Linear Inviscid Damping for Couette Flow in Stratified Fluid

TL;DR

This paper investigates the inviscid damping and decay rates of Couette flow in stratified fluids, providing new results for the full Euler equations and analyzing how stratification affects decay.

Contribution

It extends the understanding of inviscid damping to stratified fluids, including the full Euler equations, and explores the influence of stratification on decay rates.

Findings

Decay rates depend on the Richardson number similarly in both models.

Optimal decay rates are established for general perturbations with minimal regularity.

Dispersive decay due to stratification is analyzed in the absence of shear.

Abstract

We study the inviscid damping of Couette flow with an exponentially stratified density. The optimal decay rates of the velocity field and the density are obtained for general perturbations with minimal regularity. For Boussinesq approximation model, the decay rates we get are consistent with the previous results in the literature. We also study the decay rates for the full Euler equations of stratified fluids, which were not studied before. For both models, the decay rates depend on the Richardson number in a very similar way. Besides, we also study the dispersive decay due to the exponential stratification when there is no shear.