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

Flows at planetary scales are generally driven by buoyancy and influenced by rotation. Rotating Rayleigh-Bénard 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}. %geostrophic regime, where the dominant force balance is between Coriolis and pressure-gradient forces.
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 ≤ Pr ≤ 6. We study the relation between Pr and Nu at constant Ekman number Ek = 3 × 10^-7 (an inverse measure for strength of rotation) for two different diameter-to-height aspect ratios (Γ = 1/5 and 1/2) of the setup. The corresponding constant Rayleigh numbers (strength of thermal forcing) are Ra = 1.1 × 10¹² and 1 × 10¹¹, respectively. Additionally, we measure the relation between the Rayleigh number Ra and Nu for 4 × 10¹⁰ ≤ Ra ≤ 7 × 10¹¹, Ek = 3 × 10^-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.