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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2020 Volume 60, Number 8, Pages 1439–1448 (Mi zvmmf11123)

This article is cited in 5 papers

Variational method for computing ray trajectories and fronts of tsunami waves generated by a localized source

S. Yu. Dobrokhotovab, M. V. Klimenkoc, I. A. Nosikovc, A. A. Tolchennikovab

a Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 117526 Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, 141700 Russia
c Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, West Department, Russian Academy of Sciences, Kaliningrad, 236035 Russia

Abstract: A variational approach for solving the boundary value problem of computing ray trajectories and fronts of ocean waves is presented. The solution method is based on Fermat's principle (of stationary time). A distinctive feature of the proposed approach is that the Fermat functional is optimized directly without solving the Euler–Lagrange equation; moreover, the locations of the wave source and receiver are fixed. Multipath propagation in the boundary value problem is addressed by finding various types of stationary points of the Fermat functional. The technique is numerically tested by applying the method of bicharacteristics with the use of analytical seabed models. The advantages of the variational approach and the prospects of its further development as applied to ocean wave computation are described. The relations between various types of stationary points of the travel time functional, caustics, and foci are discussed.

Key words: ocean waves, tsunami, rays, fronts, Fermat's principle, functional, method of bicharacteristics.

UDC: 519.6

Received: 11.11.2019
Revised: 15.02.2020
Accepted: 09.04.2020

DOI: 10.31857/S0044466920080074


 English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1392–1401

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© Steklov Math. Inst. of RAS, 2024