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

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.

6 pages, submitted

References in corpus (2)

• Exact and quasi-resonances in discrete water-wave turbulence
• Cluster formation in mesoscopic systems

Cited by in corpus (7)

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• Rigidity of three-dimensional internal waves with constant vorticity
• On the time-evolution of resonant triads in rotational capillary-gravity water waves
• Liouville-type results for time-dependent stratified water flows over variable bottom in the $\beta$-plane approximation
• On the modelling of short and intermediate water waves
• The Lagrangian formulation for wave motion with a shear current and surface tension