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Enhanced dissipation and Taylor dispersion in higher-dimensional parallel shear flows
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abstract
We consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity $\nu$, which is assumed to be small, and the wave number $k$ in the streamwise direction, which can take arbitrary values. Under generic assumptions on the shear velocity $v$, we obtain optimal decay estimates for large times, both in the enhanced dissipation regime $\nu \ll |k|$ and in the Taylor dispersion regime $|k| \ll \nu$. Our results can be deduced from resolvent estimates using a quantitative version of the Gearhart-Pr\"uss theorem, or can be established more directly via the hypocoercivity method. Both approaches are explored in the present example, and their relative efficiency is compared.
Forward citations
Cited by 2 Pith papers
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Exponentially mixing flows with slow enhanced dissipation
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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Sampling and Optimization meet Enhanced Flows
New first- and second-order transport-diffusion dynamics with deterministic alternating shear flows converge to a given Gibbs measure at an enhanced O(ν^{1/2}) rate, faster than classical Langevin sampling at O(ν).
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