Abstract
A set of wave equations derived on the basis of a variational principle in consideration of both strong nonlinearity and strong dispersion of surface/internal waves is numerically solved through a finite difference method to simulate generation and propagation of tsunamis in the vertical two-dimension. The velocity potential in each fluid layer is expanded into a power series of vertical position z, such that the accuracy of vertical distribution of velocity depends on the number of expansion terms, N. The tsunami generation in the existing experiment is successfully represented using the numerical model when N = 2 or 3. Shorter oscillation in a tsunami tail cannot be expressed in tsunami generation using the set of nonlinear shallow-water equations, where N = 1, as well as a long wave group, which consists of many waves especially in distant-tsunami propagation, leading to overestimation of both the wave height and wave steepness of the first wave. The wave height becomes larger in a stratified ocean than that in the one-layer case, although the present density distribution hardly affects the tsunami phase even after a travel of a long distance.
