Centrifugal instability and Taylor vortices
Taylor number: —
Taylor-Couette flow occurs between two coaxial rotating cylinders. When the inner cylinder spins fast enough, the Rayleigh centrifugal criterion is violated and the laminar flow becomes unstable, forming stacked toroidal vortices (Taylor vortices). The Taylor number Ta = (Ω₁r₁d/ν)²(d/r₁) governs transition; Tac ≈ 1708. Above this, beautiful patterns of counter-rotating vortex pairs emerge, and at higher speeds, wavy vortices, modulated waves, and eventually turbulence appear.