STABILITY OF SLIDING COUETTE-POISEUILLE FLOW IN AN ANNULUS SUBJECT TO AXISYMMETRICAL AND ASYMMETRIC DISTURBANCES

The linear stability of pressure-driven flow between a sliding inner cylinder and a stationary outer cylinder is studied numerically. Attention is restricted to axisymmetric disturbances (n = 0), and asymmetric disturbances with azimuthal wave numbers n = 1,2, and 3. Neutral stability curves in the Reynolds number versus the wave-number plane are presented as a function of the sliding velocity of the inner cylinder for select values of the radius ratio-kappa. Overall, the sliding velocity of the inner cylinder has a net stabilizing effect on all modes studied. Results presented for kappa = 2 show that individual disturbance modes can be completely stabilized by increasing the sliding velocity. In particular, when the sliding velocity is approximately 25% of the maximum Poiseuille velocity, the neutral curve for the n = 2 mode vanishes; at 36% of the maximum Poiseuille velocity, the neutral curve for the n = 0 mode vanishes, and at 65%, the neutral curve for the n = 1 mode vanishes. For a stationary inner cylinder the asymmetric modes are generally the least stable, though this conclusion does depend on the magnitude of kappa. As kappa --> 1 the axisymmetric mode found to be the most dangerous.