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

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 IM Ư L A T IO 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 RIVKR 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 tm 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 llcg e o f S c ie n c e , V N U A s t r a c t A three dim cntionaỉ mathcmatical model ùH presented to computc the ivatcr levcl, velocity and salinity distributions in stratified Coastal Lvaters a n d tid a lly m o d u la te d p lu m c o f th c rivcr en tra n cc region T h e m o d c ỉ sy s tc m c o n s is ts of hydrodynamìc, transport and turbulence closure modcls In the hydrodyn am ìc m o d e l co m p o n cn t, th e N a v ic r -S to k c s cq u a tio n s a re so lved 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 ssin csq a p p ro xim a tio n T kc tr a n s p o r t m o d cl coruĩists o f th c ivatcr tc m p c tu rc a n d s a lin ity tra 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 ity in fĩu en ce th e Uỉater d e n sity , a n d in rc tu r n th e velo 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 arc soỉvccl n u m e r ic a lly u s in g th e m o d c -s p littin g tcch n iq u e A s th e tu rb u len ce m odel, a o n e-eq u a tio n k -e p siỉo n tu rb u le n c e m o d e l is a p p lied ỉn th e tra n sp o rt rnodel th e th r c e -d im c n tio n a l tíd v c c tiv c d iffu Ìo n e q u a tio n are solved The m o d el is a p p lie d to a rec ta n g le b a s in en clo sed by a Coastal b o u n d a ry a n d 'th ree opcn sea b o u n d a ries, tid a l fo r c ỉn g is im p o se d in th c fo rm o f CI /ric tio n less K elvin w a ve 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, frc sh 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 cu tio n o f one river m o u th , Uỉhich rcached a to ta l o f lOOOm1 s 1 I n t r o d u c t i o n A n e stu a r y is an a r ea o f in ter a c tio n betvveen s a lt a n d ír e s h vvater T ho nnơ)§t c o m m o n d e fin itio n u sed t h a t s t a t e s "an estu a ry is a s e m i-e n c lo s e d C oastal b o d y of vvater vvhich h a s a free c o n n e c tio n w ith the open sea and vvithin vvhich s e a w a t e r is m e a s u r a b ly d ilu te d w ith fresh w a te r derived from ia n d d r a in 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 in a g e but b ey o n d th e c o n íìn e s o f e m e r g e n t land - m a s s e s T h e c la ss ic d e fin itio n of an estu a r y in c lu d e s t h e s e th r e e c h a r a c t e r is t u c s : s e m ie n c lo s e d , free c o n n e c tio n vvith th e open sea , and ír e s h w a te r d e r iv ed from laind d r a in a g e T hese th r e e c h a r a c te r is tic s govern th e c o n c e n tr a tio n of s e a w a t; e r , therefore, s a lin ity is th e key to e s tu a r in e c la ss iíìc a tio n T h e m ixing o f fresh V, a \ter and sea w ater p rodu ces d e n s ity g r a d ie n ts th a t d r iv e d is tin c t iv e e stu a r in e ( g r a v ita tio n a l) c irc u la tio n p a tte r n s T h e s e c irc u la tio n ancỉ s h o a lin g p a tte rn s differ w ith e a ch e s t u a r y sy stc e m accorcỉing to th e d ep th , tid a l a m p litu d e and p h a se at t h e m o u th , and th e a m o u n lt of fresh w a te r flo w in g in to th e basin 30 A t h r c c - d i m c n t i o n a l s ir n n la t ÌOĨI o f th c 31 T ho tid e t h a t a p p r o a c h e s t h e m ou th of th e e s tu a r y is th e r e s u lt o f all th e a str o n o m ic a l, m e te ọ r o lo g ic a l, se is m ic , and m a n -m a d e íactors a ffe c tin g am plit.ude and (Yequency o f t h e vvave A s th e tide e n te r s th e e s tu a r y , it is g r ea tly in flu e n c e d bv th e river d e p th , w id th , an d d isc h a r g e S u p e r im p o s e d on t h is tid a l action is th e fr e s h w a t e r /s a ltw a te r in ter a c tio n S a lt w ater w ill a d v a n c e up a s y s t e m u n til th e tidal flơw can no longer o v e rc o m e th e riverflow D e p e n d in g on th e r ela tio n s h ip betvveen tid al flow a n d river flow, th e estu a r y c a n be c la s s if ie d by its s a lin ity s tr u c tu r e a n d r e s u ltin g c irc u la tio n p a tte r n s 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 im u lt e w ind d r iv e n circ u la tio n and d e n s ity c u r r e n ts th a t occur in Coastal w a ters e s p e c ia lly in e s t u a r y s tr a tifie d bv s a lin itv and te m p e r a tu r e la y e r s c a u s in g s ig n iíìc a n t la te r a l d e n s ity g r a d ie n ts , th r e e -d im e n tio n a l m a th e m a tic a l m odel are n ecessa ry T he d e v e lo p e đ th r e e -d im e n tio n a l m a th e m a tic a l model is c a p a b le of co m p u tin g th e w a te r lev el a n d vvater particle v e lo city clistribution in th r e e princip al directio n s by s o lv in g ap p ro x im a tio n and th e th e N a v ie r -S to k e s a s s u m p tio n of e q u a tio n s ve rtica l u s in g h y d ro sta tic th e B o u s s in e s q e q u ilib r iu m , th e c o n tin u itv e q u a tio n an d e q u a tio n s of te m p e r a tu r e and s a lin ity 2.1 G o v e r n in g eiỊ uations o f the m odel T h e b a sic e q u a t io n s in th e th ree-cỉim en sion a l c a r te s ia n co o rd in a te s y s t e m are: du cu — + // — ct dx cu du d/ y\ ỉ ri ỵ r õp p tí dx õ + V — + Ví' — - A' = — Đz dv «h' cv —- + // — + V dí dx dy õv d2 —— -+ dp ~ (1 dz p(] õ y cu T ortz d_ du dz ( 1) ơy dx +~ rx r*y + õy (2 ) yy V 02 - - - + - ds PS d.S ( cỉ rx Õz Õz \ (7s -+ I I -■> + V’ — + H' -— A) c p d z dz dĩ ar õx ■H (~ :x ~ + — + Ạ — (2 ) /a H o r iz o n ta l diffusion te r m s are m e a n t to p a r a m e t e r iz e s u b g r id s c a le p r o c esses, in practice th e h o rizo n ta l d iffu s iv itv scale c o m p u ta tio n a l n o is e th e y sp a cin g s an d th e m a g n itu d e V ịị and are ta k e n Ả ịị a re u s u a lly r e q u ir e d to d am p sm a ll p ro p o rtio n a l to o f th e velo citv d e íb r m a tio n t h e h o r iz o n ta l te n s o r in griđ a n a lo g y w ith S m a g o rin ky*s (1963) p a r a m e te r is a tio n V'// = C m0Ax Ay D T a nd /.,/ = c o Ax Ay D T (2.26) 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 sta l b o u n d a r ie s are c o n s id e r e d as im p r e g n a b le w a lls T h is m e a n s currrents, a d v e c tiv e and d iffu s iv e flu x es are s e t to zero h a t all Nguy en Minh Hucềìn u = 0, w = y = Q' V= , Juiị/ =0, ẢH— = (2.27?) Jvtỵ = , ẢH— = ( 2 Ỉ ) ôx õy O pen s e a (or river) b o u n d a r y co n d ition for the 2-1) m o d e n eed to be s u p p ỉie c 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 for a t western a n d u conditions T h e y h a v e th e form o f a d ia tio n co n d itio n d e r iv e d u s in g th e m e t h o d cof c h a r a c te r is tic s [H e d str o m [Rancỉall J L eV e q u e 1979), [Roed and Cooper, 1987], [R uddick, 19 95Ị] 1997] T h is is b a se d on the in te g r a tio n o f th e e q u a t io n s for t h ie incoming and o u tg o in g R ie m a n n v a r ia b le s le, s p e c ia liz e d at t h e vvestern bou n d a rv , th e n ta k e s th e form (3 ) R = u +cỊ = c F |Mr = 2cA e ,v/c coso)~t , w h e r e th e C oriolis fr e q u e n c y is e v a lu a te d at a l a t i t u d e o f , (0 is th e tiđal ír eq u e n c y , A = m a n d , r, c are th e d e p t h -in te g r a t e d a lo n g s h o r e cu r re n t, th e barotropic vvave s p e e d and th e s u r ía c e e le v a t io n T h e a m p ỉit 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 ia llv vvith d is ta n c e to th e c o a s t vvith a d e c a v s c a le g iv e n hy th e barotropic R o ssb y r a d iu s c / f - 120 km T h e a m p lit u d e A e ' o f th e harm onic fu n ction Flíflr is storecỉ for e a ch o p e n boundary node A zero n o r m a l graciient co n d itio n is s e le c te d at th e e a s t e r n a n d northorn bouncỉaries, i.e ~ ự /