Resonantly interacting water waves
- 1 June 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 191 (-1) , 529-534
- https://doi.org/10.1017/s0022112088001685
Abstract
Coupled nonlinear equations are derived for the amplitudes of two small-amplitude resonantly interacting gravity waves in water of non-uniform depth. Such resonance is possible only for wavelengths long compared to the depth. It is shown that the same equations are obtained from the exact Euler equations, from the nonlinear shallow water theory, and from the Boussinesq equations.Keywords
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