The effect of radius ratio on the stability of Couette flow and Taylor vortex flow

The effect of radius ratio on the stability of Couette flow to axisymmetric and nonaxisymmetric disturbances and the stability of Taylor vortex flow to nonaxisymmetric disturbances is considered. It is assumed that the outer cylinder is at rest. As the ratio η of the radius of the inner cylinder to the radius of the outer cylinder is decreased, it is found that (i) the number of unstable normal modes for Couette flow at a fixed Taylor number decreases rapidly, and (ii) there is a critical value of η equal to about 0.65, below which there is no instability of the Taylor vortex flow for the range of Taylor numbers considered here. Recent experimental observations are summarized.