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× 10⁶≤ Ra ≤ 5× 10¹³ , 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 ~ Ek1/3 , 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 RaEk4/3 200 , we have reached the diffusion-free geostrophic turbulence regime.