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An example of mixing and enhanced dissipation in the whole plane

Michele Dolce
Imperial College
Friday, December 4, 2020 - 16:00

When adding milk to coffee, we all know that if we stir the two they get mixed in a much faster way with respect to simply waiting for the milk to diffuse in the coffee by itself. The heuristic behind this phenomenon is that stirring helps the milk to pass from large scale structures to small ones where diffusion is more effective. An advection-diffusion equation can be considered as a first mathematical toy model to investigate the problem. In the talk, we consider the case of a passive scalar advected by a radial flow in the whole plane. We show that on a time-scale much faster with respect to the diffusive one the passive scalar first converges to an axisymmetric state and then diffusion takes over.

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