Density homogenization of a stratified exact coherent structure at high Prandtl number

We study a family of stably stratified unstable equilibria in plane Couette flows as the Prandtl number Pr — the ratio of viscosity to thermal diffusivity — varies. In both the small and large Pr limits, these states persist at high global Richardson numbers (>> 1/4) without being disrupted by stratification. For large Pr, the channel interior becomes well-mixed, forcing strongly stably stratified boundary layers to form near the walls. This layering makes the equilibria indifferent to the imposed density difference between the walls in the limit. As far as we are aware, this is the first example of layering in an exact numerical solution to the stratified Navier-Stokes equations.