Numerical Methods for Nonlinear Interactions between Water Waves

On Nonlinear Water Waves in a Channel

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...

Nonlinear water waves.

This introduction to the issue provides a review of some recent developments in the study of water waves. The content and contributions of the papers that make up this Theme Issue are also discussed.

Numerical methods for fluctuation-driven interactions between dielectrics.

We develop a discretized theory of thermal Casimir interactions to numerically calculate the interactions between fluctuating dielectrics. From a constrained partition function we derive a surface free energy, while handling divergences that depend on system size and discretization. We derive analytic results for parallel plate geometry in order to check the convergence of the numerical methods...

Nonlinear Resonances of Water Waves

In the last fifteen years great progress has been made in the understanding of nonlinear resonance dynamics of water waves which is the main subject of discrete wave turbulence. Notions of scaleand angle-resonances have been introduced, new type of energy cascade due to nonlinear resonances in the gravity water waves has been discovered, conception of a resonance cluster has been much and succe...