d at t h e f i f t h input line y o u c a n press e n t e r t o s t a r t t h e d e m o f i l m . If t h e file w i t h t h e data e x i s t s in t h e c u r r e n t d i r e c t o r y , t h e p r o g r a m w i l l c o n t i n u e . T h e p r o g r a m c a n be t e r m i n a t e d by p r e s s i n g ESC.
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3. Summary.
T h i s m a n u a l gives i n f o r m a t i o n a b o u t h o w t o use t h e P . C . - m o d e l O D I F L O C S . T h e w a v e a c t i o n o n and in s e v e r a l t y p e s o f c o a s t a l s t r u c t u r e s c a n be c o m p u t e d . T h e n e c e s s a r y i n p u t data and t h e o u t p u t data h a v e been d e s c r i b e d . A l t h o u g h m a n y p h e n o m e n a are i m p l e m e n t e d in t h e m o d e l , w h i c h r e s u l t e d in rather a c c u r a t e p r e d i c t i o n s of several p r o p e r t i e s , f u r t h e r v e r i f i c a t i o n and f u r t h e r r e s e a r c h are r e q u i r e d t o i m p r o v e t h e a c c u r a c y o f t h e m o d e l . C o m p a r i s o n w i t h several m e a s u r e m e n t s s h o w e d t h a t t h e m o d e l p r e d i c t s r u n - u p levels, v e l o c i t i e s and s u r f a c e e l e v a t i o n s rather w e l l . It m u s t be v e r i f i e d w h e t h e r s u c h results w i l l be o b t a i n e d f o r o t h e r cases as w e l l . See also t h e a p p e n d i c e s of t h i s m a n u a l . F u r t h e r r e s e a r c h w i l l c o n t a i n m o r e v e r i f i c a t i o n w i t h m e a s u r e m e n t s , a v e r i f i c a t i o n w h e t h e r f o r c e s o n u n i t s o f t h e s t r u c t u r e s c a n be p r e d i c t e d a n d t h e i m p l e m e n t a t i o n o f irregular w a v e s .
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M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C SA cknowledgemen ts
T h e d e v e l o p m e n t of t h e n u m e r i c a l m o d e l is c o - s p o n s o r e d by t h e C o m m i s s i o n o f t h e E u r o p e a n C o m m u n i t i e s w i t h i n t h e f r a m e w o r k o f t h e M A S T - G 6 S p r o j e c t ( c o n t r a c t 0 0 3 2 - C ) . T h e s t u d y is c a r r i e d o u t u n d e r s u p e r v i s i o n of Prof. K. d ' A n g r e m o n d and Dr. J . W . v a n der Meer. I w o u l d like t o e x p r e s s m y a p p r e c i a t i o n also t o t h e p a r t n e r s in t h e M A S T - g r o u p , in p a r t i c u l a r t o Prof. A . T o r u m , Prof. A . L a m b e r t i , M r . H . A . H . Petit, Prof. F . B . J . B a r e n d s , Dr. S . E . J . S p i e r e n b u r g , M r . F. Engering and M r . M.Z. V o o r e n d t .TU Delft
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slopes, J . o f W P C & O E , A S C E , V o l . 1 1 3 , n o . 3 .
K o b a y a s h i , N. and K.D. W a t s o n ( 1 9 8 7 ) , Wave reflection and runup on smooth
slopes, Proc. C o a s t a l H y d r o d y n a m i c s .
K o b a y a s h i , N. and A . W u r j a n t o ( 1 9 8 9 ) , Numerical model for design of impermeable
coastal structures, Research r e p o r t no. C E - 8 9 - 7 5 , C e n t e r f o r A p p l i e d C o a s t a l
R e s e a r c h , D e p a r t m e n t o f Civil E n g r g . , U n i v e r s i t y o f D e l a w a r e .
M a d s e n , D.S. and S . M . W h i t e ( 1 9 7 5 ) , Reflection and transition characteristics of
porous rubble mound breakwaters, Report n o . 2 0 7 , R . M . Parsons L a b , D e p t . o f
Civil E n g r g . , M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y , C a m b r i d g e , M a s s .
M e e r , J . W . v a n der, and M . Klein Breteler ( 1 9 9 0 ) , Measurements and computation
of wave induced velocities on a smooth slope, A S C E , P r o c . I C C E ' 9 0 , D e l f t , T h e
N e t h e r l a n d s .
M e e r , J . W . v a n der ( 1 9 8 8 ) , Rock slopes and gravel beaches under wave attack, P h . D . - t h e s i s , D e l f t U n i v e r s i t y of T e c h n o l o g y and Delft H y d r a u l i c s .
S h i h , R.W.K. ( 1 9 9 0 ) , Permeability characteristics of rubble material, new formulae, Proc. ICCE 1 9 9 0 D e l f t , V o l . 2 , p p . 1 4 9 9 - 1 5 1 2 .
T o r u m , A ( 1 9 9 1 ) , Wave induced water particle velocities and forces on an armour
unit on a berm breakwater, M A S T - G 6 S r e p o r t .
T o r u m , A and M . R . A . v a n G e n t ( 1 9 9 2 ) , Water particle velocities on a berm
breakwater, t o be p u b l i s h e d in Proc. I C C E ' 9 2 , V e n i c e , I t a l y .
TU Delft
M A N U A L O F T H E P . C . - P R O G R A M O D I F L O C SEquations
T h e basic e q u a t i o n s f o r t h e c o u p l e d m o d e l are p r i n t e d b e l o w . T h e e q u a t i o n s f o r t h e p o r o u s f l o w m o d e l m a y s l i g h t l y d i f f e r , d e p e n d i n g o n t h e area o f t h e p o r o u s m e d i u m : in w h i c h t h e y are a p p l i e d . H Y D R A U L I C M O D E L : dhu dhu 2 , . a l / , I I + —— = -g —— -g h tan 0. - —f u \u\ + q qdx " dx " x = q dh dhu— +
dt dx POROUS F L O W M O D E L : M .dhu dh I dhu2 d \ h l fl , K flf«,( 1 +cA)——-cAu—+ — = -ng—— -nghtanQ -ngh(cvu+c2u \u
)-9/t + }_§hu_ q dt n dx n w h e r e h : w a t e r - d e p t h . u : d e p t h - a v e r a g e d h o r i z o n t a l (filter) v e l o c i t y . 9 : angle o f t h e s l o p e , f : f r i c t i o n c o e f f i c i e n t . q : f l o w b e t w e e n h y d r a u l i c m o d e l and p o r o u s m o d e l ( m / s ) . qx : x - c o m p o n e n t o f t h e v e l o c i t y of q . n : p o r o s i t y . cA : c o e f f i c i e n t f o r added m a s s . c, : F o r c h h e i m e r c o e f f i c i e n t ( s / m ) . c2 : F o r c h h e i m e r c o e f f i c i e n t ( s2/ m2) .
TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
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M A N U A L OF T H E P . O . - P R O G R A M O D I F L O C S
Figures:
Examples output (ODIDEMO) berm breakwater.
Input ODIFLOCS: Breakwaterdata : N u m b e r o f S l o p e - S e c t i o n s : 7 S l o p e s e c t i o n L e n g t h T a n of A n g l e F r i c t i o n c o e f f . 1 0 . 1 8 5 0 0 . 0 0 5 0 0 . 1 5 0 0 2 0 . 6 1 0 0 0 . 8 1 8 0 0 . 1 5 0 0 3 0 . 5 4 0 0 0 . 2 3 1 5 0 . 1 5 0 0 4 0 . 3 3 5 0 0 . 2 6 8 7 0 . 1 5 0 0 5 0 . 4 0 5 0 0 . 3 8 2 7 0 . 1 5 0 0 6 0 . 3 0 0 0 0 . 6 6 6 7 0 . 1 5 0 0 7 0 . 1 0 0 0 0 . 0 0 5 0 0 . 1 5 0 0 N u m b e r of C o r e - S e c t i o n s : 3 C o r e s e c t i o n L e n g t h T a n of A n g l e 1 1 . 0 0 0 0 0 . 0 0 2 5 2 1 . 4 5 0 0 0 . 6 6 6 7 3 0 . 2 0 0 0 0 . 0 0 2 5 Wave data : W a v e t h e o r y : S t o k e s B1 : 0 . 1 0 0 0 B2 : 0 . 0 1 3 9
W a v e h e i g h t W a v e p e r i o d Still W a t e r Level W a v e l e n g t h Ursell
0 . 2 0 0 0 1 . 5 0 0 0 0 . 7 9 0 0 3 . 2 0 9 3 4 . 1 7 8 0 I n c l u d e Porous F l o w m o d e l l i n g ? Y e s Internal w a t e r l e v e l at l a n d w a r d b o u n d a r y : 0 . 7 9 0 0 Porosity D-Eq W m a x A l p h a ( c 1 ) B e t a ( c 2 ) c A cl cF 0 . 4 0 0 0 0 . 0 3 4 0 . 1 0 0 6 5 0 0 7 . 0 0 2 . 6 3 7 7 0 . 0 0 1.00 1.00 2 6
TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
Numerical computation :
Dx (m) Dt (s) Final T i m e Labda Delta (m) S M a x 0 . 0 1 5 0 0 . 0 0 1 5 9 . 0 0 0 0 . 1 4 0 1 0 . 0 0 5 0 1 6 4 N u m b e r o f Delta V i s u a l : 2 0 . 0 1 0 0 0 . 0 1 5 0 A l l o w O v e r t o p p i n g ? Y e s N u m b e r of S n a p s h o t s : ( A t T = .. s ) 1 0 4 . 6 5 0 0 4 . 8 0 0 0 4 . 9 5 0 0 5 . 1 0 0 0 5 . 2 5 0 0 5 . 4 0 0 0 5 . 5 5 0 0 5 . 7 0 0 0 5 . 8 5 0 0 6 . 0 0 0 0 N u m b e r o f S l o p e p o i n t s : ( A t X = .. m ) 3 0 . 6 0 0 0 1 . 4 0 0 0 2 . 2 0 0 0 F r e q u e n c y of t i m e s t e p s s a v e d f o r T i m e h i s t o r i e s : 4
4*
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M A N U A L O F T H E P . C . - P R O G R A M O D I F L O C S O D I F L O C S 5 . 2 5 D s "SS 2 8TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S O D I F L O C S 5 . 1 Ü Ü s O D I F L O C S 5 . 5 S O s. 2 9J s o o i d i a o j s O S 8 ° S
J soo-idiao I —
ik*
TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S O O I F L O C S T i n e : 6 . 3 D O ÊËMÊÊÊÊÊ & . 4 5 D s O D I F L O C S " ]-TU Delft
M A N U A L O F T H E P . C . - P R O O R A M O D I F L O C S
Figures:
Examples output (ODIDEMO) submerged structure.
Input ODIFLOCS: Breakwaterdata : N u m b e r o f S l o p e - S e c t i o n s : 7 S l o p e s e c t i o n L e n g t h T a n o f A n g l e F r i c t i o n c o e f f . 1 0 . 5 0 0 0 0 . 0 6 0 0 0 . 1 5 0 0 2 0 . 6 2 5 0 0 . 8 0 0 0 0 . 1 5 0 0 3 0 . 2 0 0 0 0 . 4 0 0 0 0 . 1 5 0 0 4 1 . 8 0 0 0 0 . 0 0 5 0 0 . 1 5 0 0 5 0 . 2 5 0 0 - 0 . 4 0 0 0 0 . 1 5 0 0 6 0 . 3 6 0 0 - 0 . 8 0 0 0 0 . 1 5 0 0 7 1 . 0 0 0 0 0 . 0 6 0 0 0 . 1 5 0 0 N u m b e r o f C o r e - S e c t i o n s : 1 C o r e s e c t i o n L e n g t h T a n o f A n g l e 1 5 . 5 0 0 0 0 . 0 6 0 0 Wave data : W a v e t h e o r y : S t o k e s B1 : 0 . 1 2 5 0 B2 : 0 . 0 2 1 5
W a v e h e i g h t W a v e p e r i o d Still W a t e r Level W a v e l e n g t h Ursell
0 . 2 5 0 0 ' 1 . 5 0 0 0 0 . 8 0 0 0 3 . 2 1 8 1 5 . 0 5 6 8 I n c l u d e P o r o u s F l o w m o d e l l i n g ? Y e s Internal w a t e r l e v e l at l a n d w a r d b o u n d a r y : 0 . 2 9 1 0 P o r o s i t y D-Eq W m a x A l p h a ( c 1 ) B e t a ( c 2 ) c A cl cF 0 . 4 0 0 0 0 . 0 3 4 0 . 1 0 0 6 5 0 0 7 . 0 0 2 . 6 3 7 7 0 . 0 0 1 . 0 0 1 . 0 0 Numerical computation : Dx (m) Dt (s) Final T i m e Labda 0 . 0 5 0 0 0 . 0 0 5 9 . 0 0 0 0 . 1 5 6 6 Delta (m) 0 . 0 0 5 0 S M a x 9 4
TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S N u m b e r o f Delta V i s u a l : 2 0 . 0 1 0 0 0 . 0 1 5 0 A l l o w O v e r t o p p i n g ? Y e s N u m b e r o f S n a p s h o t s : ( A t T = .. s ) 1 0 4 . 6 5 0 0 4 . 8 0 0 0 4 . 9 5 0 0 5 . 1 0 0 0 5 . 2 5 0 0 5 . 4 0 0 0 5 . 5 5 0 0 5 . 7 0 0 0 5 . 8 5 0 0 6 . 0 0 0 0 N u m b e r o f S l o p e p o i n t s : ( A t X = .. m ) 0 F r e q u e n c y o f t i m e s t e p s s a v e d f o r T i m e h i s t o r i e s : 4TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
TU Delft
M A N U A L OF T H E P . C . - P R O G R A M O D I F L O C S
T H E M O D E L L I N G OF W A V E A C T I O N O N AND I N COASTAL STRUCTURES
Marcel R.A. van Gent1
ABSTRACT
Description of the wave action on and in coastal structures can lead to a prediction of flow properties and forces on elements of those structures. For permeable structures several aspects concerning the interaction between the external flow and the internal flow have to be described accurately in order to predict for instance velocities and run-up levels. Wave action can be described by the numerical model ODIFLOCS, developed at Delft University of Technology within the framework of the European MAST-Coastal Structures project. The computer program ODIFLOCS which runs on a P . C , describes the wave motion on and in several types of structures. This structure can be an impermeable or a permeable structure. For instance dikes, breakwaters and submerged structures can be dealt with. The model is a one-dimensional model based on long wave equations. The program takes various phenomena into account such as reflection, permeability, infiltration, desorption, overtopping, varying roughness along the slope, linear and non-linear porous friction (Darcy- and turbulent friction), added mass, internal set-up and the disconnection of the free surface and the phreatic surface. How those aspects have been implemented in the model is described in this paper.
1. I N T R O D U C T I O N
Within the framework of the European MAST-G6-Coastal Structures project, it was decided to develop two numerical models for the description of wave motion
1 Delft University of Technology, Department of Civil Engineering, P.O. Box
5048, 2600 GA Delft, The Netherlands.
on and in coastal structures. The first model, called SKYLLA, is a research model that uses a two-dimensional description of the flow, based on adapted Navier-Stokes equations. This model describes the flow in a detailed way which requires research for a relatively long period. See Broekens and Petit (1991). The second model that was decided to be developed, should describe the flow in a more simple way and should be ready in a relatively short period. ODIFLOCS is such a model that simulates the wave action both on, and in coastal structures. In this numerical model ODIFLOCS, One Dimensional Flow on and in Coastal Structures, a hydraulic model is coupled to a porous flow model. For the hydraulic model long wave equations have been used. Kobayashi et al. (1987) and Broekens (1988) showed that those equations can be applied successfully to describe the wave motion on a coastal structure. The model ODIFLOCS, which will be described in this paper, uses long wave equations not only for the hydraulic model but adapted long wave equations for the porous flow model as well. The coupling of those two models requires some attention for aspects like for instance the disconnection of the free surface and the phreatic surface. Those aspects will be discussed as well. Results and interpretations of the results will be given to show the possibilities of the model.
2. DESCRIPTION OF T H E H Y D R A U L I C M O D E L
For the hydraulic model, simulating the external flow, long wave equations are used. The hydraulic model is similar as those described by Kobayashi et al. (1987) and Broekens (1988). This one-dimensional description of the flow includes hydrostatic pressures, the use of depth-averaged velocities (u) and a simulation of a breaking wave like a bore. The following equations are used:
dh -g h — -g h tan 6 - - ƒ u \u\ +q qx X
(1)
9 dhu + dhu2 dt + dx dh + dhu dt dxIn the first equation, the momentum equation, the influence of the pressure gradient as a result of the slope of the free surface and as a result of the slope of the bottom elevation (with angle 8) as well as the influence of the bottom friction (with coefficient f ) , are taken into account. The model for the external flow partially overlaps with the porous flow model. The q (m/s) stands for the flow between the external and internal flow per unit of length where the length is taken along the x-axis. This flow transports momentum from the external flow to the internal flow and visa versa which is represented by the term q • qx where q* is the
x-component of the velocity of this interactive flow. The long wave equations are
solved with an explicit second-order method (Lax-Wendroff), using a constant grid space and a constant time-step.
The slope of the structure is divided in a number of slope sections where for each slope section the angle of the slope and the friction coefficient, are taken constant. A t the boundaries between those slope sections the effect of the abrupt change in the angle is diminished by a special treatment of those boundary points.
On the seaward boundary an incident wave is computed with either the Stokes second-order wave theory or the Cnoidal wave theory. This seaward boundary allows a reflected wave to leave the computational domain. This is calculated with the method of characteristics. This method allows water and momentum to leave the computational domain.
The boundary at the slope is based on work by Kobayashi et al. (1987) and applied in the numerical model IBREAK. It uses a minimum water depth A at the wave front, below which level the slope is set dry at that particular point. I f the water depth becomes lower than A at another point along the slope the
computation proceeds with R j Boundary at the slope,
one volume of water while
the other volume is taken away because the model can not compute two separate volumes of water. Run-up levels Rt and run-down levels can be calculated using
several levels Aj parallel to the slope. For such a level A;, the slope is assumed to
be dry in case the water-level is lower than this value (see also the Figure 1). Figure 1 shows the level A which is the level that is actually used in the computation. The other values of A; are just levels to determine run-up levels and
have no influence on the computation itself. A good verification of the model results in a prescription of the value Aj to be used for the run-up and run-down levels. Other values of A; can show the sensitivity of the computed up and
run-down levels to the choice of a certain A;. Calibration and verification of the model IBREAK shows that such an approach can be applied. See Broekens (1991).
The model can compute overtopping. For the boundary at the slope in case of overtopping, a non-reflecting boundary is chosen. This makes the model also applicable for submerged structures.
3. DESCRIPTION OF T H E COUPLED POROUS F L O W M O D E L 3.1 Adapted equations
Several aspects of the coupling are described in detail in the next section. In this section the adapted equations and the general lay-out of the model will be discussed.
Long wave equations are used for the porous flow model as well. These equations have to be written with filter velocities u instead of pore velocities. This means that the velocities u and q, have to be replaced by respectively u/n and q^/n wherein n is the porosity. The porosity is taken constant in all directions. The flow q has to be replaced by q/n because this flow gives an increase in volume of q/n per unit of length. The phenomenon added mass is implemented in the momentum equation using the coefficient cA. The linear- and non-linear friction terms,
together called the Forchheimer terms, are implemented as well. The coefficients for added mass and the coefficients for the Forchheimer friction terms are taken constant in time and space. A complete derivation of these equations is given by Van Gent (1992-b). The equations can be written as follows:
.dhu dh 1 dhu2 d \ h Z . , i u Mx
( l + c , ) — - c A u - • _ _ = -ng— -ngh(c,u • c2« | « | ) - — ^
dh 1 dhu _ q
dt n dx n
The long wave equations are solved with an explicit second-order method (Lax-Wendroff), using a constant grid space. Expressions for c, and c2 are prescribed
by many authors. See discussions by Hannoura and Barends (1981) and Van Gent (1992-a). cx = a ( 1" ") 2 —— with a = ƒ ( Re , KC ) n 3 g d2 (3) c2 = P —r —j with p = ƒ ( Re , KC ) n3 g d
where d is a representative diameter of the particles, v is the kinematic viscosity. The non-dimensional parameters a and j8 depend on the Reynolds number (Re) and the Keulegan-Carpenter number (KC).
3.2 General lay-out of the model
The porous part can be seen as a layer that partially overlaps with the hydraulic layer. The porous part of the model is sub-divided into several area's that are
varying in size during the computation. The final equations depend slightly on the area in which they are applied because not all phenomena are present in the entire porous part.
Fig.2 Area's with different treatment.
The part of the porous medium that is always overlapped by the hydraulic model is area P I (see Figure 2) in which the thickness of the porous layer hp is time-independent. The pressure gradient in this area is caused by the slope of the free surface. The term -ng 9(V2h)/3x describing the pressure gradient becomes: -nghp
d(hh+hp)/3x where hh is the thickness of the hydraulic layer and hp is the thickness
of the porous layer. The part in which infiltration through a partially saturated area appears is area P2. In case the phreatic level reaches the slope, the boundary of the structure, while no layer of water is present there, desorption appears in this area. Both infiltration and desorption are assumed not to transport significant momentum in the x-direction. In area P2 the slope of the free surface has no direct influence on the water in the porous medium. In area P3 the terms with q and are zero because no direct flow from, or towards the hydraulic model, is present here.
The slope of the structure is already discussed in the description of the hydraulic model. For the internal area an impermeable underlayer has to be described. This is done in a similar way as for the slope sections. The impermeable underlayer can be horizontal, resulting in a homogeneous structure, or can be given a shape like an impermeable core. This core is again divided in several core sections with a constant angle of the slope for each section. This core can penetrate through the phreatic water-level. In this case the last point of the porous water-layer is treated in a similar way as for the last point of the water-layer of the hydraulic model. The treatment of this internal boundary point is done in a more simple way to save computing time. In case overtopping of the impermeable core takes place (phreatic level higher than the crest of the core), a non-reflecting boundary is chosen at this internal boundary. This boundary requires that a surface elevation has to be given towards the phreatic level converges, hp( x = 0 0 ). For this value the surface elevation
