Fast Computation Algorithm for Discrete Resonances among Gravity Waves

Abstract

Traditionally resonant interactions among short waves, with large real wave-numbers, were described statistically and only a small domain in spectral space with integer wave-numbers, discrete resonances, had to be studied separately in resonators. Numerical simulations of the last few years showed unambiguously the existence of some discrete effects in the short-waves part of the wave spectrum. Newly presented model of laminated turbulence explains theoretically appearance of these effects thus putting a novel problem - construction of fast algorithms for computation of solutions of resonance conditions with integer wave-numbers of order $10^3$ and more. Example of such an algorithm for 4-waves interactions of gravity waves is given. Its generalization on the different types of waves is briefly discussed.