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Hydroelastic solitary waves in deep water

Published online by Cambridge University Press:  19 May 2011

PAUL A. MILEWSKI ,
J.-M. VANDEN-BROECK  and
ZHAN WANG
PAUL A. MILEWSKI*
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA
J.-M. VANDEN-BROECK
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
ZHAN WANG
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA
*
†Email address for correspondence: milewski@math.wisc.edu
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Abstract

The problem of waves propagating on the surface of a two-dimensional ideal fluid of infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use a nonlinear elastic model that has been used to describe the dynamics of ice sheets. Particular attention is paid to forced and unforced dynamics of waves having near-minimum phase speed. For the unforced problem, we find that wavepacket solitary waves bifurcate from nonlinear periodic waves of minimum speed. When the problem is forced by a moving load, we find that, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. In unsteady computations, we find that if the problem is forced at a speed in this range, very large unsteady responses are obtained, and that when the forcing is released, a solitary wave is generated. These solitary waves appear stable, and can coexist within a sea of small-amplitude waves.

JFM classification

Waves/Free-surface Flows: Elastic waves Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 628 - 640
Copyright
Copyright © Cambridge University Press 2011

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References

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