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

• Michele Coti Zelati (Imperial College)
• Monday 07 February 2022, 14:00-15:00
• CMS, MR13.

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 $\nu\gg |k|$. Some of these concepts can be used also in the Navier-Stokes equations to understand stability thresholds for small perturbations of the Poiseuille and Kolmogorov flows.

This talk is part of the Partial Differential Equations seminar series.