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CATEGORIES:Fluid Mechanics (DAMTP)
SUMMARY:Optimal stirring for maximal mixing (NB: Batchelor
Lecture) - Charlie Doering (University of Michiga
n)
DTSTART;TZID=Europe/London:20170505T160000
DTEND;TZID=Europe/London:20170505T170000
UID:TALK72342AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72342
DESCRIPTION:We study incompressible flows designed to best mix
an initially inhomogeneous distribution of passiv
e tracers as measured by a measured by a 'mix-norm
' equivalent to the variance of a low-pass filtere
d image of the tracer concentration field. Unlike
the scalar concentration variance\, this is a use
ful gauge even in the absence of molecular diffusi
on: the mix-norm quantifies the stirring flow's mi
xing property in the sense of ergodic theory. For
the case of a periodic spatial domain with prescri
bed energy or power constraints on the stirring\,
we determine the flows that instantaneously maximi
ze decay of the mix-norm\, i.e.\, the instantaneou
s optimal stirring. A shell model is devised to p
robe the finite-time horizon optimal control probl
ems for maximal mixing\, The effect of molecular
diffusion on maximal mixing is investigated where\
, not unexpectedly\, suitable generalizations of t
he Bachelor scale appear prominently.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Doris Allen
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