A Note on Enhanced Dissipation and Taylor Dispersion of Time-dependent Shear Flows

Daniel Coble; Siming He

A Note on Enhanced Dissipation and Taylor Dispersion of Time-dependent Shear Flows

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arxiv 2309.15738 v2 pith:ZLGBWEOL submitted 2023-09-27 math.AP

Daniel Coble , Siming He This is my paper

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keywords dispersiondissipationenhancedsheartaylorflowstime-dependentanalysis

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This paper explores the phenomena of enhanced dissipation and Taylor dispersion in solutions to the passive scalar equations subject to time-dependent shear flows. The hypocoercivity functionals with carefully tuned time weights are applied in the analysis. We observe that as long as the critical points of the shear flow vary slowly, one can derive the sharp enhanced dissipation and Taylor dispersion estimates, mirroring the ones obtained for the time-stationary case.

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Exponentially mixing flows with slow enhanced dissipation
math.PR 2025-07 conditional novelty 8.0 of 10

Random alternating shear flows on the torus mix exponentially with diffusivity-independent rates yet have dissipation time of order 1/κ, showing enhanced dissipation is not implied by exponential mixing for merely C0 flows.

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