On variable viscosity and enhanced dissipation

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.

arXiv comment30 pages

References in corpus (8)

• Inviscid dynamical structures near Couette flow
• Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems
• Linear inviscid damping in Gevrey spaces
• Metastability of Kolmogorov flows and inviscid damping of shear flows
• Convergence to Stratified Flow for an Inviscid 3D Boussinesq System
• Linear inviscid damping and enhanced dissipation for the Kolmogorov flow
• Stability of Couette flow for 2D Boussinesq system with vertical dissipation
• Solvability of the two-dimensional stationary incompressible inhomogeneous Navier-Stokes equations with variable viscosity coefficient