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.