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THIS SEMINAR IS PART OF THE CNLS WORKSHOP: NEW DIRECTIONS IN TWO-DIMENSIONAL TURBULENCE BEING HELD AUGUST 28 - SEPTEMBER 1, 2006 AT CNLS. We discuss Lagrangian vortex mechanisms for the two-dimensional turbulent cascades of enstrophy and energy. These are the Batchelor (1969) picture of the forward enstrophy cascade as due to stretching of vorticity-gradients (extended to inertial-range fields), and the Kraichnan (1976) picture of the inverse energy cascade as due to "thinning" of small-scale vorticity by large-scale strain. We also present results of a systematic approximation scheme, a multi-scale gradient (MSG) expansion, that is consistent with these mechanisms. Quantitative comparison will be made with both numerical simulations and laboratory experiments. The physical interpretation in terms of vortex mechanisms suggests an important role of Kelvin's Theorem (1869) in the cascade dynamics. We shall show that conservation of circulations can break down in two-dimensional turbulence, via a cascade dynamics of its own. A strong statistical version seems to survive, however, which may suffice to explain the classical 2D cascades of enstrophy and energy. Host: Misha Chertkov |