Stability of sliding Couette–Poiseuille flow in an annulus subject to axisymmetric 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 κ. Overall, the sliding velocity of the inner cylinder has a net stabilizing effect on all modes studied. Results presented for κ=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 κ. As κ→1 the axisymmetric mode is found to be the most dangerous.