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SUMMARY:Optimal stirring for passive scalar mixing - Charlie Doering (Univ
 ersity of Michigan)
DTSTART:20110304T160000Z
DTEND:20110304T170000Z
UID:TALK28855@talks.cam.ac.uk
CONTACT:Doris Allen
DESCRIPTION:We address the challenge of optimal incompressible stirring to
  mix an initially inhomogeneous distribution of passive tracers.  As a mea
 sure for mixing we adopt the H^{minus1} norm of the scalar fluctuation fie
 ld.  This 'mix-norm' is equivalent to (the square root of) the variance of
  a low-pass filtered image of the tracer concentration field\, and is a us
 eful gauge even in the absence of molecular diffusion.  We show that the m
 ix-norm's vanishing as time progresses is evidence of the stirring flow's 
 mixing property in the sense of ergodic theory.  For the case of a periodi
 c spatial domain with a prescribed instantaneous energy or power budget fo
 r the stirring\, we determine the flow field that instantaneously maximize
 s the decay of the mix-norm\, i.e.\, the instantaneous optimal stirring --
 - when such a flow exists.  When no such 'steepest descent' stirring exist
 s\, we determine the flow that maximizes that rate of increase of the rate
  of decrease of the norm.  This local-in-time stirring strategy is impleme
 nted computationally on a benchmark problem and compared to an optimal con
 trol approach utilizing a restricted set of flows.  Joint work with Zhi Li
 n (University of Minnesota) and Jean-Luc Thiffeault (University of Wiscons
 in).
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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