A toy model of wave turbulence

Abstract: A novel model of wave turbulence is presented which allows to explain in the same frame various nonlinear wave phenomena: intermittency, form and direction of the energy cascades, formation of a zero-frequency band with non-zero energy, etc. as an effect of initial conditions, without any statistical assumptions. Classical Kolmogorov-Zakharov spectra are obtained as a particular case of the more general form of energy spectra. One of the most important phenomenological consequences of the model is the termination of a cascade not due to dissipation but because of the growth of nonlinearity. The model is quite general and can be exploited for the description of an arbitrary wave turbulent system.