Journal of Fluid Mechanics

The superharmonic instability of finite-amplitude water waves

P. G.  Saffman a1
a1 Applied Mathematics, California Institute of Technology, Pasadena, CA 91125

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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.

(Published Online April 20 2006)
(Received January 7 1985)