Taylor-Couette Flow
Vortex instability between rotating concentric cylinders
Geometry
Inner radius r₁
0.5
Outer radius r₂ = 1.0 (fixed)
Inner Ω₁
2.0
Outer Ω₂
0
Kinematic viscosity ν
0.05
Vortex pairs shown
4
Pause
Taylor-Couette flow:
Between r₁ (inner, Ω₁) and r₂ (outer, Ω₂).
Base flow: v_θ(r) = Ar + B/r
A=(Ω₂r₂²−Ω₁r₁²)/(r₂²−r₁²)
Taylor number:
Ta = Ω₁²r₁(r₂−r₁)³/ν²
Instability at Ta > Ta_c ≈ 1708 (Rayleigh criterion: dL²/dr < 0 ⟹ unstable).
Above critical Ta, Taylor vortices appear — toroidal counter-rotating rolls.
Taylor number:
—
Ta_critical:
1708
Status:
—
Gap width:
—
Base flow type:
—