Testing Asymptotic Scaling Trends in Laboratory-Numerical Rotating Convection and Dynamo Experiments

Asymptotic analysis of rotating convective turbulence, as exists in planets and stars, yields scaling predictions that all hinge on the value of the convective Rossby number, $Ro_C = \sqrt{Ra E^2/Pr}$ (e.g., Julien et al., GAFD 2012; Aurnou et al., PRR 2020), where the Rayleigh number $Ra$ estimates the buoyancy forcing, the Ekman number $E$ the rotation period and the Prandtl number $Pr$ the thermomechanical fluid properties. Here, we test these asymptotic scalings using a broad compilation of laboratory-numerical rotating convection and dynamo experiments in planar, cylindrical, and spherical systems. We find good agreement between the different rapidly rotating and slowly rotating $Ro_C$-dependent trends for convective heat transfer, convective velocities, length scales, and local Rossby numbers in Boussinesq fluids. Further, we show that the predicted rapidly rotating velocity trend also holds in anelastic systems, albeit with an additional dependence on the density stratification. Our tests demonstrate that, given reasonable estimates of $Ro_C$ in a geophysical fluid system, accurate first-order predictions of the convective flows and dynamics can be made.