Tsunami Waveforms and Runup of Undular Bores in Coastal Waters

Abstract

This paper carries out the numerical simulation of tsunami propagation based on the fully nonlinear and highly dispersive Boussinesq model. The numerical results indicate that the waveforms of a tsunami are quite different on steeply and mildly sloping beaches, which cannot be predicted by the analytical solution of the nonlinear shallow water equations. Long wave trains form on the steeply sloping beaches while undular bores emerge on the mildly sloping beaches. The simulation of hypothesized tsunamis in the China Seas provide different wave patterns in the near shore regions, including long wave trains, undular bores, and solitons. In order to study the propagation and run-up of undular bores, a series of undular bores is proposed by sinusoidal and attenuation functions. The properties of the run-up and energy budget of these undular bores are investigated.