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Clockwise Phase Propagation of Semi-Diurnal Tides in the Gulf of Thailand

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Clockwise Phase Propagation of Semi-Diurnal Tides in the Gulf of Thailand Journal of Oceanography, Vol. 54, pp. 143 to 150. 1998 Clockwise Phase Propagation of Semi-Diurnal Tides in the Gulf of Thailand 1 2 TETSUO YANAGI and TOSHIYUKI TAKAO 1Research Institute for Applied Mechanics, Kyushu University, Kasuga 816, Japan 2Department of Civil and Environmental Engineering, Ehime University, Matsuyama 790, Japan (Received 4 August 1997; in revised form 3 December 1997; accepted 6 December 1997) The phase of semi-diurnal tides (M and S ) propagates clockwise in the central part of Keywords: 2 2 ⋅ the Gulf of Thailand, although that of the diurnal tides (K1, O1 and P1) is counterclock- Clockwise wise. The mechanism of clockwise phase propagation of semi-diurnal tides at the Gulf of amphidrome, ⋅ natural oscillation, Thailand in the northern hemisphere is examined using a simple numerical model. The ⋅ natural oscillation period of the whole Gulf of Thailand is near the semi-diurnal period tide, ⋅ Gulf of Thailand. and the direction of its phase propagation is clockwise, mainly due to the propagation direction of the large amplitude part of the incoming semi-diurnal tidal wave from the South China Sea. A simplified basin model with bottom slope and Coriolis force well reproduces the co-tidal and co-range charts of M2 tide in the Gulf of Thailand. 1. Introduction phase propagation of semi-diurnal tides at the Gulf of It is well known that the phase of tides propagates Thailand in the northern hemisphere using a simple numeri- counterclockwise (clockwise) in gulfs or shelf seas such as cal model. the North Sea, the Baltic, the Adria, the Persian Gulf, the Yellow Sea, the Sea of Okhotsk, the Gulf of Mexico and so 2. Gulf of Thailand on in the northern (southern) hemisphere and such a phe- The Gulf of Thailand is situated in the southwestern nomenon is well explained by the superposition of incoming part of the South China Sea and the length from the shelf and reflecting Kelvin waves (Taylor, 1920). But the phase of edge to the head of the gulf, L, is about 1,500 km; its width, semi-diurnal tides in the Black Sea propagates clockwise B, is about 460 km and its average depth, H, is about 40 m and Sterneck (1922) explained this remarkable phenomenon (Fig. 2). Because the phase speed of the long wave in the gulf in terms of the phase lag between the east-west natural –1 C = gH is about 20 m s , the wavelength of the semi- oscillation forced by the east-west component of tide-gen- diurnal tidal wave l = CT (T is the semi-diurnal pe- erating force and the north-south one forced by the north- M2 M2 M2 riod) is 890 km and that of diurnal one l is about 1,700 km. south component of tide-generating force in the Black Sea, K1 neglecting the Coriolis force. After high water along the east These are nearly one half of and the same as the length of the π coast, the high water occurs along the south coast of the gulf L, respectively. The inertia period Ti (=2 /f, f; the ω φ ω Black Sea because the natural oscillations in east-west and Coriolis parameter = 2 sin , ; the angular velocity of the φ ° north-south directions have the phase difference of π/2. The earth’s rotation, ; the latitude = 9 N in this case) of the gulf λ counterclockwise phase propagation of diurnal tides (K1 is 76.6 hours. The Rossby deformation length (= gH /f ) and O1) in the Black Sea is also explained by the same theory of the gulf is 870 km. (Sterneck, 1922). Semi-diurnal and diurnal tidal periods are much shorter The phase of diurnal tides (K1, O1 and P1) propagates than the inertia period and the width of the gulf is narrower counterclockwise at the central part of the Gulf of Thailand than the Rossby deformation length in the Gulf of Thailand. in the northern hemisphere, as shown in Fig. 1(b) but that of These facts suggest that the tidal phenomena are not seriously semi-diurnal tides (M2 and S2) propagates clockwise there affected by the Coriolis force in the Gulf of Thailand. as shown in Fig. 1(a) (Yanagi et al., 1997).The observed directions of the phase propagation of diurnal and semi- 3. Numerical Model diurnal tides are well reproduced by numerical experiments The horizontal two-dimensional momentum and con- (Yanagi and Takao, 1997). tinuity equations for tide and tidal current of a homogeneous In this paper we reveal the mechanism of the clockwise fluid under Cartesian coordinates are as follows; 143 Copyright The Oceanographic Society of Japan. (a) (b) Fig. 1. Co-tidal and co-range charts of M2 (a) and K1 (b) tides in the South China Sea. Phase is referred to 135°E (Yanagi et al., 1997). Fig. 2. Gulf of Thailand. Numbers show the depth in meters. 144 T. Yanagi and T. Takao (a) (b) Fig. 3. Co-tidal (full line) and co-range (broken line) charts of M2 and K1 tides in the simplified gulf with flat bottom in the cases of no rotation (a) and rotation (b). ∂u γ 2 u u horizontal gradient operator, k the locally vertical unit vec- + ()u ⋅∇ u + fk × u =−g∇η − b + ν∇2u,1() ∂ + η tor, η the sea surface elevation from the mean sea surface, t H 2 6 γb (=0.0026) the bottom frictional coefficient, ν (=10 cm2s–1)the horizontal eddy viscosity and H the local water ∂η +∇×{}()H + η u = 0.() 2 depth. ∂t Equations (1) and (2) can be approximated by finite difference and solved by the primitive method. Numerical Here u is the depth averaged velocity vector, t the time, ∇ the experiments have been conducted in basins with different Clockwise Phase Propagation of Semi-Diurnal Tides in the Gulf of Thailand 145 (a) (b) (c) Fig. 4. Same as Fig. 3 except with bottom slope. Numbers in the upper panel show the depth in meters. bottom topography, shown in Figs. 3 and 4, which simplify time step of the calculation is 2 minutes. The quasi-steady the horizontal and vertical geometry of the Gulf of Thailand, state is obtained in four tidal cycles after the beginning of the with a length of 1500 km, a width of 460 km and an open calculation and the harmonic analysis of sea surface elevation boundary along the eastern end. The grid size is 10 km × 10 and current field is carried out at the fifth tidal cycle. km. The uniform amplitude (15 cm for M2 tide and 35 cm for K1 tide) and phase lag (330 degree for M2 and K1 tides) are 4. Results given along the eastern open boundary on the basis of The calculated results in the case of a constant depth of observed amplitude and phase lag along the shelf edge of the 40 m and in the absence of the Coriolis force are shown in Gulf of Thailand shown in Fig. 1 (Yanagi et al., 1997). The Fig. 3(a). Two amphidromic points of the M2 tide and one of 146 T. Yanagi and T. Takao the K1 tide exist in the gulf. The northern amphidrome of the propagation of diurnal tide at the central part of the Gulf of M2 tide has a counterclockwise phase propagation, but the Thailand on the basis of the calculated results with simple southern one propagates clockwise. The phase of the K1 tide models shown in Figs. 3 and 4. N-S propagates clockwise in the central part of the gulf. Results The natural oscillation periods Tw i along the north- in the presence of the Coriolis force are shown in Fig. 3(b). south direction in the western part of the simplified gulf with The direction of phase propagation of the M2 tide in the the constant depth shown in Fig. 3 and those along the east- E-W southern part of the gulf changes from clockwise to coun- west direction in the northern part Tn i are calculated by terclockwise. The position of the amphidrome and the the following equation for a closed basin, direction of phase propagation of K1 tide change drastically from east to west and clockwise to counterclockwise, re- = 2Lb () spectively. Ti 3 igH Figure 3 suggests the existence of natural oscillation nodes where the co-tidal lines gather and the amplitude decreases, that is, the natural oscillation along the east-west where i denotes the mode number, Lb (=880 km along the direction dominates for the M2 tide with no Coriolis force. north-south direction and 460 km along the east-west direc- The natural oscillation along the north-south direction tion) the length of the basin and g (=9.8 m s–2) the gravita- dominates for the K1 tide and those along the north-south tional acceralation. The natural oscillation periods along the and east-west directions couple for the M2 tide with the north-south direction in the western part are N-S N-S N-S Coriolis force. Tw 1 = 24.7 hours, Tw 2 = 12.4 hours and Tw 3 = 8.2 The results in the simplified gulf with a bottom slope hours, those along the east-west direction in the northern N-S N-S are shown in Fig. 4. The amphidromic point of the M2 tide part are Tw 1 = 12.9 hours and Tw 2 = 6.5 hours. E-W in the northern part of the gulf shown in Fig. 3(a) disappears The natural oscillation periods Ts i along the east- when the bottom slope is included, as shown in Fig.
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