The paper “Resonance theory of water waves in the longwave limit“, by Takeshi Kataoka, has been published in the Journal of Fluid Mechanics. The instability due to resonant interactions of finiteamplitude water waves is examined in the longwave limit. In contrast to the wellknown case of a smallamplitude limit in which the resonance is considered for a flat surface, the paper considers a periodic approximate of the finiteamplitude solitary wave which is the longwave 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 finiteamplitude periodic waves in shallow water are located along these unstable resonance curves. A link to the paper is here.

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