Explicit asymptotics for tsunami waves in framework of the piston model

S. Yu. Dobrokhotov, and S. Ya. Sekerzh-Zenkovich
Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

B. Tirozzi
Department of Physics, University "La Sapienza", Rome, Italy

B. Volkov
Department of Physics, Moscow State University, Moscow, Russia


[1]  An asymptotically numerical description of tsunami waves propagation in a basin with non-uniform depth in a neighborhood of wavefronts that can have caustics is proposed. The piston model and the long wave approximation are used. It is assumed that the size of the area of the initial disturbance is small in comparison both with the characteristic length of interval of the varying of the bottom depth and the distance from the observation point. The description is based on a generalization of asymptotic approach known as the Maslov canonical operator. We find formulas that are relatively simple and can be transformed in a computer program for fast calculating wave profiles. Some features of the tsunami waves propagation in basins of non-uniform depth are illustrated by graphics.

Received 25 September 2006; accepted 27 October 2006; published 7 November 2006.

Keywords: tsunami, asymptotics, dispersion-less piston model, wavefront, wave-profile.

Index Terms: 4564 Oceanography: Physical: Tsunamis and storm surges; 4594 Oceanography: Physical: Instruments and techniques; 4599 Oceanography: Physical: General or miscellaneous.


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