Direct numerical simulations of rapidly rotating Rayleigh–Bénard convection with Rayleigh number up to

Three-dimensional direct numerical simulations of rotating Rayleigh–Bénard convection in the planar geometry with no-slip top and bottom and periodic lateral boundary conditions are performed for a broad parameter range with the Rayleigh number spanning in 5 10^6 Ra 5 10^13, Ekman number within 5 10^-9 Ek 5 10^-5 and Prandtl number Pr=1. The thermal and Ekman boundary layer (BL) statistics, temperature drop within the thermal BL, interior temperature gradient and scaling behaviours of the heat and momentum transports (reflected in the Nusselt Nu and Reynolds numbers Re) as well as the convective length scale are investigated across various flow regimes. The global and local momentum transports are examined via the Re scaling derived from the classical theoretical balances of viscous–Archimedean–Coriolis (VAC) and Coriolis–inertial–Archimedean (CIA) forces. The VAC-based Re scaling is shown to agree well with the data in the cellular and columnar regimes, where the characteristic convective length scales as the onset length scale Ek^1/3, while the CIA-based Re scaling and the inertia length scale (ReEk) ^1/2 work well in the geostrophic turbulence regime for Ek 1. 5 10^-8. The examinations of Nu, global and local Re, and convective length scale as well as the temperature drop within the thermal BL and its thickness scaling behaviours, indicate that for extreme parameters of Ek 1. 5 10^-8 and 80 RaEk^4/3 200, we have reached the diffusion-free geostrophic turbulence regime.