The Stability of Viscous Flow between Horizontal Concentric Cylinders

The critical conditions for the formation of Taylor vortices between horizontal concentric cylinders are considered in detail. (1) Where the flow is unidirectional round the annular space and is caused entirely by the rotation of the inner cylinder. (2) Where the flow is caused entirely by pumping round the annular space. (3) Where a liquid is caused to reverse its flow at a free surface, the flow being entirely caused by the rotation of the inner cylinder. The last case is analyzed by the method of small disturbances and the conditions under which Taylor vortices will form are found. Results for the first two cases are already available in the literature. From examination of the three criteria a dimensionless number is proposed to correlate the critical values of the various parameters at the onset of these Taylor vortices. The proposed number has the advantage that it is insensitive to the velocity distribution in the annulus. It is subsequently used to predict the critical conditions for the onset of Taylor vortices under conditions that have not been analyzed, i.e. where flow is due to pumping and rotation of the inner cylinder. The criterion is found to predict successfully the results of various experiments carried out. In addition experimental verification of the theoretical work of Dean (1928) and of the additional analysis carried out in this paper is also given.