VISCOUS COUETTE FLOW

Taylor-Couette flow between concentric cylinders. For laminar flow, the azimuthal velocity profile is v_θ(r) = Ar + B/r where A = (Ω₂R₂² − Ω₁R₁²)/(R₂² − R₁²) and B = R₁²R₂²(Ω₁ − Ω₂)/(R₂² − R₁²). The stress τ = 2ηB/r². When inner cylinder rotates fast enough (Taylor number Ta > 1712), the flow becomes unstable and Taylor vortices appear.