Instability in centrifugally stable shear flows

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 (Phys. Rev. E, vol 95, 2017, p. 021102(R)) 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.