3-D numerical simulation of the tidal circulation in the gulf of Tonkin, Vietnam

Vietnam Journal of Mechanics, NCST of Vietnam Vol. 23, 2001, No 2 (116 - 128) 3-D NUMERICAL SIMULATION OF THE TIDAL CIRCULATION IN THE GULF OF TONKIN, VIETNAM PHAN NGOC VINH(l), NGUYEN KIM DAN(2) (l) Institute of Mechanics, 264 Doican, Hanoi, Vietnam <2l Laboratoire de Mecanique, Universite de Caen, France ABSTRACT. The purpose of this paper is to present 3-D numerical simulation of the tidal circulation in the Gulf of Tonkin. A sigma-coordinate system transformation is used to make possible a total fit ting between the computing point-grid and the bottom topography as well as the free water surface. A turbulence-closure sub-model K-L which permits the parameterization of the turbulence mixing is also included. The studied domain, the whole Gulf of Tonkin, extends from the coastal zone of Quang-Ninh into ThuaThienHue province and as far as Hai-Nam (China) island seawards. The model have been calibrated and verified by the observed data at six different stations for a three and seven-day periods. The results are in good agreement with the obseved data. The kinetic energy distribution was eonsidered. Keywords. 3-D numerical simulat ion, finite-difference scheme, the Gulf of Tonkin. Introduction The Gulf of Tonkin, one of the two largest gulfs in the South China Sea, is situated between Hai-Nam Island of China and the north coast of Vietnam. This is a rather shallow sea area with the average depth of about 45 m and the maximum one of 100 m at the mouth ~ (Fig. 1). It is known that the tide regime. ~ 19 is diurnal nearly in the whole gulf. The largest tide amplitude can reache 2.5 m at the head of the gulf. 18 17 1 6 1 1 The aim of this paper is to present a 3-D numerical study of the tidal cir- culation in the Gulf of Tonkin. In the model, the Navier-Stockes equations, which are simplified by the hydrostatic approximation and by Boussinesq's one . for the density distribution, have been solved with the help of a two-mode Fig. 1. Depth contours Map the Gulf of Tonkin technique: the water levels are determined in the external mode and the velocity 116 and scalar variables are then evaluated in the internal mode. The advect.ion terms have been handled by a characteristic method to prevent numerical oscillations and artificial diffusions (Nguyen and Martin 1988). I. MATHEMATICAL MODEL 1. Governing equations The governing equations are ~: follows: Continuity equation: (1.1) Moment.nm equations: au au au au 1 {) p {) ( au ) -+u-+v-+w-+-- = fv+- KM- +Fx at ax ay oz p ax 8z oz ' (1.2) av av av av 1 {) p {) ( av ) -+u-+v-+w-+--=-fu+- KM- +F: at ax ay ' oz . p oy az oz YI (1.3) aP az =-pg, (1.4) where, the x, y axes are horizontal and the z axis is taken positive upwards and the coordinate origin is placed at the mean water level; t is time variable; u, v, w are velocity components in the x, y and z direct.ions, respectively; Pis the pressure which can be obtained by: 0 P = Po + Po9T/ + g j pd~ (1.5) z where, pis the in-situ water density; p0 is the reference water density; g is the accel- eration of gravity; j is the Coriolis parameter, defined as j = 20 sin, where n is the angular frequency of earth rotation and¢ is latitude of the studied location; KM is the vertical turbulent viscosity coefficient; Fx, Fy are the horizontal diffusivities, which are defined as follows: (1.6) where, AM is the horizontal turbulent diffusivity, which is assumed constant in the present study. 2. Initial conditions At the initial time t = 0, velocity components of u, v, w, surface water level rt and other variables are given. 117 3. Boundary conditions - At the water surface: - At the bottom: (3.1) (3 .2) wher~, Us, Vs, Ws are velocity components at the water surface; ·ub, vb, wb are velocity components at the bottom; ( Tsx , Tsy) is wind stress at the water surface and ( Tbx, Tby) is bed shear stress; 77 is the water surface elevation; h is the bottom depth. - At the land boundary: The velocity co:m,ponents normal to walls are null, i.e. Un = 0. In addition, for the tangential component of velocity, a no-slip condition at the wall is used. - At the open _!)Oundary: Commonly, at the open boundaries, tide surface eleva- tion is a priori prescribed as Dirichlet's conditions at all times. 4. Turbulent closure sub-model K-L The governing equations contain the parameterized Reynolds stress and the flux terms, which take into account the turbulent diffusion of momentum, salt. The parameterization of turbulence in the model described here is based on the work of Li et al. (1997). This is an one equation sub-model, in which the turbulence kinetic energy, k has been determined from a transport equation as follows: 8k 8k 8k 8k [(8u)2 (8v)2] . _ -+ u-+ v-+ w-=2KM - + -at ax 8y az az az a ( 8k) 2gKzs 8p +-KM- +----E+Fk 8z 8z Po 8z (4.1) with Fk = :x (AH~~) + :y (AH~~) and the turbulent mixing length, L has been computed from the following equations proposed by Nihoul et al. (1989): k2 c: ~ ak 16KM, ak ~ 1.0, ( 4.2) with K = ~ ,.,, i /4 "k L · L (l R )L ( ) M 2 uck Y K', mi m = - f mO Z , here, Lmo(z) .is the mixing length in the neutral case. We used the formula proposed by Escudier (1966): Lmo(z) =min [Ka(77 - ZJ ), K(z - ZJ ), K(77 - z)], ( 4.3) 118 where z1 is the bottom elevation, K is the Karman constant (= 0.4) and a is a coefficient (= 0.19). R1 is the flux Richardson number: R1 = - [(8u)2 z (8v)2] · KMPo - + -8z oz (4.4) The boundary conditions for equation (4.1) are (Galperin and Mellor 1990): (4.5) with Bis an empirical constant and taken as 16.1, Uw is the wind velocity .and u. is friction velocity at the bottom: u,.. = (Tb/ p) 112 , Tb is the friction stress. At the open boundaries, the energy flux is considered equal to zero: (~~' ~~) = o. At the land boundaries: klland = u!/ JG:; Cµ is a constant (= 0.09), (Rodi, 1980). Kzs is defined from KM (Nihoul et. al, 1989) : Kzs = 1sJl - R1 KM; {s is constant ( = 1.1). 5. Vertical coordinate transformation It is desirable to introduce a non-dimensional vertical coordinate, which trans- forms both the surface and the bottom into the coordinate surfaces. The relationship bet.ween the old coordinate system and the new one is (Blumberg A. F. and G. L. Mellor, 1987): z -ry a=-- h+ry' x* = x, y* = y , t* = t, (5.1) where, a ranges from 0 at z = ry to -1 at z = -h; H = h + rJ is the flow depth. The derivative of an arbitrary variable G in the old system can be dei:ermined from the following relationships: ac = ac _ ac Ax ax ox* 8a ac = ac _ ac Ay f}y f}y* 8a aG 1 8G (5.2) 119 where, (]' 8H 1 8TJ Ax=--+--H ox• H ox•' A new vertical velocity can now be defined as: w = w -uAxH - vAyH -ArH, which transforms the boundary condition (1.6) and (1.7) into w = 0 at. a = 0 and (1 = -1. Equations (1.1)+(1.3) and (4.1) may now be written as (all asterisks will be dropped for notational convenience) OTJ auH avH aw _ 0 8t + Bx + 7iiJ + 8a - ' (5.4) 8uH + au2 H + ouvH + ouw + gHOTJ = _ fvH +!.___(KM Bu) Bt ox By Ba Bx · Ba . H Ba 0 0 gH2 a ; · gH fJH J op --- pda+-- a-da+HFx, p ax p ax Ba (5.5) ovH + ouvH + 8v2H + 8vw + gHOTJ = fuH +!.__(KM ov) ot ox oy oa oy oa H OCT 0 0 gH2 a j gH aH j. op --- pdCT+-- CT-dCT+HFy, p f)y p oy aa (5.6) 8Hk + BuHk + 8vHk + owk = 2KM -l(8u)2 + (8v)2] ot ox oy 8a H 8a 8a + ~ (Kzk ok) + 2gKzs op_ He+ HFki OCT H OO' Po OCT (5.7) where, the horizontal viscosity and diffusion terms are defined as: OTxx a ) OTyx a (A ) HFx = ~ - £l(AxTxx + -8 - -8 yTyx uX uCT y a OTyy a ) OTxy a (A ) H Fy = oy ~ OCT (AyTyy + ax - {}a xTxy (5.8) Bqx a ( ) 8qy 8 (A ) H Fk = ox - oa Axqx + By ~ Ba yqy ' with 120 6. Mode splitting Technique It is desirable in terms of computer economy to seperate out vertically inte- grated governing equations (external mode) from the full vertical equations (internal mode). Thus, the governing equations have been solved by a two-successive-mode technique: the water-surface elevations are calculated in the external mode by a 2-D Saint-Venant equation (Nguyen and Ouahsine, 1997), and then, the scalar vari- ables, including the components of velocity vectors, will be determined in the internal mode. The splitting technique in terms and in directions combined with a semi-implicit finite-difference scheme proposed by Nguyen and Ouahsine (1997) is used here to solve the depth-averaged Saint-Venant equation in the external mode. In the internal mode, diffusion terms have been discretised by a finite-difference scheme, which is explicit in the horizontal x and y directions but implicit in the vertical. This is to overcome the restriction of the time steps due to numerical stabilities caused by the small vertical grid-spacings. The convections terms have been calculated by a characteristic met.hod (see Nguyen and Mart.in, 1988) to prevent. numerical oscillations and artificial diffusion. II. APPLICATION The computation do!Ilain covering the whole Gulf of Tonkin extends from 105°30'E to 110°30'E and 16°00'N to 21°45'N is discretized by a 116 x 144 x 10 uniform grid. The horizontal grid spacings are 4050 m in the x-direction and in the y-direction as well. The vertical distribution of grid-points is irregular. Six data sets observed in the field survey in 1993, 1994, 1996 and 1997 have been used to calibrate and verify the model. Amongst them, the two first data sets c_ollect.ed in a 3-day and a 7-day field surveys at stations: T10-LeThuy96 and T20- LeThuy96 have been used to calibrate the model. The three other data sets of a 7-day period observed at st.at.ions: T14-HaiTr~eu93, T20-HaiTrieu93, T20-CuaSot.94 and on€ data set of a 3-day period, T10-LeThuy97 have been used to verify the model. Location in longitude and latit.ud,e of J.he observation stations and of the periods of observation are shown in Table 1. Calibration and verification Several benchmarks tests .(hydrostatic case and soliton case) were done to valide the mode (see [10)). The calibration have been done by adjusting the horizontal turbulent viscosity and the Chezy coefficient. Kalkwijk (1985) estimated that: for a sea flow of mean ve- locity U = 1 rns- 1 , and of depth h = 50 m, with the Chezy coefficient., Ch= 70 m2s-1 and the horizontal turbulent viscosity is given by AH = 13.4 m2s-1 . Values of An · will decrease when the water depth diminishes. In the present study, as the sea depth mainly varies from 20-45 m, a uniform value of .the horizontal turbulent viscosity, 121 AH = 10 m2s-1 is taken. Different values of the Chezy coefficient were adjusted to fit the model solution into t.he measured data obtained from 2 observation stations T10-LeThuy96 and T20-LeThuy96 in 1996 and the best value of Ch is 65.0 m2s-1• Af. the open boundaries, tide water level prescribed as Dirichlet's conditions at all times is determined from TIDE-FLOW2D based on the system of 2D shalow water non-linear equations. Table 1. Location of the observation stations and the periods of observation Location No. Station Observation time Longitude Latitude 1 T10-LeThuy96 106°54'00" E 17°15'00"N 15h 31/07/96-T12h 03/08/96 2 T20-LeThuy96 · 106°54'35"E 17°15'08"N 06h 28/07 /96-;-05h 04/08/96 3 Tl4-Hai'frieu93 106°19'35"E 20°04'14"N 16h 15/07 /93-T15h 22/07 /93 4 T20-Hai'frieu93 106°21'2l"E 20°02'36"N 15h 15/07 /93-;-14h 22/07 /93 5 T20-CuaSot94 106°04'00"E 18°30'00"N 07h 22/05/94-;-06h 29/05/94 6 T10-LeThuy97 106° 54 '00" E 17°15'00"N 08h 30/06/97-;-24h 02/07 /97 Figures 2a, 2b, 3a and 3b present the computed velocity values as a time se- ries of a 3-day period frorri 15h 31/07/96-T12h 03/08/96 and of a 7-day period from 06h 28/07 /96-;-05h 04/08/96 in comparison with the observations at station T10-LeThuy96 and T20-LeThuy96. A good agreement between the computed and observed values in both amplitude and phase was obtained in the calibration case. Five other data sets have been used for verification of the model, while preserving the model configuration obtained from the calibration step. Fig. 4a-;-7b show a comparison between the computed velocity values and the observations. A good enough agreement of amplitude and phase is also again obtained in the verification case, especially at stations T14-Haitrieu93 and T20-Haitrieu93 (see Fig. 4a, 4b, 5a and 5b). 15h 21h 3h 9h 15h 21h 3h 9h 15h 21h 3h 9h 3117 . ,__..;.1:.:;;_16 -~__,..--,--'2'-'-/6 --=,-----..,.,316 --Calculated -. - - - - - - - Observed Fig. 2a. Comparison of velocity intensity at St. TlO-LeThuy96, 15h31/ 7-12h3/8/ 96 122 dog nie 360 240 120 ---4: \: 0+-.....-....,.....;.........---.---..---.~ ........... ....--.....-~-,.- 15h 21h 3h Sh 15h 21h 3h Sh 15h 21 h 3h Sh 3117 316 l.---_-_-_-c-.1c-u_h_t• d- __ - __ - __ - __ - 0-bs- trv- t--,d I 1 /6 216 Fig. 2b. Comparison of velocity direction at St. TlO-LeThuy96, 15h 31/7-12h 3/8/96 cmls 30 20 . .. .. 10 0 6h 18h 6h 18h 6h 18h 6h 18h 6h 18h 6h 18h Sh 18h 2817 2917 3017 31(7 . 1.S 2.S 318 --- Calculated · • • · • • • • Observed Fig. 3a. C~mparison of velocity intensity at St. T20-LeThuy96, 6h 28/ 7-5h4/8/ 96 cmls 30 16h 4h 16h 4h 16h 4h 16h 4h 16h 4h 16h 4h 16h 4h 1 517 1617 1 717 1 817 1 917 2017 2117 2217 --- Calculted ... . .... Observed Fig. 4a. Comparison of velocity intensity at St. T14-HaiTrieu93, 16h 15/7-15h 22/7 /1993 cmls 30 15h 3h 15h 3h 15h 3h 15h 3h 15h 3h 15h 3h 15h 3h 1 517 1 617 1 717 1 817 1917 2017 2117 2217 --- Calculated . - . - . · · · Observed Fig. Sa .. Comparison of velocity intensity at St. T20-HaiTrieu93, 15h 15/ 7-14h 22/7 /1993 degree 360 240 120 r- 18h 6h 18h 6h 18h 6h 18h 6h 18h 6h 18h 6h 18h -1202 17 2917 3017 3117 118 2.S 3.S ---Calculated · · · · - - - - O bserved Fig. 3b. Comparison of velocity direction at St. T20-LeThuy96, 6h 28/7-5h 4/ 8/96 Degree 16h 4h 16h 4h 16h 4h 16h 4h 16h 4h 16h 4h 16h 4h 15171617 1717 1817 1917 2017 2117 2217 --- Calculed . . . . .. .. Observed Fig. 4b. Comparison of velocity direction at St. T14-HaiTrieu93, 16h 15/ 7-15h 22/ 7 / 1993 Degree 360 240 120 1 h 3h 15h .3h 15h 3h 15h 3h 15h -1201 17 1617 1717 1817 1917 ---Calculated . - - - - - . - Observed Fig. Sb. Comparison of velocity direction at St. T20-HaiTrieu93, 15h 15/ 7-14h 22/ 7 / 1993 Fig. 8 and 9 present the velocity fields on the surface, at the mid-depth and on the bottom at LW(Lowest water)+6 and HW(Highest water)+6, respectively. Obviously, tide currents are fairly uniform and their predominant direction is parallel to the shore line. The flow becomes stronger and more complicated near the Strait 123 of QuynhChau and in the South-West. of the coast.al zone of HaiNam island due to the irregularity of the topoporaphy. 30 omls . ' • " 20 10 0+-~.......;,,.--..,-....:,........;..,~.i,.--.-~~~-.--....~.,1---.--4 7h 19h 7h 19h 7h 1Sh 7h 1Sh 7h 19h 7h 1Sh 7h 1Sh 22S 23S 24S 25S 26i5 27 i5 28i5 ---- Calcu la t•d Ob u.-ed D•grH 360 240 120 !Sh 7h 1Sh 7h 1Sh 7h Sh 7h -12 i5 23S 24i5 25i5 26i5 Sh 7h 1 h 7h !Sh 27S 28i5 ---- Calculat•d - - - - - - - - Observ ed Fig. 6a. Comparison of velocity intensity at St. T20-CuaSot94, 7h 22/5-6h 29/5/1994 Fig. 6b. Comparison of velocity direction at St. T 20-CuaSot94, 7h22/5-6h 29/ 5/ 1994 cm.ls 30 8h 14h 20h 2h 8h 28i6 14h 20h 2h 8h 2Si6 14h 20h ----Calculated . . .. . . . . O b s e rve.d Dt grtt 3601 -' . ; ' h[Hb 240 ; ---- .. .. :. : -- --- -- · .. . . ' ro~. . . ~ •' 0 . ' ' 8h 14h 20h 2h 8h 14h 20h 2h 8h 14h 20h 2816 2Si6 I --- Calculated Obs e rved I Fig. 1a. Comparison of velocity intensity at St. T l O-LeThuy97, 8h 27 / 6-24h 30/ 6/97 Fig. 1b. Comparison of velocity d irection at St. TlO-LeThuy97, 8h 27 / 6-24h 30/ 6/ 97 On t h e bottom . . .................... .. . .. 1 1/ \ ~: ~: :: : : : : : :: : : : : :: : : : : :: : : : : :: : : ~~ ~~, : :::::::::::::::::::::::::::: : :::::.._~~ "'''' ' '''''' "' ' ''"''' ' '' ' '' ' __....,,.~ . . ..... , . .... 111'1••••"''''" '' '' - ........ . ,.,,,,,,, .................... , . . ...... 111111111111111 1 11 1111111 .. , •• • •• ' ' '"''"" ' " ' '"'11111111111•• ••,.•••• ''""""''''''11\ll•Ullllll •I••"'' . : :::::~:~:::~::::::::::::::::ii j l; I' ...... "'"""""""""'""' 'ull ......... ,.'"''''"\\\\\\\\\\\\\\\\}~j :::::~~~:~~~~ ~~~~~~ ~~ ~ ~ ~~~~~\\\\. ~ ............... "''' '" '''"'''"'"''''""'""'" -''"'''''' '''''"'''''f'..''''"~_.....___ '"''''"''''''"''''""'''''- --· -· · '""''"'''''' "'' ''""'''''---- ···· ''''"'"''''''"''''""'''"'·-.......... _ ... . ,,,,,,,,.;:,,,, .... ,,,, ... ,, .. ,_, __ ........ -... . ........... .............................................. _ ........ -... . .................................................... _ .......... _ ... . ......................... , ....... , .. .............. _ ...... '".-···· ,,..,,_, ............................ _.. ...... .. _ ... . 30 cm/ • .......... ,, ............. ........... _ ........... . . ''''"'''''"''" .... -.. .... .. .. - ... . At the mid dept.h On the sur face -----..---- -----------, ""'" ' "'' ' r" ' ''""'''" 11\lll•I HUll lllHl""'"lil ''' '"" '""''''" ''''"""" " \\\~ ''''' '""""'''' ''''''"1111""'~'1 \1111111111111111111111"'"'""''" ~ ~:::::::::::::: :: ::::::::::::: :~ , • 111\ I I I II I I I I Iii II II JI 1111 '' ' '"--r---- • • • • • 111 \I I\\ I l I I Ill ti I/ H Ill I •H• • • -_, , ,.,, , 111\\ \\Hllllll llll ll ll / IJ /11;,. , .. ""\\\\\\\\\\\\\\\ll/tll/ff/J/1/111,,u .::::::::::::i::::n:1111il["'fv· o\1\\\\\\\\\\\\\\\\\\\\\\1 '""""""'"\\\\\ \ \\\\\ .... "'"'"""''"''''\II '''''"''''"''''"'''~' ~~~~~~~~*"\\~\\ .,.a......''""'"""'"\! . --->--'"'"""'"''~~ :--~-......__ ... '""'"'"'"~'"''''''~ ..... . '"""'"'"'~'"''''''' ..... , .. 1\\\\\\"'"'''~'''''''~ '''' ''""""'''~~,,,,,,,,........_~_...,.,, "''''"'''''~''''""''~''~-........ -,,,, -'''''''''"'''''''''''''t-..~-.... ........ ~,, \' '(\'''"~'''''''''""*'"''~' ...... '''' ,,,,,,,,,,,,,, .... ~-.. .. . ,.....,~, .... ,,"''''"""'~ .... . 30 cm/11 ' "-~:t~---: : :: """ " ' '''"' "' '''""'' 1 I;;:~:: : : :: : : : : :: : : : : :: : : ~ ;: f '' '''" '"""" ' "' ''' "' ' " 11111'~! \l11111111•r111111111111.,1111 11 \\\~· 1 \11 1 111111111111111111111u1111~"'. 111111111111111111111 1 1111111'1 "'~ 1111111 1 1 1 11111 tlllll/l l ll l tl•• .. :::::::::~::::::~::::::~~:::::::::~ . . ... 11111\\\\111111\ 11//1/lll//ll;;,,._ 1• 1 11 1 11\\\ \ \\\\\\\\ 11 /11/f/J// ///N;_,~# ::::~::::::::i!§il!!lllL'f' .:::::::::::~~~~~~~l~l'l'l'I· ; w, "~~~~~~~i~1~ -~''"~""""' .. -~~\\\\\\\\\\'\~ ~'ll§ ;:,_ ... \\\~~~~~~,~~~ ~~~~ '''''"~"'''""''"''~ ~'''' \~~~~~~~~~~~~ -~~'''''~''''''''''"*'"""""''''-''b."' . "'''"'''~{\...''''~ ................. ,,,, ""'''~'"''''~-.... . , ...... ,,,,,,"'''''~----·-· · 30 cm/• ~~" _:::.:: Fig. 8. Velocity field at 09h 30/ 7/ 96 (LW+6) 124 On lhe bottom At the mid_ dliplh On the 1urfa~e , •... , ''"" "'IN1111• *" V;"I' HIHIHl#l#Hllll_,,,,'11'/ 11111111111111N,,Ulfllll/I 111111111, """'""'"'""' \lllfll/lllNllllllllllllllllH/llllW V11 1" 1111 U1111111111111101 1tllll\\\' """"""""'"""'""'''111 1 1\\~~ W llllNIUIN1l1lllllllllll 11111 1 I I\~~\\.. , -~,:::::~~~~~:~:~~:~:!::::::::::::z;: ~~~ '""""''""""'""'"'""""_,, •HllllllllJlllllll/ 11//11/NllllHIHHI ' 11111 11 11fl l llllllllllllllt lllU/llllll lllltlll l lllllflfll/llUl/lllllllllUI :: : ::: : :~: :: : : : : :: : :: :rn::~;Nlll/~ '' '''"''''"''''"'''''"''''f,j)t\l' ''"\ l llllUUl l\UHll\ llll llj \ I ••111111111111111011 1111111111 k 111\\\\ \\\\\\\ H\\1\\\\\ I \\\\\ IH \\\\\\1\ \ \ \ \\\\\11\ \\\\\\\\\ \ .,..,\\\\\\\H\\\11\\\\\\\\\\\\\\'-: """'' """"'\\\1111\H\'I\\\\\""'\''" ... -"' ••• ., ,,, \\\\\1\\\ \\\ \\\\\ \ \1\\"""'""''''-"· • • ••••• • 111\"\\" lll \YI\\\\"""""""'""'"'.,.. .. " . . ... ,., , 1 1\ \ I 1 1\\ 1 1 \\\\\\1\\ " \\ ' " "'""' '" .. "•••• .. ,, ' ' "'" ''"'' ''''"''''' '''"'""""'"""' ......... . _, . ,, ............... "' ......................... ......... . ............. .............. , ................... _.,, . """''' ' "'"'"" ''""'"' ......... .. _ .. ___ __ , .. . ,,, ................ .......... -........ -........... . .. , ... ,._,, ......... "'""'"'' .. ... . ... .. . . SO cm/1 . , .... ............... ...... ...... . .................. , .. _ ........ .. . Fig. 9. Velocity field at 21h 30/7 /96 (HW +6) .21.0 zo.a 19.0 f8.ll 17.0 1!l.U. ..lO_~~ -101. 5 . 1Ll&.L-.tD.9.5 . Fig. 10. Distributionofthe turbulent energy on the botfom at 9h30/7 /96(LW+6) .... ... ... ... ... 1 g, . .. 18 . 10_5,s -~l . to.z.1_ .. ..lilB.~ . ms_. Fig. 11. Distributionofthe turbulent energy on the bottom at 21h30/7 /96(LW+6) In order to understand the hydrodynamic regime of the tidal circulation, the distribution of kinetic energy in the studied domain has been determined. Figures 10 and 11 present the contour-map of kinetic energy on the bottom at two different times: LW +6 and HW +6, respectively. We remark that the kinetic energy becomes strongest near the Strait of QuynhChau and in the South-West of the coastal zone of HaiNam island where the tide currents reach their maximum values. Figures 12, 13, 14 and 15 show the distribution of kinetic energy together with the flow pattern on the transverse and longitudinal section at LW +6 and HW +6, respectively. Obvim1sly, the kinetic energy is stronger near the bottom and decreases gradually to the free _surface. 125 s )<;!' ... ·)) e ..., N ~ -10 "' ·lO E ... N -50 ·70 0 - so · lOO • lSO 0 so to.3:mm/e WO llO 150 X(iml) Fig. 12. Distribution of the turbulent energy & velo. field on the transverse section at 9h 10/7 / 96 io.3mm/s 100 150 JJO 2i0 llO ~00 ~50 X(iml) Fig. 13. Distribut ion of the turbulent energy & velo. field on the transverse section at 2lh 30 /7 /9.6 lOO lSO 200 X( i.m) 2SO .}00 Fig . 14. Dist ribution of the turbulent energy & velo. field on the longitudinal section at 9h 30 /7 /96 126 .}50 L0.00 .:> .oo 2 .00 --: .L .00 O . .:>O 0 . 25 o .oo •50 ·!.00 Conclusions X(km) Fig. 15. Distribution of the turbulent energy & velo. field on the longitudinal section at 2lh30/7 /96 ••••• 'I'.•• .i..•• 3 .00 .1.00 ···°' ..... 1) o . .i.s - A numerical simulation for the tidal circulation in the Gulf of Tonkin has been performed. The model was calibrated and verified by 6 observed stations when setting the horizontal diffusivity constant and tuning the Chezy coefficient. 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