Short-wavelength local instabilities of a circular Couette flow with radial temperature gradient

Abstract

We perform a linearized local stability analysis for short-wavelength perturbations of a circular Couette flow with a radial temperature gradient. Axisymmetric and non-axisymmetric perturbations are considered and both the thermal diffusivity and the kinematic viscosity of the fluid are taken into account. The effect of asymmetry of the heating both on centrifugally unstable flows and on the onset of instabilities of centrifugally stable flows, including flows with a Keplerian shear profile, is thoroughly investigated. It is found that an inward temperature gradient destabilizes the Rayleigh-stable flow either via Hopf bifurcation if the liquid is a very good heat conductor or via steady state bifurcation if viscosity prevails over the thermal conductance.