A three dimentional simulation of the tidally modulated plume in the rever entrance region

VNU JOURNAL OF SCIENCE... ỉ: The computational domain... A threc-dirncntional sirntỉlntion of thc.

VNU JOURNAL OF SCIENCE Nat S c i & Tech T XIX N01 2003

A T H R E E - D I M E N T I O N A L S I M Ư L A T I O N O F T H E T I D A L L Y

M O D Ư L A T E D P L Ư M E IN T H E RIV K R E N T R A N C E R E G I O N

N g u y ê n Minh H u a n

D e p a r t m e n t o f H y d r o -M e te o r o lo g y a n d O c e a n o g r a p h y

C o llc g e o f S c ie n c e , V N U

A s t r a c t A three d im cn tion aỉ mathcm atical model ùH presen ted to com putc the

ivatcr levcl, velocity a n d sa lin ity distributions in stra tifie d Coastal Lvaters a n d

ti d a lly m o d u la te d p lu m c o f th c riv c r e n tra n cc region T h e m o d c ỉ s y s tc m c o n s is ts

of h ydrodyn am ìc, tran sport an d turbulence closure modcls In the h y d ro d yn a m ìc

m o d e l c o m p o n c n t, th e N a v ic r -S to k c s c q u a tio n s a re s o lv e d iv ith th e h y d r o s ta tíc

a s s u m p tio n (Itìd th e B o u s s in c s q a p p ro x im a tio n T k c tr a n s p o r t m o d c l coruĩists o f

th c iv a tcr tc m p c r a tu r c a n d s a lin ity tr a n sp o rt mocleLs T h e v a r ia tio n s in th e Lưatcr

te m p c r a tu r e a n d s a lin i ty in fĩu e n c e th e Uỉater d e n s ity , a n d in r c tu r n th e v e lo c ity

fic ld T h e e q u a tio n s o f m o m e n tu m a n d c o n tin u ity a rc soỉvccl n u m e r ic a lly u s in g

th e m o d c -s p littin g tc c h n iq u e A s th e tu rb u le n ce m o d el, a o n e -e q u a tio n k -e p s iỉo n

tu r b u le n c e m o d e l is a p p lie d ỉn th e tr a n s p o r t rnodel th e th r c e - d im c n tio n a l

tíd v c c tiv c d iffu 8 Ìo n e q u a tio n are solved The m o d e l is a p p lie d to a re c ta n g le

b a s in e n clo se d by a Coastal b o u n d a ry a n d 'th ree opcn sea b o u n d a r ie s , ti d a l

fo r c ỉn g is im p o s e d in th c fo r m o f CI /ric tio n le ss K e lv in w a v e w ith o Ị fr c q u e n c y

c n te r in g a t th e ivestcrn b o u n d a rỵ , fr c s h w a te r lo a d in g w a s ta k c n in to a c c o u n t a t

lo c u tio n o f one r iv e r m o u th , Uỉhich rcached a to ta l o f lOOOm1 s 1

1 I n t r o d u c t i o n

A n e s t u a r y is a n a r e a o f in t e r a c tio n betvveen s a l t a n d ír e s h vvater T h o nnơ)§t

c o m m o n d e f in it io n u s e d t h a t s t a t e s "an e stu a r y is a s e m i - e n c l o s e d C o a sta l b o d y of vvater vvhich h a s a fr e e c o n n e c t io n w ith th e op en se a a n d vvithin vvhich s e a w a t e r is

m e a s u r a b l y d ilu t e d w ith fr e sh w a t e r d erived from ia n d d r a i n a g e ” T h e e s t u a r i m e

inHuence may extend to nearshore Coastal waters vvhere seavvater is diluted by Ịaind

d r a i n a g e b u t b e y o n d t h e c o n í ì n e s o f e m e r g e n t la n d - m a s s e s

T h e c la s s ic d e f in it io n o f a n e st u a r y in c lu d e s t h e s e t h r e e c h a r a c t e r i s t u c s :

s e m i e n c l o s e d , fr e e c o n n e c t io n vvith th e open s e a , a n d í r e s h w a t e r d e r iv e d fro m lain d

d r a i n a g e T h e s e t h r e e c h a r a c t e r is t ic s g o v e rn t h e c o n c e n t r a t i o n o f s e a w a t ; e r , therefore, s a lin it y is t h e k ey to e s t u a r in e c la s s iíìc a t io n T h e m ixing o f fr e sh V, a \te r

a n d s e a w a t e r p r o d u ce s d e n s it y g r a d ie n ts t h a t d r iv e d i s t i n c t i v e e s t u a r i n e ( g r a v it a t io n a l) c ir c u la t io n p a t t e r n s

T h e s e c ir c u la t io n ancỉ s h o a l i n g p a t te r n s differ w i t h e a c h e s t u a r y sy stc e m accorcỉing to t h e d e p t h , tid a l a m p lit u d e and p h a s e a t t h e m o u th , and t h e a m o u n l t of

fr e sh w a t e r flo w in g in t o t h e b a sin

3 0

A t h r c c - d i m c n t i o n a l s i r n n l a t ÌOĨI o f th c 3 1

T h o t id e t h a t a p p r o a c h e s t h e m o u th o f t h e e s t u a r y is th e r e s u l t o f all t h e

a s tr o n o m ic a l, m e t e ọ r o l o g ic a l, s e is m ic , and m a n - m a d e ía c to r s a f f e c t in g am p lit.ud e and (Yequency o f t h e vvave A s th e tid e e n t e r s t h e e s t u a r y , it is g r e a t ly in f lu e n c e d bv

t h e river d e p t h , w id t h , a n d d is c h a r g e

S u p e r i m p o s e d on t h i s tid a l a c tio n is t h e f r e s h w a t e r / s a l t w a t e r in t e r a c tio n S a l t

w a ter w ill a d v a n c e up a s y s t e m u n til th e tid a l flơw c a n no lo n g er o v e r c o m e t h e riverflow D e p e n d i n g o n t h e r e la t io n s h ip betvveen tid a l flow a n d river flow, t h e

e st u a r y c a n b e c l a s s i f i e d by i t s s a lin it y s t r u c t u r e a n d r e s u l t i n g c ir c u la tio n p a t t e r n s

2 T h e o r e t i c a l c o n s i d e r a t i o n s

To s i m u l t e w in d d r iv e n c ir c u la tio n a n d d e n s i t y c u r r e n t s t h a t occur in Coastal

w a te r s e s p e c ia lly in e s t u a r y s t r a t if ie d bv s a lin it v and t e m p e r a t u r e la y e r s c a u s i n g

s i g n i í ì c a n t la t e r a l d e n s i t y g r a d i e n t s , t h r e e - d im e n t io n a l m a t h e m a t ic a l m o d el a re

n e c e s s a r y T h e d e v e lo p e đ t h r e e - d im e n t io n a l m a t h e m a t ic a l m od el is c a p a b l e of

c o m p u tin g t h e w a t e r le v el a n d vvater p a r tic le v e lo c ity clistribution in t h r e e p r in c ip a l

d ir e c tio n s by s o l v i n g t h e N a v ie r - S t o k e s e q u a t io n s u s i n g t h e B o u s s i n e s q

a p p r o x im a tio n a n d t h e a s s u m p t i o n o f v e r t ic a l h y d r o s ta tic e q u ilib r iu m , t h e

c o n t in u it v e q u a t io n a n d e q u a t i o n s of te m p e r a t u r e a n d s a lin it y

2.1 G o v e r n i n g e iỊ u a ti o n s o f th e m o d e l

T h e b a sic e q u a t i o n s in t h e th r e e -c ỉim e n s io n a l c a r t e s ia n c o o r d in a te s y s t e m are:

— + // — + V — + Ví' — - A' = — ——

/ 1 \ ỉ r i ỵ

0

- +

cu

«h' c v

—- + // — + V

< ỉ

~\

( z

du

dz + ~ r*y +r x

d_

(2.3)

(2.4)

— + tỉ —— + V —— +

1 dJ d

- +

-A) c p d z d z

d ĩ

õ x ■H

a r

a r

-+ 5 I I - + V’ — + H' -—■>

ơ Õz

( ~ <• \ ò

-T- -t- 11 ~ + — +s 11 X "

vvhere ( u ,v tw ) a r e t h e c o m p o n e n t s of t h e c u r r e n t , T d e n o te s t h e t e m p e r a t u r e , s th e

s a l i i i t y , f = 2 0 s i n 0 t h e C o r io lis ír e q u e n c y , ũ =271/86164 racl/s th e r o ta tio n

32 N g u y en Minh Hu a n

(Yequencv of t h e E a r th , g t h e a c ce le ra tio n o f g r a v ity , p t h e p r e s s u r e , VT a n d ẢT th e

v e r t i c a l e d d y v i s c o s i t y a n d d iffu sio n c o e f fic ie n ts , Ản t h e h o r iz o n t a l d iffu sion

c o e f f ic ie n t for s a ỉ i n i t y a n d te m p e r a t u r e , p th e d e n s it y , Po a r e f e r e n c e d e n s it y , cft th e

s p e c ií ic h e a t o f s e a w a t e r a t c o n s t a n t p r e s s u r e a n d 1 (x, y, z, t) s o la r irracliance.

T h e h o r iz o n t a l c o m p o n c n t s of t h e s t r e s s t e n s o r a r e d e f in e d by

- 2 v

■5

du

y x XV' = V', du ô v

d V õ x

ỡ y

(2.8)

(2.9)

w h e r e VH is t h e h o r iz o n t a l d iffu sio n co effic ien t for m o m e n t u m

T h e n u m e r ic a l s o l u t i o n s o f t h e m o d el e q u a t i o n s a r e g r e a t l y s im p liíle d by

i n t r o d u c in g a n e w v e r t ic a l c o o rd in a te t h a t t r a n s íb r m s b oth t h e s u r fa c e and th e

b o t t o m in to c o o r d in a t e o f s u r f a c e s (P h illip s 19Õ7).

Suríàce ơ 1

u

Bottoni o 0

F ig u re 1.1 T h e a-coorcỉinate tr a n sfo m a tio n in t h e v ertical

T h e f o llo w in g c o o r d in a t e tr a n s fo r m a tio n is app lied:

vvhere

ơ = z + h z + h

is t h e c o m m o n ly usecỉ a - c o o r d in a t e v a r y in g b e t w e e n 0 a t t h e b o tto m and 1 at th e

s u r ía c e T a k i n g /(0 ) = 0 a n d / ’(1) = 1 t h e e q u a t io n o f t h e b o tto m t a k e s th e sim p le

A t hrcc-dirtient iotial simu la tio n o f the. 33

form z* = 0 w h i l e t h e m o v in g s u r fa c e tr a n s ío r m s in t o z * = L T h is is íu r t h e r

i llu s t r a t e d in F i g u r e 1 .1 .

T h e t r a n s í o r m e d v e r s i o n s of t h e e q u a t io n s o f h o r iz o n ta l m o m e n t u m ,

h y d r o s ta tic e q u i ỉ i b r i u m , t e m p e r a t u r e , s a lin it y and c o n t in u it y a r e g iv e n by

I (

7 ( i

—7 Ụu) + ^7 - ^ ụ i r

= - » - p r - t - 4 + Q\ + , ~ r

r X p u õ x J c z

\ ũ , , x ì D , v

V j d u

J õz*

(2.12)

- 7 — r ( » + 7 7 7 ( - / w v ) + — - - ~ ự v ) + - 7 v ) + fu

c C 1 r‘/ >, ^ 1 p í I^r r v

(■>' />i, (>>' J (í: V J d z ,

(2.13)

L Ũ S l

J (V

J d t + 77 7 7 ^ + - 7■! d V/ ;ạ + - 7/ #-<■*•*•>^ 7

_L -ẼL I g

J p íi c p d z ’ J d z *

JÀT

d ĩ '

L _ L

./ í V /í

L A

./ d.v 7 /

Ỡ7' '

H r> •

^ >

(2.15)

1 ổ í

./ rV

1 í)

J cy

Jk i r-s \

Xi

ỡ r fl.v

1 a

J d x ' JẢ

ÕS , \

II ,

d x

(2.16)

34 Nguyên Minh Hucunì

2.2 T u r b u l e n c e s c h e m e s

O n e of t h e m o s t i n t r i c a t e p r o b le m s in o c e a n o g r a p h ic m o d e llin g is a n a đ e q u a tee

p a r a m e t e r i s a t i o n o f v e r t ic a l e x c h a n g e p r o c esses In t h e p r e s e n t m o d el th e y a.ree

r e p r e s e n t e d t h r o u g h t h e e d d y c o e f fic ie n ts VT a n d Ả r V a l u e s for t h e s e tvvco

p a r a m e t e r s a r e to b e p r o v id e d by a tu r b u le n c e s c h e m e

A large v a r i e t y o f t u r b u l e n c e p a r a m e t e r i s a t i o n s w ith a s u b s t a n t i a l r a n g e o:>f

c o m p le x it y h a v e b e e n p r o p o s e d a n d v a lid a t e d in t h e lit e r a t u r e T h e s e le c t io n o f ía

s u i t a b l e s c h e m e is o f t e n a d if fic u lt t a s k s in c e it d e p e n d s o n t h e t y p e o f p h y s i c a i l

p r o c e s s e s sp ecific for t h e s i m u a t e d a rea (e g tid e s , t h e r m o c l i n e s , r iv er íron ts, ).

In a n a lo g y w it h m o le c u la r d iffu sio n w h e r e t h e eddy v is c o s it y a n d d i f f u s i o m

c o e f f ic ie n t s a re p r o p o r tio n a l to t h e m e a n v e lo city t i m e s a n d t h e m e a n free p a t h cof

t h e m o le c u le s , t h e e d d y c o e f f c i e n t s VT a n d Ả T a r e c o n s id e r e d a s t h e product off :a

t u r b u l e n t v e lo c it y s c a l e a n d a le n g t h sca le / u s u a l l y d e n o t e d by t h e K o lm o g o r o v

/-P r a n d t l “m ix in g l e n g t h ” A c o m m o n ly u s e d v e lo c ity s c a l e is t h e sq u a r e root ooĩ

t h e t u r b u le n t k in e t ic e n e r g y T h i s p a r a m e te r c a n b e o b t a in e d by s o lv in g a t r a n s p o r r t

e q u a t io n T h e m o s t g e n e r a l form o f t h is e q u a t i o n s , a s u s e d in t h e p ro g r a m , iis vvritten as

w h e r e t h e t i m e d e r i v a t i v e , t h e h o r iz o n ta l a n d v e r t i c a l a d v e c t io n a s t h e d iffu sic o n

o p e r a t o r s are d e f in e d by

1 d

T ( k ) = ^ ( J k )

J õt

( 2 1 8?a)

( 2 1 8 íb )

A J k ) = \ ~ ( J w k )

J dz

( 2 1 8 k )

(2.18^d)

N 2 a n d Af2 a r e s q u a r e d b u o v a n c v and s h e a r fr e q u e n c ie s g iv e n by

A thrce-dimcntional simu lơtio n o f thc. 35

a n d /; d e n o t e s th e d i s s i p a t i o n r a t e o f t u r b u l e n c e e n e r g y T h e d i s s i p a t i o n r a t e is

p a r a m e t e r i s e d acco rd in g to

k' 2

w h e r e cu is a c o n s t a n t d e t e r m i n e d by L\, = 0 1 8 8

AU t u r b u l e n c e t r a n s p o r t e q u a t io n s are s o l v e d vvith t h e s a m e h o r ỉz o n t a l

d if fu s io n c o e f fic ie n t Ả f Ị vvhich is th e s a m e a s t h e o n e u s e d in t h e e q u a t i o n s o f

t e m p e r a t u r e a n d s a lin it y

T h e e d d y c o e f fic ie n ts a r e t h e n e x p r e s s e d as

w h e r e vht Ảh a r e p r e sc r ib e d b a c k g r o u n d c o e f f i c i e n t s f Vi = / 0 7 [ m 2!s]; Ảfj = 7 0 5 Ị m 2/ s j

a n d s m, S), a r e u s u a lly r effed a s t h e s t a b ili t v íu n c t i o n s T h e ir e x p lic it íò rm s are

0 l() X ^ ( )0 2 2 9 q v

‘ " ” 1+ 0 4 7 l aV + 0 0 2 7 5 a ỉ

0.177

U 0 4()3av

k *

o

O n e - e q u a t io n k - e p silo n tu r b u le n c e m od el is u s e d for p a r a m e t e r i s a t i o n for t h c

m ix in g l e n g t h and d i s s i p a t i o n ra te W h e n o n e - e q u a t i o n m o d e l i s c h o s e n , t h e

k-e q u a t io n is s t ill s o lv k-e d vvith c m o d k-e llk-e d a c c o r d in g to (2 2 1 ) w h i l k-e / is d k-e t k-e r m in k-e d

u s in g t h e ío r m u la tio n , in i t i a l l y p r o p o se d by B la c k a d a r (1 9 6 2 ), h a s t h e form

/ /> Ạ /a

H o r iz o n ta l d iffu sio n t e r m s a r e m e a n t to p a r a m e t e r i z e s u b g r id s c a l e p r o c e s s e s ,

in p ractice t h e h o r iz o n ta l d if f u s iv it v V ị ị a n d Ả ị ị a r e u s u a l l y r e q u ir e d to d a m p s m a ll sca le c o m p u t a t io n a l n o is e t h e y are t a k e n p r o p o r tio n a l to t h e h o r iz o n t a l griđ

sp a c in g s a n d t h e m a g n i t u d e o f t h e v e lo citv d e íb r m a t io n t e n s o r in a n a lo g y w ith

S m a g o r in3ky*s (1 9 6 3 ) p a r a m e t e r i s a t i o n

2.3 B o u n d a r V a n d i n i t i a l c o n d i t i o n s

C o a s t a l b o u n d a r ie s a re c o n s id e r e d as i m p r e g n a b l e w a lls T h is m e a n s h a t all

c u rrren ts, a d v e c tiv e a n d d if f u s iv e flu x es a r e s e t to zero

N g u y en Minh Hucềìn

ô x

õ y

O pen s e a (or riv er) b o u n d a r y c o n d itio n for th e 2-1) m o d e n e e d to be s u p p ỉ i e c d

for u a t w estern a n d eastern b o u n d a r ie s a n d for V a t S o u t h e r n a n d n o r t h e r r n

boundaries A selection can be made between different types of open b o u n d a r - y

co n d itio n s T h e y h a v e t h e form o f a r a d ia tio n c o n d itio n d e r iv e d u s i n g th e m e t h o d cof

c h a r a c t e r is t ic s [ H e d s tr o m 1 9 7 9 ), [Roed a n d C ooper, 1 9 8 7 ], [R u d d ick , 1 9 9 5 Ị] [Rancỉall J L e V e q u e 1997] T h is is b a s e d on th e in t e g r a t io n o f t h e e q u a t i o n s for t h i e

incoming an d o u t g o i n g R i e m a n n v a r ia b le s

< K K ) = ( Ũ ± cỉ ; V t c C ) (2 2 Í 9 )

3 N u m e r i c a l s i m u l a t i o n

T h e a i 111 o f t h e t e s t i s to s i m u l a t e th e e v o lu tio n o f a t id a lly m o d u la te d riveer

p lu m c u s i n g t h e f o ll o w i n g c o n d i t i o n s o f a b a s in w ith vvater d e p t h r a n g in g from 3im

in th e s h o r e li n e to 2 0 m in t h e o ffsh o r e b o u n d a ry T h e c o m j ) u t a t io n a l d o m a in , h a i s

th e form o f a r e c t a n g l e b a s i n e n c lo s e d by a Coastal (solicỉ) b o u n d a r y a n d th r e e opoĩn

s e a b o u n d a r ie s For c o n v e n i e n c e , t h e Coastal b o u n d a r y w ill be d e n o t e d b y th ìe

S outhern b o u n d a r y , t h e l a t t e r by th e vvestern, e a s t e r n c r o s s - s h o r e b o u n d a r i e s a n u l

th e n ortb ern a l o n g s h o r e b o u n d a r y T h e b a s in h a s a le n g t h o f 120 km , a w id th o f 410 kin, in th e Southe rn b o u n d a r y t h e r e is th o r iv er m outh s i t u a t e d in th e d i s t a n c e o f fí)0

km from th e vvestern b o u n d a r y and d is c h a r g e vvator to b a s in in sid o ono h a b ío r

c o n str u c ted by 2 g r o in s T h e h o r iz o n t a l r e s o lu t io n o f g r id is 5 0 0 m a n d 2 0 l e v e ỉ s aire used in th e v e r t ic a l T h e a r e a is rillecl in i t ia lly w ith sea v v a ter h a v i n g a unifor*m

s a lin it y o f 3 0 PSƯ

ỉ ỉ iittsei I

Km

4 0

30

20

10

Hi ve ì n u m ỉ h

F i g u r e 3 ỉ: The computational domain

A threc-dirncntional sirntỉlntion of thc. 37

Ticlal ĩo r c in g is i m p o s e d in t h e form of a f r i c t i o n l e s s K elv in w a v e with

ír e q u e n c v of Oj e n t e r i n g at th e vvcstern b o u n d a r y a n d p r o p a g a t i n g a lo n g th e const [V a n Rijn, 1 9 8 9 a n d Rudciick et al., 1995] T h e i n c o m i n g R ic m a n n varial>le,

s p e c i a l i z e d at t h e vvestern b o u n d a r v , t h e n ta k e s t h e form

R = u + cỊ = 2 c F |Mr = 2cA e ,v/c coso)~t , ( 3 1)

w h e r e th e C o r io lis fr e q u e n c y is e v a l u a t e d at a l a t i t u d e o f 2 0 , (0 is th e 0 tiđal

ír e q u e n c y , A = 0 8 m a n d ư , r, c are t h e d e p t h - i n t e g r a t e d a l o n g s h o r e c u r r e n t , th e

b a ro tro p ic vvave s p e e d a n d t h e s u r í a c e e l e v a t i o n T h e a m p ỉ i t u d e o f th o w a v e

d e c r e a s e s e x p o n e n t i a l l v vvith d i s t a n c e to th e c o a s t vvith a d e c a v s c a l e g iv e n hy th e

b a rotrop ic R o s s b y r a d i u s c / f - 120 km T h e a m p l i t u d e A e ' o f t h e h a rm o n ic

fu n c tio n Flíflr is storecỉ for e a c h o p e n b o u n d a r y n od e.

A zero n o r m a l graciien t c o n d it io n is s e l e c t e d at t h e e a s t e r n a n d n o rth orn

b ou ncỉaries, i.e.

~ ự / - c £ ) = 0

<\x

(3.2)

4 - ( V - c O = 0

r y

T h e l a t e r c o n d it io n is j u s t i f í e d bv t h e fact t h a t t h e vviđth o f t h e b a s in is m u ch

sm aller than t h e external Rossby radius c / f

S in ce t h e v a l u e o f Q is unknovvn at th e r iv e r m o u t h , t h e o p e n b o u n d a ry

concỉition a t t h e i n l e t is n o lo n g e r d e íìn e d in t e r m s o f t h e in c o m i n g R ie m a n n

v a r ia b le b u t by s p e c i f y i n g t h e c r o s s - s h o r e c o m p o n e n t o f t h e clepth in t c g r a te d

c u rren t T h is is g iv e n a s t h e s u m o f a r e s i d u a l v a l u e , r e p r e s e n t i n g t h e river cỉischarge, a n d a t id a l c o m p o n e n t

w

w h e r e Q,i = 1 0 0 0 m Vs is t h e r iv e r d is c h a r g e , vv = 5 0 0 m t h e w i d t h o f t h e i n l e t and Á,

= 0.6 m/s t h e a m p l i t u d e o f t h e t id a l c u r r e n t a t t h e m o u t h o f t h e riv er T h e p h a s e tp,

is d e te r m in c d bv

c 2

w here D = 2 6 0 k ĨTÌ so t h a t D, l c r e p r e s e n t s t h e t i m e t r a v e l l e d bv t h e K e lv in w a v e

from the w e r s t e r n b o u n d a r y to t h e r iv er m o u th O b s e r v a t i o n s in th o r iv er plu m e

sh ow th a t th e a lo n g s h o r e a n d c r o s s - s h o r e c o m p a n e n t a r e a n t i - p h a s e vvhich e x p la in s

th e use of t h e fa cto r 7t/ 2 [V a n Rijn, 1989].

38 N g u y en Minh Ị ỉ U an

III a d d itio n to thi' p r e v i o u s c o n d it io n s for th e 2 -D m od e, o p en b o u n d a r y

c o n d it io n s h a v e to be i m p o s e đ d u r in g th e fin al run for t h e h o r iz o n t a l v e lo c ity

d e v i a t i o n s (u\ V9 a n d the s a l i n i t y s.

A t th e o p e n s e a b o u n d a r i e s a zero n orm a l g r a d ie n t c o n d it io n is t a k e n for all

q u a n t i t i e s In th e c a s e o f s a l i n i t y th is p ro ced u re is a r e a s o n a b l e a p p r o x im a tio n

s in c e th e p lu m e n e v e r i n t e r s e c t s th e vvestern and n o rth orn b o u n d a r y w h ile th e cro ss-b ou n clary g r a d ie n t i s m u ch s m n lle r th a n t h e a lo n g b o u n d a r y g r a d ie n t a t th e

e a s t e r n b o u n d a r y

T h e d e í a u l t c o n d i t i o n s a r e no lo n g er a p p lic a b le a t th e riv er m o u th w h e r e u'

a n d s a r e s p e c ií ìe d in t h e form o f a tvvo-layer s tr a tific a tio n

v ’ = - 0 2 [m s ‘] i f - H < 2 < - 5, ( 3.5)

vvhere ổ = 5 m is t h e s p e c i í ì e d d e p th o f th e p lu m e la y e r a t t h e m o u th In t h i s vvay

fresh w a t e r is r e le a s e d t h r o u g h th e su rfa ce la y e r vvhereas s a l t i c r s e a w a t e r flow s

in to t h e e s t u a r y t h r o u g h t h e b o tto m layer A zero g r a d ie n t c o n d it io n is a p p lie d for

s a l i n i t y in th e b o tto m la y e r

4 D i s c u s s i o n

A lth o u g h th e d e v e l o p e d p rogram is a b le to e x a m i n e th e role of d if fe r e n t

p h y s ic a l ío r c in g n i e c h a n i s m ( b a t h y m e t r y , tid e s , w in d , w a v e ) on t h e p lu m e s tr u c tu r e ,

th o in t e n t i o n h e r e is to t e s t s o m e o f th e a b o v e -m e n tio n e d fo rcin g a n d th e role o f th e

S m a g o r iỉ is k y í o r m u l a t io n for h o r iz o n ta l d iffu sio n and th e u p w in d s c h e m e for th e advort.ion o f m o m e n t u m

F ỉg u res 4.1 Su rface d is tr ib u tio n o f current and sa lin ity after õOh s im u la tio n (fmal run)

F ig u r e s 4.1 - 4 5 c l e a r l y sh o w how th e p lu m e e v o lv e s d u r in g a tidal cycle At

th o t im e w h e n th e a l o n g s h o r e c u r r e n t r e v c r s e s s ig n a n d th o o u t flo w roa ch es its

A three-dimentional simulation of the.

20

10

m a x im u m , a nevv blob o f ír csh w a te r e n t e r s th e b a s in m o v in g seavvard s (ỈMgure

á 1 ì

xO.Skm *°

20

F ig u re 4 3 : S u r ía c e distrib u tion o f c u r r e n t a n d s a lin it y a fter 54h s im u la t io n

F ig u res 4.2 S u rfa ce distribu tion o fc u r r e n t and s a lin it y a fter Õ2h s im u la t io n

A s t h e e a s t w a r d d ir e cted tid al w a v e b e c o m e s s t r o n g e r , t h e fr e sh vvater p atch

is d e fle c te d to th e r ig h t (F ig u r e 4 3 ).

x0.5km

D u r in g t h i s p h a s e of th e tid e both th e b u lg e a n d th e C o a s t a l p lu m e expancl

s e a w a r d s W h e n t h e t id a l c u r r e n t r e v e r s e s s i g n a g a i n a n d t u r n s to t h e w e s t , th e

c u r r e n t i n s id e th e p l u m e is first s o u t h e a s t w a r d s p u s h i n g t h e b u lg e t o w a r d s th e

c o a s t (F ỉg u r e 4.4).