The stability of Couette flow between rotating cylinders in the presence of a radial temperature gradient

Abstract The effects of viscosity and density variations due to an imposed radial temperature gradient on the stability of Couette flow between rotating cylinders are investigated. The annular spacing between the cylinders is assumed to be small compared with the mean radius. The fluids considered are water and 50% aqueous glycerol. Free convection due to gravity is not considered. Approximate solutions to the stability equations are obtained by the Galerkin method. Computations are restricted to the case where the outer cylinder is at rest. For the cases studied, the effects of radial convection were found to be small but the effects of the temperature dependence of viscosity were appreciable. The critical Taylor number based on the mean temperature viscosity was found to decrease as the viscosity variation became more pronounced and as the Prandtl number increased.