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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 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.
Ivanov, R. & Martin, C. (2019). On the time-evolution of resonant triads in rotational capillary-gravity water waves. Physics of Fluids, 31, 117103. doi:10.1063/1.5128294