Enhanced Dissipation, Taylor Dispersion, and Inviscid Damping of Couette flow in the Boussinesq system on the Plane

Ryan Arbon

Paper

Enhanced Dissipation, Taylor Dispersion, and Inviscid Damping of Couette flow in the Boussinesq system on the Plane

Abstract

We consider the quantitative asymptotic stability of the stably stratified Couette flow solution to the 2D fully dissipative nonlinear Boussinesq system on

with large Richardson number

, viscosity

and density dissipation

. For an initial perturbation

of size

in a low-order anisotropic Sobolev space, for

roughly

and

comparable, we demonstrate asymptotic stability with explicit enhanced dissipation and Taylor dispersion rates of decay. We also give inviscid damping estimates on the velocity

and the density

. This is the first result of its type for the Boussinesq system on the fully unbounded domain

. We also translate some known linear results from

, and we give an alternative theorem for the nonlinear result.