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Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth

Published online by Cambridge University Press:  21 April 2006

Juan A. Zufiria
Juan A. Zufiria
Affiliation:
Applied Mathematics Department, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

A weakly nonlinear model is developed from the Hamiltonian formulation of water waves, to study the bifurcation structure of gravity-capillary waves on water of finite depth. It is found that, besides a very rich structure of symmetric solutions, non-symmetric Wilton's ripples exist. They appear via a spontaneous symmetrybreaking bifurcation from symmetric solutions. The bifurcation tree is similar to that for gravity waves. The solitary wave with surface tension is studied with the same model close to a critical depth. It is found that the solution is not unique, and that further non-symmetric solitary waves are possible. The bifurcation tree has the same structure as for the case of periodic waves. The possibility of checking these results in low-gravity experiments is postulated.

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Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 183 - 206
Copyright
© 1987 Cambridge University Press

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