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The superharmonic instability of finite-amplitude water waves

Saffman, P. G. (1985) The superharmonic instability of finite-amplitude water waves. Journal of Fluid Mechanics, 159 . pp. 169-174. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:SAFjfm85

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Abstract

Zakharov's (1968) Hamiltonian formulation of water waves is used to prove analytically Tanaka's (1983) numerical result that superharmonic disturbances to periodic waves of permanent form exchange stability when the wave energy is an extremum as a function of wave height. Tanaka's (1985) explanation for the non-appearance of superharmonic bifurcation is also derived, and the non-existence of stability exchange when the wave speed is an extremum is explained.


Item Type:Article
Additional Information:Copyright © 1985 Cambridge University Press. Reprinted with permission. (Received 7 January 1985) I have benefited from discussions with Dr H.C. Yuen, Dr P.A.E.M. Janssen and Mr J. Zufiria. This work was supported by the Office of Naval Research (NW14-79-C-0412 NR062-639).
Record Number:CaltechAUTHORS:SAFjfm85
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SAFjfm85
Alternative URL:http://dx.doi.org/10.1017/S0022112085003159
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10132
Collection:CaltechAUTHORS
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Deposited On:14 Apr 2008
Last Modified:26 Dec 2012 09:57

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