Dispersive tsunami waves in the ocean: Model equations and sensitivity to dispersion and Coriolis effects

We derive fully nonlinear, weakly dispersive model equations for propagation of surface gravity waves in a shallow, homogeneous ocean of variable depth on the surface of a rotating sphere. A numerical model is developed for the weakly nonlinear version of the model based on a combined finite-volume and finite-difference method with a fourth-order MUSCL-TVD scheme in space and a third-order SSP Runge-Kutta scheme in time. In the context of tsunami generation and propagation over trans-oceanic distances, a scaling analysis reveals that the importance of frequency dispersion increases with a decrease of the source width, while the effect of the Coriolis force increases with an increase of the source width. A sensitivity analysis to dispersive and Coriolis effects is carried out using the numerical model in a series of numerical experiments in an idealized ocean using Gaussian and di-polar sources with different source sizes. A simulation of the Tohoku 2011 tsunami is used to illustrate the effects of dispersive and Coriolis effects at large distances from the source region. (C) 2012 Elsevier Ltd. All rights reserved.