TaylorCouette

Taylor-Couette flow refers to the viscous flow of a fluid in the annular gap between two coaxial cylinders, where the inner cylinder of radius a and the outer cylinder of radius b rotate at angular velocities Omega_i and Omega_o, respectively. The gap width is d = b − a and the radius ratio is eta = a/b. The fluid has density rho and dynamic viscosity mu. The flow stability is described by dimensionless parameters such as the Reynolds numbers Re_i = rho Omega_i a d / mu and Re_o = rho Omega_o b d / mu, the radius ratio eta, and the axial aspect ratio Gamma = L/d, where L is the cylinder length. A key composite parameter is the Taylor number, which combines rotation, viscosity, and geometry to gauge centrifugal versus viscous effects.

At low rotation rates the flow is circular Couette flow: steady, laminar, with purely azimuthal motion. When the inner cylinder rotates sufficiently fast (for given Re_o and eta), the laminar state becomes unstable and axisymmetric toroidal vortices, known as Taylor vortices, appear in the gap and extend along the axis. The number and arrangement of these vortices depend on geometry and speeds. With further increases in rotation, the flow undergoes secondary instabilities to non-axisymmetric states such as wavy vortices and modulated wavy vortex flow, eventually leading to chaotic turbulence.

Taylor-Couette flow is a canonical system for studying hydrodynamic stability, nonlinear pattern formation, and transition to turbulence. It is widely used in fundamental fluid dynamics research, precision viscosity measurements, and experimental investigations in magnetohydrodynamics, including studies of magnetorotational instability with liquid metals.