  We investigate an effect of the resonant interaction in the case of
one-directional propagation of capillary-gravity surface waves arising as the
free surface of a rotational water flow. Specifically, we assume a constant
vorticity in the body of the fluid which physically corresponds to an
underlying current with a linear horizontal velocity profile. We consider the
interaction of three distinct modes and we obtain the dynamic equations for a
resonant triad. Setting the constant vorticity equal to zero we recover the
well known integrable three-wave system.
