On the stability of shear flows in bounded channels, II: non-monotonic shear flows

TL;DR

This paper proves linear inviscid damping and vorticity depletion for non-monotonic shear flows with a single critical point in bounded periodic channels, providing quantitative rates without symmetry assumptions.

Contribution

It offers a rigorous proof of stability phenomena for non-monotonic shear flows in bounded channels, extending previous results to more general flow profiles.

Findings

Proved linear inviscid damping in bounded channels

Established vorticity depletion rates without symmetry constraints

Demonstrated stability for shear flows with a critical point

Abstract

We give a proof of linear inviscid damping and vorticity depletion for non-monotonic shear flows with one critical point in a bounded periodic channel. In particular, we obtain quantitative depletion rates for the vorticity function without any symmetry assumptions.