Abstract
Conditions are derived under which asymptotic solutions of the Cauchy problem for the wave equation can be applied to the computation of a piston model of tsunami in a basin of constant depth. The derivation is carried out for the initial displacement of the bottom in the form of Gaussian exponentials by comparing the results of numerical integration with computations using asymptotic formulas.
Similar content being viewed by others
References
S. Dobrokhotov, S. Sekerzh-Zenkovich, B. Tirozzi, and T. Tudorovski, “Description of Tsunami Propagation Based on the Maslov Canonical Operator,” Dokl. Akad. Nauk 409(2), 171–175 (2006) [Doklady Mathematics 74 (1), 592–596, (2006)].
S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zenkovich, B. Tirozzi, and B. Volkov, “Explicit Asymptotics for Tsunami Waves in Framework of the Piston Model,” Russ. J. Earth. Sci. 8, ES4003 (2006).
V. P. Maslov, Perturbation Theory and Asymptotic Methods (Izdat. Moskov. Univ., Moscow, 1965) [in Russian].
F. I. González, “Tsunami! Predicting Destruction by Monster Waves,” Sci. American 21, 58–65 (May 1999).
S. S. Voit, “Tsunami Waves,” in Oceanology, Physics of the Ocean, Part 2: Hydrodynamics of the Ocean (Nauka, Moscow, 1978), pp. 229–254.
E. N. Pelinovsky, Tsunami Wave Hydrodynamics, (Nizhny Novgorod Ins. Applied Physics Press, 1996) [in Russian].
E. Bryant, Tsunami. The Underrated Hazard (Cambridge University Press, 2001).
V. S. Vladimirov, Generalized Functions in Mathematical Physics (Nauka, Fizmatgiz, Moscow, 1976).
H. Lamb, Hydrodynamics (Cambridge University Press, London, 1930).
N. E. Kochin, I.A. Kibel, and N. V. Roze, Theoretical Hydrodynamics, Part 1 (Fizmatgiz, Moscow, 1963).
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the Russian Foundation for Basic Research, project 05-01-00968.
Rights and permissions
About this article
Cite this article
Sekerzh-Zenkovich, S.Y., Volkov, B.I. Application of asymptotic solutions for the computation of the piston model of tsunami. Russ. J. Math. Phys. 14, 319–331 (2007). https://doi.org/10.1134/S1061920807030077
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1061920807030077