What can go wrong when applying wave turbulence theory

Abstract: Many new models of wave turbulence -- frozen, mesoscopic, laminated, decaying, sand-pile, etc. -- have been developed in the last decade aiming to solve problems seemingly not solvable in the framework of the existing wave turbulence theory (WTT). In this Letter we show that very often the reason of these discrepancies is that some necessary conditions of the WTT are not satisfied: initial energy distribution is not according to the assumptions of the theory; nonlinearity is not small enough; duration of an experiment is not sufficient to observe kinetic time scale; etc. Two alternative models are briefly presented which can be used to interpret experimental data, both giving predictions at the dynamical time scale: a) a dynamical energy cascade, for systems with narrow initial excitation and weak and moderate nonlinearity, and b) an effective evolution equation, for systems with distributed initial state and small nonlinearity.