Centrifugal instability of decelerating swirl-flow within finite and infinite circular cylinders

Centrifugal instability of the flow within a circular cylinder which is spun down is investigated. The cylinder is assumed to be infinitely long so that the flow is governed by simple viscous diffusion alone and the basic state is pure azimuthal flow. Cylinders of finite length are also considered. In this case, the basic state is fully three dimensional, being dominated by the effects of the endwall Ekman layers. The stability of this flow is examined by means of numerical experiments performed for a variety of Reynolds numbers, aspect ratios, and container spin histories. The axisymmetric Navier-Stokes equations are integrated using an existing program. Disturbances due to round-off and truncation errors are found to be sufficient to trigger centrifugal instabilities. Onset times for instabilities, vortex wavelength variation, torque and angular momentum histories, and the applicability of Rayleigh's criterion to this unsteady viscous flow are emphasized.