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Dynamics of steep two-dimensional gravity–capillary solitary waves

Published online by Cambridge University Press:  01 November 2010

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: [email protected]
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Abstract

In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type solitary waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation solitary waves, which were known to be linearly unstable, are shown to evolve into stable depression solitary waves, together with a radiated wave field. Depression waves and certain large amplitude elevation waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.

JFM classification

Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 466 - 477
Copyright
Copyright © Cambridge University Press 2010

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References

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