Stability of the Spiral Flow in the Annulus between Concentric Cylinders

Abstract

Subject of this paper is the stability of the spiral flow (flow with helical streamlines) in the annulus between concentric circular cylinders (see figure below). This is the fully developed flow in the annulus when both axial pressure gradient and rotation of one of t he cylinders, either the inner or outer one, are simultaneously present. Its stability is studied through the linearised equations for small disturbances. The dispersion relation of the eigenvalue problem contains as parameters of the basic flow the Reynolds number of the through flow, the ratio of the gap width to cylinder radius and the ratio of the circumferential to through flow (axial) velocities. The temporal and spatial eigenvalue problem has been solved numerically by the spectral collocation method to obtain the growth/decay rates of small disturbances and thus the wave numbers of neutrally stable disturbances. The focus of attention in this work is the region on the surface of neutral stability over which transition changes character from one close to Taylor instability (axial pressure gradient is zero) to the one closer to the instability of the channel flow (no rotation of either cylinder, gap width small compared to radius).