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1.3 PHYSICAL SCIENCES, 1.1 MATHMATICS
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.
Ivanov, I. & Martin, C. (2019) On the Time-Evolution of Resonant Triads in Rotational Capillary-Gravity Water Waves, Physics of Fluids, 31 (2019) 117103 DOI:10.1063/1.5128294