Laminated Wave Turbulence: Generic Algorithms I

TL;DR

This paper introduces a unified model of wave turbulence that combines statistical and discrete effects across the entire spectrum, and presents a generic algorithm for efficient computation in large integer domains.

Contribution

It develops a generic algorithm for polynomial dispersion functions applicable to various wave systems, enabling fast computations over extremely large spectral domains.

Findings

Unified model of wave turbulence incorporating discrete effects

Development of a generic algorithm for polynomial dispersion functions

Application to gravity and planetary waves

Abstract

The model of laminated wave turbulence presented recently unites both types of turbulent wave systems - statistical wave turbulence (introduced by Kolmogorov and brought to the present form by numerous works of Zakharov and his scientific school since nineteen sixties) and discrete wave turbulence (developed in the works of Kartashova in nineteen nineties). The main new feature described by this model is the following: discrete effects do appear not only in the long-wave part of the spectral domain (corresponding to small wave numbers) but all through the spectra thus putting forth a novel problem - construction of fast algorithms for computations in integers of order $10^{12}$ and more. In this paper we present a generic algorithm for polynomial dispersion functions and illustrate it by application to gravity and planetary waves.