Stability of a viscous fluid between rotating cylinders with axial flow and pressure gradient round the cylinders

The stability of a viscous fluid between two concentric cylinders with an axial flow is investigated for the case in which the azimuthal velocity is the sum of a velocity distribution due to the rotation of the cylinders and a “pumping” velocity distribution due to the pressure gradient acting round the cylinders. The outer cylinder is stationary and the spacing between the cylinders is assumed small. For various small Reynolds numbers associated with the axial flow the Taylor number is computed for a large range of values of the ratio of the average pumping velocity to the average velocity of the rotation.