Random walks, random flows, and enhanceddiffusivityin advection-diffusion equations

Michael Taylor

doi:10.3934/dcdsb.2012.17.1261

Article Contents

2012, Volume 17, Issue 4: 1261-1287. Doi: 10.3934/dcdsb.2012.17.1261

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Random walks, random flows, and enhanced diffusivity in advection-diffusion equations

Michael Taylor^1,

1.
Mathematics Department, University of North Carolina, Chapel Hill, NC 27599

Received: May 31, 2010

Revised: July 31, 2011

Published: May 2012

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Abstract

We study the phenomenon of enhanced diffusivity, introduced by G. I.Taylor, for a class of advection-diffusion equations, modeling, for example, the spread of an ink drop in a fluid engaged in Poiseuille flow. We consider such flow in a pipe of general cross section, and compute variances and covariances of certain random flows associated with the advection-diffusion. We examine both long time behavior, including a central limit theorem, and short time asymptotics.

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Mathematics Subject Classification: Primary: 35K20, 35Q30; Secondary: 60J60.

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References

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