The role of non-linear terms in the shallow water equation with the application in three-dimensional tidal model of the Malacca Strait and Taylor's Problem in low geographical latitude

Abstract

Numerical experiments were done with the tides in Malacca Strait using a three-dimensional model, based on finite-difference and a semi-implicit numerical scheme. The numerical experiments were carried out as follows: firstly the discreted shallow water equations were solved without non-linear terms. Secondly, the case with non-linear terms was run. The results are then compared and we show that the non-linear terms play a dominant role in the Malacca Strait. They also suggest that one must be careful when ignoring these terms in order to maintain the stability of the model. Kelvin wave propagation using the analytical model is also discussed. It is found that the pattern of M 2 amplitude’s lines is greatly influenced by small value of Coriolis parameter in Malacca Strait (∼3°), while the pattern of M 2 co-tidal lines is controlled by the bottom friction parameter. It is also proposed to calculate energy balance directly using the ratio of reflected and incident Kelvin wave in open boundary of analytical model. From this direct calculation, the displacement of amphidrome can be determined exactly. It can then be concluded that the Malacca Strait has actually the virtual amphidromic point, where the position of this point is away roughly 2097 km northeastward from the middle of the Strait. The total loss of energy due to bottom friction, calculated by analytical model, coincides well with that calculated by numerical model in the Malacca Strait.