On variable viscosity and enhanced dissipation

TL;DR

This paper studies 2D Navier-Stokes equations with variable viscosity, showing that shear flow can enhance dissipation even when viscosity varies, with decreasing viscosity strengthening this effect.

Contribution

It establishes linear enhanced dissipation near non-affine stationary states for variable viscosity flows, revealing the counterintuitive effect of viscosity on dissipation strength.

Findings

Decreasing viscosity leads to stronger enhanced dissipation.

Shear flow overcompensates for viscosity weakening effects.

Enhanced dissipation persists near non-affine stationary states.

Abstract

In this article we consider the 2D Navier-Stokes equations with variable viscosity depending on the vertical position. As our main result we establish linear enhanced dissipation near the non-affine stationary states replacing Couette flow. Moreover it turns out that the shear flow overcompensates for weakening viscosity: decreasing viscosity leads to stronger enhanced dissipation and increasing viscosity leads to weaker dissipation than in the constant viscosity case.