Resonance theory of water waves in the long-wave limit

solitarywaveThe paper “Resonance theory of water waves in the long-wave limit“, by Takeshi Kataoka, has been published in the Journal of Fluid Mechanics.  The instability due to resonant interactions of finite-amplitude water waves is examined in the long-wave limit. In contrast to the well-known case of a small-amplitude limit in which the resonance is considered for a flat surface, the paper considers a periodic approximate of the finite-amplitude solitary wave which is the long-wave limit of the periodic wave. The resonance conditions for the corresponding perturbations yield a new family of resonance curves .  The results are verified numerically by showing that the instability bands for finite-amplitude periodic waves in shallow water are located along these unstable resonance curves. A link to the paper is here.

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