Stability of viscous three-dimensional stratified Couette flow via dispersion and mixing

TL;DR

This paper investigates the stability of viscous three-dimensional stratified Couette flow, analyzing how mixing and gravity-induced dispersion influence nonlinear transition thresholds in fluid dynamics.

Contribution

It combines mixing effects and internal gravity wave dispersion to establish a quantitative bound for the nonlinear transition threshold in stratified viscous flows.

Findings

Transition threshold exceeds inverse Reynolds number

Stronger stratification increases stability threshold

Mixing and gravity effects are fundamentally different mechanisms

Abstract

This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves. These mechanisms are of fundamentally different nature and relevant in complementary dynamical regimes. Our study combines them to establish a bound for the nonlinear transition threshold, which is quantitatively larger than the inverse Reynolds number $\nu$, and increases with stronger stratification resp. gravity.