SPECIAL MATHEMATICS-SCS-GFDI COLLOQUIUM
Speaker: Charles Doering
Title: Stirring Up Trouble: Multi-Scale Measures of Mixing for
Steady Scalar Sources
Affiliation: University of Michigan
Date: Monday, April 24, 2006.
Place and Time: Room 018 - Keen Building, 3:00 pm.
Abstract.
We study the evolution of passive scalar fields maintained by steady
but spatially inhomogeneous sources and sinks and stirred by
statistically stationary, homogeneous and isotropic incompressible
flows, including "familar" turbulence. The effectiveness of a flow
field to enhance mixing over molecular diffusion is measured by the
suppression of the space-time averaged scalar variance, the gradient
variance (stressing small scales), and the inverse gradient variance
(focusing on large scale fluctuations).
Ratios of these variances without stirring to the corresponding
variances with stirring provide non-dimensional measures of the "mixing
efficiency" of the flow on different scales. In this work we derive rigorous
estimates on these multi-scale mixing efficiencies for a variety of
source distributions with general stirring flows including
statistically homogeneous and isotropic velocity fields, and compare
them with conventional (eddy diffusion) theory, direct numerical
simulations and exact calculations for sample problems.
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