Effect of outer-cylinder rotation on the radially heated Taylor-Couette flow

A Taylor-Couette setup with radial heating is considered where a Boussinesq fluid is sheared in the annular region between two concentric, independently rotating cylinders maintained at different temperatures. Linear stability analysis is performed to determine the Taylor number for the onset of instability. Two radius ratios corresponding to wide and thin gaps with several rotation rate ratios are considered. The rotation of the outer cylinder is found to have a general stabilizing effect on the stability threshold as compared to pure inner-cylinder rotation, with a few exceptions. The radial heating sets up an axial flow which breaks the reflection symmetry of isothermal Taylor-Couette flow in the axial coordinate. This symmetry breaking separates linear stability thresholds, and we find the fastest growing modes with both positive and negative azimuthal numbers for different parameters. Another important finding of the current study is the discovery of unstable modes in the Rayleigh-stable regime. Furthermore, closed disconnected neutral curves (CDNCs) are observed for both wide and thin gaps which can separate from or merge into open neutral-stability curves. Alternatively, CDNCs can also morph into open neutral stability curves as the rotation rate ratio is changed. CDNCs are observed to be sensitive to changes in control parameters, and their appearance/disappearance is shown to induce discontinuous jumps in the critical Taylor number. For both wide and thin gaps, the fastest-growing modes found in the pure corotation case are shown to have their origins in the instability islands at smaller values of rotation rate ratios.