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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 1, Pages 23–35
DOI: https://doi.org/10.15372/SJNM20170103 (Mi sjvm633) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach

An. G. Marchuk

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva, 6, Novosibirsk, 630090, Russia
Full-text PDF (2417 kB) Citations (3)
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DOI: https://doi.org/10.15372/SJNM20170103
Abstract: In this paper, the kinematics of the tsunami wave ray and the wavefront above an uneven bottom is studied. The formula to determine the wave height along a ray tube has been obtained. The exact analytical solution for the wave-ray trajectory above the parabolic bottom topography has been derived. Within the wave-ray approach this solution gives the possibility to determine the tsunami wave heights in an area with a parabolic bottom relief. The distribution of the wave-height maxima in the area with the parabolic bottom was compared to the one obtained by the numerical computation with a shallow-water model.
Key words: tsunami propagation, shallow-water equations, wave ray, wavefront kinematics.
Received: 30.05.2016
Revised: 02.09.2016
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 1, Pages 17–27
DOI: https://doi.org/10.1134/S1995423917010037
Bibliographic databases:
Document Type: Article
UDC: 550.344.42
Language: Russian
Citation: An. G. Marchuk, “The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach”, Sib. Zh. Vychisl. Mat., 20:1 (2017), 23–35; Num. Anal. Appl., 10:1 (2017), 17–27
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sjvm/v20/i1/p23
    • This publication is cited in the following 3 articles:
    1. E. D. Moskalensky, “The novel class of exact solutions of the two-dimensional eikonal equation when the velocity in a medium depends on one spatial coordinate”, Num. Anal. Appl., 11:3 (2018), 208–219  mathnet  crossref  crossref  isi  elib  elib
    2. K. Hayashi, An. Marchuk, A. Vazhenin, “Generating boundary conditions for the tsunami propagation calculation on imbedded grids”, Num. Anal. Appl., 11:3 (2018), 256–267  mathnet  crossref  crossref  isi  elib  elib
    3. S. I. Kabanikhin, O. I. Krivorotko, “An algorithm for source reconstruction in nonlinear shallow-water equations”, Comput. Math. Math. Phys., 58:8 (2018), 1334–1343  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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    Abstract page:209
    Full-text PDF :74
    References:29
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