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The Effect of Mean Flows on Enhanced Diffusivity in Transport by Incompressible Periodic Velocity Fields

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Avellaneda and one of the authors ([1], [3]) have recently established that an upper bound for the enhanced diffusivity in the large scale, long time advection‐diffusion with periodic steady incompressible velocity fields has the form where Pe is the Peclet number and is the reciprocal of the Prandtl number. In this paper, flow fields with maximal and minimal enhanced diffusion are studied. Maximal enhanced diffusion requires that in some directions the enhanced diffusion tensor also has the lower bound . For minimal enhanced diffusion, the effect of the velocity field is to boost the enhanced diffusivity by a negligible amount that is bounded by a fixed constant times the bare diffusivity regardless of Peclet number. Stieltjes measure formulas are used to develop a simple, necessary, and sufficient condition for maximal enhanced diffusion and also to characterize minimal enhanced diffusion.
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Document Type: Research Article

Affiliations: Princeton University

Publication date: August 1, 1993

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