Volume 86, Number 2, April 2009
|Number of page(s)||6|
|Section||Geophysics, Astronomy and Astrophysics|
|Published online||24 April 2009|
Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
Faculty of Mathematics, University of Vienna - 1090 Vienna, Austria, EU
2 RISC, J. Kepler University - Linz 4040, Austria, EU
Accepted: 31 March 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.
PACS: 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
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