Abstract
A linear hydrodynamic problem concerning the generation of gravitational waves on the free surface of a liquid by a source (defined as an initial instant vertical displacement of the bottom of the basin) is studied, where the displacement is defined by a rather simple axially symmetric function of the horizontal coordinates. A solution to the problem is obtained in the form of single integrals and is regarded as a distribution (a “generalized function”) with respect to time. These integrals are evaluated numerically and asymptotically. In this part of the paper, using the results of numerical evaluation carried out for each source (having a given characteristic radius in a wide range of values), we find the initial instantaneous displacement of the fluid, determine the parameters of the leading crest of the created surface wave, and estimate the minimal radius which a source must have to be referred to tsunami generators.
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References
S. S. Voit, “Tsunami Waves,” Oceanology, Physics of the ocean, Part 2: Hydrodynamics of the Ocean, Nauka, Moscow, 229–254 (1978) [in Russian].
S. Wang, B. Le Mehaute, and Chia-Chi Lu, “Effect of dispersion on impulsive waves,” Marine Geophysical Researches 9, 95–111 (1987).
I. M. Gel’fand and G. E. Shilov, “Generalized Functions,” Vol. I (Fizmatgiz, Moscow, 1959; Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1964 [1977]).
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This work was supported by the Russian Foundation for Basic Research, project 11-01-00973-A.
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Sekerzh-Zen’kovich, S.Y. Analytical study of a potential model of tsunami with a simple source of piston type. 1. Exact solution. Creation of tsunami. Russ. J. Math. Phys. 19, 385–393 (2012). https://doi.org/10.1134/S1061920812030107
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DOI: https://doi.org/10.1134/S1061920812030107