Centrifugal buoyancy driven turbulent convection in a thin cylindrical shell

Centrifugal buoyancy driven convection is closely related to Rayleigh–Bénard convection, and offers another approach to the ultimate regime of thermal convection. Here, we perform direct numerical simulations (DNSs) of centrifugal convection in a cylindrical shell rotating about its axis at constant angular velocity. The walls undergo solid-body rotation, and the flow is purely driven by the temperature difference between the cold inner wall and the hot outer wall. We invoke the thin-shell limit where radial variations in centrifugal acceleration can be neglected. The Prandtl number is 0.7 corresponding to air. For this setup we have two input parameters: 1) the Rayleigh number Ra characterising the driving by centrifugal (buoyancy) effect, and 2) the Rossby number Ro characterising the Coriolis effect. Here, we vary Ra from 10⁷ to 10¹⁰, and the inverse Rossby number Ro⁻¹ from 0 (no rotation) to 1. We find that the flow dynamics is subjected to an interplay between the driving buoyancy force and the stabilising Coriolis force, similar to that of Chong et al. (Phys. Rev. Lett., vol. 119, 2017, 064501), but with an important difference owing to the different axis of rotation. Instead of the formation of highly coherent plume-like structures at optimal condition that maximises heat transport, here, the formation of strong bidirectional wind at optimal condition (Ro⁻_opt¹ ≈ 0.8) minimises heat transport. By increasing Ra at Ro⁻_opt¹, the mean flow approaches the Prandtl–von Kármán (logarithmic) behaviour, yet full collapse on the logarithmic law is not reached at Ra = 10¹⁰.