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arXiv · 2108.11192

Enhanced dissipation and Taylor dispersion in higher-dimensional parallel shear flows

Michele Coti Zelati·Thierry Gallay
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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.

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Michele Coti Zelati, Thierry Gallay. 2021-08-25. Enhanced dissipation and Taylor dispersion in higher-dimensional parallel shear flows. https://arxiv.org/abs/2108.11192

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