Hydrodynamic Stability of a Tangential Flow Between Cylinders Induced by Rotation and External Pumping

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Abstract
Consideration is given to the conditions marking the onset of instability for flow that is induced between concentric cylinders by simultaneous rotation of the cylinders and an imposed tangential pressure gradient. Critical Taylor numbers and corresponding disturbance wavenumbers have been determined by an analytical method that is applicable for arbitrary spacing between the cylinders. Numerical results are presented for a wide range of rotation and pumping conditions for cylinder radius ratios ranging from 0.95 to 0.35. The critical Taylor numbers are found to exceed those predicted on the basis of the narrow‐spacing hypothesis.