Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-03-23
Physical Review E 78, 016304 (2008)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
10 pages, 12 figures, accepted to PRE
Scientific paper
10.1103/PhysRevE.78.016304
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) {\it angle-resonances} which cannot directly cascade energy but which can redistribute it among the initially excited modes and (2) {\it scale-resonances} which are much more rare but which are the only ones that can transfer energy between different scales. We find such resonant quartets and their clusters numerically on the set of 1000 x 1000 modes, classify and quantify them and discuss consequences of the obtained cluster structure for the wavefield evolution. Finite box effects and associated resonant interaction among discrete wave modes appear to be important in most numerical and laboratory experiments on the deep water gravity waves, and our work is aimed at aiding the interpretation of the experimental and numerical data.
Kartashova Elena
Nazarenko Sergey
Rudenko Oleksii
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