Rayleigh–Bénard convection instabilities in a cylindrical container with a rotating lid

This study employed the spectral element method for systematically linear stability analysis on Rayleigh–Bénard convection (RBC) instabilities in a cylindrical container with a rotating lid, determining the complete critical stability curves. Critical Rayleigh numbers Ra c range from a minimum of 2461 at rotating Reynolds number Re =0 to peaks exceeding 16,000 at higher Re . Four distinct instability modes are identified in the parameter space 0< Re <3000 and 0< Ra <16500, and the corresponding critical stability curves form a closed area where the steady axisymmetric base flow is linearly stable. The propagation velocity of disturbance increases almost linearly with Re , and the propagation directions of instability Mode 1, Mode 2, and Mode 3 are the same as the lid rotation, while the propagation direction for Mode 4 is opposite to the lid rotation. In addition, the instability mechanisms were deeply revealed through the perturbation energy budget analysis. Thermal buoyancy plays a dominant role in inducing flow instability at small rotating Reynolds numbers ( Re <200) and large Rayleigh numbers ( Ra > Ra c ), while the centrifugal instability mechanism is responsible for flow instability at small Rayleigh numbers ( Ra <16000) and large rotating Reynolds numbers ( Re > Re c ). For 200< Re <3000 and Ra > Ra c , flow instability is triggered by the mechanism coupling of thermal instability, elliptical instability, and centrifugal instability.