Numerical Study of Tsunami Waves with Sloping Bottom and Nonlinear Friction

In this paper we investigate the breaking of long-waves propagating on shallow water with nonlinear friction on the sloping bottom. A complete set of equations is presented and a numerical method is developed to simulate the wave propagation. The method uses an up-wind difference scheme for the nonlinear convective term and the central difference scheme for other derivative terms. Various numerical examples have been conducted to investigate the effect of nonlinear friction and drag coefficient on wave propagation and breaking. By analyzing the numerical results, we find that in order to overcome wave breaking, nonlinear friction needs to be below certain level.