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arXiv · 1911.05213

On the time-evolution of resonant triads in rotational capillary-gravity water waves

Rossen I. Ivanov·Calin I. Martin
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Abstract

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.

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Rossen I. Ivanov, Calin I. Martin. 2019-11-13. On the time-evolution of resonant triads in rotational capillary-gravity water waves. https://doi.org/10.1063/1.5128294

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