Connections between slowly and rapidly rotating convection scalings: Rise of the Rossby numbers*

We will present transport scalings for slowly and rapidly rotating turbulent convection systems, with the end goals of both explaining differences and forging connections between the regimes. Through the selection of physically relevant estimates for length $\ell$, velocity $U$ and temperature scales $\vartheta$ in each regime, turbulent scalings are developed for the local Reynolds $Re_\ell = U \ell /\nu$; local P\'eclet $Pe_\ell =  U \ell /\kappa$; and Nusselt number $Nu = U \vartheta/(\kappa \Delta T/H)$. Emergent from the scaling analyses is a unified continuum based on a single external control parameter, the convective Rossby number, $\RoC = \sqrt{g \alpha \Delta T / (4 \Omega^2 H)}$, which is found to scale with the local Rossby number $\Rol \sim \RoC$ in both the slowly and rapidly rotating regimes, explaining the ubiquity of $\RoC$ in studies of rotating convection dynamics, convection-driven zonal jet generation and planetary dynamo generation.