A proof that Couette flow in the stably stratified Boussinesq system on R^2 is asymptotically stable for Richardson number R>1/4, with explicit enhanced dissipation, Taylor dispersion, and inviscid damping rates.
Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces
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abstract
We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $\mathbb{T} \times \mathbb{R}$ with small viscosity $\nu$. We establish nonlinear stability in $H^s$ for $s \geq 2$ with a threshold of size $\epsilon \nu^{1/3}$ for time smaller than $c_*\nu^{-1}$ with $\epsilon, c_* \ll 1$. Additionally, we demonstrate nonlinear inviscid damping and enhanced dissipation.
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Enhanced Dissipation, Taylor Dispersion, and Inviscid Damping of Couette flow in the Boussinesq system on the Plane
A proof that Couette flow in the stably stratified Boussinesq system on R^2 is asymptotically stable for Richardson number R>1/4, with explicit enhanced dissipation, Taylor dispersion, and inviscid damping rates.