THE EFFECTS OF CENTRIFUGAL FORCE ON THE STABILITY OF AXISYMMETRICAL VISCOUS-FLOW IN A ROTATING ANNULUS

Axisymmetric flow in a rotating annulus with differential heating is computed for a high-kinematic-viscosity fluid, such as silicone oil, by numerical integration of the Navier-Stokes equations. Linear stability analysis of the steady axisymmetric flow with respect to a wave perturbation gives a transition curve from the axisymmetric regime to the wave regime; the transition curve is similar to that obtained experimentally by Fein & Pfeffer (1976). However, if we neglect the centrifugal force term, the transition curve is not similar, but it resembles the curve for water (a familiar 'anvil shape' in the regime diagram). A dimensionless parameter v2(a+b)/8g(b-a)4 (where a and b are the radii of the inner and outer cylinders, d the depth of the fluid, v the kinematic viscosity, g the acceleration due to gravity), which equals the ratio of the centrifugal force to the gravity force divided by the Taylor number, is more fundamental than the Prandtl number in determining the shape of the transition curve.