A Numerical Simulation of Tides and Tidal Currents
in the South China Sea
 
Tetsuo YANAGI1 and Toshiyuki TAKAO2
 
(received 1998/1/28, revised 1998/4/14, accepted 1998/4/27)
 
Abstract

Semi-diurnal and diurnal tides and tidal currents in the South China Sea are well reproduced by a horizontal two-dimensional numerical model. Diurnal tides are more dominant than semi-diurnal tides in the South China Sea because the natural oscillation period of the South China Sea is 19.2 hours. Tidal types of tides and tidal currents in the South China Sea are revealed using the calculated results, and their characteristics are discussed.
 

(Keywords: tide, tidal current, natural oscillation, South China Sea)
1 Research Institute for Applied Mechanics, Kyushu University, Kasuga 816, Japan
2 Department of Civil and Environmental Engineering, Ehime University, Bunkyo 3, Matsuyama 790, Japan
 
 
Introduction
 
The South China Sea (SCS) is a marginal sea with shallow shelves less than 200 m in depth, such as the Gulfs of Thailand and Tongking in the western part, and with a deep basin of about 4000 m in depth in the central part (Fig.1). The characteristics of tides in the SCS have been investigated by Fang (1986) and Huang et al. (1994) using observed tide gauge data at coastal stations, by Mazzega and Berge (1994) and Yanagi et al. (1997) using satellite altimetric data, and by Ye and Robinson (1983) using a numerical experiment.

It is well known that diurnal tides are more prevalent than semi-diurnal tides in the SCS. Yanagi et al. (1997) pointed out that the resonance of diurnal tides there resulted in its predominance relative to semi-diurnal tides in the SCS. However, the detailed mechanism of resonance in the SCS is not yet elucidated. The characteristics of diurnal and semi-diurnal tidal currents in the whole area of the SCS have also not yet been studied, except for co-amplitude charts of K1 and M2 tidal currents: in the northern part of the SCS by Fang (1986), based on field observations; and in the whole area by Ye and Robinson (1983), based on numerical calculation.

In this paper we show the characteristics of tides and tidal currents of four major tidal constituents (M2 , S2 , K1 , and O1) in the SCS using a two-dimensional numerical model under the Cartesian coordinate of the ?-plane. Next we compare our calculated results with the results observed by Yanagi et al. (1997) and the results calculated by Ye and Robinson (1983) under the spherical co-ordinate including the tidal potential. By these comparisons, we investigate the effects of the earth's curvature and tidal potential on the tidal phenomena in the SCS.

The mechanism of the predominance of diurnal tides in the SCS is also investigated using our numerical model. Finally, we examine the tidal types of tides and tidal currents in the SCS using our calculated results.
 

 
 
Numerical model
 
The horizontal two-dimensional momentum and continuity equations for tide and tidal current of the homogeneous fluid under the Cartesian coordinate are:

where u is the depth averaged velocity vector; t is the time; Ñ is the horizontal differential operator; f is the Coriolis parameter (f = 2w sin?; w is the angular velocity of the earth'srotation and ? is the latitude); K is the locally vertical unit vector; g (= 980 cm s-2) is the gravitational acceleration; ? is the sea surface elevation from the mean sea surface; ?b2 (= 0.0026) is the bottom frictional coefficient; ? (= 10 7 cm 2 s ?1) is the horizontal eddy viscosity; and H is the local water depth.

Equations (1) and (2) are approximated by finite difference and are solved by the primitive method (Yanagi et al., 1983). The grid size is 40 km x 40 km. The observed tidal amplitude and phase lag are given along three open boundaries: the Taiwan Strait, the Bashi Channel and the Sunda Shelf, as shown in Fig.1, on the basis of co-tidal and co-range charts by Yanagi et al. (1997). We exclude the water exchange between the SCS and Sulu Sea across the channels between Luzon Island and Kalimantan Island because their cross-sectional areas are very small. The quasi-steady state is obtained four tidal cycles after the beginning of the calculation and the harmonic analysis of sea surface elevation and current field is carried out for the fifth tidal cycle.
 

Results
 
Tides

Calculated co-tidal and co-range charts of semi-diurnal tides (M2 and S2) are shown in Figs 2 and 3 along with the ones observed by Yanagi et al. (1997). The semi-diurnal tidal waves enter the SCS from the Bashi Channel and propagate northeastward to the Taiwan Strait, southwestward to the Gulf of Tongking and to the Gulf of Thailand. The phase speed in the deep part of the SCS, which can be estimated from Fig. 2(b) and (d) and Fig. 3(b) and (d), is about 800 km / 30o, which is 800 km / 1 hour, or 220 m s-1. This value is nearly the same as the phase velocity of a long wave; (gH)1/2 = 198 m s?1 (H = 4000 m, the water depth in the deep part of the SCS). There is a clockwise amphidromic point of semi-diurnal tide in the central part of the Gulf of Thailand. The calculated phase distribution of semi-diurnal tides coincides well quantitatively with the observed one except at the central part of the Gulf of Thailand. The calculated phase is ahead of the observed one at the central part of the Gulf of Thailand by 60 to 90 degrees. The generation mechanism of the clockwise amphidrome of semi-diurnal tides at the central part of the Gulf of Thailand has been given by Yanagi and Takao (1997) using a simple numerical model.

? The amplitude of semi-diurnal tides is largest in the Taiwan Strait and is large along the southern coasts of China and the Indo-China peninsula, and along the eastern coast of Malaysia and the southwestern coast of Kalimantan. The amplitude calculated for semi-diurnal tides quantitatively reproduces that observed except along the southern coasts of China and the Indo-China peninsula, at the head of the Gulf of Tongking and along the southwestern coast of Kalimantan Island. The calculated amplitude for these are much larger than those observed.

The Calculated co-tidal and co-range charts of diurnal tides (K1 and O1) are shown in Figs 4 and 5 with observed ones by Yanagi et al. (1997). The diurnal tidal waves enter the SCS from the Bashi Channel and Taiwan Strait, and they propagate southwestward to the Gulf of Tongking and to the Gulf of Thailand. The phase speed of diurnal tidal waves in the deep part of the SCS, which can be estimated from Fig. 4(b) and (d) and Fig. 5 (b) and (d), is about 1,600 km / 30 o, that is 1,600 km / 2 hours or 220 m s -1. This value is also nearly the same as the phase speed of the long wave in the deep part of the SCS. There is a counter-clockwise amphidromic point of diurnal tides in the central part of the Gulf of Thailand. The calculated phase distribution of diurnal tides coincides well quantitatively with the observed one.

The amplitude of diurnal tides is the largest at the head of Gulf of Tongking. This is due to the local resonance of diurnal tides in the Gulf of Tongking (Manh and Yanagi, 1997). Off the southern coast of the Indo-China peninsula and at the head of Gulf of Thailand, the amplitude of diurnal tides is large. The calculated amplitude of diurnal tides reproduces well quantitatively that observed. The reproduction of diurnal tides is better than that of semi-diurnal tides.

Our calculated results are nearly the same as those from Ye and Robinson (1983), which include the tidal potential under the spherical co-ordinate with a horizontal mesh size of about 31 km. In our model, we also conduct numerical experiments including the tidal potential, but the results are nearly the same as those obtained without the tidal potential. These facts suggest that the tidal potential and the earth's curvature do not have any serious effect on the tidal phenomena in the SCS. We can understand that the tidal phenomena in the SCS are mainly governed by incoming tidal waves from the Pacific Ocean through the Bashi Channel (See Figs 2 to 5).

In both this study and that by Ye and Robinson (1983), the reproduction of diurnal tides is better than that of semi-diurnal tides. Ye and Robinson (1983) pointed out that the shorter wave length of semi-diurnal tides resulted in poor reproduction of semi-diurnal tides near coasts with irregular geometry by the numerical model with coarse mesh size of about 31 km. The mesh size of 40 km of our numerical model is a little coarser than that of Ye and Robinson (1983). We will try another numerical experiment using a finer mesh size in the near future.

The reproductions of amplitude and phase in the whole area are very good in our numerical experiments, except for the small discrepancy near the coast especially on semi-diurnal tides, as shown in Figs 2 to 5. Therefore we will discuss the characteristics of tides and tidal currents based on our calculated results in the whole area of the SCS.

Tidal currents

The calculated amplitude of semi-diurnal tidal currents is shown in Fig.6 (a) and (b) with observed M2 tidal current amplitude in the northern coastal area of the SCS by Fang (1986) (Fig.6 c) and one calculated for the whole area by Ye and Robinson (1983) (Fig.6 d). There is no published chart of observed S2 tidal current amplitude in the SCS. The amplitude of M2 tidal current is large in the Taiwan Strait (about 60 cm s?1), off the southern coast of China (about 20 cm s?1), at the head of the Gulf of Thailand (about 20 cm s?1), off the southern coast of Indo-China peninsula (about 40 cm s?1), and off the northern coast of Kalimantan Island (about 60 cm s?1). Our calculated result for M2 tidal current amplitude is nearly the same as that by Ye and Robinson (1983). The accuracy of calculated tidal current amplitude near the coast is not high because the irregular bottom topography and/or horizontal geometry near the coast may generate strong tidal current locally. However, we cannot resolve such local amplification of tidal current amplitude by the numerical model with a coarse mesh size of 30 to 40 km.

Fig. 2 (a-b) ; (c-d) Calculated amplitude (a) and phase (b) of M2 tide by our numerical model and observed amplitude (c) and phase (d) of M2 tide by Yanagi et al. (1997) in the South China Sea. Phase is referred to 135oE. The calculated amplitude of diurnal tidal currents are shown in Fig.7a and 7b, with observed K1 tidal current amplitude in the northern coastal area of the SCS by Fang (1986) (Fig.7c) and one calculated for the whole area by Ye and Robinson (1983) (Fig.7d). There is no published chart of observed O1 tidal current amplitude in the SCS. The amplitude of diurnal tidal currents is large in the central parts of the Gulfs of Tongking and Thailand (about 30 cm/s), and off the southwestern coast of Kalimantan Island (35 cm/s). Results calculated by our model and that of Ye and Robinson (1983) are nearly the same and they reproduce well those observed by Fang (1986). Fig. 3 Calculated amplitude (a) and phase (b) of S2 tide by our numerical model and observed amplitude (c) and phase (d) of S2 tide by Yanagi et al. (1997) in the South China Sea. Phase is referred to 135 oE.

Fig. 4 Calculated amplitude (a) and phase (b) of K1 tide by our numerical model and observed amplitude (c) and phase (d) of K1 tide by Yanagi et al. (1997) in the South China Sea. Phase is referred to 135 oE.
Discussions
 
Diurnal tides are more dominant than semi-diurnal tides in the SCS and Yanagi et al. (1997) pointed out the possibility of the resonance of diurnal tides in the SCS. The period of the first mode of natural oscillation Tn1 along the long axis of the SCS, which is calculated from Tn1 =4L / (gh)1/2 (L=2500 km, the distance from the Bashi Channel to the east coast of the Malay peninsula; g=9.8 m s?1 , the gravitational acceleration and h=1500 m, the mean depth of the SCS), is 22.9 hours. However, the value for the mean depth of the SCS (1500 m) is a rough estimate and the natural oscillation period of 22.9 hours is not reliable. We examine quantitatively the natural oscillation period of the SCS using our numerical model. The tidal waves with amplitudes of 16 cm and different periods are given at the Bashi Channel, and the amplitude in the central part of the SCS is calculated using the radiation conditions at the other two open boundaries -- Taiwan Strait and the Sunda Shelf. The results are shown in Fig.8. The amplitudes are 69.8 cm, 70.5 cm and 66.9 cm for the periods of 18.8 h, 19.2 h, and 19.6 h, respectively. From this result, we can understand that the natural oscillation period of the SCS is 19.2 h and the diurnal periods are near the natural oscillation period of the SCS.
  Fig. 6 Calculated amplitude of M2 tidal current (a), that of S2 tidal current (b) by our numerical model, observed amplitude of M2 tidal current by Fang (1986) (c) and calculated amplitude of M2 tidal current by Ye and Robinson (1983) (d). The calculated distribution of tidal type F (which is (H K1 +H O1) / (H M2 +H S2), where H is the amplitude) of tide and tidal current in the SCS are shown in Fig.9. The diurnal type is defined as F > 1.25, the semi-diurnal type as F < 0.25 and the mixed-type as 1.25 > F > 0.25. In the entire area of the SCS, there is no region where semi-diurnal tides dominate and diurnal tides dominate nearly. On the other hand, semi-diurnal tidal currents dominate in the Taiwan Strait and the area of mixed-type tidal current is wider than that of tide. This is because with the same amplitude of tide, the periods of semi-diurnal tides are about half that of diurnal tides, and the amplitudes of semi-diurnal tidal currents are twice that of diurnal tidal currents.

Fig. 7 Calculated amplitude of K1 tidal current (a), that of O1 tidal current (b) by our numerical model, observed amplitude of K1 tidal current by Fang (1986) (c) and calculated amplitude of K1 tidal current by Ye and Robinson (1983) (d).

 
 
 Fig. 8 Amplitude versus period diagram.
 

Fig. 9 Tidal types of tide (a) and tidal current (b) in the South China Sea.

  
Acknowledgements
 
This study is partly supported by a research fund from the Ministry of Education, Science and Culture, Japan.
 
References
 
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