Instabilities and transition in flow between concentric rotating cylinders

The stability and transitions of viscous incompressible flow between concentric rotating cylinders is considered as the speed of one or both cylinders is increased, with attention to the case of the outer cylinder at rest. Consideration of the instability of Couette flow and the growth of the Taylor vortex secondary flow demonstrates that as the Reynolds number is increased, the Taylor vortices become unstable at a second critical Reynolds number and a new flow is established with traveling azimuthal waves superimposed on the Taylor vortices. Experiments which in the past six years have shown that further instabilities occur before the fluid becomes turbulent are discussed with regard to the higher instabilities and the transition to turbulence.