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arXiv · 2410.02252

Instability in centrifugally stable shear flows

Kengo Deguchi·Ming Dong
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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.

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Kengo Deguchi, Ming Dong. 2024-10-03. Instability in centrifugally stable shear flows. https://doi.org/10.1017/jfm.2025.114

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