Instability in centrifugally stable shear flows

TL;DR

This paper explores the surprising linear instability of centrifugally stable shear flows, revealing mechanisms involving vortex interactions and boundary layer effects through advanced asymptotic theories and numerical analysis.

Contribution

It develops large Reynolds number asymptotic theories to identify and explain instabilities in stable rotating flows, extending understanding of flow stability mechanisms.

Findings

Instability caused by vortex and viscous flow interactions.

Theories confirm instability mechanisms in boundary layers.

Numerical results support the theoretical predictions.

Abstract

We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories. Our theoretical results not only aid in detecting instabilities previously reported by Deguchi (2017) across a wide parameter range but also clarify the physical mechanisms behind this counterintuitive phenomenon. Instability arises from the interaction between large-scale inviscid vortices and the viscous flow structure near the wall, which is analogous to Tollmien-Schlichting waves. Furthermore, our asymptotic theories and numerical computations reveal that similar instability mechanisms occur in boundary layer flows over convex walls.