Grimshaw, RHJ;
Yuan, C;
(2016)
Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation.
Natural Hazards
, 84
(2)
pp. 493-511.
10.1007/s11069-016-2479-6.
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Abstract
Although tsunamis in the deep ocean are very long waves of quite small amplitudes, as they propagate shorewards into shallow water, nonlinearity becomes important and the structure of the leading waves depends on the polarity of the incident wave from the deep ocean. In this paper, we use a variable-coefficient Korteweg–de Vries equation to examine this issue, for an initial wave which is either elevation, or depression, or a combination of each. We show that the leading waves can be described by a reduction of the Whitham modulation theory to a solitary wave train. We find that for an initial elevation, the leading waves are elevation solitary waves with an amplitude which varies inversely with the depth, with a pre-factor which is twice the maximum amplitude in the initial wave. By contrast, for an initial depression, the leading wave is a depression rarefaction wave, followed by a solitary wave train whose maximum amplitude of the leading wave is determined by the square root of the mass in the initial wave.
| Type: | Article |
|---|---|
| Title: | Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11069-016-2479-6 |
| Publisher version: | http://dx.doi.org/10.1007/s11069-016-2479-6 |
| Language: | English |
| Additional information: | Copyright © The Author(s) 2016. Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Tsunami, Solitary wave, Shoaling |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1522169 |
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