Scaling regimes in spherical shell rotating convection

Rayleigh-Bénard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use threedimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning 3 × 10−7 ≤ E ≤ 10−1, Rayleigh numbers within the range 10 < Ra < 2 × 10 and a Prandtl number unity. The radius ratio ri/ro is 0.6 in all cases and the gravity is assumed to be proportional to 1/r. We investigate the scaling behaviours of both local (length scales, boundary layers) and global (Nusselt and Reynolds numbers) properties across various physical regimes from onset of rotating convection to weakly-rotating convection. Close to critical, the convective flow is dominated by a triple force balance between viscosity, Coriolis force and buoyancy. For larger supercriticalities, a small subset of our numerical data approaches the asymptotic diffusivity-free scaling of rotating convection Nu ∼ RaE in a narrow fraction of the parameter space delimited by 6Rac ≤ Ra ≤ 0.4E−8/5. Using a decomposition of the viscous dissipation rate into bulk and boundary layer contributions, we establish a theoretical scaling of the flow velocity that accurately describes the numerical data. In rapidly-rotating turbulent convection, the fluid bulk is controlled by a triple force balance between Coriolis, inertia and buoyancy, while the remaining fraction of the dissipation can be attributed to the viscous friction in the Ekman layers. Beyond Ra ' E−8/5, the rotational constraint on the convective flow is gradually lost and the flow properties continuously vary to match the regime changes between rotation-dominated and non-rotating convection. We show that the quantity RaE provides an accurate transition parameter to separate rotating and non-rotating convection.