Mathematical Modelling of Tsunami Propagation

The generation of tsunamis with the help of a simple dislocation model of an earthquake and their propagation in the basin are discussed. In this study, we examined the formation of a tsunami wave from an initial sea surface displacement similar to those obtained from earthquakes that have generated tsunami waves and its propagation through the sea to the shore. Linear shallow water wave equations were employed to explain the propagation of the waves in the open sea while nonlinear wave equations were introduced to explain the behaviour of the wave near the shore. The influence of the Coriolis force on the propagation of tsunami was shown to become very important when the tsunami travel distance is significant in relations to the earth’s complete rotation time. The group velocity of tsunami waves which is the velocity of wave energy propagation and its independence on the wave number was demonstrated. @ JASEM