We present high-precision experimental and numerical studies of the Nusselt number $\mathrm{Nu}$ as functions of the Rayleigh number $\mathrm{Ra}$ in geostrophic rotating convection with the domain aspect ratio $\mathrm{\Gamma }$ varying from 0.4 to 3.8 and the Ekman number $\mathrm{Ek}$ varying from $2.7\times {10}^{-5}$ to $2.0\times {10}^{-7}$. With decreasing $\mathrm{Ra}$ our heat-transport data $\mathrm{Nu}\left(\mathrm{Ra}\right)$ reveal a gradual transition from buoyancy-dominated to geostrophic convection at large $\mathrm{Ek}$, whereas the transition becomes sharp with decreasing $\mathrm{Ek}$. We determine the power-law scaling of $\mathrm{Nu}\sim {\mathrm{Ra}}^{\gamma }$, and find an unexpectedly strong $\mathrm{\Gamma }$ dependence of the scaling exponent $\gamma$. We further show that the boundary flows formed near the lateral wall give rise to pronounced enhancement of $\mathrm{Nu}$ over a broad range of the geostrophic regime, leading to reduction of $\gamma$ in small-$\mathrm{\Gamma }$ cells. A very steep scaling with $\gamma >3$ is observed when the periodic lateral boundary condition is used, which manifests the significant differences between laterally confined and unconfined rotating thermal convection. The present work provides insight into the heat-transport scaling in geostrophic convection.

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• Heat transfer
• Rayleigh-Bénard convection
• Rotating geophysical flows