Transition from rotation to buoyancy dominated regime in rotating Rayleigh-Bénard convection

The transition process from rotation-dominated to buoyancy-dominated regime in rotating Rayleigh-Bénard convection is investigated via direct numerical simulation, with laterally periodic domains of both no-slip and free-slip top and bottom boundary conditions. The comprehensive transition pathways from rotationally dominated to the buoyancy-dominated flows are realized by increasing the thermal deriving force (Rayleigh number, Ra) over five orders of magnitude, i.e. 10⁶≤Ra≤10¹¹ for one decade of Ekman number 10^-6 ≤Ek≤10^-5 with the Prandtl number Pr=1. During the transition, the horizontal and vertical convective length scales display different scaling relations in rotation-dominated and buoyancy-dominated regimes. A local Rossby number defined by combining these two different length scales is demonstrated to well quantify the transition point between the two flow regimes. Moreover, this local Rossby number is shown to match well with the transition between the thermal and viscous Ekman boundary layer (BL) thicknesses. The heat and momentum transport scaling relations during the transition are examined and agree well with the recent unifying transition scaling theory proposed based on the balance of the thermal and viscous Ekman BL thicknesses (Ecke & Shishkina, Annu. Rev. Fluid Mech. 55 (2023)). Instead of using the BL thickness, we extend the transition scaling theory based on the convective length scale, which is applicable to both no-slip and free-slip boundary conditions.