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

The influence of an underlying current on three-wave interactions of capillary water waves is studied. The fact that in irrotational flow resonant three-wave interactions are not possible can be invalidated by the presence of an underlying current of constant non-zero vorticity. We show that: 1) wav...

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Bibliographic Details
Published in:Europhysics letters 2009-04, Vol.86 (2), p.29001-29001p6
Main Authors: Constantin, A, Kartashova, E
Format: Article
Language:English
Subjects:
47.15.ki
47.35.Pq
91.10.Vr
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Summary:The influence of an underlying current on three-wave interactions of capillary water waves is studied. The fact that in irrotational flow resonant three-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 and 4) the magnitude of a positive constant vorticity triggering a resonance cannot be too small.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/86/29001