Wave turbulent statistics in non-weak wave turbulence

TL;DR

This paper derives closed equations for wave turbulence without assuming weak nonlinearity or time scale separation, extending the weak turbulence theory using the Direct-Interaction Approximation.

Contribution

It introduces a DIA-based framework that generalizes weak turbulence theory to non-weak wave turbulence, removing key assumptions.

Findings

DIA equations recover weak turbulence kinetic equations under weak nonlinearity

The framework extends turbulence analysis beyond weak interaction regimes

Provides a more general description of wave turbulence dynamics

Abstract

In wave turbulence, it has been believed that statistical properties are well described by the weak turbulence theory, in which nonlinear interactions among wavenumbers are assumed to be small. In the weak turbulence theory, separation of linear and nonlinear time scales derived from the weak nonlinearity is also assumed. However, the separation of the time scales is often violated even in weak turbulent systems where the nonlinear interactions are actually weak. To get rid of this inconsistency, closed equations are derived without assuming the separation of the time scales in accordance with Direct-Interaction Approximation (DIA), which has been successfully applied to Navier--Stokes turbulence. The kinetic equation of the weak turbulence theory is recovered from the DIA equations if the weak nonlinearity is assumed as an additional assumption. It suggests that the DIA equations is a natural extension of the conventional kinetic equation to not-necessarily-weak wave turbulence.