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

Abstract

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.