Heat transport by rotating Rayleigh-Bénard convection in cylindrical cells with various aspect ratios*

Rotating convection has been of interest for decades, yet there exists no generally accepted scaling law for heat transfer behavior in the geostrophic turbulence regime. We present high-precision measurements of the Nusselt number Nu as functions of the Rayleigh number Ra and the Ekman number Ek using cylindrical cells with various aspect ratio $\Gamma$. For a given $\Gamma$ data for Nu(Ra, Ek) in the geostrophic regime can be represented through one single power function $Nu{=}(Ra/Ra_c)^{\gamma}$, where $Ra_c{=}8.7Ek^{-4/3}$ is the critical Ra for the onset of convection. However, our experimental and numerical results reveal that the exponent $\gamma$ increases steeply with increasing $\Gamma$, leading to various parameter scaling for the transition towards the geostrophic regime. The present study may provide hints to reconcile previous results of the heat-transport scaling relationship in geostrophic turbulence.