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CATEGORIES:Fluid Mechanics (DAMTP)
SUMMARY:Optimal stirring for passive scalar mixing - Charl
ie Doering (University of Michigan)
DTSTART;TZID=Europe/London:20110304T160000
DTEND;TZID=Europe/London:20110304T170000
UID:TALK28855AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28855
DESCRIPTION:We address the challenge of optimal incompressible
stirring to mix an initially inhomogeneous distri
bution of passive tracers. As a measure for mixin
g we adopt the H^{minus1} norm of the scalar fluct
uation field. This 'mix-norm' is equivalent to (t
he square root of) the variance of a low-pass filt
ered image of the tracer concentration field\, and
is a useful gauge even in the absence of molecula
r diffusion. We show that the mix-norm's vanishin
g as time progresses is evidence of the stirring f
low's mixing property in the sense of ergodic theo
ry. For the case of a periodic spatial domain wit
h a prescribed instantaneous energy or power budge
t for the stirring\, we determine the flow field t
hat instantaneously maximizes the decay of the mix
-norm\, i.e.\, the instantaneous optimal stirring
--- when such a flow exists. When no such 'steepe
st descent' stirring exists\, we determine the flo
w that maximizes that rate of increase of the rate
of decrease of the norm. This local-in-time stir
ring strategy is implemented computationally on a
benchmark problem and compared to an optimal contr
ol approach utilizing a restricted set of flows.
Joint work with Zhi Lin (University of Minnesota)
and Jean-Luc Thiffeault (University of Wisconsin).
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Doris Allen
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