1206.2472 (Elena Kartashova)
Elena Kartashova
A novel model (D-model) of weakly nonlinear wave interactions possible due to a singly mode excitation is presented. It allows to reproduce in a single theoretical frame various nonlinear wave phenomena such as intermittency and discrete and continuous energy spectra. Conditions for the formation of a D-cascade, direction of discrete and continuous energy D-cascades, conditions for D-cascade termination, etc. are obtained as a direct outcome from the initial state. No statistical assumptions are needed as all effects are derived from the interaction of distinct modes. In the example given -- gravity surface waves $\o^2=g\,k$ with small nonlinearity -- D-model predicts asymmetrical growth of side-bands for Benjamin-Feir instability; transition from discrete to continuous energy spectrum yields the saturated Phillips' power spectrum $\sim g^2\o^{-5}$, for specific choice of the parameters of initial excitation. D-model can be applied to the experimental and theoretical study of numerous weakly nonlinear wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, convection theory, etc.
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http://arxiv.org/abs/1206.2472
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