Multiple states in centrifugal convection

We systematically investigate the multiplicity of flow states in centrifugal convection in water at about $40\,^\circ$ C with Prandtl number $Pr = 4.3$ in a vertically aligned annulus in which the inner radius, the gap between the cylinders and the height all coincide (6 cm). This leaves two independent control parameters: the thermal driving, quantified by the Rayleigh number ${\textit{Ra}}$ , and the rotation strength, expressed by the Froude number ${\textit{Fr}}$ . We explore the range $2\times 10^{5} \le {{\textit{Ra}}} \le 10^{7}$ for ${{\textit{Fr}}} = 10$ and $100$ with direct numerical simulations (DNS). The states are characterised by the number of convection rolls in the mid-height cross-section. We show that the final state sensitively depends on the initial condition, leading to pronounced multistability and substantial variations in heat and momentum transport, while the range of attainable states is strongly restricted. We derive a theoretical estimate of the admissible roll numbers based on the Poincaré–Friedrichs inequality and demonstrate quantitative agreement with the DNS. We further show that, for larger ${\textit{Ra}}$ , the range of possible states shrinks systematically due to an elliptical instability, providing a predictive framework for the selection and disappearance of coherent roll states in centrifugal convection.