The very notion of energy cascade in large bodies of water belongs to the English mathematician, physicist and meteorologist L.F. Richardson, who introduced it in 1922 and also suggested a qualitative heuristic model of this process. This conceptual model has been turned into a mathematical theory by A.N. Kolmogorov in 1941, for fully developed turbulence, and by V.E. Zakharov in 1967, for weak wave turbulence of weakly nonlinear amplitude. The model of a dynamic energy cascade presented in this talk covers a range of moderate nonlinearities not covered by any of the previous theories. The main physical mechanism generating a dynamical cascade is modulation instability. Analytical and numerical results will be presented, and also briefly compared with experimental observations.
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