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Wave Trains Associated with a Cascade of Bifurcations ofSpace-Time Caustics over Elongated Underwater Banks

Published online by Cambridge University Press:  17 September 2013

S. Yu. Dobrokhotov ,
D. A. Lozhnikov  and
V. E. Nazaikinskii
S. Yu. Dobrokhotov*
Affiliation:
A. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences Moscow Institute of Physics and Technology
D. A. Lozhnikov
Affiliation:
A. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences Moscow Institute of Physics and Technology
V. E. Nazaikinskii
Affiliation:
A. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences Moscow Institute of Physics and Technology
*
⋆ Corresponding author. E-mail: dobr@ipmnet.ru
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Abstract

We study the behavior of linear nonstationary shallow water waves generated by aninstantaneous localized source as they propagate over and become trapped by elongatedunderwater banks or ridges. To find the solutions of the corresponding equations, we usean earlier-developed asymptotic approach based on a generalization of Maslov’s canonicaloperator, which provides a relatively simple and efficient analytic-numerical algorithmfor the wave field computation. An analysis of simple examples (where the bank and sourceshapes are given by certain elementary functions) shows that the appearance and dynamicsof trapped wave trains is closely related to a cascade of bifurcations of space-timecaustics, the bifurcation parameter being the bank length-to-width ratio.

Keywords

linearized shallow water equationsasymptoticswave front singularity evolutiontrapped nonstationary waveunderwater ridgeunderwater bank
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 1 - 12
Copyright
© EDP Sciences, 2013

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