A numerical model for the tidal oscillation and current in the gulf of tonkin

Vietnam Journal of Mechanics, NCST of Vietnam Vol. 23, 2001, No 1 (25 - 33) A NUMERICAL MODEL FOR THE TIDAL OSCILLATION AND CURRENT IN THE GULF OF TONKIN TRAN THI NGOC DUYET, PHAM VAN NINH, Do N Goe QuYNH Institute of Mechanics, NCST of Vietnam ABSTRACT. in this paper results of a numerical model, based on the TIDEFLOW-2D Software, for the tidal oscillation and current in the Gulf of Tonkin (GT) are presented . The model was tested as follows: i) the observed values of the four main tidal constituents M2 , S2, K i, 01 at the 44 coastal stations and islands were compared with computed ones; ii) . the computed tidal levels ware compared with the correlative ones in the Tide Tables at t he six stations: Hon Gai, Cua Ong, Hon Dau, Cua Hoi, Cua Gianh and Cua Tung in many monthly periods; iii) t he results of computed tidal levels and currents were compared with the observed data. The results of testing show a good agreement between the available data and computed values , therefore we can use t his model for simulation t ide level and current of GT. The results of using thjs model in GT: distribution of t he major harmonic const ituents ; the tidal elevation and current patterns; the extremal values of the tidal level and ci.i.rrent, ... will be published later. 1. Introduction Up to now, in Vietnam, tidal regime for the Gulf of Tonkin (GT) has been studied and simulated by many authors . In the Gulf, there exist six national tidal stations measuring tidal oscillation: Cua Ong, Hon Gai , Hon Dau, Cua Hoi, Cua Gianh and Cua 1\mg. However, research results on tidal current in the region are limited. Very few comparisons between observed tidal currents and computed ones had been done for GT. There exist several 2D models (4] for tidal, wind drift level and current have been deyeloped by Center for Marine Survey, Research and Consult ation (CMESRC), Hanoi Institute of Mechanics, whic4 have overcome quite well this lack. In this paper we present op.ly the software TIDEFLOW-2D, provided by Hy- draulics Research Wallingford Ltd (UK) [1]. A numerical model for GT based on this softwar~ has been established since nearly ten years in CMESRC. The testing for the simulation of the tidal oscillation and currents has been made. The results of testing show a good agreement between the available data and computed values and therefore we can use this model for simulation tide level and current of GT [5]. Soine results of usipg this tested numerical model in GT: 25 • the major harmonic constituents M2, 82, K1, 0 1 for tidal level and current, • the tidal elevation and current pat.terns, • the extremal values of the tidal level and current [6, 7] will be published later. 2. Basic equations, initial and boundary conditions In order to simulate the tidal regime in GT, TIDEFLOW-2D software is used. The basic equations for ,,the software are the following two-dimensional nonlinear shallow water equations: Conservation of mass az a a fJt + fJx (ud) + a)vd) = 0. Conservation of momentum au au au az 'l.l 2 2 1/2 [a2u . a2v] at + u ax + v ay = -g ax - f d ( u + v ) + D ax2 + ay2 + nv + TsxPd av fJv av az V( 2 2)1/2 [a2u a2v] T8 y -+u-+v-=-g--f- u +v +D-+- -Ou+- at ax ay ay d 8x2 8y2 pd where: u, v are depth...:averaged components of velocity in the x-direction and y- direction (m/s), z - water surface elevation above reference datum ( m), h - water depth below reference datum ( m), d - total water depth (d = h+ z) (m), 0 - Coriolis parameter (s-1), which is derived from the latitude specif;ied when setting up the model, g - gravity acceleration (m/s2), D - horizontal eddy viscosity coefficient (m2 /s), T5x, Tsy - the components of wind stress in x-and y-directions (kg/ms2), f - the friction coefficient calculated by the models usin:g the rough channel law: . 1 . . . 2 f = 32 [1og10(14.8d/ks)J- , here ks is roughness length (m). • At t = 0 an eqllilibrium is assumed. •For the solid boundary: u = v = 0. • At the liquid boundaries water levels are prescribed as follows: n Z(t) = Zo + LFi(t)hicos(ait - 9i + ~(t)) i=l 26 where: Z0 is value of the average water level (m), hi - Amplitude harmonic constant of the i-tide constituent (m), 9i - phase harmonic constant of the i-tide constituent (degree) (the above constants are varied along the open boundaries), Fi(t) - amplitude astronomical constant, ?; ( t) - phase astronomical constant (degree) (the above constants are varied with time at all open boundaries) , (Ti - angle velocity of the i-tide constituent (degree/second) , t - time (s), n - tide wave number. For GT water elevation values at liquid boundaries were computed according to the distribution of amplitudes and phases for the four main tidal constituents: M 2 , S2 , K1 , 0 1 at two bounds: + Quynh Chau Strait +GT Month Cross Section. This distribution was obtained by CMESRC thanks to the tidal simulating of the South China Sea [2, 3] , and calibrating with some data resources of field survey at the Gulf Mouth Cross Section. The bathymetry for the simulation was compiled by many maps and given by the Data Bank of GIS department of CMERSC. In using TIDEFLOW-2D software, patching technique has been applied. Accord- ing to this technique, the computed region can be divided into areas of difference grid size. The size of the fine grid is three times less then the adjacent coarse one. In this way, we can choose desired space size of grid for the simulated area and it equals 1/ 3n the size of the beginning course grid, if number of patching times is n. For instance, if we need to make 100 m for the space size of the finest grid and will do 4 patching times , so we need to take 8100 m for the beginning grid size. 3. The model testing 3.1. Comparison between computed and observed harmonic constituents Values of the fmJ.r main tidal constituents M2 , S2 , K 1 , 0 1 at the 44 coastal stations, and islands were compared with computed ones. The result of comparison is given in Table 1. We can see that the errors of the comparison at majority of the stations are acceptable not only for amplitudes but also for the phases of the four cons ti t1 ients. 3.2. Comparison with Tide Tables Computing for the tidal level in GT has been carried out at any moment of the year and in any monthly period. The computed tidal levels was compared with the correlative ones in the Tide Tables at the six stations: Hon Gai, Cua Ong, Hon Dau, 27 Table 1. Computation between given and computed harmonic constituents No Station's name M2 S2 (1) (2) (3) (4) (5) (I) (2) (3) (4) I Lo Chuc San 25 145 5 2 18 7 186 3 48 2 Co To 20 138 2 6 8 5 198 2 36 3 Thien Mon 19 150 5 -3 26 7 200 I 37 4 Ke Bao 20 145 3 2 15 10 190 -3 50 5 Van Hoa 26 166 -I -19 -5 5 205 3 32 6 Dao Rua 12 130 4 20 29 2 148 3 89 7 Cua Ong 13 157 I -10 6 4 158 0 88 8 Hon Gai 8 115 -4 74 -47 4 128 -2 214 9 Cua Binh Yen 5 146 -1 22 -20 2 144 -I 230 10 Cat Ba 4 102 -2 0 -55 3 137 -2 -89 11 Long Chau 0 0 2 135 0 0 0 I 51 12 Bach Long 9 103 -3 -13 -32 4 133 -2 17 13 Cua NamTrieu 0 0 3 216 0 0 0 2 33 14 Do Son 4 102 -2 126 -50 3 136 0 -94 15 Hon Dau 6 38 -4 301 -67 5 101 -2 -53 16 Ba Lat 13 32 -3 304 -22 5 123 1 -69 17 Van Ly 17 357 0 -18 -1 9 91 0 -34 18 Hon Ne 18 351 5 9 28 7 112 4 -49 19 Hon Me 20 357 7 -12 35 10 100 2 -34 20 Lach Truong 23 I I 344 5 II 94 0 -31 21 Lach Trao 25 17 0 328 -2 9 73 2 -7 22 Hon Ngu 30 2 I 343 3 10 84 3 -12 23 Cua Hoi 29 5 1 340 4 9 76 4 -4 24 Cua Sot 28 306 1 39 4 10 64 2 8 25 Vung Chua 20 10 3 -10 15 10 15 -I 57 26 Ron 21 355 3 -10 13 8 71 2 2 27 Cua Gianh 23 355 0 5 -I 6 53 3 19 28 Nhat Le 22 356 0 4 I 6 21 2 51 29 Cua Tung 17 353 2 -14 13 5 46 I 20 30 Con Co 19 351 0 -15 I 5 356 I 67 31 Thuan An 18 322 -2 5 -10 4 28 0 23 32 Chon May 17 310 -3 5 -18 3 0 0 33 33 Da Nang 17 301 -4 8 -24 6 340 -3 35 34 Long Mon 30 160 15 -16 50 10 195 7 36 35 Bae Hai 38 165 8 -24 21 12 201 5 24 36 Vi Chau 30 185 10 -47 33 10 225 5 -3 37 Dieu Thach 20 195 6 -63 30 15 260 -5 -41 38 Xin In 22 200 I -59 5 15 240 -6 -15 39 Duong Pho 20 180 0 -66 0 12 220 -5 -28 40 Tung Hai Tan 18 62 -3 -32 -17 3 138 2 -27 41 Tang LouChiao 20 205 -9 -40 -45 20 250 -14 17 42 13 353 I -59 5 4 50 I -44 43 Cu Lao Cham 17 300 -5 3 -29 6 340 -3 24 44 Kikuik 17 292 -6 8 -35 6 339 -3 27 (1) Given amplitude( cm) (2) Given phase (degree) (4) Absolute error for phase (degree) 28 Kl 01 (5) (I) (2) (3) (4) (5) (I) (2) (3) (4) (5) 37 80 68 2 16 2 79 18 7 6 8 30 75 83 3 4 4 91 18 -9 10 -10 14 72 81 9 6 13 81 16 4 II -30 70 83 II 4 16 80 18 5 9 48 84 92 -2 -5 -3 91 29 -6 -2 163 75 84 2 3 3 87 15 -6 12 8 81 92 -4 -2 -5 87 39 -5 -12 -51 73 90 I I I 82 28 -3 -I -50 69 78 4 12 6 74 22 4 5 -67 72 89 -1 I -1 79 26 -2 I 0 70 88 0 2 0 70 24 6 3 -55 77 82 -14 5 -18 78 17 -7 7 0 70 85 3 5 4 70 27 8 0 0 72 89 0 I 0 70 26 7 4 -38 70 91 0 -I 0 78 26 -2 4 22 62 102 3 -9 4 73 38 -2 -5 -1 51 89 10 7 20 69 25 -I II 57 68 92 -9 7 -13 69 17 -3 19 20 60 92 -5 13 -8 60 38 3 I -2 52 96 7 6 14 66 29 I 7 20 55 94 3 8 6 64 40 I -4 30 50 87 I 24 2 59 30 0 12 40 47 106 3 5 6 56 34 2 8 22 38 94 9 20 23 55 33 0 12 -10 20 130 12 -7 60 40 37 0 8 20 20 100 14 23 68 34 32 7 16 43 23 106 8 20 34 33 34 5 14 38 19 107 10 22 51 26 39 8 12 30 6 103 12 35 181 14 39 8 15 13 6 66 9 69 142 14 33 6 15 -5 3 255 6 -99 173 2 5 8 55 0 16 285 -5 -39 -31 9 247 -7 -31 -48 20 290 -4 -32 -18 13 244 -5 -22 70 90 71 -2 10 -2 90 30 -I -6 42 3 72 -16 6 -16 13 38 -25 -20 50 80 73 2 2 3 80 30 5 -12 -33 65 75 6 -15 9 70 20 2 -8 -40 70 75 -7 -6 -10 73 15 0 6 -42 65 70 0 2 0 70 10 5 8 67 52 57 -4 6 -8 62 356 -3 13 -70 60 76 -3 -28 -5 60 25 -4 -19 14 28 354 -2 -36 -7 26 312 -2 -30 -50 23 294 -4 -33 -17 17 247 -5 -16 -50 27 298 -5 -34 -19 23 251 -7 -17 (3) Absolute error for amplitude (cm) (5) Relative error for amplitude(%) 5 6 -6 -6 -6 -4 5 -3 9 -9 11 10 -2 -3 -1 -4 5 I 2 0 4 -I 0 21 17 29 54 45 335 -78 -38 -I -22 6 3 0 7 -5 -7 -6 -29 -30 Cua Hoi, Cua Gianh and Cua 'I\mg. The results of the comparison are acceptable. Fig. 1, Fig. 2 are examples of the c~mparison at Cua Ong St . .' in 7 /1994, and 12/1994. H(cm) 500 400 300 ' 200 100 0 Day 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 H(cm) 500 400 300 200 100 1· · · · · · · Tide Tables -- Compu~~d - -I Fig. 1. Comparison between Tiell' Tabks and computed tidal level at Cua Ong in .July HJ!J4 • .. 0+--+-+-+-+--f-11--tl-i-+-+-+-+-+--+--+--+--+-+-+-+-+-...._~1--1'-'--1--+-+-+-- 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 ·--- ---- - --· --- --------1 · · · · · · Tide Tables Computed Fig. 2. Comparison between Tide Tables and computed tidal level at Cua Ong in December 1994 3.3. Comparison with observed data The software had been tested also by comparison between computed results and the data observed by ·CMESRC since 1993 up to now. Tlie data series are observed tidal levels and tidal currents measured continuously for 1, 3, 5 or 7-days periods. For GT, the comparison between computed tidal levels and observed values was carried out at about 10 stations. Nevertheless , it was done for tidal current at nearly 20 stations located along the coastal zone of GT. The figures, from Fig. 3 to Fig. 8, are examples of the comparison. Satisfying result for tidal regime comparison shows high simulation ability of TIDEFLOW-2D. However this remark denotes also high reliability of the CMESRC's observed data. 29 300 250 200 150 100 ff(cm) 50 O-t---t---t-:-r--t--t---il--+--+-+~..,._;4--t---il--+-.:..f.!.-+~+---+-~~ i; ..c: - H(cm) 250 200 150 100 50 0 ..., ~~ -N V(cm/s) 35 30 25 20 15 10 I'- ' M °' s r-- M °' - - - - ~r..~g:~ ..c: r '-- ., • • • · • ·Observed I ..c: ' ..c: ~- ------ -~ ---Computed I . I Fig. 3. Comparison between observed and computed tidal lewl at Nam Dinh from 16 to 21 July 1993 \.c ~ - \0 N ..c:~ ---- - ~-------, - -· ~ ! • • • • • ·Observed Computed i ..c:~ - 00 N Fig. 4. Comparison betwee11 observed and computed tidal level at Vung Ang from 25 to 28 August 1996 s N .c 5 0+-1'4-~+-+-l-1~~+-+-1-1~+-1-+-+-+-<~+-1-+-+-+-1-++-1-+-+-+-1-++-1-+-+-+-~+-+-l-1~~+-+-l-1~~ I'- <"\ 0\ 00 !"' M O'\ 00 --M- -:;;:- .c .c Fig. 5.1. Comparison between observed and computed velocities at Le Thuy (T20) from 28 July to 4 August 1996 30 G(degree) 360 300 240 180 120 60 . ·--. 01-Ht-t-t-+-H-t+H-++Hf-++++f-'t+H-++Hf-t+++f++H-++-H-i+i-H++~"+· ++-1-4-1-+ Fig. 5.2. V(cm/s) 40 30 20 10 0 M O'I ~r-- M O'I ~r-- r, 0\ ~ .c: .c: .c: Comparison betwPen observed and comp11tC"d current directions at Le Thuy (T20) from 28 July to 4 August ' 19U6 / L · · · · · ·Observed - _-_-Computed l G(degree) Fig. 6.1. Comparison hetw1-e11 obsen·ed and computed velocities .at Le Thuy (T 10) from 31 July to 3 August 1996 360 300 240 180 120 \ 1r ···----v J; ••••'"'"' '"'"• •., I \..:..,••'"'0,......•-:'• -:°.":" • ..,,.., .. . . . \F 1.-..,_,..._-::.-..-.. -:-. -:-. • . . • 60 0-t--t--t--+---t~t--+-+--t--+--+-+---lt--t--f--t--+--+--+---l~+--+--+--+- 35 30 25 20 15 10 5 1--=~ ·Observed ---Computed J -· - - --- - - -- - --- -- Fig . 6.2. Comparison between observed and computed current directions V(cm/s) at Le Thuy (TIO) from :H July to 3 August 1996 0 .+-li-4-+-1-J-+-+~+-+-+-+-+-+-~+-1~+-1-+-+-+-+-+-+-+-+-+-+-1-++-1~+-1-+-+-1-+-+-+-+-+-+-+-+-+-+-1-+-+-~ t'-MO'l~t--MO'l~t'-MO\.C:t'-r"JO'l.C:t'-r"lO'l~t'-M~.C:~M~.C: ~~ ~~ ~~ ~~ ~~~ .c: [ • • • • • • Obsered --. -. Computed Fig. 7.1 . C~mp~iso~ between observed and computed velocities at Cua Sot from 22 to, 29 May 1994 31 360 300 240 180 120 G(degree) 60 I I ~-"' O+t-r=H++++-tH-T++l-+t++l-+-H-+++rl++++-+.!t-t-++++-tr++++t!-H-H-+-+-lH4-+4--+- Fig. 7. 2. Comparison between observed and computed current directions V(cm/s) at Cua Sot from 22 to 29 May 1994 25 20 15 IO 5 0++++t-Hr-+-t++++++-1-H-+++++++-Hr-+-t++++++t-H-++++++~r!H+++++4-~ ~~~-~~~~~~~-~~~-~~~-~~~~~ ~~ ~~ ~~~ ~~~ ~~~ ~ 360 300 240 180 120 ' 60 ~ N N N ~ ~ 1-~--:-0bse-;~ed . C~d-] ..::: Fig. s: 1. c~~lparis~~-betw~n obse;;ed a~d com;~tPd Yelocities at Hoang Hoa from 25 January 1 February l!J99 G(degree) '• 0+-t-Hrt-t-+t++++t+t-Hrt-H-H-+++t+i:+.:i~l-+-+-+++-!o=ll-+++4~~14-......... 44...j:!...l.44-+-1- Fig. 8.2. Comparison between observed and computed current directions at Hoang Hoa from 25 January to 1 February 1999 4. Conclusion The numerical model based on TIDEFLOW-2D for the tidal levels and currents for the Gulf of Tonkin was established and tested carefully. The testing results show a good agreement and this model can be used for simulation the tidal movement in the Gulf. Results of such like simulation will be published later . The paper was accomplished partly thanks to the National Project: "Basics Studies on Marine Hydrological Problems for 1999 year KT.04-3.2.4". 32 REFERENCES 1. Soft.ware TIDEFLOW-2D. Hydraulics Research Ltd Wallingford, UK 1991. 2. Data Collection on Tidal Harmonic Constants. Report of the National Project KT.03.03. The Appendix. Vietnam Marine Programme, Hanoi, Vietnam 1993. 3. Tide and Water Level Rising in Coastal Zone of Vietnam. Final Report of the National Project KT.03.03, Hanoi 1995. 4. Nguyen Thi Viet Lien. Numerical Model of the Tide and Storm Surge. Ph.D. Thesis, Hanoi 1996. 5. Tran Thi Ngoc Duyet, Nguyen Thi Viet Lien, Pham Van Ninh, Nguyen Minh Son. Simulation of current and water level oscillation in the Halong bay Area. Proceedings of 6-th National Mechanics Conference. Hanoi 12/1997. 6. Do Ngoc Quynh, Pham Van Ninh, Tran Thi Ngoc Duyet. Special Report on the Tidal Computation in the Gulf of Tonkin. National Project KT.06.10. Hanoi 3/1999. 7. Do Ngoc Quynh, Pham Van Ninh, Tran Thi Ngoc Duyet. Special Report on the Computation of Extremum Tidal Oscillation in 19-year period in the Gulf of Tonkin. National Proje_ct KT.06.10. Hanoi 3/1999. Received October 20, 2000 ,.. .. ,.,, "' ' ...... ' ... "' ~ ,... MO HINH SO TR~ VE THUY TRJEU VA DONG TRIEU T ~ V~NH BAC BQ Bai nay trlnh bay ket qua d1.a vi~c thiet l~p m6 hlnh so tr! dl.ra tren phan mem TIDEFLOV/-2D nham tinh toan m\rc trieu t~i v!nh Blic B9. Mo hlnh duqc kiem d!nh bang each: i) SO sanh so li$u quan trac Va tfnh toan hang SO dieu hoa m\fC rnrac trieu d1a 4 song chinh: M2 , 8 2 , K1 , 0 1 t~i 44 tr~m quan trac ven ba va cac dao d1a V!nh; ii) so sanh gifra ml.re trieu tong hqp tinh duqc v&i m\fC rnr&c ghi trong bang thl'iy trieu t~i 6 tr~m quan trlic quoc gia: Clra Ong, Hon Gai, Hon Dau, Clh H(>i, Cl'ra Gianh va Clra Timg t~i thOi diem bat dau bat·ky trong cac chu ky keo dai hang thang; iii) SO sanh ID\fC IllfOC trieu va dong trieu gifraclo d<;tC Va tinh toan t~i nhieu tr~m khac nhau trong CaC khoang thai gian quan trac lien tl.lC va dai ngay ke tir narn 1993 den nay. Cac ket qua thir nghi~m neu tren cho thay mo hlnh duqc thiet l~p tot va c6 the Slf dl,mg de mo phong cac bai toan khac nhau ve chuyen d¢-ng trieu & V!nh Bae B9 nhu i) hang so dieu hoa, ii) b\rc tranh dong trieu, iii) m\rc trieu cl.re tr! v.v ... Cac ket qmi d6 se duqc cong bo sau nay. 33