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.

中文翻译：

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具有不同纵横比的地转旋转对流中的传热缩放和转变

我们提供了 Nusselt 数的高精度实验和数值研究 $怒$ 作为瑞利数的函数 $镭$ 在具有域纵横比的地转旋转对流中 $\mathrm{\Gamma }$ 从 0.4 到 3.8 以及 Ekman 数 $\mathrm{EK}$ 不一样 $2.7\times {10}^{-5}$ 到 $2.0\times {10}^{-7}$. 随着减少$镭$ 我们的传热数据 $怒\left(镭\right)$ 揭示了从以浮力为主的向地转对流的逐渐转变 $\mathrm{EK}$，而转变变得尖锐 $\mathrm{EK}$. 我们确定幂律缩放$怒～{镭}^{\gamma }$，并发现一个意想不到的强大 $\mathrm{\Gamma }$ 缩放指数的相关性 $\gamma$. 我们进一步表明，在侧壁附近形成的边界流引起了显着增强$怒$ 在广泛的地转区域，导致减少 $\gamma$ 在小-$\mathrm{\Gamma }$细胞。非常陡峭的缩放$\gamma >3$当使用周期性横向边界条件时观察到，这表明横向限制和非限制旋转热对流之间的显着差异。目前的工作提供了对地转对流中热传输尺度的深入了解。