Variational Boussinesq model for simulation of coastal waves and tsunamis

In this paper we describe the basic ideas of a so-called Variational Boussinesq Model which is based on the Hamiltonian structure of gravity surface waves. By using a rather simple approach to prescribe the profile of vertical fluid potential in the expression for the kinetic energy, we obtain a set of dynamic equations extended with one additional elliptic equation for the amplitude of the vertical profile. All expressions in the energy contain at most first order derivatives, which makes a numerical implementation with finite elements relatively easy. The applicability of the code is illustrated for two different applications in this paper. One application deals with tsunami simulations, for which we show the phenomenon of tsunami waveguiding before the coast of Lampung in Indonesia. Another application deals with simulations of coastal waves entering the small harbour of Cilacap on the south-coast of Java, Indonesia; we will show that the simulations indicate a resonance phenomenon in the small inner harbour.