Research using the 2 d model to evaluate the changes of riverbed

V N U JO U R N A L 0 F S C IE N C E Nat., S ci & Tech I XIX N.,1 2003

R E SE A R C H Ư S IN G T H E 2-1) MO DEL TO EVA L Ư A T E T H E

C H A N G E S O F 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 e p a rtm e n t 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 p la 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 r m a tio n m o d e ls vvere b u il t t o 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 - 6 , 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 t ig a tc th e s e d im e n t tr a n s p o r t a 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 t io n Som e 2 -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 2 1 h a ve o n ly ío c u s e d on th e d is t r ib u t io 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 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

a n d o rth o g o n a l d ir e c tio n s , in m a n y re g io n s , th e r iv e r b a n k e ro s io n is v e ry

im p o r ta n t, because th e v h a v e a ffe cte cỉ 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 T h u s i t is n e c e s s a ry to

u n d e r s ta n đ a n d s im u la te t h is p rocess u s in g 2 -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 it e C o n tro l V o lu m e (F C V ) m e th o d a n d im p l i c it sch e m e o f C ra n k -

N icolson The resu lts of tho m odel arc tho values of bod elev a tio n , 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 ea ch 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 i li t 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

1 B a s i c E q u a t ỉ o n s

a F lu id flo w e q u a tio n s

I n C a rte s ia n c o o rđ in a te , th e c ỉo p th -a v e ra g e d tw o - d im c n s io n a l s h a llo v v -v v a te r

e q u a tio n s in c lu d e th e c o n t in u it y e q u a tio n a n d 2 m o m e n tu m e q u a tio n s :

•17

( U ) Ổ/ õx õy

ÕM ôuM õvM ÕZS rbx õ / ~ã~t\ d ( - t ĩ z \ /1

ÔN 5uN dvN ,Õ Z S ĩby ô ( ~ r r \ ô ị ~rTL\ / , o\

c + ì t v v h r T - \ - u v h ì (1-3)

w h e re : t: tim e ; x ,y : th e s tre a m v v is e 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 vva te r 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 ra tio n (= 9 8 1 m /s 2),

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 ra 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 r e s p e c tiv e ly ,

48 N g u y e n H u u K h a i , N g u y ê n T i e n G i a n g , T r a n N g o e A n h

- u '2 , - u ' v f, - v ' 2 : x ,y c o m p o n e n ts o f d e p th -a v e ra g e d R e y n o ld s s tre s s

te n s o rs ,

' ô u } 2

V õx ) 3

u 'V'= D h

V'2 = 2D.

4* V dx dx J

(1.5)

(1.6)

à y )

w h e re : I ) h: th e e d dy v is c o s ity ; k: d e p th -a v e ra 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 t io n v e lo c ity (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)

6 Sccỉim cn t c o n tin u ity equation

T h e s e d im e n t c o n t in 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 ra l c o o rd in a te s y s te m c a n e x p re s s e d b y:

R e s e a r c h u s ỉ n g t h e 2-1) to c v a ỉ u n t c t h e c h a n g e 49

ĐZ I

-' M

vvhere: T|: b e d e le v a tio n ( w a te r s u rfa c e e le v a tio n s u b tr a c t w a te r d e p th ),

VỊ/, <p: g e n e ra l c o o r d in a te a x is ,

Â: p o r o s ity o f th e bed m a te r ia l,

J : J a c o b ia n o f th e tr a n s íb r m a tio n fro m C a r te s ia n c o o rd in a te to non-

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 I t is c o m p u te d by:

(1 9 )

w here: xv, x<p ,yv ,v\p: í ỉ r s t p a r t i a l d e riv a tiv e s of X, y,

QĨ ' 9 Ĩ : lo a d đ is c h a rg e p e r u n it o f v v id th in vjy a n d cp, re s p e c tiv e lv

T h e y a re c a lc u la te đ fr o m th e bed loacl đ is c h a rg e in s (s tre a m w is e d ir e c tio n ) ,

a n d n (th e d ir e c t io n o r th o g o n a l to th e s tre a m v v is e d ir e c tio n ) Processes o f c o n v e r tin g

is p re s e n te d as fo llo w s :

à ¥ s â „ ( õx

r í = , 9 Ầ + ~ t ch = — + Vfy

õ ỵ }

à ; II ( õx õ y > s ( dx (ỵ '

•ồ * ) 1 + ) 1 * r ì + <px — + <pv

ơn V Oò Uò { (71 õ n j0 »

vvhere: y 1( \ ị / y , ( Ị > „ , <py: f i r s t p a r t ia l d e r iv a tiv e s o f \ụ a n d < J >

A f t e r c h a n g e , o b ta in s :

Ị7 + ụfy ~ (ỊỈ + [ - yrx “ + V y prjí/fc" = — - u v ch ) ( 1 1 2 )

■ í3* 77 + p y 77 <76 = 7 7 7 - « „ 9 * " ) í 1 - 1 3 )

\ (

+

c tr a n s p o r t eq u a tio n s:

I n o r d e r to a c c o m p lis h th e s e d im e n t tr a n s p o r t c o n t in u it y e q u a tio n , th e

c o m p o n e n t o f bed lo a d t r a n s p o r t in s tre a m w is e d ir e c tio n (s) a n d th e d ir e c tio n

orthogonal to (s) direction m ust be sp eciíled before hand In the stu d y, Ikeda’s

e q u a tio n s fo r s e d im e n t tr a n s p o r t r a te w h ic h c o u p le s th e e ffe c t o f s p ir a l flo w a n d th e

lo n g itu d in a l s lo p e o f r iv e r b e d a re a d o p te d T hose e q u a tio n s h a v e th e fo r m of:

5 0 N g u y e n H u u K h a i , N g u y e n T i e n G i a n g , T r a n N g o e A n h

=

Me &

r r < n + J - ậ ĩ >CO

1/2

= - — ( r -*■«,)(*■ - r „ ) ặ - - Ị - ( 4 )c o \ 1/2 d*7

w h e re : q ‘ , q “ : n o n - d im e n s io n a l be d lo a d s e d im e n t t r a n s p o r t r a te in (s) a n d (n)

d ir e c tio n s in th e c u r v ilin e a r c o o rd in a te s y s te m

T* : no n d im e n s io n a l bed s h e a r s tre s s

r ^ : n o n - d im e n s io n a l c r it ic a l bed s h e a r s tre s s , i t c a n be c o m p u te d by a n y

m e th o d , i n t h is s tư d y , th e Iw a g a k i’s ĩo r m u la ( 1958) is u se d ,

Ịic: C o u lo m b í r i c t i o n fa c to r , v a lu e o f 0.7 w a s ta k e n fo r c o m p u ta tio n ,

ul,v*b : th e d im e n s io n le s s s lip v e lo c ity c o m p o n e n t in s tre a m v v is e and tra n s v e rs e d ir e c tio n s in th e c u r v ilin e a r (s,n ) c o o rd in a te s y s te m

A l l o th e r s y m b o ls h a v e been d e íìe d p r e v io u s ly

d T r a n s fo r m a tio n o f bed lo a d eq u a tio n s

I n s o lv in g th e c o n t in u it y e q u a tio n in th e g e n e ra l n o n -o rth o g o n a l c o o rd in a te

s y s te m , e q u a tio n (1 1 4 ) a n d (1 1 5 ) s h o u ld be tr a n s íb r m e d a c c o rd in g ly to (vị/,< p)

c o o rd in a te in s te a d o f (s, n ) c o o rd in a te E a c h te r m in th o s e e q u a tio n s a re

tr a n s ío r m e d s u b s e q u e n tly as íbllovvs:

( l) T e r m Ẽ 1

( 2 ).T e rm Ẽ 1

õn

Ể ? = _ L l Ẽ l u * - Ẽ l i r ) Ẽ l = - L t Ẽ l

Ôn J V d ọ dy/ dn J V õ ọ

_ £ n _ U P ) (1 17)

d [ị/

-— u - — V

{õụ/ dịị/

\ /

+ U 9 — dv u -Võu

e The c o n ti n u i ty e q u a tỉo n o f s u s p e n d e d s e d im e n t

In C a r te s ia n c o o r d in a te s y s te m , th e c o n t in u it y e q u a tio n o f suspendeci lo a d has

th e fo rm as d e s c rib e d in íb llo v v in g e q u a tio n :

ô(Ch) d ( Q xC) d (Q yC) õ

ôt dx õy õx d x ) õy h s

ÕC

õy ) - { Er - / ) * ) = 0 (1.19)

U s in g th e a s s u m p tio n o f lo c a lly c o n s ta n t d iffu s io n c o e ffic ie n t in h o r iz o n ta l

d ir e c tio n , r e s u lt in g in a tr a n s íb r m e d e q u a tio n :

R e s e a r c h u s i n g t h c 2 - D t o c v a l u a t e t h e c h c in g c 51

vvhere: C: s u s p e n d e đ c o n c e n t r a t io n a t le v e l z

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

a C oncept o f d is c r e tiz a tio n in F V M

T h e b a s ic o f f i n it e v o lu m e m e th o d ( F V M ) is b a se d o n th e c o n s e r v a tio n r u le

a p p lie d fo r í ì n it e c o n tr o l v o lu m e T h e g e n e tic c o n s e r v a tio n e q u a tio n fo r a s c a la r ộ

tr a n s p o r te d b y th e flo w h a s th e in t e g r a l fo rm of:

In th e e q u a tio n ( 1 2 1 ), o a n d s a re th e v o lu m e o f a n d s u ría c e e n c lo s in g c v ,

re s p e c tiv e ly ,

n: u n it vector o rt ho go na l to sur fac e s a nd direction outvvard, V is fluid velocity

v e c to r,

p: th e d e n s ity o f m ix t u r e o f w a t e r a n d s u s p e n d e d s e d im e n t,

Term ( 1 ) is th e r a te o f c h a n g e o f th e p r o p e r ty v v ith in th e c o n tr o l v o lu m e ,

T e r m ( 2 ) is n e t f lu x o f th e q u a n t it y ộ tr a n s p o r t e d th r o u g h th e c v b o u n d a ry by

c o n v e c tiv e m e c h a n is m ,

T e r m (3) is n e t f lu x o f th e q u a n t it y <ị> t r a n s p o r t e d th r o u g h th e c v b o u n đ a ry by

d iffu s iv e m e c h a n is m ,

T e r m (4 ) is to ta l s o u rc e s o r s in k s o f q u a n t it y ộ o c c u r v v ith in th e c v

T h e F V M ’s d is c r e t iz a t io n in v o lv e s in to w s te p s T h e f i r s t s te p is

ip p r o x im a t io n o f in t e g r a ls in e q u a tio n ( 1 2 1 ) a n d th e se co nd s te p is th e

n te r p o la tio n T h e f in a l o u tc o m e o f d is c r e t iz a tio n p ro ce ss is a n a lg e b r a ic s y s te m

h a t n e eded to be s o lv e d b y a n y c o n v e n tio n a l m e th o d s G e n e r a lly s p e a k in g , F V M is

in a d v a n c e d a p p ro a c h o f f i n it e d if f e r e n t m e th o d ( F D M ) , w h e re th e m ass :o n s e rv a tiv e c h a r a c t e r is tic is s t r i c t l y re s e rv e d fo r each c v s u r r o u n d in g a

ĩo m p u ta tio n a l node

— Ị p ộ d í ì + Ị pộVndS = Ị rgradộndS + ị q ệd í ì

(1.21) (4)

52 N g u y ê n H u u K h a iy N g u y ê n T i e n G i a n g , T r a n N g o e A n h

C o n t in u it y e q ư a tio n o f s u s p e n d e d s e d im e n t c o n c e n tr a tio n in th e g c n c ra l

c o o rđ in a te s y s te m h a s fo rm :

J — ( C h ) + — Ụ c Q * )+ — Ụ c ọ * —

cỉ

d(p he

+ Ụ c Q ¥)+ ị - Ụ c Q * ) - 4 - ^ h

( 1 22 )

(1.23)

U s in g C r a n k - N ic o ls o n sch e m e in th e in t e g r a l, th e c o rre s p o n d in g fo rm o f

e q u a tio n ( 1 2 2 ) c a n be p re s e n te d as:

J { c h ) n ; ' + — — { j c q v Ỵ 1 + - - ? - ( j c q ọ Ỵ '

<7^ ^ J o\ự J Õ<p y

g n g c Ỵ " 1

+Ẻ.JLhc(ễạ.Ẽl-SiLẼ£.T' + ị 4 -hsẨ ẳ ỉi.Ẽ £ -ỉiL Ĩ£ T ' +Jịch)r‘ 0.

2 ^ / 7 2 <7<ơ ^ J d(p J S ụ / ) I J

b N in e - d ia g o n a l coefficient m a tr ix solver

F ro m p re v io u s ly d e riv a tio n s , th e susp en d e d s e d im e n t tr a n s p o r t e q u a tio n in non-

o rth o g o n a l c o o rđ in a te s y s te m in d is c re tiz e d fo rm v v ritte n fo r c o n tro l v o lu m e (i j ) is:

+ í7ó S \ j ) + 7 + M Ml.Vl + ữ 9^-|M.y + l ’ (1.2 4 )

w h e re : a r a 9 : a re c o e ffic ie n ts *

B q u a tio n (1 2 4 ) is g e n e ra liz e d as:

(1.25)

T h e r e s u lte d s y s te m o f e q u a tio n s in v o lv e s u n k n o w n fo r s in g le e q u a tio n in

e ach tim e s te p a n d h a s th e fo r m o f b a n d m a t r ix T h e a lg o r ith m s fo r s o lv in g t h a t

s y s tc m o f e q u a tio n c a n be a n y in t e g r a tio n m e th o d H e re b y , th e re s e a rc h acỉopted

th e lin e - b y - lin e te c h n iq u e to s o lv e th o s e r e le v a n t e q u a tio n s

R e s e a r c h u s i n g t h e 2-1) t o c v a lỉ i c ĩt e th e c h a n g e 5 3

c I)iscretizatio?i o f E x n e r 's eq u a tio n

R rv v rito E x n e r*s c q u a t io n in th e fo rm :

./

( 1.26)

A p p ly in g th e s a m e r u le o f d is c r e tiz a tio n , w e h a v e :

(1.2 7 )

)

(<p

U J )

A(p

S u b s t it u t c e q u a tio n (1 2 7 ) , (1 2 8 ) in t o e q u a tio n (1 2 6 ), o b ta in s :

At

A n =

-0 - W i

a , , + b , ì + j * ( e , 1, - d 1J I

(1 2 8 )

(1 2 9 )

E q u a tio n (1 2 9 ) is th e f in a l d e s c re tiz e d fo r m o f E x n e r* r e q u a tio n I t is s o lv e d

b y e x p lic it sch e m e T h e o u tc o m e is th e c h a n g e i n r iv e r b e d e le v a tio n a t each t im e

s te p a t c e n te r o f ea ch c o m p u ta tio n g r id T h e n e w bed e le v a tio n is u p d a te d , a n d flo w

m o d u le is s ta r te d c o m p u t in g fo r th e n e x t tim e s te p

<? D e t e r m i n i n g t n e a s u r e o f s t r c a m - b a n k e r o s i o n

C ro s s s e c tio n s , a f t e r s c o u rin g , w i l l c re a te a n e w r o o f w it h g r e a te r s lo p e U s in g

s lip c o m p u ta tio n m e th o d o f s o il m e c h a n ic s c a n d e te r m in e m e a s u re o f s tr e a m - b a n k

e ro s io n S lip fo rm c a n be f l a t s lip o r s lip c u rv e , u n d e r e ffe c t o f s lip a n d a n t i- s lip forces:

„ Z c.l, +Ĩ N,'gv.

- 1 T, - '

w h e re : N u m e r a to r is a n t i- s lip fo rce , a n d d e n o m in a to r is s lip fo rc e ,

c ,: s tic k y fo rc e ; 1 ,: le n g th o f i th s lip c u rv e ,

N fc: a n t i- s lip fo rc e (s h e a r d ir e c tio n ) ,

T ,: s lip fo rc e ( n o r m a l d ir e c tio n )

(1 3 0 )

54 N g u y ê n H ư u K h a i y N g u y ê n T i c n G i a n g , T r a n N f * o c A n n h

In a p p r ồ x im a b ilitv fo rm , a p p ly in g p r in c ip le o f s tr o n g b a la n c e o f C o u lo m l c a n n

c o m p u te th e needed slope to g u a ra n te e s te a d y in g s tro n g b a la n c e :

w h e re : |í: slope o f s te a d y in g s tr o n g b a la n c e ,

<p: in s id e í r ic t io n a n g le ; C: s tic k y íorce,

H : ỉ ỉ c i g h t o f slop e ro o f; y: s p e c ific w e ig h t o f s a n d v s o il

III Test mocỉol to curved bend oí’ Red river

T h e m o d el w as d e v e lo p e d a n d a p p lie d fo r te s tin g in S o n T a y c u r v e d b e n d < o f Red R iv e r ( f Ì £ l) In o rd e r to c ie te rm in e th e u p s tre a m a n d d o v v n s tre a m b o u n d a r y y ,

r iv e r n e tvvơ rk is ro u te d b y H E C -6 m ơdel T o p o g ra p h ic a l c ia ta is a đ o p te đ fro n m

m e a s u re d d a ta d u r in g th e e n d o f 1997 a n d b e g in n in g 1998 T h e g r iđ s y s te m w e r r e

g e n e ra te d b v so ítvva re G c n G rid O õ o f C A F L A B (Y u e n g n a n ì U n iv - S o u th K o r e a a )

T im e s te p fo r c o m p u ta tio n flo w vvas 0 2 5 second a n d fo r s e d iirìe n t c o m p u t a t io n vvaas

2 se co nđ R e s u lts o f d is t r ib u t io n o f bed e le v a tio n , v e lo c ity f ie ld a n d d e p t h o f th a e

s e g m e n t vvere shovvn in ta b le 1 a n d fig 2 R a tin g c u rv e a n d bed c h a n g e a fte e r

c o m p u ta tio n a re co in c ic ỉe d w it h o b se rve d re s u lts a t S o n T a y s ta tio n t h a t lo c a te e c ỉ

w it h i n th e s e g m e n t T h is is th e p r e lim in a r y te s t so th e e r o s io n - c r u m b lin g o f b a n k k s

w as n o t c o m p u te d y e t

Figure 1. S o n T a y c u rv e d bend o f Red R iv e r

R e s e a r c h u s i n g t h c 2 - D to c v a l u a t c t h c c h a n g c 55

T a b l e 1 C o m p u ta tio n re s u lts ơ f d is tr ib u tio n o fv e lo c ity , d e p th a n d bed e le v a tio n o f

r iv e r reach

CROSS SECTION OF SONTAY STATION PASS EROSION

Z(nn)

Pigure 2. C ross se ctio n o f S o n T a y s ta tio n pass flo o d days

56 N g u y ê n H ư u K h a i , N g u y e n T i c n G i a n g , T r a n N g o e A n h

IV C om m ents

1 R e c e n tly , th e e ro s io n o f r iv e rb e d is th e h o t p ro b le m so a tv v o - d im c n s io n a l

m o d e l to a n a lv z e a n d s im u la te th o s e processes is n e eded

2 M o d e l c o m p u te d t r a n s p o r t o f bed a n d s u s p e n d e d s e d im e n ts to o r th o g o n a l

d ir e c t io n a n d d is t r ib u t io n fo llo w in g d e p th o f s u s p e n d e d s e d im e n t, r e f le c t in g rnore

a d e q u a te re s a s o n s a n d p re s e n t c o n d itio n o f r iv e r e ro s io n a n d s e d im e n t tr a n s p o r t

b a la n c e

3 M o d e l uses f in it e c o n tro l v o lu m a n d C ra n k -N ic o ls o n s c h e m e t h a t has

e ffe c te r to s e d im e n t tr a n s p o r t

4 T h is is b e g in in g te s t,th e re fo re e ro s io n -c ru m b le p ro b le m n o t is in v e s tig a te d y e t

R eferences

1 C h ih T e d Y a n g , Secỉim ent Transport, T h e o ry a n d p ra c tic e, M c G r a w - H i l l , 1996

2 H ydrologic E n g in e erin g Centrc, ư s A r m y C ops H E C - 6 , S co u r a n d D ep o » sitio n in

r iv e r a n d r e s e rv o ir, 1994

3 N T G ia n g , S e d im e n t tra n sp o rt balance a n d b a n k in Son Tay c u r v e d b e n d , R ed

R iv e r V ietn a m , A T h e s is fo r th e degree o f M a s te r o f E n g in e e rin g , A s ia n I n s t it u t e

o f T e c h n o lo g y , 2 0 0 0

4 T r a n T h u c , N g u y e n T h i N ga, Rỉver D ynam ics, U n iv e r s ity o f S c ie n c e -V N U , 2*001

TẠP CHỈ KHOA HỌC ĐHQGHN, KHTN & CN, T XIX, Nọ1.2003

N G H I Ê N CỨU ỨNG D Ụ N G MỒ H ÌN H 2 C H lỂ U T Í N H T O Á N

B IẾN DẠNG LÒNG D A N

N guyễn Hữu K h ả i, N guyễn T iề n G iang, T rầ n Ngọc A n h

Khoa K h í tượng T h u ỷ văn & H ả i dương học Đại học Khoa học T ự n h iê n, Đ H Q G H à Nội

V iệ c n g h iê n cứu xó i lở lò n g sông đả dược t iế n h à n h ỏ n h iề u n ơ i t r ẽ n t h ế g ió i, ở nưỏc ta đã sử d ụ n g m ộ t sô m ô h ìn h n h ư H E C - 6 , M I K E 1 1 đế p h â n tí c h , t í n h to á n xói

lở T u y n h iê n các m ô h ìn h tr ê n m ỏ i c h ỉ g iả i q u y ế t b à i to á n 1 c h iể u M ộ t sô mô h ìn h

th ủ y lự c 2 c h iể u n h ư T E L E M A C h a y M IK E 2 1 c ủ n g m ố i c h ỉ x é t ở p h ạ m v i p h ả n bố

tố c độ d ò n g c h ả y

Cho đến nay hệ th ô n g sông ngòi V iệ t N a m bị xói lở theo cả chiều dọc v à chnểu ngang

r ấ t m ạ n h mẽ và ch ú n g có tác động tương hỗ với n h a u V ì vậy cần th ié t có m<ột nnô h ìn h 2

ch iế u dò g iả i q u y ế t bài toán này M ô h ìn h b iê n d ạng lò n g dẫn 2 chiểu tr o n g hộ t.oạ độ phi

tu y ê n k h ô n g trự c giao T R E M (Tvvo-dim ensional R ive rb e d E v o lu tio n M ọ d e l o o n s tru c te c l in

th e n u n -o rth o g o n a l c u rv ilin e a r coordim ate system ) cho phép xác đ ịn h sự p h â n bô tóc độ

c ù n g như b iế n đổi đáy sông theo cả hướng dọc và hướng ngang