Experiments on rapidly rotating convection: the role of the Prandtl number

Abstract

Flows at planetary scales are generally driven by buoyancy and influenced by rotation. Rotating Rayleigh-B\'enard convection (RRBC) is a practical and simple model that can be used to describe these systems. In RRBC, thermally induced convection occurs, which is influenced by the constant rotation it experiences. We study RRBC in a cylinder in the \red{transition region between rotation-affected and rotation-dominated (also called geostrophic) convection}. Experiments are performed to assess the dependence of the Nusselt number $\Nu$ (efficiency of convective heat transfer) on the Prandtl number $\Pr$ (ratio of kinematic viscosity over thermal diffusivity), a relation that is not explored much for geostrophic convection. By using water at different mean temperatures we can reach $2.8\le \Pr\le 6$. We study the relation between $\Pr$ and $\Nu$ at constant Ekman number $\Ek=3\times10^{-7}$ (an inverse measure for strength of rotation) for two different diameter-to-height aspect ratios ($\Gamma=1/5$ and $1/2$) of the setup. The corresponding constant Rayleigh numbers (strength of thermal forcing) are $\Ra=1.1\times 10^{12}$ and $1\times 10^{11}$, respectively. Additionally, we measure the relation between the Rayleigh number $\Ra$ and $\Nu$ for $4\times10^{10}\le \Ra\le 7\times10^{11}$, $\Ek=3\times10^{-7}$ and $\Pr=3.7$. It is found that $\Nu$ exhibits a significant dependence on $\Pr$, even within this limited range. Increasing $\Pr$ by a factor 2 resulted in a decrease of $\Nu$ of about $25 \%$. We hypothesize that the decrease of $\Nu$ is caused by the changing ratio of the thermal and kinetic boundary layer thicknesses as a result of increasing $\Pr$. We also consider the anticipated contributions of the wall mode to the heat transfer using sidewall temperature measurements.