### 1. Introduction

### 2. Numerical Simulation

_{2}, S

_{2}, K

_{1}, O

_{1}, N

_{2}, K

_{2}, P

_{1}and Q

_{1}. An additional experiment using Platzman resonant iteration scheme was conducted to investigate the free oscillation modes in the SCS.

### 3. Model Validation

_{2}amplitude: 21.0 cm, M

_{2}phase: 25.9 degree, S

_{2}amplitude: 8.23 cm, S

_{2}phase: 29.4 degree, K

_{1}amplitude: 9.5 cm, K

_{1}phase: 20.1 degree, and O

_{1}amplitude: 10.8 cm, O

_{1}phase: 16.0 degree. The differences are attributed to disagreement between the observation stations and calculation grid points, irrelevant bottom friction coefficients, and the effect of shallow water depths.

### 4. Results and Discussion

### 4.1 Tide Prediction System

_{2}, S

_{2}, K

_{1}and O

_{1}with minor constituents, N

_{2}, K

_{2}, P

_{1}and Q

_{1}. The small figure in this figure indicates the enlarged image of tides in Tacloban City. The tidal distributions of four major constituents are similar to the previous studies (Cai et al., 2006; Fang et al., 1999; Zu et al., 2008). The largest M

_{2}tide amplitude is found in the Taiwan Strait and the large ones are found in the south of Guangdong around Leizhou Peninsula, the northwest coast of Kalimantan, south of the Indo-China Peninsula, and around the western and southern parts of the Malay Peninsula. The amphidromic points are shown in the shelves including Gulf of Thailand. The S

_{2}tidal chart is similar to M

_{2}tidal chart. The highest amplitudes of S

_{2}tide are shown near the positions displaying the highest M

_{2}amplitude. In the case of S

_{2}tide, the high values are also found in the southeast coast of Kalimantan and Celebes Sea. The K

_{1}and O

_{1}tidal charts show the amphidromic points in Gulf of Thailand and the K

_{1}and O

_{1}tidal amplitudes are larger than S

_{2}tide. The phase directions of semi-diurnal tides are shown in clockwise propagation and the phase directions of diurnal tides are shown in counterclockwise propagation at the Gulf of Thailand. Yanagi and Toshiyuki (1998a) reported the mechanism of clockwise phase propagation of semidiurnal tide and counterclockwise phase propagation of diurnal tide at the central part of the Gulf of Thailand.

_{2}and S

_{2}are high in the east of Leizhou Peninsula, while those of K

_{1}and O

_{1}tides are high in the west of Leizhou Peninsula. Fang et al. (1999) reported that the amplification of semi-diurnal tides in the shelf sea east of the Leizhou Peninsula is much greater that diurnal tides. This pattern was described by Cao and Fang (1990) by means of the theory of Clarke and Battisti (1981). Both K

_{1}and O

_{1}tidal charts show the degenerate amphidromic system centered at the middle of Vietnam coast. This feature is also depicted in Fang et al. (1999). The tidal charts of four minor constituents were also obtained from the simulation. The amphidromic points of N

_{2}and K

_{2}constituents are shown near the positions of M

_{2}and S

_{2}constituents. In addition, the spatial distribution of high or low amplitude is similar to those of M

_{2}and S

_{2}constituents. Maximum tidal amplitude (> 30 cm) of N

_{2}constituent is calculated in the north-west coast of Kalimantan, and maximum one (> 10 cm) of K

_{2}are found in the same coast. The spatial patterns of P

_{1}and Q

_{1}showing the amphidromic system and co-tidal line are similar to K

_{1}and O

_{1}tides. Generally, the tidal amplitudes of P

_{1}and Q

_{1}constituents are less than 30 cm and 20 cm, respectively.

### 4.2 Free Oscillation

*F*is calculated as

*F*= (A

_{K1}+ A

_{O1})/(A

_{M2}+ A

_{S2}), where

*A*

_{constituent}is the tidal amplitude of each constituent. If F < 0.25, tides are semi-diurnal. In the cases that

*F*ranges from 0.25 to 1.50 or from 1.50 to 3.0, tides are dominantly semi-diurnal or dominantly diurnal, respectively. If

*F*> 3, there is diurnal tides. Fig. 5 depicts the tidal regimes in the SCS, classified by tidal form factor,

*F*, which was computed from modeled tidal amplitudes (Fig. 4). Overall, this distribution is similar to the figure of van Maren and Gerritsen (2012) computed with the TPX06 ocean tide model. The difference of types between our study and van Maren and Gerritsen (2012) is shown the west of Luzon Island, Sulu Sea, Celebes Sea, Java Sea and the east of Philippine Islands, however its difference is just one grade and the type like semi-diurnal or diurnal tides is approximately equal each other. Comparing Fig. 5 with cotidal charts (Fig. 4), the regions characterized by semi-diurnal tide are the Taiwan Strait, the east of Leizou Peninsula, the south-east of Indo-China Peninsula, the north-west of Kalimantan Island, Celebes Sea and Philippine Sea, especially the strong semi-diurnal tide in the Taiwan Strait. On the other hand, the regions classed as diurnal tide are the overall SCS excluding the regions with semi-diurnal tide, and in particular, the very predominant diurnal tide are shown in the Gulf of Tonkin, the west of Luzon Island, Gulf of Thailand, Karimata Strait and a part of the Java Sea.

_{1}inside the Gulf of Tonkin, P6 at Leizhou outside the Gulf of Tonkin, P2 and P5 inside SCS, P3 and P4 inside the Gulf of Thailand, P9 and P

_{1}0 inside Java Sea, P8 inside Celebes Sea and P9 inside Sulu Sea. These 10 points correspond to the representative of regions classified by tidal form factor (center of Fig. 5). Here, water elevations were stored in at intervals of 10 minutes and the ones recorded for the early two days were discarded for the computation of free oscillation mode.

_{1}in Fig. 5) has the periods of around 10 hours, 20 hours and 31 hours. The periods of around 57 hours are shown in the center of Gulf of Thailand (P4 in Fig. 5) and the periods of around 49 hours are shown in the Java Sea (P9 in Fig. 5). Blackman-Turkey method’s frequency spectra distribution were different from FFT’s results, however the peak periods were quite similar to FFT’s ones on the whole region.

_{2}tide decreases in the SCS basin after propagating from the Pacific Ocean through the Luzon Strait, while that of K

_{1}tide increase remarkably. According to Zu et al. (2008), the K

_{1}tide is amplified by the Helmholtz resonance inside the SCS, considering that the phase and amplitude of the K

_{1}tide are nearly constant, and based on the resonant frequency for a Helmholtz oscillator and basin shape information (area and length) of the SCS and Luzon Strait, the resonant period of the basin is calculated as 24.8 hours, which is close to the diurnal tidal periods of K

_{1}(23.93 h) and O

_{1}(25.82 h). The co-amplitude and co-phase patterns of the S

_{2}and O

_{1}tides are similar to the M

_{2}and K

_{1}tides, respectively. The amplitude of the S

_{2}tide is much smaller than that of M

_{2}tide, whereas the amplitude of O

_{1}tide is comparable to that of K

_{1}tide. O

_{1}tide also responds to Helmholtz resonance in the SCS basin. Our study shows that the prevailing peak periods are approximately 20 hours in the SCS, which is comparable to Zu et al. (2008).

_{2}, is quite large in the Taiwan Strait in many studies (Cai et al., 2006; Fang et al., 1999; van Maren and Gerritsen, 2012; Zu et al., 2008) as well as our study (Fig. 4 and 5), thus the computed free oscillation period of 10 hours demonstrates the near-resonant characteristics of this area which responds to semi-diurnal tidal period.

*L*(length of the Gulf of Tonkin) = 500 km and

*h*(water depth) = 60 m at the entrance of the Gulf of Tonkin assuming that its basin has a rectangular type horizontally and non-uniform depth with a constant slope vertically (Rabinovich, 2009). If considering the Coriolis force, the period becomes smaller, i.e., 29 hours. In addition, Minh et al. (2014) estimated the resonant modes of this basin using the numerical simulation that the single tidal force of O

_{1}constituent was imposed, the forcing period varied from 4 to 56 hours and the model run length was 360 hours. The model result showed the resonant peak was seen around a period of approximately 29 hours. This period was very close to the other period, i.e., 29 hours obtained assuming the basin has a rectangular type and the constant slope and the effect of earth rotation. Our study exhibits the free oscillation period of about 30 hours in the Gulf of Tonkin, which is nearly the same as the result of Minh et al. (2014).

### 4.3 Residual Transport

_{2}, S

_{2}, K

_{1}and O

_{1}(Yanagi and Takao, 1998b).

_{2}, S

_{2}, K

_{1}and O

_{1}(Fig. 7). The tidal energy dissipation is estimated by converting the maximum bottom shear stress caused by the bottom friction into work per unit area. Comparing with tidal charts of semi-diurnal and diurnal tides (Fig. 4), the distributions of M

_{2}and S

_{2}, and K

_{1}and O

_{1}are similar. The maximum tidal energy dissipation (> 10

^{4}N/m) due to M

_{2}tide is shown in the Taiwan and Malacca Straits, small channels connecting Sulu and Celebes Seas, and northwestern Kalimantan Island. The large tidal energy dissipation of about 0.5 N/m is seen in the southeastern Indo-China Peninsula. The pattern of tidal energy dissipation of S

_{2}constituent is similar to that of M

_{2}tide, but the magnitude of S

_{2}is much smaller.

_{1}and O

_{1}is large in small channels between Sulu and Celebes Seas, the Gulf of Tonkin, the Hainan Strait, the Gulf of Thailand, the Karimata Strait and the Java Sea. In the Gulf of Thailand, the Karimata Strait and the Java Sea, energy dissipation of O

_{1}tide is distinctly smaller than that of K

_{1}tide, whereas in the Gulf of Tonkin including the Hainan Strait, that of O

_{1}tide is nearly equal or comparable to that of K

_{1}tide.