On the time-evolution of resonant triads in rotational capillary-gravity water waves
Fluid Dynamics
2019-11-14 v1 Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1911.05213,
title = {On the time-evolution of resonant triads in rotational capillary-gravity water waves},
author = {Rossen I. Ivanov and Calin I. Martin},
journal= {arXiv preprint arXiv:1911.05213},
year = {2019}
}
Comments
20 pages, 1 figure