A. Constantin, Elena Kartaschova,
"Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves"
, in EPL, Vol. 86, Seite(n) 29001--6, 2009, ISSN: (print edition): 0295-5075 ISS
Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
Sprache des Titels:
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.