Luận án tiến sỹ " Tính toán dòng chảy vùng biển ven bờ - nước sông " pptx

Dl).IHOC Qu6c GIA TP. H6 CHI MINH
TRU<JNGDl).IHOC KHOAHOC TV NmEN

V() THANH TAN
, " ?
'fINI-I TOAN DONG CI-IAY
, ~ , , ~
VUNG UIEN VEN nO - NUDCNONG
Chuyen nganh : H<liDLtdngHl)c
Mii 86 : 1.07.07
TOM TAT LU~N AN TIEN si V~T LY
TP. H6 ChiMinh -2004
Cong trinh hoan thanh t~i: Bc) m6n V~t Ly MOi Trd<tng, khoa
Vl)t Ly, trdi1ng D~i HQc Khoa HQc TV Nhit}n, D~i HQc Qu6c
Gia TP.HCM.
NgtfC1ihtf(1ng d~n khoa hQc:
PGS. TS. IJt}Quang To~i
PMn bit;n 1:
PGS. TS.Dinh VAnu'u
PMn bit;n 2:
TS. Nguyen HOO NhAn
PMn bit;n 3:
TSKH. Phon VAnHoijc
I
j
Lu~n an dtf<JcbaG vt? tnidc HQi B6ng chii'm lu~n an cii'p
Nha Ntfdc, hQp t~i: tnt<'fngB<;tiHQc Khoa HQc Tt! Nhien TP.HCM
VaGhie: 14 gi<'f30 ngay 24 thang 9 Dam 2004
C6 the am hieu lu~nan ~i thtfvit;n:
~ Khoa HQcT5ng H<JpTP.HCM
- Tnt<'fngB<;tiHQc Kltoa HQc Tt! Nltien TP.HCM

1
M(1 DAU
Khu v1!cbie'n yen 1XJDam Vi~t Nam c6 mQt vai tro ra-t
quaDtrQngtrong nhi~u lanh v1!ckhac nhau. Cae nghi~n cll'u,khllo
sat va do d~c cac d~c tntng hili dudng hQc ngay ding nhi~u hdn
tr~n wng bien yen 1XJ.Tuy nhi~n, cac bai loan mo blah cho vung
bie'nnay vancon tltdngd6i it.Cae qua trlnhtltdngtae bie'n-1XJ 1£1
nhfi'ng trd ng~i Idn eho cac bai loan mo blah. Ngoai fa, ding c6
the' ke' th~m blah d~ng du<'1ng1XJva s1!sii'd1}ngcac di~u ki~n bi~n
d6i vdi mi~n tinh c6 bi~n rQng hudng v~ phia bie'n cling 1£1nhfi'ng
kh6 khan kIDthi€t l~p mo blah.
Phudng phap pMn tii'hfi'uh~n vdi tinh ~m deo trong vi~c
thi€t k€ m~ng ludi to ra thich h~p d6i vdi khu v1!cc6 du<'1ng1XJ
bie'n phrtc ~p, c6 nhi~u dao nM. M(ic du v&ntdn ~i nhfi'ngh~n
ch€dang ke ciia n6 d6i vdi cae bai loan mo blah thiiy dQng11!c.
Ngay nay, phudng phap pMn tii' hfi'u h~n dang du~c ap
d1}ngngay cRag nhi~u hdn vao cac bai loan thiiy dQng 11!chQc
bie'n, tU'nhfi'ngmo blah kich thudc nho, yen b<'1(lscandarani, 1993
- Le Provost, 1994 - Kapolnai, 1996) cho d€n cae bai toaD hoao
hm d~i dttdng ba chi~u Dch thudc Idn (Greenberg, 1997).
L~n lu~t cac bai toaD mQt,hai va ba chi~u thllYdQng 11!c
hQc bien sii'd1}ngphudng phap phitn tii'hfi'u h~n du~c trlnh bay
trong nQidung ciia lu~n an.
Cung vdi vi~c ap d1}ngphudng phap so'tri ph~n tii'hfi'uh~n
de' tinh toaDM th6ng hoan lttu gi6 mila ~i dai yen 1XJva th~m 11}c
dia Dam Vi~t Nam, lu4n an nay con sii' d1}ngphudng phap tach
mi~n khong giait cho bai toaDhoRnhm ba ehi~u.
2
A
CHUdNG 1: TONG QUAN

1.1 GiO'ithi~u chung v~ khu vqc ven 1XIDamVi~t Nam
Vung biin ven 1X7Dam Vi~t Nam du'<;1egidi h~n tit Nha
Trang d6n dao Phd Qu6e du'QechQnlam khu vf{.enghi~n eU'u
M
th6ng dong ehiy trong cae thang gi6 mua (tMng 1 va thang 7) va
cae thang gi6 chuyin mUa(thang 4 va thang 10). Khu vf{.enghi~n
eU'uohm trong vUngkinh tuy6n tit 1O3~ d6n 111°Eva vi tuy6n tit
7,5~ d6n 13~. Df{.avao cae d~e diim v~ khi tu'Qngva hii van,
ngu'Cfita ehia khu vf{.enay thanh ba vUng. Vung 1 tit Nha Trang
d6n Viing Tau; vung 2 tit Viing Tau d6n Ca Mau va vung 3 lit
vUngyen 1X7biin uty DambQ.
1.2 Cac nghi~n CUDh~ th6ng dong chsy ven I.XI
Mc}t86 dQtkhao sat va do d~e dong ehiy yen 1X7tit cae
tr~m do li~n t1;1edii du'Qeti6n hilnh. Trong d6 e6 thi ki d6n cae
dQt "Dilu Ira khao sat tdng hf/p cae dilu ki~n tT!nhien t{li vung
biin Kien Giang
- CaMau" vitomua kho va mua mu'aDam1998
va ehuy6n khao sat vung biin Phan Thi6t vao thang 10/1999.
1.3 MOtviti m6 hJnh tinh toaD ng~n CUDBi~n D6ng
Cae bili toaD mo hlnh eho vUngbiin yen bCfkhong nhi~u.
Do d6, cae k6t qua tinh loan eua roOhlnh Biin Bong va vjnh Thai
Lan eung ea'p nhii'ngthong tin eiin thi6t eho bili loan yen 1X7.
Mc}ts6 k6t qua tu'dng tf{.nhau tit cae lac gia khae nhau.
Ching h~n. mc}th~ th6ng dong eMy ~nh yen 1X7DamVi~t Nam
tit Phan Thi6t d6n Ca Mau (vUng 1 va vUng2) hu'dngv~ Damtrong
tru'Cfnggi6 mUa dong - Me va hu'dngl~n bifc trong tntCfnggi6 mua
uty - nam; dong ehiy yen bCfvjnh Thai Lan (vUng3) pMt triin
3
ye'u trong tru'(Jnggi6 mila dong - Me nhu'ngpMt trieD ~nh trong
tru'(Jng gi6 mila tay - Dam;

1.4 NQidung lu{in an va phddng phap nghi@ncoo
1.4.1 Cae n6i dung thu'cbien
M11etieu chinh: tlnh toaD h<%th6ng dong chciy gi6 trung
blnh hai chi~u va ba ehi~u khu v1f.eyen b(JDamVi<%tNam tll'Nha
Trang de'n vnng bien tay Damva dao Phti Qu6c trong cae tru'(Jng
gi6 mila d~c tru'ngbhng phu'dng pMp phin tit htru hc,tnvdi mc,tng
lu'didu'~cxay d1f.ngg6m cae pMn to'tam ghic bit ky.
Ngoai fa, phu'dngpMp phin tit htru hc,tncon du'~e ap d11ng
vao bai toaDdong chay troi mQtchi~u vdi roOhlnh Ekman.
Cae ke't qua tlnh toaDtru'£1ngdong chciytu'dng !tng vdi cae
thang gi6 miIa d~c tru'ng va cae thang gi6 ehuyen mila du'~e th~
hi<%ntren cae ban d6.
1.4.2 Phu'dngpMp nghien eltu
Mi~n tlnh yen b(Je6 bien long rit rQng. Phu'dngpMp tinh
hai llin du'~e ap d11ng.LiD diu, vdi mi~n tlnh rQng hdn, khu vJ!.e
nam Bi~n Bong. Ke't qua cua bai toan Dam Bi~n Bong du'~e sit
d11nglam di~u ki<%nbien eho bai toaDyen b(J.
Phu'dng pMp phin tit htru hc,tnd1f~eap d11ngd~ thJ!.Chi<%n
dnh toaD eho cae bai toaD mQtchi~u, hai chi~u va ba chi~u. Cae
mc,tnglu'di hai chi~u du'~exiiy d1f.ngteen cd sd phep dJ!.ngtam giae
Delaunay, vdi thu~t toaDDelaunay Refinement.
Phu'dng phap tach mi~n khong gian va phep bie'n ddi tQa
dQ khong th!t nguyen sigma du'~c ap d11ngde tinh dong ehciyba
chi~u. Bai toaD ba chi~u du'~e philn ra thanh cae bai toaD mQt
ehi~u theo phu'dng thing d!tng va cae bai toaD hai ehi~u theo
phu'dngngang.
4
CHUONG2:Cd Sa LY THuvET
2.1 H~ th6ng cae pbddng trlnb xua't pMt
Hc$th6ng cae phu'dng trinh xu(t pMt mo ta cae hoan h.tu

trong d~i du'dng bao gdm cae phu'dng trinh bio loan dQnghtc;Jng,
bao loan kh6i htc;Jng,khue'ch tan mu6i va ehuy€n v~n entropi. B6i
vdi nhung chuy~n dQng kich thu'deldn trong d~i du'dng,hc$th6ng
phu'dng trinh xu(t pMt du'c;Jevie't trong hc$tQa dQe~u (A,(j),R) e6
d~ng r(t phtte ~p.
2.2 Cae phep xa'p xi
Sa d~ng phep ehie'u leD ~t phing [3,cae phep g~n dung
thuy tinh va phep g~n dung Boussinesq d€ du'a M cae phu'dng
trinh xu't pMt v~ d~ng ddn gian hdn.
2.3 Cae m6 hlnb Hob toaD dong coy trong d{tidddng
2.3.1 Mo hlnh ba ehi~u
Phu'dng trinh bio loan dQng 1u'c;Jngd6i vdi thanh phh
thing drtng rut l~i thanh phu'dngtrinh thuy tinh va thanh pMn v~n
t6e thing drtng du'c;Jetinh tit phu'dng trinh lien t~e. Cae phu'dng
trinh chuy€n dQnge6 d~ng:
00 00 00 00 1 Op. ac. g a
~ / a
(
00
)
-+u-+v-+w fv= g jpdz+- A - +A Au
Ot Ox. Oy Oz Po Ox. Ox. Po Ox.z Oz ZOz t
Ov Ov Ov Ov 1 Op. ac. g a
f
~ / a
(
Ov
)
-+u-+v-+w-+fu= g pdz+- A - +AtAv
Ot Ox. Oy Oz Po Oy Oy Po Oy Z oz ZOz

(2.1)
Phu'dng trinh lien t~e d~ tinh thanh ph~n v~n t6e thing
drtng:
aw' au av
- =
az ax ay
(2.2)
5
Thanh ph~n thing dli'ng eua veetd v~n t6e dong eMy t~i
day bien Wbva dao dQng ro1,1'enUdel,;dli<;fCtinh tit cac di~u ki~n
dQnghQc~i day bien va tren ~t bien:
aH aH .
Wb = -Ub Vb- khl z=-H
ax ay
al,; al,; al,; .
-+u -+v - = W khl Z= r
at sax Say S ""
2.3.2 Sli trung blnh h6a theo phlidng thing dli'ng va rod hlnh hai
chi~u
V~n t6c dong cMy trung blnh theo dQsdu dli<;fcdjnh nghia:
1 /; 1 /;
11=
J
udz v=
J
vdz (2.5)
(H + l;LH (H + l;LH
Tich pMn cac phu'dog trlnh (2.1) va (2.2) theo phu'dng
thing dli'ng,ta c6 rod bloh hai chi~u:
au au au 1 Cpa 8l; g /; /;api

-a+U ax+v oy -fv=-p;:- ax -g ax- Po(H+l;) ifax dzdz+
'tS 'tb
+ x x +Al~u
Po(H+l;) Po(H+~)
av av av 1 ape 8l; g
J
/;
J
/;api
-at+uax +v ay +fu=- Po ay -gay PO(H+l;)-HZ ay dzdz+
'ts 'tb
+ y y + A ~V
l
Po(H+l;) Po(H+l;)
au(H + l;) + av(H + l;) + al; = 0
ax ay at
2.3.3 Phlidng phap pMn fa cua rod hloh ba chi~u
C6 nhi~u phu'dng phap pMn fa rod hlob ba chi~u ohhro
dlia bai toaDv~ d~og ddn giiin hdo. MQt troog 86 d6 la 81,1'tach cac
thanhpMn nhroogangu va v cuadongcMy thanhcac thanhph~n
(2.3)
(2.4)
(2.6)
(2.7)
(2.8)
6
dong chay trung blnh U,v va cac dQI~ch cua n6 Uf,v' quanh gia
tri trung blnh:
u=u+ui V=V+Vf (2.9)
U,v duQcgQila cac thAnhpMn chInh ap cua dong chay va uf, v'

duQCgQila cac thiinh ph~n ta ap.
Thanh ph~n chInh ap cua dong chay U,v va dao dQngmlfc
nudc ,duQctioo tU'mo hlnh hai chi~u. Cac thAnbpMn ta ap uf, v'
duQc Hnhvdi budc th<'Jigian Idn bdn, c6 the ga'p mu<'JiI~n, so vdi
budc th<'Jigian tinh cac thanh pMn chinh ap.
2.4 Trao d6i rffi thing dUng
Thong thu<'Jng,ngu<'Jita danb gia
M 86 trao d6i r6i th~ng
dd'ngAztU'phudng trlnh dQngDangr6i:
oE+uoE+voE+woE;:::A
[(
OU
)
2 +
(
fJv
)
2
]
+~
(
A OE
)
-!D oP-e
at Ox Oy Oz Z Oz Oz oz ZOz P zoz
(2.10)
Trong sd dd Mellor
- Yamadab~c2, cac M s6 traod6i r6i
va khutch tan r6i duQc tlnh to' pbudng trlOOditng cua dQngmlng
r6i:

A{(:r+(:)'] -:D, :-e =0
(2.11)
Trong 8d dd Mellor - Yamada b4c 2V2,1cichthudc r6i duQc
tinh tU'phudng trlnb chuyen dQng:
D(q2p)=~
(
K oq2P
)
+EIPf Az
[(
8u
)
2 +
(
fJv
)
2
]
+ ! Dz api
}
-e (2.12)
Dt Oz q Oz 1 Oz oz Po oz
-
Cac h~ s6 trao d6i r6i Az.trao d5i khutch tan Dz:
Az =lqSM
Dz =lqSH'
(2.13)
7
CHt1<1NG3: AP DVNG PHt1<1NG PHAP
PRAN Tit HOO ~N VAo CAC MO HINH

TiNH TOANDONGCHAY
3.1BMtoan m()tchi~u
3.1.1 Thi€t lap bAiloan
Hc$th6ng cae ph\tdng trlnh xutt pMt eua bai toan m(>t
ehi~u Ozmidov e6 dl;\ng:
au
fv
at
av
-+fu
at
= ~(A au)
az Z az
= ~(A av)
az Z az
(3.1)
(3.2)
cae di~u kic$nbi~n:
- Tl;\im~t biin eho tr\tde tr\t{Jng\fng Stitt tie'p tuye'n gi6
tr~n ~t biin:
A au(z, t)
- A av(z, t) -
Po z az - 'tx Po Z az - 'ty
- Tl;\iday biin vdi di~u kic$ndinh:
u(-H) =v(-H) =0
va di~u kic$nban ddu:
(3.3)
(3.4)
u(z,t=O)=0 va
trongd6:

u va v la cae thanhphdnohmngangeua v~nt&-edongehay.
Sir d~ng ph\tdngpMp phdn ttl hii'uhl;\n,gia tri gdn dung
eua cae thanhpMn v4n t6e dong ehay u va Y d\t<;1extp xi quanh
cae nut eua phdntii':
U
-(1) -
U
<1>(1)+ U <1>(1)
- 1 1 2 2
U-(n) - U <I>(n)+ U <I>(n)
- N.l N+1 2
v(z,t=O) = 0
y(l) - v <1>(1)+ v <1>(1)
- 1 1 2 2
-
V
(n) -
V n,.(n) + v <I>(n)
- N""'1 N+1 2
8
V.di c1>lk)va c1>r)la cae ham d~ng dng vdi ph~n ur (k):
c1>lk) = zk+l-z va c1>~k)= Z - Zk (3.5)
L L
Ap d\lDg phtidng phap Galerkin. m3i pUn td' dti<;Jebi~u
di~n dtfdi ma tr~n:
[
L/
3
L/
]{

~
J
i
-A ~~I+A (Uhl-Uk) + Lf
(
Vk + Vk+l
))
/3 16 Uk - zfulk zk L 3 6
L/ LI ~ - A
~
u -A (Uk+l-U\::)+ Lf
(
VI:: + VI::+l
)
/6 13 Uk+l Zoz zk L 6 3
.1::+1
[
L/
3
L/
jl
~
\
i
-A ov-I +A (Vk+l-VI<) Lf
(
UI:: + Uhl
)!
7316 Vk - zOZlk zk L 3 6 (3.6)
L/ L/ ~ - A Ov

l
-A (Vk+l-Vk)-Lf
(
Uk+Uk+l
)
/6 13 Vk-l z OZ zk L 6 3
1<+1
San khi lien ke't ta't ea cae pUn tU'd~ ~o thanh m<}tma
tr~n loan eve cho ml,tng ltidi. ta dti<;Jchai M phtidng trlnh dnh cae
thAnh ph~n v~
r
t6e u va v rieng bi~t e6 dl,t
~
~hti san:
[A] U}={Bu} va [A] VJ={BJ (3.7)
Dtfa c c ai€u ki~n bien vao M (3. ) va chung dti<;Jcgiiii
bhng sai philn tie'n theo thCligian dng vdi mMbtide l~p.
3.1.2 Cae ke't qua cua bai loan mot chi€u
1. TrtiClngdng sua't tie'p tuye'n gi6 kMng d5i: ke't qua tinh
toaD nMn dti<;JedtiClngxoAn 6e Ekman dng v"i cae vi de] khae
nhau
2. TrtiClngh<;JptrtiClngdng sua't tie'p tuye'n gi6 thong d5i
phtidng va de]!dn bie'n thien di€u bOa:cae kh6i nti"e l~i loon xoay
htidng eung chu ky eua trtiClnggi6. eung chi€u kim d6ng h6 d BAc
Ban C~u va ngti<;Jcl~i ~i Nam Ban C~u.
9
B~u mut cac vecto dong chay cac t~ng ve Den mQtdu'<Jng
eHip. Khi T = To (chu ky dao dQngrieng cac kh6i nu'dc) du'<Jng
eHip trd thanh mQtdu'<Jngiron co ban kinh r!t Mn.
3. Tru'{jnggio xoay hu'dng vdi chu ky T: cac kh6i nu'dc

trong d~i du'ongding xoay hu'dngcling chu ky vdi tru'<Jnggio. Cac
d~u mut cua vecto dong chay t~o thanh mQt du'<JngtrOll.Ne'u gio
xoay hu'dng cung chi~u kim d6ng h6 thi dong chcly m~nh hon
nhi~u. Tru'<Jngh<,1pT
= To,vdi 811cQnghu'dngcua tru'<Jnggio va
cac kh6i nu'dc trong d~i du'ong, dong chay cac t~ng co dao dQng
cung pha vcsibien dQra'tMn.
3.2 Phudng phap xay d\ffig m~ng Idm trong cae bai toaD hai
chi~u stt d\1ng phddng phap phdn ttt hii'u h~n
DlIa ireD ph§n m€m Triangle vcsi thu;%ttoaD Delaunay
Refinement di xay dllng ~ng lu'oi dnh roan cho bai toaD Dam
Biin Bong va khu vllc yen b(JDam Vi~t Nam voi goc d dinh tam
giac khong nM hon 27°.
M~ng lu'oi Dam Biin Bong g6m 1.602 diim nut, 3.031
ph~n t11'va 4.633 c~nh. M~ng lu'oi yen b<JDamVi~t Nam g6m 947
diim nut, 1.769 ph~n tti'va 2.716 c~nh.
3.3 BM toaD roo hinh hai chi~u
3.3.1 He phu'ong trinh xu!t pMt. cac di€u kien bien va di€u kien
ban dh
H~ th6ng cac phu'dng trinh xu!t pMt cho bai roan hai chi€u
co d~ng:
ou ou OU at;, 1:~ 1:~
(
3 8
)
-+u-+v fv = -g-+ - +A,dU'
ot ox oy ox pQ(H+t;,) Po(H+ t;,)
s b
ov ov ov tJ(, 'y 'y
(3 9)

-+u-+v-+fu=-g-+ - +AfJ)v,
ot ox oy oy Po(H+(,) Po(H+(,)
10
ou(H+l;;) + ov(H+l;;) + ol;; =0
ox' oy ot
Bi~u ki~n ban d~u:
u(x,y,t = 0) = 0 v(x,y,t = 0) = 0 i; (x,y,t = 0) = 0
Bi~u ki~n bien:
Tren bien do, di~u ki~n bien tru'<;ftdu'<;feap d\lng eho ea
hai ~ng Iu'~iDamBien Bong va yen bCl:Y.n
I Gl =0 (3.12)
Tren bien long, d6i v~i bai loan dong ebily nam Bien
Bong, di~u ki~n bien pMt x~ Orlanski d6i v~i thiinh phh v~n t6e
pMp tuye'n du'<;feap d\lng eho ea du'Cfngbien phia bAeva phia Dam
cua ~ng Iu'~i:
(3.10)
(3.11)
a<p a<p
-+c -=0
at P an
B6i v~i bai toaD dong cbily yen bCI,do da c6 cae ke't qua
tU'bai loan nam Biin Bong nen mQt trong hai di~u ki~n bien
Dirichlet du'<;fcap d\lng de tinh toaD:
-Cho tru'~e thanh ph~n v~n t6e pMp tuye'n v~i bien:
Vo(x,y,t)IG2= f(x,y,t) (3.14)
- Cho tru'dcdao dQngmlfc nu'dcbien tren bien:
i;(x,y,t)lo2=g(X,y,t) (3.15)
3.3.2 Ap dung phu'dngpMp phh to'hifu ban vao bai toan mOhlnh
hai ehi~u
Cae thanh ph~n v~n t6c dong eM y trung blob u, v, dao

dQng mlfe nu'~e i;, cae thanh ph~n \tng sult tie'p tuye'n gi6 'tx, 'ty
du'<;fexlp xi quanh cae diim nut i,j, m \tog v~i m6i pMn to':
U=Ui <Pi + Uj<Pj+Um<Pm V=Vi<Pi+ Vj<Pj+Vm<Pm
~=i;i <Pi + i;j q>j + i;m <Pm
trong d6 q>Iii ham d~ng:
(3.13)
11
<I>j=aj +bjx+cjY
2L\
(3.16)
vdi aj = XmYi- XiYm ; bj =Ym- Yi;Cj =Xi - Xmva L\la di~n tich
cua m3i ph~n tit.
Ap d',lUgph1.fdngpMp Galerkin cho cae ph1.fdngtrinh (3.8)
- (3.10) va san khi lien ktt cac ma tr~n c\tc bQd~ ~o ma tr~n toaD
c\te cho ~ng lu'di, eu6i ding, M phu'dng trlnh trd thiloh:
[P]{~~}={Q,} [P]{~~}={Q.r [P]{~;}=pJ
(3.17)
Cae phu'dog moh (3.17) d1.f<.1egilii bhog sai pMo lito theo
thCfigiao.
3.4 BM toan m6 hlnh ba chi~u
3.4.1 He ph1.fdngmoh xua't pM!. cae di~u kien bien va di~u kien
ban d~u
H~ ph1.fdngtrinh xua't pMt co d!,\og:
Ou+uOu+vOu+wOu-fv=-got;-JL~lpldz+~
(
A au
)
+A Llu
at Ox Oy oz ox PoOxz f}z z& £
av av av av at; g 0 7- I 0

(
av
)
-+u-+v-+w-+fu=-g jpdz+- A - +A Llv
at Ox Oy f}z oy PoOy z & z & £
(3.18)
Tru'CJngnhi~t - mu6i d1.f<.1eeho tr1.fdctU'cae tili li~u. H~ s6
nhdt r6i th£ng dti'ngd1.f<.1etinh trong di~u ki~n bO qua stf trao d6i
khutch tao nhi~t
-mu6i:
A, =£'.1(::J' + (:: r
(3.19)
12
vdi f=f~(I-Rf) la kich thudc r6i va fo =K(H+Z{I-~{I+ ~)]
la kich thudc r6i phan !lng trung dnh vdi K
= 0,4 la hAngs6
Karman.
Thanh pMn th!ng dd'ng cua dong chay w du'<;1cdnh to'
phudng trinh li~n D:tc:
au +av + aw = 0
ax ay az
Phudng trlnh d6i vdi dao dQngmtfc nu'dc:
at:" at:" at:" .
-+u-+v-=w khl z=t:"
at ax ay
(3.20)
(3.21)
Bi~u ki~n bi~n:
T~i m~t biln:
Cho tru'dcd'ngsutt ti€p tuy€n gi6 ~i m~t biln t: va t~:

a
5
a
15
A ~ =~ va A -2 =.2
z az Po z az Po
(3.22)
T~i da y biln:
Dng sutt tru'<;1t~i day biln dU<;1cdnh theo c<>ngthd'c:
1~ = rpou~u2 +V2 va 't~ = rpo V~U2+V2 (3.23)
Bi~u ki~n bi~n ~i biJ r4n va bi~n long trong m<>hlnb ba
chi~u du'<;1cpMt bilu tudng tI! nhu m<>hlnh hai chi~u.
3.4.2 Su' tach mMn kMn!: !:ian troD!:m<>blnh ba chi~u
Thanh ph~n DAmngang cua dong chay trong d<;lidu'dng c6
thl du<;1cxem 18t6ng cua hai thanh ph~n:
{
U=Uh +uz
V=Vh +vz
Do d6, phu'dngtrlnh chuylo dQngding du<;1ctach ra thanh
cac phu'dogmoh bai chi~u va mQtchi~u tUdngd'ng:
(3.24)
auh=-u au-Vau +fv-g at;_JL~
f
1;p/dz+At Au
at ax ()y ax Poax
z
auz =a
(
A au
)

-w au
at a Zaz az
avh=-uav -vav -fu-gat;_JL~
f
1;p/dz+AtAV
at ax ()y ay Po By
z
avz =~
(
A av
)
-w av
at a zaz az
Cac ph\fdng trlnh (3.26) va (3.28) d\f(jcgiii b~ng bai loan
mQt chi~u thing dltng va cac ph\fdng trlnh (3.25) va (3.27) d\f(jc
giiHb~ng bili toaDhai chi€u n~m ngang.
3.4.3 Phltdng phap bie'n d6i loa do sigma
Ph\fdng phap bie'n d6i tQa dQ sigma chI th~t s1f.pM h(jp
cho khu V1f.cc6 dQ d6c day bi~n nM. Tuy nhi~n, n6 cho mQt
phltdng phap tinh ddn gian khi th1f.Chi<%nbAi loan ba chi€u. S1f.ap
d~ng ph\fdng phap bie'n d6i tQa dQ sigma vito cac bAi toaD nlt~c
DongvAkhu v1f.cven b()IAmQtphltdng phap tinh hi<%uqua cho cac
mo hlnh ba chi€u.
Th1f.c hi<%nphep bie'n d6i d, tit b€ m~t bi~n z =t; de'n day
bi~nz =- H c6 tQadQkhong thlt nguy~n d =0 vAd =-I:
13
I
X =x
I
Y =y

I z-t;
0" =-
H+t;
(3.25)
(3.26)
(3.27)
(3.28)
(3.29)
Sau khi th1f.chi<%nphep bie'n d6i sigma, ap d~ng phltdng
phap tach mi€n khong gian thAnhcac bai loan mQtva hai chi€u:
14
{
Ul =Uhl +Uol
Vi =Vhl +Vol
(3.30)
Do d6. cae bili toaD mQt chi~u 1£,)thAnh:
a1uol 1 al
(
a1u/
)
1 a1ul
att= (H+<;)2&/ Ao &/ -w ac/
(3.31)
a'vol = 1 al
(
A alv'
)
-w' alv'
ae (H + <;)200' 0 00' 001
(3.32)

va cae bili toaDhai chi~u:
aluh' , auf 1auI I al<;
- =-u - -v -+fv -g
ae axl ay' axl
0 , 1 0 al I
- g(H + <;)Ja~ dcrl + JL JQx ~dcrl + At !:1.u' (3.33)
Po cI ax Po d 00
al Vh' I (}V, , (}vI I al <;
-=-u v fu -g
ae &/ ayl ayl
0 I , 0 I I
- g(H + <;) Ja~ dcrl + ~ JQy a~ dcrl + At !:1.v' (3.34)
Po ",' ay Po cI 00
3.4.4 Ap dung phtfdng phap pMn tU'hU'uban vao hili toaDba chi~u
Bili toaDba chi~u Ia tc5ngh<jpcua cae bili toaD mt')tchi~u
(g6m 6 clog sigma theo phtfdng thing d11'ng)vil cae bili toaD hai
chien 1£~ncae clog ding sigma ttfdngtl1nhtfhili toaDhai chi~u.
So sanh giua cae bili toaDmQtva hai chi~u dtf<jctach ra tit
hili toaD ba chi~u va cae m6 hlob mQtchi~u 1£ong3.1 va m6 blob
hai chi~u trong 3.2. c6 nhung khac bi~t:
Bai toaD mQtchien dtf<jctach ra kh6ng c6 thanh phin
l11cCoriolis.
15
Bid toaD hai chi~u du<Jctach ra khong c6 thanh ph~n
trao d6i r6i thing d\tng.
Slf tach mi~n trong bai toaD ba chi~u cho th!y hic$u\tog
cua bai toaDba chi~u g6m t6ng cae hic$u«ng cua cae bili to<1nmQt
chi~u va hai chi~u. Trong d6, hic$u\tng mQt chi~u la sf! xoay
hutJng dong chclyxu6ng cae t~ng san va hic$u«ng hai chi~u la slf
trtt<Jtdong chcly~i cae bCJr4n va sf!t<Jothanh cae xoay trong d<Ji

dudng. .
San khi ap dl,mgphudng pMp Galerkin d6i vtJi m6i phh
tir va lien ke't cae pMn tir cua tOaDbQ ffi<JnglutJi de ~o cae M
phudng mnh d(ic tntng, cae bai tOaDmQtva hai chi~u e6 dl.lngnhu
san:
[A]~ a/(n)} {a~n-I) ~e + [A]~ a/(n-I) }
[A ]{va/(n) } {a~n-I)}le + [A ]{va/(n-I) }
(3.35)
va
[p ~ h/(n)} ~~n-I) }It + [p]~ h/(n-I)}
[pHvh/(n)}= ~~n-I) }It + [p ]{vh/(n-I) }
(3.36)
Trong d6,
[A] la ma tr4n vuong 6x6, cae ma tr4n cQt {Bu}va {Bv}
g6m 6 pMn tir.
[P] la ma tr~n vuong 16O2x1602va cae ma tr~n cQt {Qn}
va {Qv}g6m 1602 ph~n tircho bai toan DamBien Bong. so' phh
ttr tu'dog \tog cua chUng cho bai toan ven bCJl~n lu<Jtg6m 947x947
va 947.
Thanh pMn v~n t6c thing d«ng ~i clog day du<JCHnh ttt
di~u kic$ndQnghQc:
16
aH aH
Wb = -Ub- -Yb-
ax ay
va ding du'<Jcap d1}ngphu'dngphap ph~n hi'hU'uh~n.
Thanh ph~n v~n t6c thing d11'ng~i cac clog tren du'<Jcunh
tft'phu'dng trlnh lien t1}c(3.20) va du'<Jcap d1}ngphu'dng phap sai
pMn hU'uh~n.
Bi~u kic$nbien dQnghQc tren M ~t bi~n (3.21) du'<Jcap

d1}ngd~ unh dao dQngm1!cnu't1cl;;va cling du'<Jcunh theo phu'dng
phap ph~n tli'hU'uh~n.
Bu't1cthiJi gian trong bai toaDmQtchi~u L\e Rhohdn bu'dc
thiJi gian L\ttrong bai toaD hai chi~u. MQtvong l~p cua bai toaD
hai chi~u c6 nhi~u vong l~p bai toaD mQtchi~u. Do d6, s1!tach
mi~n khong gian d~ lam ro hic$u11'ngbai toaD ba chi~u ma con
tang t6c dQunh toaD.
3.5 St1li~n k~t giila m6 binh Dam Bi~n D6ng va m6 binb ven 1XI
Dam Vi~t Nam
Bai toaD yen b(J Dam Vic$tNam du'<Jcth1!chic$nvdi di~u
kic$nbien long la ktt qua nMn du'<JCti'tbai toaDDamBi~n Bong.
Chu'dng tdnh cho bai toaD Dam Bi~n Bong du'<Jcyilt vt1i
thu t1}cghi l~i ktt qua unh toaD ti'tnggi<'Jlen mQt ~p tin. Gia tri
dao dQngm1!cnu'dc l;;ho~c thanh pMn v~n Wcphap tuytn Vntren
bien long cua bai toaD yen b(J DamVic$tNam c6 du'<Jcbhg cach
sd'd1}ngt~p tin ktt qua d~ dQCcac gia trj san ti'tnggi<'Jdnh cung
vdi cac ham nQiguy theo khong gian va thiJigian.
Cac bai toaD mQtchi~u va hai chi~u du'<Jcth1!chic$nmQt
cach dQcl~p, cac thanh ph~n Ubva ~ tren cac clog cling du'<Jcth1!c
hic$ndQcl~p Den kha Dang l~p trlnh song song tren cac ~ng may
tfnh la hic$nth1!cnhhm tang nhanh qua trlnh dnh toaD.
(3.37)
17
CHUdNG 4:
CAC KET QuA TINH TOAN vA NH!N XET
Trong m6 hlnh hai chi~u, bu'<1cth<1igian dnh .:1t= 6O0scho
bai roan DamBien E>6ngva .:1t= 240scho bai loan ven b<1.Trong
m6 hlnh ba chi~u, bai loan thing dti'ngmQtchi~u va bai tmin DAm
ngang hai chi~u c6 bu'<1cdnh I~n 1u'<;1tla .:1r= 25s va .:1t= 6OOscho
bili loan Dam Bi~n E>6ng.E>6ivdi bai loan ba chi~u ven b(1cae

bu'<1cdnh I~n 1u'<Jtla .:1r= 30s va .:1t= 240s.
4.1 Cae ke't qua cua b8i toaD hai ehi~u
T~i miii Cll Mau lu6n c6 mQt h~ th6ng dong char m~nh
trong cae thang gi6 mua. Gifi'aBi~n E>6ngva vinh Thai Lan lu6n
c6 h~ th6ng dong chay xoay. Stf xu!t hi~n cae xmly d~u lien quaD
d6n stf tu'dnglac eua tru'<1nggi6 va y6u 16dia hlnh cua khu vf!.cva
e6 th~ giai thich sf!.xu!t hi~n cae xoay ireD cd sObao roan th6ng
1u'<Jngnu'detrong d~i du'dng.
H~ th6ng dong chay ~nh ven b(1DamVi~t Nam tUNha
Trang d6n miii Cll Mau, hu'<1ngv~ Damtrong tru'<1nggi6 mua d6ng
- Me va hu'dng leu Me trong tru'<1nggi6 mua Hiy - Dam.
T~i khu vtfe Hiy - Dam fir miii Ca Mau dtn dao Phli Qu6e
c6 ffiQth~ th6ng dong chay m~nh vito thang 7. Tuy nhien, v<1i
tru'<1nggi6 nn)a d6ng
- Me (thang I), dong ehiiy ndi d:iy l~i c6 gia
tri nM hdn rtt nhi~u.
MQt xoay Rho hlnh thilnh ch~y dQe su6t b(1bien fir Nha
Trang d€n C~n Gi<1trong tru'<1nggi6 mua Hiy-Dam va sri tdn ~i
mQtdong chay nghich v~ hu'dngDam~i d:iy trong tru'<1nggi6 mua
Hiy- Dam.
18
Dougduiy tMug 1
V.n t6<:- 2Ocmls
Mile n~c
.
~
1
Ifmh 4.8: Dong eMy trung binh va ml/e mille thang 1
Doug cluiy tbang 7
V$nt6<: - 2Ocmls

Mite nulk
-
Ifmh4.10:DOngehiytrungbinhvaml/enlillethdng7
19
Tht!e nghi~m HnhtoaDvdi hai di~u kic;nbien Vn(x,y,t)eho
tru'de va ~(x,y,t) eho tru'de dO'i.ydibai toaD yen bCl.Trong do, cae
thanh ph~n v~n to'e phap tuye'n Vn(x,y,t) va dao dQng mt!e mtde
~(x,y,t) tren bien long du\1erot tU'tai li~u Hnh eua bai loan nam
Bi~n Bdng. Ke't qua nh~n du'<jeeho thty di~u ki~n bien vdi dao
dQngmt!c nu'de~(x,y,t) du'<jeeho tru'dctren bien co dQ6n dinh eao
hdn.
4.2 Cac k~t qui cUa bai toaD ba chi~u
V~n sii' dt}ngdi~u ki~n bien dao dQng mt!e nu'de ~(x,y,t)
du'<jerot tU'tai li~u tinh loan dong ehay Dam Bi~n B6ng vao bai
loan yen bi1.
Khu vt!c tU'eii'a sdng H~u Giang de'n miii Ca Man ludn co
mQt M thO'ngdong ehiiy ml}-nh.Dong ehay ~ng ~t dl}-tde'n
31,5emls vao thang 1 va khoang 23,5emls vao thang 7.
Dong chay tl\ng m4t
tbiing 1
H'mh 4.30: Dong chdy tIlng milt thang 1 ven b(j nam Viit Nam
20
H'mh 4.40: Dong chiy tilng mijt thang 7 ven bu nam Vwt Nam
Hai m6 hinh hai chi~u va ba chi€u ddng nhit cho k€t qua
tudng t1fnhu nhau v€ hudng, v4n t6c dong chciy ding nhtt dao
dQngmlfc mtdc. Tuy nhien, slfkhae bi~t cM ytu gifta hai m6 hinh
tlnh d thanh ph~n v4n t6e tl1lDgbiBb khi c6 dong ehciy clng m~t
Phat tri~n ~nh.
4.3 So sanh klt qua v8i cae tAi Ii~u tinh tmin kluic
Nhii'ngdi~m phu h<;1p:

- Huang va dQ Idn dong ehciy yen bC1d6ng Dam be}trong
tru'C1nggi6 thang 1 va 7 (httdng v€ Damvao thang 1 va hudng leu
Me thang 7)
-Httdng va dQ Idn dong ehciyvung bi~n fay DambQ. C6
gia trj Idn vao thang 7 nhung l~i nhiSvao thang 1.
- Mfii Ca Mau lu6n c6 v~n t6e dong chciy Ian trong cae
thang gi6 mua.
21
-Sf! hlnh thanh cae xoay thu4n va nghjeh vinh Thai Lan
va gifi'aDamBi~n Bong trong cae thang gi6 mila.
Cae di~m khong phil h<;1p:
-H~ th6ng dong ehiiy vilng Cdn Gi(j, ed'a song Sai Gon
trong tru'(jnggi6 thang 7. Mi).edil khu vf!e nay e6 nhi~u song, tuy
nhi{;n cae mo hlnh ttnh eh1fath~ hi~n du'<;1cvai tro eua cae song
l{;n
M th6ng dong ehiiy.
- Vi trt cae xoay trong tru'(jnggi6 ehuy~n mila.
4.4 M()t viti nh$n xet v~ tinh 6n dinh va phu'dng phIlp tinh CUB
cae m6 hinh Huh toaD
M;~mglu'~i du'<;1edy df!ng va kich thu'~e eua cae pMn tii'
n!m tr{;nbien anh hu'dng r!t !dn d6i voi sf!6n djnh eua bai toaDsii'
dq.ngphu'dngphap ph.in tii'hfi'uh~n.
Sf!phil h<;1pgifi'atru'(jnggi6 va di~u ki~n bi{;nlam gia tang
tinh 6n djnh eua bai tmin. Trong tr1f(jngh<;1psf!phil h<;1pnay kMng
t6t, sf! thay d6i kich thu'~e pMn tii' n~m tr{;n bi{;n la mQt trong
nhfi'ngphu'dngeach lam bai toaD 6n djnh t6t hdn (~ng lu'~idQc
bien long eua bai toaDven b(JDamVi~t Nam).
Sf! ap d\mg cae di~u ki~n 6n djnh Courant - Friedrichs -
Lewy (Llt:s;
~) eho bai toaD hai chi~u vao m~ng lu'~icae tam

v2gH
giac chi mang mQt
ynghla tu'dngd6i.
Sf! 6n djnh eua ~ng lu'~i tam giac phq. thuQcnhi~u vao
di~n tfch eua cae phh tii'va dQs~u day bi~n. MQtso'm~ng lu'~idii
du'<;1cthie'tke'ma trong d6 sf!hdn kern v~ di~n tich eua cac ph~n tii'
e6 th~ l{;nde'n khoang tir vai ch1,lcde'n vai tram Idn ph1,lthuQcvao
dQs~u day bi~n.
22
4.5 Cae h\1neh6 ena phddng ph3p tinh
Phu'dng phap pMn tIt hii'u vAncon c6 nhung nhu'<,1cdiim
quaDtn;mgla kh6i lu'<Jngtinh tmin va th<1igian tinh r(t IOnso vdi
cae phu'dngphap sai phiin hii'uh~n.
Di kh4c pht}ctlnh tr~ng nay, c6 thi sIt dt}ng cae phu'dng
pMp xtt ly ma tr~n di nit ng4n th<1igian tinh hay sIt dt}ngphu'dng
pMp tach mien to.'bai loan ba chien thanh cae bai toaDmQtchien.
511ap dt}ng cae di~u kit$nNeumann va pMt x~ Orlanski
lam cho bai loan c6ng k~nh vi them mQt vong tinh toaD cho cae
pMn tIt tren bien va xu(t hit$n nhi~u sai so' trong qua trlnh tinh.
MQt~ng lu'dicac tam giac b(t ky tren bien long g~y Den sl1phU'c
~p trong vit$cap dt}ng cac di~u kit$nbien nay, th~m chi, khong
thi ap dt}ng du'<,1c.Do d6, di ap dt}ng du'<Jccac di~u kit$n
Neumann va.pMt x~ Orlanski cAnphai thitt kt l~i ~ng lu'disao
cho cac phSn tIt c6 kich thu'dc tu'dng d6i den d~n ~i bien long.
M~c du m~ng M1i da du'<Jcdy dJ1ngl~i nhu'v~y nhu'ngvAnkhong
lam giam sl1phU'ctC;1Ptrong qua trlnh ap dt}ngchUngva.obai toaD
mo hinh.
511ke'th<,1pcac phu'dngphap tinh, sai phiin hii'uh~n cho bai
loan flam Biin Dong (ho~c ca Biin Bong) va pMn tii'hii'uh~n, vdi
tinh HnhdQngtrong sl1thitt l~p ~ng lu'di, cho bai loan yen b<1c6

thi la mQtphu'dngan t6t khi thl1chit$ncae bai toaDmo hinh.
Phu'dng pMp bie'n d6i tQa dQ sigma chi th~t sl1pM h<Jp
cho cae mo hinh tinh mAdQd6c day biin c6 sl1bitn thien nM. Di
tinh loan du'<Jcdong chay cac tSng san cua khu vl1c Biin Dong,
phep bitn d6i tQadQsigma c~n du'<Jcthay the' bAngmQtsd d6 tinh
pM h<Jphdn.
23
KET LU!N
Nhfi'nglu~n di~m mdi ma lu~n an da:d~t du'<;1e:
1. Giai quytt du'<;1ebai toaDdong cMy ven 1x'1DamVit$tNam troog
di~u kit$ndia hinh phU'c~p, g6m ca vuog bi~o pbia d60g va pbfa
my DambQvdi bien long fQOgva dai.
2. Ap d1;l0gphu'dng pMp s6 trj pMo tt.i'hfi'uh<;tovao cae m6 bioh
hai ehi~u va ba chi~u cho cac bai loan DamBi~n B60g va ven b<'1
DamVit$tNam.
3. Bhng tb1;l'cnghit$ms6 trj, so saoh nnb 6n dinh cua hai di~u kit$n
bien: cho tru'dc m1;l'cnu'de l;IG=f(x,y,t) va cho tru'de thaoh pb§n
pMp tuytn cua v~n t6e ~i bien VnIG=g(x, y, t).
4. Bhng th1;l'enghit$ms6 tri, so saoh ktt qua doh dong chiiy truog
biBbtheo hai m6 hinh hai cbi~u va m6 hioh ba chi~u.
5. 51;1'tach mi~o kh60g gian cua rei toaD ba chi~u thaoh cac bai
loan mQtehi~u va hai cbi~u de' rut ngdn th<'1igian tinh va lam n6i
b~t cae hit$uU'ngmQtchi~u va hai chi~u trong bai loan ba chi~u.