Coriolis effect on centrifugal buoyancy-driven convection in a thin cylindrical shell

We study the effect of the Coriolis force on centrifugal buoyancy-driven convection in a rotating cylindrical shell with inner cold wall and outer hot wall. This is done by performing direct numerical simulations for increasing inverse Rossby number from zero (no Coriolis force) to (very large Coriolis force) and for Rayleigh number from to and Prandtl number, corresponding to air. We invoke the thin-shell limit, which neglects the curvature and radial variations of the centripetal acceleration. As increases from zero, the system forms an azimuthal bidirectional wind that reaches its maximum momentum at an optimal, associated with a maximal skin-friction coefficient and a minimal Nusselt number. Just beyond, the wind weakens and an axial, quasi-two-dimensional cyclone, corotating with the system, begins to form. A local 'turbulence' inverse Rossby number (non-dimensionalised by the eddy turnover time) determines the onset of cyclone formation for all, when its value reaches approximately. At, the system falls into the geostrophic regime with a sudden drop in. The bidirectional wind for is a feature of this system, as it hastens the boundary layer transition from laminar to turbulent, towards the ultimate regime. We see the onset of this transition at and, although the mean flow profile has not yet fully collapsed on the Prandtl-von Kármán (logarithmic) law.