  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.

Fluid Dynamics;Geophysics