RIASSUNTO
ABSTRACT:
The linear shallow-water equations have been used frequently to simulate transoceanic propagation of tsunamis instead of the linear Boussinesq equations. In previous studies, the physical dispersion is compensated by using the numerical dispersion generated from the leap-frog finite difference scheme. However, the linear Boussinesq equations can be directly solved because computer technique has been improved dramatically. In this study, a new finite difference scheme is proposed to discretize the linear Boussinesq equations. The newly developed model is applied to propagation of a Gaussian hump over a constant water depth. The model is then verified by comparing predicted results with analytic solutions. Predicted results agree well with analytical solutions. The model can be directly applied to simulation of transoceanic propagation of tsunamis.
INTRODUCTION
Tsunami is one of the ocean water surface waves and is generated by landslides, an undersea earthquake, a volcanic eruption and a meteor, which can disturb ocean water surface. Most of major tsunamis result from undersea earthquakes and the induced tsunami travels in all directions from the source region where the water surface is disturbed. When a tsunami propagates over a long distance, in general, the frequency dispersion and Coriolis force may play some roles(Kajiura and Shuto, 1990). However, the nonlinear advective inertia force is not significant comparably and can be ignored because the wave slope of a typical tsunami is very small(Imamura et al., 1988). Thus, the linear Boussinesq equations including the Coriolis force may be adequate to describe the propagation of distant tsunamis (Imamura et al., 1988; Liu et al., 1994). When the linear Boussinesq equations are simulated with numerical methods, it may require a small mesh size to suppress the numerical dispersion, and consume a huge computer memory space and excessive computational time to deal with frequency dispersion terms expressed by higher order derivatives.