Stability of axial Poiseuille-Couette flow between concentric cylinders

Abstract

The linear stability of axial parallel Poiseuille-Couette flow in an annulus between concentric circular cylinders is considered. Using a long-wave version of the axisymmetric Orr-Sommerfeld equation the stability chart of this flow in the velocity ratio-radius ratio plane is derived. It is shown that pure sliding Couette flow can become unstable if the radius ratio is below a specific threshold value. Finally, applying the results to other flow geometries, it is shown that the boundary layer along a slender cylinder can become unstable in a confined region downstream the leading edge only.