RESUMEN
While the heat transfer and the flow dynamics in a cylindrical Rayleigh-Bénard (RB) cell are rather independent of the aspect ratio Γ (diameter/height) for large Γ, a small-Γ cell considerably stabilizes the flow and thus affects the heat transfer. Here, we first theoretically and numerically show that the critical Rayleigh number for the onset of convection at given Γ follows Ra_{c,Γ}â¼Ra_{c,∞}(1+CΓ^{-2})^{2}, with Câ²1.49 for Oberbeck-Boussinesq (OB) conditions. We then show that, in a broad aspect ratio range (1/32)≤Γ≤32, the rescaling RaâRa_{â}≡Ra[Γ^{2}/(C+Γ^{2})]^{3/2} collapses various OB numerical and almost-OB experimental heat transport data Nu(Ra,Γ). Our findings predict the Γ dependence of the onset of the ultimate regime Ra_{u,Γ}â¼[Γ^{2}/(C+Γ^{2})]^{-3/2} in the OB case. This prediction is consistent with almost-OB experimental results (which only exist for Γ=1, 1/2, and 1/3) for the transition in OB RB convection and explains why, in small-Γ cells, much larger Ra (namely, by a factor Γ^{-3}) must be achieved to observe the ultimate regime.
RESUMEN
For rapidly rotating turbulent Rayleigh-Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one, whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra^{1/4}Ek^{2/3} where the Ekman number Ek decreases with increasing rotation rate.