An. G. Marchuk, “The assessment of tsunami heights above the bottom slope within the wave-ray approach”, Sib. Zh. Vychisl. Mat., 18:4 (2015), 377–388; Num. Anal. Appl., 8:4 (2015), 304

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2015, Volume 18, Number 4, Pages 377–388
DOI: https://doi.org/15372/SJNM20150404 (Mi sjvm590)

This article is cited in 12 scientific papers (total in 12 papers)

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

An. G. Marchuk

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev pr., Novosibirsk, 630090, Russia

Full-text PDF (272 kB) Citations (12)

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DOI: https://doi.org/15372/SJNM20150404

Abstract: In this paper, the kinematics of the tsunami wave ray and wave front above an uneven bottom is studied. The formula to determine the wave height along a ray tube is obtained. The exact analytical solution for the wave-ray trajectory above the bottom slope is derived. This solution gives the possibility to determine within the wave-ray approach the tsunami wave heights in an area with a sloping bottom relief. The distribution of the wave-height maxima in the area with the sloping bottom is compared to the one obtained by the numerical computation with a shallow-water model.

Key words: tsunami propagation, shallow-water equations, wave ray, wave front kinematics.

Received: 24.03.2015
Revised: 19.05.2015

English version:
Numerical Analysis and Applications, 2015, Volume 8, Issue 4, Pages 304–313
DOI: https://doi.org/10.1134/S1995423915040047

Bibliographic databases:

Document Type: Article

UDC: 550.344.42

Language: Russian

Citation: An. G. Marchuk, “The assessment of tsunami heights above the bottom slope within the wave-ray approach”, Sib. Zh. Vychisl. Mat., 18:4 (2015), 377–388; Num. Anal. Appl., 8:4 (2015), 304–313

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sjvm590

https://www.mathnet.ru/eng/sjvm/v18/i4/p377

This publication is cited in the following 12 articles:

Mikhail Lavrentiev, Andrey Marchuk, Konstantin Oblaukhov, “Low power computation of transoceanic wave propagation for tsunami hazard mitigation”, Ocean Modelling, 192 (2024), 102459
A. G. Marchuk, “Capture of Wave Energy by Islands”, jour, 21:3 (2023), 20
An. G. Marchuk, “Restoration of the ocean depth using recorded tsunami arrival times”, Num. Anal. Appl., 14:1 (2021), 83–89
Lavrentiev M., Lysakov K., Marchuk A., Oblaukhov K., Shadrin M., “Algorithmic Design of An Fpga-Based Calculator For Fast Evaluation of Tsunami Wave Danger”, Algorithms, 14:12 (2021), 343
Lavrentiev M.M., Marchuk A.G., “Fast Modelling of Tsunami Wave Propagation Using Pc With Hardware Computer Code Acceleration”, J. Sib. Fed. Univ.-Math. Phys., 14:4 (2021), 433–444
M. Lavrentiev, K. Lysakov, A. Marchuk, K. Oblaukhov, M. Shadrin, “Hardware acceleration of tsunami wave propagation modeling in the southern part of japan”, Appl. Sci.-Basel, 10:12 (2020), 4159
V. V. Churuksaeva, A. V. Starchenko, “Numerical modelling of pollution transport in tom river”, Vestn. Tomsk. Gos. Univ.-Mat. Mek., 2020, no. 64, 48–62
M Lavrentiev, An Marchuk, K Oblaukhov, A Romanenko, “Comparative testing of MOST and Mac-Cormack numerical schemes to calculate tsunami wave propagation”, J. Phys.: Conf. Ser., 1666:1 (2020), 012028
Mikhail Lavrentiev, Konstantin Lysakov, Andrey Marchuk, Konstantin Oblaukhov, Mikhail Shadrin, OCEANS 2019 - Marseille, 2019, 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
Konstatntin Lysakov, Mikhail Lavrentiev, Andrey Marchuk, Konstatntin Oblaukhov, Mikhail Shadrin, 2018 OCEANS - MTS/IEEE Kobe Techno-Oceans (OTO), 2018, 1
An. G. Marchuk, “The assessment of tsunami heights above the parabolic bottom relief within the wave-ray approach”, Num. Anal. Appl., 10:1 (2017), 17–27

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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