Numerical Study of Tsunami Waves with Sloping Bottom and Nonlinear Friction

Abstract

Abstract: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.

Nonlinear processes in tsunami simulations for the Peruvian coast with focus on Lima/Callao

“…All these types of nonlinearity play different roles in wave propagation near and on the coast. As shown in the work of Androsov et al (2013), on a steep slope of the bottom when approaching the coast, the momentum advection plays a prominent role; in the shelf zones, there is already a nonlinearity in the continuity equation and, near the coast and on it, friction at the bottom (Ribal, 2008).…”

The Role of Sine and Cosine Components in Love Waves and Rayleigh Waves for Energy Hauling during Earthquake

“…Tsunami waves or long waves are also the surface waves. However, these waves are dissimilar with Rayleigh waves or Love waves (Ribal, 2007;2008).…”