The superharmonic instability of finite-amplitude water waves

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 (19...

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Bibliographic Details
Published in:Journal of fluid mechanics 1985-10, Vol.159 (1), p.169-174
Main Author: Saffman, P. G.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic waves
Physics
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112085003159