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arXiv · 0903.4813

Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves

Adrian Constantin·Elena Kartashova
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Abstract

The influence of an underlying current on 3-wave interactions of capillary water waves is studied. The fact that in irrotational flow resonant 3-wave interactions are not possible can be invalidated by the presence of an underlying current of constant non-zero vorticity. We show that: 1) wave trains in flows with constant non-zero vorticity are possible only for two-dimensional flows; 2) only positive constant vorticities can trigger the appearance of three-wave resonances; 3) the number of positive constant vorticities which do trigger a resonance is countable; 4) the magnitude of a positive constant vorticity triggering a resonance can not be too small.

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Adrian Constantin, Elena Kartashova. 2009-03-27. Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves. https://doi.org/10.1209/0295-5075/86/29001

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