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arXiv · 1512.01562

The instability of Wilton ripples

Olga Trichtchenko·Bernard Deconinck·Jon Wilkening
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Abstract

Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phenomenon that alters the order at which the resonant harmonic mode enters in a perturbation expansion. We compute such solutions using non-perturbative numerical methods and investigate their stability by examining the spectrum of the water wave problem linearized about the resonant traveling wave. Instabilities are observed that differ from any previously found in the context of the water wave problem.

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Olga Trichtchenko, Bernard Deconinck, Jon Wilkening. 2016-08-09. The instability of Wilton ripples. https://doi.org/10.1016/j.wavemoti.2016.06.004

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