Volume 86, Number 2, April 2009
Article Number 29001
Number of page(s) 6
Section Geophysics, Astronomy and Astrophysics
Published online 24 April 2009
EPL, 86 (2009) 29001
DOI: 10.1209/0295-5075/86/29001

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

A. 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. - Inviscid flows with vorticity.
47.35.Pq - Capillary waves.

© EPLA 2009