# Nonstationary distributions of wave intensities in Wave Turbulence

## TL;DR

This paper derives a general solution for wave intensity distributions in non-stationary Wave Turbulence, revealing how wave statistics evolve over time and under different conditions, including steady states and decay.

## Contribution

It provides a comprehensive analytical framework linking wave intensity distributions to the evolving wave action spectrum in non-stationary turbulence.

## Key findings

- Wave statistics tend to Gaussian in steady-state forced systems without wave breaking.
- Initial Gaussian statistics remain Gaussian over time.
- Non-Gaussian initial conditions can persist indefinitely in decaying turbulence.

## Abstract

We obtain a general solution for the probability density function of wave intensities in non-stationary Wave Turbulence. The solution is expressed in terms of the wave action spectrum evolving according the the wave-kinetic equation. We establish that, in absence of wave breaking, the wave statistics asymptotes to a Gaussian distribution in forced-dissipated wave systems that approach a steady state. Also, in non-stationary systems, if the statistics is Gaussian initially, it will remain Gaussian at any time. Generally, the statistics that is not Gaussian initially will remain non-Gaussian over the characteristic nonlinear time of the wave spectrum. In freely decaying wave turbulence, substantial deviations from Gaussianity may persist infinitely long.