The onset of convection in rotating circular cylinders with experimental boundary conditions

Convective instabilities in a fluid-filled circular cylinder heated from below and rotating about its vertical axis are investigated both analytically and numerically under experimental boundary conditions. It is found that there exist two different forms of convective instabilities: convection-driven inertial waves for small and moderate Prandtl numbers and wall-localized travelling waves for large Prandtl numbers. Asymptotic solutions for both forms of convection are derived and numerical simulations for the same problem are also performed, showing a satisfactory quantitative agreement between the asymptotic and numerical analyses.