Optimal stirring for maximal mixing (NB: Batchelor Lecture)

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• Charlie Doering (University of Michigan)
• Friday 05 May 2017, 16:00-17:00
• MR2, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Doris Allen.

We study incompressible flows designed to best mix an initially inhomogeneous distribution of passive tracers as measured by a measured by a ‘mix-norm’ equivalent to the variance of a low-pass filtered image of the tracer concentration field. Unlike the scalar concentration variance, this is a useful gauge even in the absence of molecular diffusion: the mix-norm quantifies the stirring flow’s mixing property in the sense of ergodic theory. For the case of a periodic spatial domain with prescribed energy or power constraints on the stirring, we determine the flows that instantaneously maximize decay of the mix-norm, i.e., the instantaneous optimal stirring. A shell model is devised to probe the finite-time horizon optimal control problems for maximal mixing, The effect of molecular diffusion on maximal mixing is investigated where, not unexpectedly, suitable generalizations of the Bachelor scale appear prominently.

This talk is part of the Fluid Mechanics (DAMTP) series.

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