Nonstationary distributions of wave intensities in Wave Turbulence

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.