Asymptotic De-‎scription for Tsunami Waves in Framework of the Piston Model: General ‎Construction and Explicit Solvable Cases

Dobrokhotov S.Yu., Volkov B.I., Sekerzh-Zenkovich S.Ya., Tirozzi B.

An asymptotically numerical description of tsunami wave propagation in a basin with nonuniform depth ‎in a neighbourhood 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 with both the characteristic length of the bottom depth variation interval and the distance ‎from the observation point. The description is based on the generalization of an asymptotic approach ‎known as Maslov canonical operator. For special disturbances relatively simple explicit formulas are ‎presented that can be transformed in a computer program for wave profiles fast calculating. Some ‎features of the tsunami wave propagation in basins of nonuniform depth are illustrated by graphics with ‎the help of these formulas.

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