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Asymmetric gravity–capillary solitary waves on deep water

Published online by Cambridge University Press:  04 November 2014

Z. Wang ,
J.-M. Vanden-Broeck  and
P. A. Milewski
Z. Wang*
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
P. A. Milewski
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
*
†Email address for correspondence: [email protected]
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Abstract

We present new families of gravity–capillary solitary waves propagating on the surface of a two-dimensional deep fluid. These spatially localised travelling-wave solutions are non-symmetric in the wave propagation direction. Our computation reveals that these waves appear from a spontaneous symmetry-breaking bifurcation, and connect two branches of multi-packet symmetric solitary waves. The speed–energy bifurcation curve of asymmetric solitary waves features a zigzag behaviour with one or more turning points.

JFM classification

Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Surface gravity waves
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 759 , 25 November 2014 , R2
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Copyright
© 2014 Cambridge University Press 

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