“Fast” Nonlinear Evolution in Wave Turbulence

Modeling of nonlinear random wave fields in nature (and, in particular, their most common example-wind waves in the ocean) is one of the fundamental open problems of natural sciences. The existing theoretical approaches based on the kinetic equation paradigm assume a proximity to stationarity and homogeneity. In reality this assumption is often violated and how a wave field evolves is not known. We show by direct numerical simulation that after a strong perturbation the wave field evolves on the much faster O(epsilon;{-2}) "dynamic" [rather then O(epsilon;{-4}) "kinetic"] time scale; here epsilon is the characteristic wave steepness (epsilon<<1). The phenomenon of fast evolution is universal, and it must occur whenever there is a strong external perturbation.