Separation of time-scales in drift-diffusion equations on ${\mathbb{R}}^2$

Abstract

We deal with the problem of separation of time-scales and filamentation in a linear drift-diffusion problem posed on the whole space ${\mathbb{R}}^2$. The passive scalar considered is stirred by an incompressible flow with radial symmetry. We identify a time-scale, much faster than the diffusive one, at which mixing happens along the streamlines, as a result of the interaction between transport and diffusion. This effect is also known as enhanced dissipation. For power-law circular flows, this time-scale only depends on the behavior of the flow at the origin. The proofs are based on an adaptation of a hypocoercivity scheme and yield a linear semigroup estimate in a suitable weighted $L^2$-based space.

arXiv comment14 pages, 1 figure

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Cited by in corpus (1)

• Linear stability analysis for 2D shear flows near Couette in the isentropic Compressible Euler equations