Stability Of Rayleigh-Stable Couette Flow Between Two Differentially Heated Cylinders

The stability of the circular Couette flow with two differentially heated cylinders is studied in the special cases of hydrodynamically stable rotation regimes. A one-dimensional model is developed to derive the condition of flow stability. This condition combines the curvature of the cylinders, the applied temperature difference between the two cylinders, and the diffusion properties of the fluid. The three-dimensional analysis is performed for two different rotation regimes: the Keplerian regime and the regime where the inner cylinder is stationary. The main results of this analysis is that, for a given radius ratio of the two cylinders, a single parameter combining the Prandtl number and the thermal expansion parameter can describe the critical state of the system. The description is in good agreement with the result of the one-dimensional model. An energy analysis shows a subtle role played by the shear stress in these two rotation regimes.