A method of determining the maximum height of localized circular waves in the proximity of shallow water

Abstract

The paper presents a mathematical model of the expansion of localized circular tsunami-type waves in the proximity ofshallow water. The model is based on special T-profile representations of the waves. Taking into account the relevant profile representations, we have analytically solved the system of shallow water equations for random bottom surface in the absence of azimuthal perturbations. We have suggested a method for studyingover-time changes of the profile of random initial perturbations at a given bottom surface, which allows, in particular, studying over-time changes of the maximum disturbance. The main idea is to studythe changing profile of traveling waves at certain checkpoints and to find appropriate equations for amplitude functions. For each checkpoint,we solve the Cauchy problem for ordinary differential equations. The method can be applied with regard to random initial conditions for the wave profile, the law of its movement,and different initial perturbation velocities.