Wave Turbulence on Water Surface

Abstract

We overview the wave turbulence approach by example of one physical system: gravity waves on the surface of an infinitely deep fluid. In the theoretical part of our review, we derive the nonlinear Hamiltonian equations governing the water-wave system and describe the premises of the weak wave turbulence theory. We outline derivation of the wave-kinetic equation and the equation for the probability density function, and most important solutions to these equations, including the Kolmogorov-Zakharov spectra corresponding to a direct and an inverse turbulent cascades, as well as solutions for non-Gaussian wave fields corresponding to intermittency. We also discuss strong wave turbulence as well as coherent structures and their interaction with random waves. We describe numerical and laboratory experiments, and field observations of gravity wave turbulence, and compare their results with theoretical predictions.