Enhanced dissipation and Taylor dispersion in higher-dimensional
parallel shear flows
parallel shear flows
File(s)
Working Paper
Author(s)
Gallay, Thierry
Zelati, Michele Coti
Type
Working Paper
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, 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
implemented in the present example, and their relative efficiency is compared.
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, 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
implemented in the present example, and their relative efficiency is compared.
Date Issued
2022-06-06
Citation
2022
Publisher
ArXiv
Copyright Statement
©2022 The Author(s)
Identifier
http://arxiv.org/abs/2108.11192v1
Subjects
math.AP
math.AP
35Q35, 35H10, 47B44, 76E05
Notes
26 pages, no figure
Publication Status
Published