Anomalous probability of large amplitudes in wave turbulence

Time evolution equation for the probability distribution function (PDF) is derived for system of weakly interacting waves, dominated by the four-wave process. It is shown that a steady state for such system may correspond to strong intermittency. Numerical simulation performed on the surface gravity waves equations demonstrate an order of magnitude increase of probabilities of long large-amplitude waves with respect to Rayleigh distribution. (c) 2005 Elsevier B.V. All rights reserved.