Evolution of Wave Turbulence under Gusty Forcing

We consider nonlinear evolution of a random wave field under gusty forcing, fluctuating around a constant mean. Here the classical wave turbulence theory that assumes a proximity to stationarity is not applicable. We show by direct numerical simulation that the self-similarity of wave field evolution survives under fluctuating forcing. The wave field statistical characteristics averaged over fluctuations of forcing evolve as if there were a certain constant effective wind. The results justify the use of the kinetic equations with forcing averaged over gusts as a good first approximation.