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Focusing of long waves with finite crest over constant depth
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Date
2013-05-08
Author
Kanoğlu, Utku
Titov, Vasily V.
Aydin, Baran
Moore, Christopher
Stefanakis, Themistoklis S.
Zhou, Hongqiang
Spillane, Michael
Synolakis, Costas E.
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Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from their source region. Here, we introduce a new analytical solution to study the propagation of a finite strip source over constant depth using linear shallow-water wave theory. This solution is not only exact, but also general and allows the use of realistic initial waveforms such as N-waves. We show the existence of focusing points for N-wave-type initial displacements, i.e. points where unexpectedly large wave heights may be observed. We explain the effect of focusing from a strip source analytically, and explore it numerically. We observe focusing points using linear non-dispersive and linear dispersive theories, analytically; and nonlinear non-dispersive and weakly nonlinear weakly dispersive theories, numerically. We discuss geophysical implications of our solutions using the 17 July 1998 Papua New Guinea and the 17 July 2006 Java tsunamis as examples. Our results may also help to explain high run-up values observed during the 11 March 2011 Japan tsunami, which are otherwise not consistent with existing scaling relationships. We conclude that N-waves generated by tectonic displacements feature focusing points, which may significantly amplify run-up beyond what is often assumed from widely used scaling relationships.
Subject Keywords
General Engineering
,
General Physics and Astronomy
,
General Mathematics
URI
https://hdl.handle.net/11511/39096
Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
DOI
https://doi.org/10.1098/rspa.2013.0015
Collections
Department of Aerospace Engineering, Article
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BibTeX
U. Kanoğlu et al., “Focusing of long waves with finite crest over constant depth,”
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
, vol. 469, no. 2153, pp. 0–0, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39096.