Resonant interactions of nonlinear water waves in a finite basin

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...

On Nonlinear Water Waves in a Channel

on nonlinear water waves in a channel

A Finite Element Method for Fully Nonlinear Water Waves

A Finite Element Method for Fully Nonlinear Water Waves Xing Cai,∗ Hans Petter Langtangen,† Bjørn Fredrik Nielsen,∗ and Aslak Tveito∗ ∗Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, N-0316, Oslo, Norway; and †Mechanics Division, Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316, Oslo, Norway E-mail: [email protected], [email protected], bjornn@i...

Nonlinear waves in a strongly nonlinear resonant granular chain

We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e., exponentially localized, time periodic states mounted on top of a non-vanish...