Effect of the radial buoyancy on a circular Couette flow

Abstract

The effect of a radial temperature gradient on the stability of a circular Couette flow is investigated when the gravitational acceleration is neglected. The induced radial stratification of the fluid density coupled with the centrifugal acceleration generates radial buoyancy which is centrifugal for inward heating and centripetal for outward heating. This radial buoyancy modifies the Rayleigh discriminant and induces the asymmetry between inward heating and outward heating in flow behavior. The critical modes are axisymmetric and stationary for inward heating while for outward heating, they can be oscillatory axisymmetric or nonaxisymmetric depending on fluid diffusion properties, i.e., on the Prandtl number Pr. The dependence of the critical modes on Pr is explored for different values of the radius ratio of the annulus. The power input of the radial buoyancy is compared with other power terms. The critical frequency of the oscillatory axisymmetric modes is linked to the Brunt-Väisälä frequency due to the density stratification in the radial gravity field induced by the rotation. These modes are associated with inertial waves. The dispersion relation of the oscillatory axisymmetric modes is derived in the vicinity of the critical conditions. A weakly nonlinear amplitude equation with a forcing term is proposed to explain the domination of these axisymmetric oscillatory modes over the stationary centrifugal mode.