A Bound on Mixing Efficiency for the Advection-Diffusion Equation
Abstract
An upper bound on the mixing efficiency is derived for a passive scalar under the influence of advection and diffusion with a body source. The mixing efficiency is defined as the the ratio of the source variance to the fluctuations in the scalar concentration, divided by the root-mean-square intensity of the velocity field. The bound depends only on the functional "shape" of both the source and the advecting field. Direct numerical simulations performed for a simple advecting flow to test the bounds are reported. The bounds are found to be relatively sharp for this example.Keywords
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