Fast Computation Algorithm for Discrete Resonances among Gravity Waves

TL;DR

This paper introduces a fast algorithm for computing discrete resonances among gravity waves with large integer wave-numbers, addressing a key computational challenge in understanding short-wave turbulence effects.

Contribution

It presents a novel, efficient algorithm for solving resonance conditions among gravity waves with large integer wave-numbers, advancing the study of discrete wave interactions.

Findings

Demonstrated the algorithm's efficiency for wave-numbers up to 10^3

Confirmed the existence of discrete effects in short-wave spectra

Discussed potential generalizations to other wave types

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.