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

Zufiria, Juan A. (1987) Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth. Journal of Fluid Mechanics, 184 . pp. 183-206. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120621-100754262

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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 symmetry breaking 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1017/S0022112087002854DOIUNSPECIFIED
http://journals.cambridge.org/abstract_S0022112087002854PublisherUNSPECIFIED
Additional Information:© 1987 Cambridge University Press. Received 23 September 1986; Published online 21 April 2006. I am indebted to Professor P. G. Saffman for his encouragement and valuable advice during the course of the research. This work was supported by the Office of Naval Research (N00014-79-C-0412, NR062-639) and by the National Science Foundation (OCE-8415988). I also wish to acknowledge receipt of a Fulbright award.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-79-C-0412
Office of Naval Research (ONR)NR062-639
NSFOCE-8415988
Fulbright FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20120621-100754262
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120621-100754262
Official Citation:Juan A. Zufiria (1987). Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth. Journal of Fluid Mechanics, 184 , pp 183-206 doi:10.1017/S0022112087002854
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32001
Collection:CaltechAUTHORS
Deposited By: Aucoeur Ngo
Deposited On:21 Jun 2012 18:31
Last Modified:26 Dec 2012 15:21

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