Instability islands in 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. An important finding of the current study is the discovery of unstable modes in the Rayleigh-stable regime. Furthermore, instability islands are observed for both wide and thin gaps which can separate from or merge into open neutral--stability curves. Alternatively, instability islands can also morph into open neutral stability curves as the rotation rate ratio is changed. Instability islands 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.