A novel model of wave turbulence

TL;DR

This paper introduces a new D-model for wave turbulence that captures various nonlinear phenomena without statistical assumptions, providing a flexible framework applicable across multiple physical systems.

Contribution

The novel D-model reproduces diverse wave turbulence phenomena and generalizes classical energy spectra without relying on statistical assumptions.

Findings

Reproduces intermittency and energy cascade phenomena.

Derives generalized energy spectra depending on initial conditions.

Applicable to various physical wave systems.

Abstract

A novel D-model of wave turbulence is presented which allows to reproduce in a single frame various nonlinear wave phenomena such as intermittency, formation and direction of energy cascades, possible growth of nonlinearity due to direct energy cascades, etc. depending on the initial state. No statistical assumptions are used, all effects are due to the behavior of distinct modes. Classical energy spectra $E_\o \sim \o^{-\nu}, \ \nu= \const >0,$ for dispersion function of the form $ \o \sim k^{\a}, \ \a>0$ are obtained as a particular case of a more general form of energy spectra: $E_{\o} \sim \o^{-\nu}, \ 2+\a^{-1}\le \nu \le 2(2+\a^{-1})$ where magnitude of $\nu$ is defined by the parameters of the initial excitation. D-model is a generic model which can be expanded into a hierarchy of more refined models including dissipation, forcing, etc. D-model can be applied to the experimental and theoretical study of numerous wave turbulent systems appearing in hydrodynamics, nonlinear optics, electrodynamics, convection theory, etc.