Stability of flow between rotating cylinders with axial buoyancy effect

The linear stability of a fluid confined between two coaxial cylinders rotating independently with axial buoyancy induced flow is examined. Buoyancy is included through the Boussinesq approximation. The numerical investigation is restricted to radius ratio 0.5 at Prandtl number 0.709 with co-rotation situation. The outer rotating cylinder’s Couette flow Reynolds number is restricted to 200. Zeroth-order discontinuities are found in the critical surface, which are explained as the result of the competition between the centrifugal and axial buoyancy induced shear instability mechanisms. Due to the competition, the neutral stability curves develop islands of instability, which considerably lower the instability threshold. Specific and robust numerical methods to handle these geometrical complexities are developed.