A toy model of wave turbulence

TL;DR

This paper introduces a new wave turbulence model that explains various nonlinear phenomena through initial conditions, deriving classical spectra as special cases and highlighting cascade termination due to nonlinearity growth.

Contribution

A novel wave turbulence model that explains diverse phenomena without statistical assumptions and generalizes classical spectra.

Findings

Classical Kolmogorov-Zakharov spectra are recovered as special cases.

Cascade termination occurs due to nonlinearity growth, not dissipation.

The model can describe a wide range of wave turbulent systems.

Abstract

A novel model of wave turbulence is presented which allows to explain in the same frame various nonlinear wave phenomena: intermittency, form and direction of the energy cascades, formation of a zero-frequency band with non-zero energy, etc. as an effect of initial conditions, without any statistical assumptions. Classical Kolmogorov-Zakharov spectra are obtained as a particular case of the more general form of energy spectra. One of the most important phenomenological consequences of the model is the termination of a cascade not due to dissipation but because of the growth of nonlinearity. The model is quite general and can be exploited for the description of an arbitrary wave turbulent system.