Tsunami surge in a river: a hydraulic jump in an inhomogeneous channel

Abstract

A tsunami or storm surge propogating in a river is a very energetic phenomenon and not many human constructions can resist it. We will not consider here the case of the ocean where the bathymetry plays a crucial role in fixing the wave speed but a channel or river where the depth and width vary slowly compared with the wave length. We examined the propagation of a tsunami from the deep sea where non-linearity and dispersion are small to the coastline where those parameters become significant. In particular we showed on the inhomogeneous linear wave equation the importance of bathymetry in the wave amplification.