@article{RISC3410,author = {E. Kartashova and S. Nazarenko and O. Rudenko},
title = {{Resonant interactions of nonlinear water waves in a finite basin}},
language = {english},
abstract = {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.},
journal = {Physical Review E},
volume = {78 },
number = {016304},
pages = {1--9},
publisher = {American Physical Society},
isbn_issn = {1539-3755 (print) , 1550-2376 (online)},
year = {2008},
refereed = {yes},
length = {9},
url = {http://link.aps.org/abstract/PRE/v78/e016304}
}