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Oscillatory spatially periodic weakly nonlinear gravity waves on deep water

Zufiria, Juan A. (1988) Oscillatory spatially periodic weakly nonlinear gravity waves on deep water. Journal of Fluid Mechanics, 191 . pp. 341-372. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120607-135919090

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Abstract

A weakly nonlinear Hamiltonian model is derived from the exact water wave equations to study the time evolution of spatially periodic wavetrains. The model assumes that the spatial spectrum of the wavetrain is formed by only three free waves, i.e. a carrier and two side bands. The model has the same symmetries and invariances as the exact equations. As a result, it is found that not only the permanent form travelling waves and their stability are important in describing the time evolution of the waves, but also a new kind of family of solutions which has two basic frequencies plays a crucial role in the dynamics of the waves. It is also shown that three is the minimum number of free waves which is necessary to have chaotic behaviour of water waves.


Item Type:Article
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URLURL TypeDescription
http://dx.doi.org/10.1017/S0022112088001600 DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=394336PublisherUNSPECIFIED
Additional Information:© 1988 Cambridge University Press. Received 23 April 1987 and in revised form 24 August 1987. Published Online April 21 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 an award from the Comité Conjunto Hispano-Norteamericano para la cooperacion cultural y educativa.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-79-C-0412
Office of Naval Research (ONR)NR062-639
NSFOCE-8415988
Comité Conjunto Hispano-Norteamericano para la cooperacion cultural y educativaUNSPECIFIED
Record Number:CaltechAUTHORS:20120607-135919090
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120607-135919090
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31842
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Jun 2012 21:15
Last Modified:26 Dec 2012 15:19

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