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Dynamic energy cascades in the theory of water waves

Presented by: 
E Tobisch Johannes Kepler Universität
Date: 
Monday 28th July 2014 - 14:00 to 15:00
Venue: 
INI Seminar Room 1
Abstract: 
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.
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons