This flow, which is constituted by a flow between two concentric cylinders rotating at different rates was first studied by M. Couette in 1901. Instabilities in this flow were discovered by G.I. Taylor in 1923.
If a simple approach of the solution shows that the flow remains entirely azimuthal, experiences show that, when outer cylinder is at rest and the inner one is animate by a constant increase rotating speed, for a rotating speed value, the flow is structured itself as a stacking of alternate senses rotating toroidal vortices called Taylor cells.
More complex configurations of this instability could appear during the transition to turbulence or when flow is entirely turbulent, but this study is only lead on laminar fluid case.