Interaction between mean flow and turbulence in two dimensions

Gregory Falkovich
Weizmann Institute of Science

I describe a straightforward analytic approach to the description of interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in 2 and 3 dimensions and see why the former are solvable and the latter are not (yet). I present the analytic solutions for 2d mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. I then discuss when those simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end.

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