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The superharmonic instability of finite-amplitude water waves

Published online by Cambridge University Press:  20 April 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, CA 91125
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 159 , October 1985 , pp. 169 - 174
Copyright
© 1985 Cambridge University Press

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