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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. doi:10.1017/S0022112085003159.

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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.

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Additional Information:© 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).
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Office of Naval Research (ONR)NW14-79-C-0412 NR062-639
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Deposited On:14 Apr 2008
Last Modified:08 Nov 2021 21:05

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