V N U JO U R NAL F S C IE N C E Nat., S ci & Tech I XIX N.,1 2003 RESEARCH ƯSING T H E 2-1) MO DEL TO EVALƯATE THE C H A N G E S OF IUVERBKI) N g u y ê n H u 11 K h a i, N g u y ê n T ie n G ia n g , T r a n N g o e A n h D ep artm ent o f HydroMcteorology a n d Oceanology College o f Science, V N Ư I I n t r o d u t i o n Bed e ro s io n p ro b le m w a s s tu d ie d a n d re s e a rc h e d in m a n y pla ce s a ll o v e r th e vvorld M a n y m e th o d s a n d b e d d e fo rm a tio n m o d els vvere b u ilt to s o lv e th e p r a c tic a l p ro b le m s In V ie tn a m , som e m o d e ls such as H E C - , M I K E l l w e re u se d to a n a ly z e a n d c o m p u te th e r iv e r e ro s io n B u t m o st o f th e m vvere 1-D m o d e ls , o n lv c o m p u tin g bed e ro s io n w it h th e a s s u m p tio n o f c o n s ta n t e ro s io n d e p th o v e r th e c ro s s -s e c tio n t h a t c o u ld n 't in v e s tig a tc th e s e d im e n t tr a n s p o r ta tio n a n d n o n - r e g u la r e ro s io n processes in o rth o g o n a l d ir e c tio n Some -D h y d r a u lic m o d e ls as T E L E M A C o r M IK E h a ve o n ly ío cu se d on th e d is t r ib u tio n o f vvater flo w v e lo c ity b u t th e s e d im e n t processes R e c e n tly r iv e r s o f V ie tn a m and o rth o g o n a l d ire c tio n s , in h a ve been s tr o n g ly s c o u re d i n b o th s tre a m -w is e m any re g io n s , th e r iv e r bank e ro s io n is v e ry im p o r ta n t, because th e v h a v e affe ctecỉ on m a n y te rm s o f s o c ia l a n d h u m a n life O n Red r iv e r s y s te m e ro s io n vvas s e rio u s , e s p e c ia lly a fte r th e H o a B in h H y d ro p o v v e r P ia n t th e r iv e r bed c ro s io n becom es m o re s e rio u s Thus it is n e ce ssa ry to u n d e rs ta n đ a n d s im u la te t h is process u s in g -D m o d el T h e T w o -d im e n s io n a l R iv e rb e d E v o lu tio n M o d e l- T R E M - w a s c o n s tru c te d in th e n o n -o rth o g o n a l c u r v ilin e a r c o o rd in a te s y s te m b y N Iz u m i a n d N T G ia n g M o đ e l used K in ite C o n tro l V o lu m e (F C V ) m e th o d a n d im p lic it sch e m e o f C n k - Nicolson The resu lts of tho model arc tho values of bod elevation , velocity íìeld and s c c ỉim c n t c o n c e n tra tio n a t th e g r id nodes, re s p e c tiv e ly vvith each c o m p u ta tio n tim e ste p T h e n by u s in g b a n k s t a b ilit y a n a ly s is th e r iv e r b a n k e ro s io n a n d b a n k lin e s h if t c a n be d e te rm in e d II Theoritical base o f m o d e l B a s ic E q u a t ỉ o n s a F lu id flow equations I n C a rte s ia n c o o rđ in a te , th e cỉo p th -a v e g e d tw o - d im c n s io n a l s h a llo vv-vva te r e q u a tio n s in c lu d e th e c o n tin u ity e q u a tio n a n d m o m e n tu m e q u a tio n s : •17 48 N g u y e n H u u K h a i, N g u yê n T ie n G ia n g , T r a n N goe A n h (U ) Ổ/ w h e re : õx õy ÕM ôuM õvM * dt dx õy ƠN 5uN dí dx ÕZS rbx õx dvN ,Õ Z S õy dx õ / ~ã~t\ e + £ s dxr " ĩby ô ( ~ rr\ d (- t ĩz /1 ( 2) \ 'â y ị ~rTL\ /, c + ì t v v h r T - \s- u vdy' h ì dx o\ (1-3) t: tim e ; x ,y : th e s tre a m vvise a n d la te r a l c o o rd in a te s , r e s p e c tiv e lv h: th e vvater d e p th ; z8: th e vvater le v e l, p :th e w a te r d e n s ity , g: g r a v it y a c c e le tio n (= m /s2), M ,M : x ,y c o m p o n e n ts o f d is c h a rg e flu x v e c to r, u ,v : x ,y c o m p o n e n ts o f th e d e p th -a v e g e d v e lo c ity v e c to rs , Tbl, Tby : x ,y c o m p o n e n ts o f th e bed s h e a r s tre s s re s p e c tiv e ly , - u ' , - u ' v f, - v ' : x ,y c o m p o n e n ts of d e p th -a v e g e d R e y n o ld s s tre ss te n s o rs , - u ’2 = 2Dh 'ôu} Võx ) ' Õ14 -ịK (1.4) dv u'V'= D h 4* -V dx dx (1.5) J ( 1.6) V'2 = 2D ày) Dh = ahu , w h e re : I ) h: th e eddy v is c o s ity ; (1.7) k: d e p th -a v e g e d t u r b u le n t e n e rg y , a : c o n s ta n t; u : th e ír ic tio n ve lo city(w « = — , r : th e bed s h e a r s tre s s ) \p T r a n s íb r m a tio n o f th e above th re e e q u a tio n s in t o n o n -o rth o g o n a l c u r v ilin e a r c o o rd in a te c a n be fo u n d in N a g a ta (2000) Sccỉim cnt c o n tin u ity equation T h e s e d im e n t c o n tin u ity e q u a tio n in 2-D w r it t e n fo r th e la y e r e x te n d e d fro m th e b o tto m to bed s u rfa c e in g e n e l c o o rd in a te s y s te m ca n e xp re sse d b y: R e s e a rc h u s ỉ n g th e 2-1) to c v a ỉ u n t c th e c h a n g e ĐZ I- 49 ' M c