Effect of non-zero constant vorticity on the nonlinear resonances of capillary water wavesA. Constantin1 and E. Kartashova2
1 Faculty of Mathematics, University of Vienna - 1090 Vienna, Austria, EU
2 RISC, J. Kepler University - Linz 4040, Austria, EU
received 27 March 2009; accepted in final form 31 March 2009; published April 2009
published online 24 April 2009
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.
91.10.Vr - Ocean/Earth/atmosphere/hydrosphere/cryosphere interactions; mass balance.
47.15.ki - Inviscid flows with vorticity.
47.35.Pq - Capillary waves.
© EPLA 2009