A model of laminated wave turbulence

A model of laminated wave turbulence is presented. This model consists of two co-existing layers one with continuous waves’ spectra, covered by KAM theory and Kolmogorov-like power spectra, and one with discrete waves’ spectra, covered by discrete classes of waves and Clipping method. Some known laboratory experiments and numerical simulations are explained in the frame of this model. PACS: 47.10.-g, 47.27.De, 47.27.T 1. WT in infinite domains. In [12] Kolmogorov presented energy spectrum of turbulence describing the distribution of the energy among turbulence vortices as function of vortex size and thus founded the field of mathematical analysis of turbulence. Kolmogorov regarded some inertial range of wave numbers, between viscosity and dissipation, and suggested that at this range, turbulence is (1) locally homogeneous (no dependence on position) and (2) locally isotropic (no dependence on direction) which can be summarized as follows: probability distribution for the relative velocities of two particles in the fluid only depends on the distance between particles. Using these suggestions and dimensional analysis, Kolmogorov deduced that energy distribution, called now Kolmogorov ́s spectrum, is proportional to k−5/3 for wave numbers k. Results of numerical simulations and real experiments carried out to prove this theory are somewhat contradictious. On the one hand, probably the most spectacular example of the validity of Kolmogorov ́s spectra is provided in [3] where measurements in tidal currents near Seymour Narrows north of Campbell River on Vancouver Island were described and −5/3 spectra appeared at the range of 10 (energy dissipation at a scale of millimeters and energy input at 100 meters). On the other hand, Kolmogorov ́s spectra have been obtained under the assumptions opposite to Kolmogorov ́s [4] so that exponent −5/3 corresponds to both direct and inverse cascades. With a hope to diminish established unclearness of Kolmogorov ́s theory in a more simple setting, theory of wave (or weak) turbulence (WT) in infinite domains has been developed. The problem is regarded in the very general form