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.