A Study on Residual Flow in the Gulf of Tongking

Journal of Oceanography, Vol. 56, pp. 59 to 68. 2000 A Study on Residual Flow in the Gulf of Tongking DINH-VAN MANH 1 and TETSUO YANAGI 2 1 Department of Civil and Environmental Engineering, Ehime University, Matsuyama 790-8577, Japan 2 Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan (Received 6 May 1997; in revised form 28 April 1999; accepted 1 May 1999) On the basis of observations of water temperature, salinity and wind during winter (December to following February) and summer (June to August) in the Gulf of Tongking, a robust diagnostic three-dimensional model has established that reveals the seasonal variation in residual flow, including wind-driven current, density-driven current and tide-induced residual current. It is shown that in the Gulf of Tongking the wind-driven current plays the most important role in the seasonal variation of residual flow field. Due to strong NE monsoon (9 m/s) during winter the residual flow (reaches 30 cm/s) is stronger than that in summer. At the surface the residual flow direction during winter is basically westward or southwestward, while during summer it is almost reversed. Keywords: Residual flow, diagnostic model, Gulf of Tongking. 1. Introduction The Gulf of Tongking in the northwestern part of the South China Sea is situated within the monsoon regime. During winter, a north-easterly wind prevails over the whole gulf with an average speed of about 9 m/s. A weaker southerly wind (about 6 m/s) dominates during summer. It is obvious that residual flow plays an important role in the long-term material transport process in the coastal sea. But there has been no study of the residual flow field in the Gulf of Tongking. A study concerning the tide-induced residual flow in the Gulf of Tongking has recently carried out (Manh and Yanagi, 1997). The tide-induced residual flow is stationary except the springneap modulation throughout the year. In order to increase our understanding of the residual flow field in the Gulf of Tongking, a study of the seasonal variation in residual flow, including wind-driven and density-driven currents, is necessary. In this study a robust diagnostic three-dimensional model is applied to simulate the residual flow field, including wind-driven current, density-driven current and tide-induced residual current in the Gulf of Tongking, during winter and during summer. 2. Observed Data Observational data of water temperature and salinity during summer (from June to August) and during win- Corresponding author e-mail: dinhvan@coe.ehime-u.ac.jp Copyright The Oceanographic Society of Japan. ter (from December to following February) at seven levels (0 m, 10 m, 20 m, 30 m, 50 m, and 100 m deep) from 1961 to 1974 were obtained from the Marine Environmental Atlas of Japan Oceanographic Data Center (JODC). The monthly average wind field data during summer and during winter from 1961 to 1991 were extracted from the Comprehensive Ocean Atmosphere Data Set (COADS) developed by NOAA (National Oceanic and Atmospheric Administration). Observatinal data of residual flow for 5 7 days at three stations A (from 9/1 to 14/1 1993), B (2/6 8/6/1994) and C (28/7 4/8/1996) were obtained from the Center for Marine Environment Survey, Research & Consultation of Vietnam (private communication). The observation locations and stations are presented in Fig. 1. The distributions of observed seawater temperature, salinity and density (sigma-t) during winter and during summer at three levels, the upper (0 m), middle ( 20 m) and lower ( 50 m), as well as at three vertical cross sections, at latitudes of 20, 19 and 17 30 N, are presented in Figs. 2 to 5, respectively. The surface water temperature during winter increases from 20 C in the north to 24 C in the south as shown in Fig. 2, whereas during summer the gradient is much weaker (from 27.5 C in the north to 29.5 C in the south) as shown in Fig. 3. In summer the stratification is developed and the water temperature decreases rapidly in the vertical direction (from 29.5 C at the surface to 19 C at the depth of 90 m) as shown in Fig. 5. By contrast, it is vertically well mixed in winter as shown in Fig. 4. Salinity in winter changes from 34.0 psu 59

Fig. 1. Geometry of the Gulf of Tongking and observation locations of water temperature, salinity and wind. Contours show the depth in meters. at the mouth of the gulf to 32.0 psu in the northwestern part of the gulf as shown in Fig. 2. Generally, the salinity in winter is a little higher than that in summer from Figs. 2 and 3. However, the salinity at the bottom near the mouth of the gulf in summer is higher than in winter. 3. Diagnostic Numerical Model The governing equations in Cartesian coordinates are as follows (the t and z subscripts denote partial derivatives): + = () h u w z 0 1 ut + u hu+ wuz + fk u 2 ρ 1 p A u A u F 2 = + + + ( ) h h h ζ ρo ρ p = ρogζ + g dz z ρ o v zz t () 3 3 2 ( ρ 1. 0) 10 = 28. 14 0. 0735T 0. 00469T + ( 0. 0802 0. 002T) ( S 35) ( 4) T + u ht + wt = Dh 2 ht + DvT + γ T T 5 t z zz ( ) ( ) ( ) ( ) St + u hs+ wsz = Dh 2 hs+ DvSzz + γ S S. 6 Here u is the horizontal velocity vector, w the upward velocity, f the Coriolis parameter (=2ωsinϕ, ω is the angular velocity of the earth s rotation; ϕ is latitude), k the vertical unit vector, g (=980 cm/s 2 ) the acceleration due to gravity, F t tidal stress, h the horizontal gradient operator, t time, p water pressure, ρ water density, ρ o overall mean sea water density, ζ sea level height above the mean sea surface, A h and D h horizontal eddy viscosity and diffusivity, respectively, A v and D v vertical eddy viscosity and diffusivity, respectively, T water temperature, and S salinity. 60 D.-V. Manh and T. Yanagi

Fig. 2. Horizontal distributions of water temperature, salinity and sigma-t in winter at 3 levels: upper (0 m), middle ( 20 m) and lower ( 50 m). The eddy viscosity and diffusivity coefficients are given as: A h = D h = 10 6 cm 2 /s, D v = A v = 20 cm 2 /s. The horizontal forces due to tidal stress F t are calculated 4 by F t = u i hu i, where ũi denotes the horizontal tidal i= 1 current of M 2, S 2, K 1, or O 1 tide, and the over-bar represents the average over one tidal cycle, respectively. Tidal currents have already been calculated (Manh and Yanagi, 1997). The last terms in Eqs. (5) and (6) are called γ-terms and were introduced by Sarmiento and Bryan (1982) to prevent calculated values of T and S from deviating greatly from the observed ones T* and S*. In this case, γ = 1/12 hour is used. In addition the following boundary conditions are used: A Study on Residual Flow in the Gulf of Tongking 61

Fig. 3. Horizontal distributions of water temperature, salinity and sigma-t in summer at 3 levels: upper (0 m), middle ( 20 m) and lower ( 50 m). At the sea surface: ρau ρ C WW, T 0, S 0. 7 = = = ( ) v z a d z z At the bottom: ρau βuu, T 0, S 0. 8 v z = z = z = () Here ρ a (=0.0012 g/cm 3 ) is the air density, C d (=0.0013) the sea surface drag coefficient, W the wind vector, β (=0.0026) the bottom drag coefficient. At the solid boundary: u = 0, T n = 0, S n = 0 ( r n is the unit outward vector).(9) 62 D.-V. Manh and T. Yanagi

Fig. 4. Vertical distributions of water temperature, salinity and sigma-t in winter at 3 cross sections: latitude of 20 00, 19 00 and 17 30 N. Fig. 5. Vertical distributions of water temperature, salinity and sigma-t in summer at 3 cross sections: latitude of 20 00, 19 00 and 17 30 N. A Study on Residual Flow in the Gulf of Tongking 63

At the open boundary: T and S are given on the basis of observed values and volume transports are prefixed. The initial values of T and S are obtained by interpolating or extrapolating from the above mentioned observed data. The volume transports across the open boundaries are obtained from another numerical model for studying the residual flow in the South China Sea (Manh and Yanagi, 1999). The above mentioned equation system is solved by the finite difference method. First, in order to determine the variation of sea water level, Eqs. (1) and (2) are integrated over the range from bottom to surface, so that modified shallow water equations are obtained. These equations (under the above corresponding boundary conditions) are solved approximately by an alternative direction implicit difference scheme (Ramming and Kowalik, 1980). Second, to determine the distributions of horizontal velocity components, water temperature and salinity, Eqs. (2), (5) and (6) are solved by an implicit finite difference scheme in the vertical direction on the basis of a vertically σ-stretched grid (Nihoul and Jamart, 1987). Finally, the vertical velocity is obtained by integrating Eq. (1) step by step from bottom to surface, and the sea water density is determined by the state Eq. (4). Other parameters of the numerical model are taken as follows: the horizontal space steps equal 1/6 degrees of latitude/longitude (about 18 km), the time step is 120 s and the number of layers is 25. The thickness of the layers is increased from surface to bottom and the maximum value is 10 m. 4. Results The residual flow, including wind-driven current, density-driven current and tide-induced residual current, is calculated for two cases, winter and summer. The quasisteady states are obtained about 10 days after the beginning of the calculation. The calculated residual flow in winter at three levels (upper, middle and lower) is plotted in Fig. 6. It is shown that the residual flow at the upper level is strong (reaches 30 cm/s). In the Vietnamese coastal zone from surface to bottom the flow has the same direction: along the shoreline from north to south. In the coastal zone of Hai-Nan Island, the flow at the upper level is southwesterly in the northern part and westerly in the southern part. From surface to bottom the flow direction changes and its speed is reduced significantly. In the central part of the gulf, the residual flow direction changes from westward at the upper level to northward at the lower one. A clockwise eddy exists at the middle level in the northwestern coastal zone of Hai-Nan Island. Another counter-clockwise eddy occurs at the lower level in the middle of the southern part of the gulf. At the mouth of the gulf the flow is inward at the upper level and outward at the lower level. The residual flow at the upper level in summer is smaller (about 22 cm/s in the Hai-nan coastal zone) and its direction is almost reversed in comparison with that in winter, as shown in Fig. 7. At the middle level a large counter-clockwise eddy exists in the central part of the gulf, while another small counterclockwise eddy occurs in the northwestern part of the Hai-nan coastal zone. At the mouth of the gulf the flow is outward at the upper level and inward at the lower level. The calculated results are compared with the observed data in Table 1. In winter there is only one data set at station A and the result of simulation agrees well with observation. In summer the comparison is carried out at stations B and C. At station B the calculated and observed currents have nearly the same direction but at the depth of 10 m the magnitude of the calculated flow is smaller Fig. 6. Calculated residual flow in winter at the upper (0 m), middle ( 20 m) and lower ( 50 m) levels. 64 D.-V. Manh and T. Yanagi

Fig. 7. Calculated residual flow in summer at the upper (0 m), middle ( 20 m) and lower ( 50 m) levels. Table 1. Comparison between observed and simulated residual flow at three stations. Location Season Depth (m) Observed (cm/s) Simulated (cm/s) Eastward Northward Eastward Northward Station A Winter 3 8.9 13.4 14.2 11.5 Station B Summer 10 3.7 16.2 1.7 6.0 17 1.0 6.5 1.9 7.5 Station C Summer 10 3.4 7.0 4.9 5.8 20 3.5 7.4 1.4 5.3 upwelling zones exist off the northwestern coast of Hai- Nan Island and off the southern coast of Vietnam. Another noticeable upwelling zone is in the middle near the mouth of the gulf. The maximum vertical residual flow (about 3.0 10 3 cm/s) occurs off the northwestern coast of Hai-Nan Island. We may expect a high primary production in these upwelling zones during summer. Fig. 8. Vertical residual flow (in 10 3 cm/s) in summer at the middle ( 20 m) level. than the observed flow. At station C the calculated residual flow result is acceptable. The vertical residual flow in summer at the middle ( 20 m) level is presented in Fig. 8. It is shown that 5. Discussion and Conclusion In this study we have tried to reveal the major characteristics of the residual flow in the Gulf of Tongking based on the observed data, using a robust diagnostic model with a large γ-term to prevent a great deviation of calculated water temperature and salinity from the observed values. Because of the lack of observed data to establish the hydrodynamic boundary conditions at the open boundaries, we use the water volume transports obtained from another numerical model for studying the residual flow, including wind-driven, density-driven and tide-induced residual currents, in the South China Sea (Manh and Yanagi, 1999). This numerical model covers the whole South China Sea with a horizontal grid size of 40 km. To enclose the equation system, here we apply a constant vertical eddy viscosity model. The values of A v are chosen after calibrating the model. A Study on Residual Flow in the Gulf of Tongking 65

The results on the tide-induced residual flow in the Gulf of Tongking (Manh and Yanagi, 1997) show that it is relatively small. The strongest tide-induced flow (about 10 cm/s) occurs in the northwest coastal zone of Hai-Nan Island. Another region with a considerable tide-induced residual flow (about 4 cm/s) is in the coastal zone from 16 N30 to 17 N30 of Vietnam. The tide-induced residual flow in the remainder of the gulf is about 2 cm/s or less. Generally, in the Vietnamese coastal zone the direction of the tide-induced residual flow is southerly, while in the Hai-nan coastal zone, due to the existence of tow small counterclockwise eddies in the northwestern part and southwestern part, the flow direction varies. In order to evaluate roughly the contribution of three components, wind-driven, density-driven and tide-induced, of residual flow as well as the influence of the adjacent sea on the residual flow pattern in the gulf, two more numerical experiments were carried out: (1) calculating residual flows in winter and in summer, as shown in Fig. 9, by using a modified form of Sommerfeld radiation condition (Blumberg et al., 1985) at the open boundaries while other parameters of the numerical model remained unchanged; and (2) calculating wind-driven currents in winter and in summer, as shown in Fig. 10, by using the uniform density fields (ρ = ρ o for each season) and the same radiation condition. This open boundary condition is described as follows: ζ t + (gh) 1/2 ζ n = ζ/t f, where H is water column, T f (=1 hour) the time factor. The first numerical experiment results (Fig. 9) are relatively similar to the results obtained by using the volume transport at the open boundaries (Figs. 6 and 7), except near the open boundaries. It is shown that the radiation condition at the open boundaries is good enough to Fig. 9. Calculated residual flow, using the radiation condition, in winter (a) and in summer (b) at the upper (0 m), middle ( 20 m) and lower ( 50 m) levels. 66 D.-V. Manh and T. Yanagi

simulate the residual flow in the area studied. From these numerical experiment results, it is understood that the main component of the residual flow in the Gulf of Tongking is wind-driven. Therefore, the seasonal variation of the residual flow in the gulf, especially at the upper level, is related closely to the seasonal variation of wind field. In winter under the strong NE monsoon, the residual flow direction at the upper level is basically westward or southwestward, in summer the flow direction at the upper level is almost reversed. The residual flow speed in winter is quite strong compared to that in summer. It is clear that the density driven component will become more significant in the lower levels. In summer, the counterclockwise eddy occurs at the middle and lower levels near the central part of the gulf due to existence of the colder water mass. It is difficult to recognize the ef- fect of a density driven component in winter. In summer, a low temperature (19 C) and high saline (34.5 psu) water mass exists at the bottom near the mouth of the gulf. This comes in from the deeper part of the South China Sea. In winter, the bottom water mass near the mouth of the gulf goes out. This results in the low temperature and high salinity water mass at the bottom being replaced by the warmer (23 C) and less saline (34.0 psu) one. It is noticed that along the Vietnamese coastal zone at the middle level the residual direction is southward both in winter and in summer. This agrees with the observational data obtained by the Center for Marine Survey, Research and Consultation of Vietnam. In winter, obviously, this is a result of the NE monsoon wind. In summer, due to the topography of the gulf as well as the shoreline, the SW wind field also generates a counterclockwise Fig. 10. Calculated wind-driven flow in winter (a) and in summer (b) at the upper (0 m), middle ( 20 m) and lower ( 50 m) levels. A Study on Residual Flow in the Gulf of Tongking 67

circulation at the middle level in the north part of the gulf. In the south part of the Vietnamese coastal zone, the winddriven flow is rather small, while the tide-induced and density-driven currents have the same southward direction and become more dominant. Therefore, in summer at the middle level of the Vietnamese coastal zone the residual direction is along the shoreline from north to south. On the basis of the calculated results of the residual flow in winter and in summer the following conclusions are drawn: - Wind-driven current plays the most important role in the seasonal variation of residual flow field in the Gulf of Tongking. Therefore, the residual flow direction at the upper level in winter is basically westward or southwestward, while in summer it is almost reversed. The residual flow speed in winter is quite strong in comparison with that in summer. - At the middle level of the Vietnamese coastal zone, the residual flow direction is along the shoreline from north to south in winter as well as in summer. Acknowledgements The authors express their sincere thanks to Prof. H. Takeoka of Ehime University for his help during this study. The observational data of seawater temperature and salinity used in this study have been taken from the Marine Environmental Atlas of Japan Oceanographic Data Center. The observed data on residual flow were obtained from the Center for Marine Environmental Survey, Research & Consultation of Vietnam. References Blumberg, A. F. and L. H. Kantha (1985): Open boundary condition for circulation models. J. Hydraulic Engineering, 111, No. 2, 237 255. Guo, X. and T. Yanagi (1994): Three-dimensional structure of tidal currents in Tokyo Bay, Japan. La mer, 32, 173 185. Manh, D. V. and T. Yanagi (1997): A three-dimensional numerical model of tides and tidal currents in the Gulf of Tongking. La mer, 35, 15 22. Manh, D. V. and T. Yanagi (1999): Seasonal variation in residual flow in the South China Sea (to be submitted). Nihoul, J. C. J. and B. M. Jamart (1987): Three-Dimensional Models of Marine and Etuarine Dynamics. Elsevier Publishers B.V., p. 35 54. Ramming, H. G. and Z. Kowalik (1980): Numerical Modeling of Marine Hydrodynamics. Elsevier Scientific Publishing Company, p. 112 164. Sarmiento, J. L. and K. Bryan (1982): An ocean transport model for the North Atlantic. J. Geophys. Res., 87, 394 408. 68 D.-V. Manh and T. Yanagi