Nonlinear Interactions between Gravity Waves in Water of Constant Depth

Nonlinear evolution of surface gravity waves over highly variable depth.

New nonlinear evolution equations are derived that generalize those presented in a Letter by Matsuno [Phys. Rev. Lett. 69, 609 (1992)]] and a terrain-following Boussinesq system recently deduced by Nachbin [SIAM J Appl. Math. 63, 905 (2003)]]. The regime considers finite-amplitude surface gravity waves on a two-dimensional incompressible and inviscid fluid of, highly variable, finite depth. A F...

A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity

On Nonlinear Water Waves in a Channel

On the homotopy multiple-variable method and its applications in the interactions between nonlinear gravity waves

In this talk, a homotopy-based multiple-variable method is proposed to investigate the interactions of fully-developed periodic traveling primary waves. This method does not depend upon any small physical parameters at all and thus is more general than the famous multiple-scale technique in perturbation methods. By means of this technique, it is found that, for a fully developed wave system, th...

Resonant interactions of nonlinear water waves in a finite basin.

We study exact four-wave resonances among gravity water waves in a square box with periodic boundary conditions. We show that these resonant quartets are linked with each other by shared Fourier modes in such a way that they form independent clusters. These clusters can be formed by two types of quartets: (1) Angle resonances which cannot directly cascade energy but which can redistribute it am...