Predicting the Rossby Number in Convective Experiments

Abstract

Abstract The Rossby number is a crucial parameter describing the degree of rotational constraint on the convective dynamics in stars and planets. However, it is not an input to computational models of convection but must be measured ex post facto. Here, we report the discovery of a new quantity, the predictive Rossby number, which is both tightly correlated with the Rossby number and specified in terms of common inputs to numerical models. The predictive Rossby number can be specified independent of Rayleigh number, allowing suites of numerical solutions to separate the degree of rotational constraint from the strength of the driving of convection. We examine the scaling of convective transport in terms of the Nusselt number and the degree of turbulence in terms of the Reynolds number of the flow, and we find scaling laws nearly identical to those in non-rotational convection at low Rossby number when the predictive Rossby number is held constant. Finally, we describe the boundary layers as a function of increasing turbulence at constant Rossby number.