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Dynamic energy cascades in the theory of water waves

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Theory of Water Waves

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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