DSpace at VNU: Research using the 2-D model to evaluate the changes of riverbed

V N U JO U R NAL 0 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 - 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 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 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 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 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 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 ra 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
1. 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 ra 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 2 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

ÔN

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
ô 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 ra tio n (= 9 .8 1 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 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 re s p e c tiv e ly ,
- u ' 2 , - u ' v f, - v ' 2 :

x ,y

c o m p o n e n ts

of

d e p th -a v e ra g e d

R e y n o ld s

s tre ss

te n s o rs ,

- u ’2 = 2Dh

'ôu}
Võx )

' Õ14

2

-ịK

(1.4)

3

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 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 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).
6 . 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 ra 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
rựể

=

0

( 1 .8 )

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/,


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

J a c o b ia n

of

th e

tr a n s íb r m a tio n

fro m

C a rte 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 sys te m . I t is c o m p u te d by:

(1.9)

w here: xv, x

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 ire c tio n ),
a n d n (th e d ir e c tio n o r th o g o n a l to th e s tre a m vvise d ir e c tio n ) Processes o f c o n v e rtin g
is p re s e n te d as fo llo w s :

â
„ (
+ ~ t ch = —

+

°s

\ ị / y ,

(Ị> „ ,

(

õỵ}

Oò

V

<ỉh

ÕS

õx

*•ồ
)■s 1

<

vvhere: y 1(

.

II
; -o

+

à.
ơn

õx

Vfy
ÔS

( 1. 10)

õy> s
ỵ( '
(
dx
r ì + 0»
*

s
9Ầ

) 1.

,

+

à¥

.

rí =

Uò

{


(71

õnj

< J> .

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

Ị7 + ụfy ~

(ỊỈ + [ - yrx “

\

In

- u v ch )

(112)

-« „9 *")

í 1 -1 3 )

(
+

c.

+ V y prjí/fc" = —

^

■ í3* 77 + p y 77 <76 = 7
K
Ky
K/

7

7

tra n sp o rt equations:
o rd 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 tin u ity

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

e q u a tio n ,

th e

(s) a n d th e d ir e c tio n

orthogonal to (s) direction m ust be speciíled before hand. In the stu dy, 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 ra 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 slo 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 rm of:


N g u y e n H u u K h a i, N g u y e n T ie n G ia n g , T r a n N goe A n h

50

a 1/2

n

=

ổ 77\

1

r CrO< n + J - ậ ĩ >
2 / i c õs

Me &
1/2

„•

= -—

♦
(r

(1.14)

*
♦»'!
. 1/1
c o \ 1/2 d*7
-*■«,)(*■
- r „ ) ặ - - Ị- ( 4 )

(1.15)

Ôn

w h e re : q ‘ , q “ : n o n -d im e n s io n a l bed lo a d s e d im e n t tr a n s p o r t ra te in (s) a n d (n)
d ire 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* : non 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 ic t io n fa c to r, v a lu e o f 0.7 w as 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

com ponent

in

stre a m v vise

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 re v io u s ly .

d. T r a n s fo r m a tio n o f bed load equ ations
In 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
c o o rd in a te

(1 .1 4 ) a n d (1 .1 5 ) s h o u ld be tr a n s íb r m e d

in s te a d

of

(s,

n)

c o o rd in a te .

E a ch

te r m

in

a c c o rd in g ly
th o s e

to

(vị/,< p)

e q u a tio n s

a re

tra n s ío rm e d s u b s e q u e n tly as íbllovvs:
( l) .T e r m Ẽ 1

Ể ỉ =i ( Ị ỉ r

( 2 ).T e rm Ẽ 1

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

ôs

õs

Ôn

õn

3

V õy/

i n

JV dọ

dy/

dn

-

{õụ/

dịị/

_£n_U P )

d [ị/

JV õọ

\
/
dv
du
— V +U9 —

dv

-— u

(3). T e rm — I

(1.16)

d(p

õu

u

d(p

-------V

d(p

(1 17)

(1.18)

e. The c o n tin u ity e q u a tỉo n o f su sp en d e d se d im en t
In C a rte s ia n c o o rd in a te s y s te m , th e c o n tin u ity 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 ( QxC)

d(Q yC)

õ

ôt

dx

õy

õx

dx)

õy

hs

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 riz o n ta l
d ire 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 rc h u s i n g t h c 2 - D to c v a l u a t e th e c h c in g c .

51

vvhere: C: su s p e n d e đ c o n c e n tr a tio 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. Concept o f d isc re tiza tio n in F V M
T h e b a s ic o f f in it e v o lu m e m e th o d (F V M ) is ba sed on th e c o n s e rv a tio n r u le
a p p lie d fo r í ì n ite c o n tr o l v o lu m e . T h e g e n e tic c o n s e rv a tio n e q u a tio n fo r a s c a la r ộ
tra n s p o r te d b y th e flo w h a s th e in te g r a l fo rm of:
— Ị p ộ d í ì + Ị pộVndS = Ị rgradộndS + ị qệd í ì

(1.21)

(4)
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 orthogonal to surface s and 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 te 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 rm ( 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 te 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 rm (3) is n e t f lu x o f th e q u a n t it y <ị> tr a n s p o r te 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 rm (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 .
The

F V M ’s

ip p r o x im a t io n

of

d is c r e tiz a tio n
in t e g r a ls

in

in v o lv e s
e q u a tio n

in

to w

( 1 .2 1 )

and

s te p s .
th e

The

fir s t

se cond

s te p

s te p

is

is
th e

n te r p o la tio n . T h e fin a l o u tc o m e o f d is c r e tiz a tio n p ro cess is a n a lg e b ra ic s y s te m
h a t needed 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

advanced

:o n s e rv a tiv e

a p p ro a c h

of

c h a r a c te r is tic

ĩo m p u ta tio n a l node.

f in it e
is

d if fe r e n t

s tr ic tly

m e th o d

re s e rv e d

fo r

(F D M ),
each

cv

w h e re

th e

m ass

s u r r o u n d in g

a


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 tin u ity

e q ư a tio n

o f suspended

s e d im e n t c o n c e n tra 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 :

)+ ị—- ỤỤ c Q * c) - 4 -ọ ^

+õy/ ỤỤ cc QQ *¥)+
cọ
c\ự

J — ( C h )>+ —

cỉ

a

d(p

. . . \

he

*

/

C(p

^ J

a

J

U s in g C r a n k - N ic o ls o n

_

\

*

/

a

. . .

h*

J

^

—
õ y

f

J

õ ọ

( 1. 22 )

õụỉ)

sch e m e in

th e

in te g r a l, th e c o rre s p o n d in g

fo rm

of

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; ' + — —

•'
At

2

{j c

ôụ/x

(

<7^

Ỵ1 + --? -(

q v

hl

*>y 1

^ J

o\ự

j c q ọỴ

2 d
> V '»

J

' -

fMJ

\

Õ
g n g c Ỵ" 1

2 5(0

11í

dọ

J

~AIJ{ER - I ) , x ;

,y

(1.23)

eV ) t i

J

2 õiị/

+

2 õ
4

+Ẻ.JLhc(ễạ.Ẽl-SiLẼ£.T' + ị -hsẨẳ ỉi.Ẽ £ -ỉiL Ĩ£ .T ' +Jịch)r‘ . 0.
2

^ ./

7

^ J

2 <7<ơ

d(p

J Sụ/)IJ

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 suspended s e d im e n t tr a n s p o r t e q u a tio n in nono 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:
I

! .;

+ í7ó S

+

\.j

a i '

) +

I.J

+

7

* « ♦ ! . ;

+

+

^ 4 ^

+

a s '

,.J

M Ml.Vl + ữ 9^-|M.y +l

f |

+

’

(1.24)

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 re 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
each tim e s te p a n d h a s th e fo r m o f b a n d m a tr 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 te 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 lve th o s e r e le v a n t e q u a tio n s .


R e s e a rc h u s i n g t h e 2-1) to c v a lỉic ĩt e th e c h a n g e .

53

c. I)iscretizatio?i o f E x n e r's equation
R rv v rito E x n e r*s c q u a tio n in th e fo rm :
./ N

(1

I [ ^ L ) +£ ^ L ) W(K
-Ả

o )

( 1.26)

a
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 ve :

(1.27)
)

A(p

(U.J)

(1 .2 8 )
S u b s titu tc 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 , , + b , ì + j * ( e , 1 , - d 1J I .

An = 0 - W

(1 .2 9 )

i

E q u a tio n (1 .2 9 ) is th e fin a l d e s c re tiz e d fo rm o f E x n e r* r e q u a tio n . I t is s o lve 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 tim e
ste p a t c e n te r o f each 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 tin g fo r th e n e x t tim e s te p .
C ro ss s e c tio n s , a fte r s c o u rin g , w il l c re a te a n e w r o o f w it h g r e a te r slo 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 tre a m -b a n k
e ro s io n . S lip fo rm c a n be f la 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 ti- s lip
forces:

„ Zc.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 ti- s lip fo rc e (s h e a r d ir e c tio n ) ,
T ,: s lip fo rc e ( n o rm 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 ic n G ia 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 tro n g b a la n c e o f C o u lo m l

cann

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 :
tg Ịí= tg ip + C /y .H

(1 .3 1 1 )

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

C: s tic k y íorce,

H : ỉ ỉc i g h t o f slope 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 odel 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 rre

g e n e ra te d b v soítvvare 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 re 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 seconđ. R e s u lts o f d is t r ib u tio n o f bed e le v a tio n , v e lo c ity f ie ld a n d d e p th 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 cicỉe d w it h o b serve 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 in th e se 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 le 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
I

J

X

Y

z

V

u

H

1

1

-8212.75

2989.2

8.526

0.434

•0.573

4.132

1

9

-81G3.Õ898

3033.6699

2.273

0.604

•0.822

10.385

1

3

-8114.4399

3078.1399

0.808

0.801

•1.123

11.85

1

4

•80(30.2 7 08

3122.6001

1.516

0 .8

• 1.157

11.141

1

5

-8 0 1G. 1299

3167.0701

2.489

0.741

•1.107

10.169

1

6

-7966.9702

3211.54

2.835

0.692

-1.068

9.822

1

í

.7 9 17.8198

3256.01

2.872

0 .6 6 6

-1.062

9.786

1

8

-7868.G602

3300.47

2 .8 6 8

0.647

• 1.067

9.79

1

9

-7819.5098

3344.9399

2.952

0.627

-1.072

9.705

1

10

-7770.3501

3389.1099

3.599

0.594

-1.051

9.058

1

11

■7721.2002

3433.8701

3.947

0.556

- 1.0 2

8.711

1

12

-7672.04

3178.3401

4.762

0.516

•0.981

7.896

1

13

-7622.8901

3522.8101

6.355

0.45

-0.889

6.302

1

14

-7573.73

3567.28

7.228

0.383

-0.788

5.43

1

15

-7524.5801

3611.74

10.133

0.282

-0.603

2.525

1

16

-7475.4199

3656.21

Z(nn)

10.132

0.102

-0.228

2.525

CROSS SECTION OF SONTAY STATION PASS EROSION

—♦ — zo

® z l z4 ..........2 8 ••••*—z l 9

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


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

56
IV . C om m ents

1 . R e c e n tly , th e e ro s io n o f riv 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 se processes is needed.
2. M o d e l c o m p u te d tr a n s p o r t o f bed a n d su 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 tio n a n d d is t r ib u tio 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 sa so 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

and

C ra n k -N ic o ls o n

schem e

th 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 heory a n d p ra c tic e , M c G r a w - H i l l, 1996.

2.

H ydrologic E ngineerin g Centrc, ư s A r m y Cops. H E C - 6 , S co u r a n d D ep o » sitio n in
r iv e r a n d re s e rv o ir, 1994.

3.

N .T .G ia n g , S e d im e n t transport balance a n d ban k in Son Tay c u r v e d bend , R ed

R iv e r V ietnam , 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 ra n T h u c , N g u ye n T h i N ga, Rỉver D ynam ics , U n iv e rs 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 HÌNH 2 C H lỂ U T ÍN H T O Á N
BIẾN DẠNG LÒNG D AN
N guyễn Hữu K h ả i, Nguyễn T iề n G iang, T rần Ngọc A n h
Khoa K h í tượng T h u ỷ văn & H ải 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 tiế 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 tíc 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 ch ả y .
Cho đến nay hệ th ô n g sông ngòi V iệ t N am bị xói lở theo cả chiều dọc v à chnểu ngang
rấ t m ạ n h mẽ và ch ú ng 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 yế t bài toán này. M ô h ìn h biên dạng lò n g dẫn 2 chiểu tro 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 cte cl 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
cù n g như b iế n đổi đáy sông theo cả hướng dọc và hướng ngang.