Plesio-geostrophy for Earth’s core – II: thermal equations and onset of convection

The columnar-flow approximation allows the development of computationally efficient numerical models tailored to the study of the rapidly rotating dynamics of Earth’s fluid outer core. In this paper, we extend a novel columnar-flow formulation, called Plesio-Geostrophy (PG) by including thermal effects and viscous boundary conditions. The effect of both no-slip and stress-free boundaries, the latter being a novelty for columnar-flow models, are included. We obtain a set of fully 2-D evolution equations for fluid flows and temperature where no assumption is made regarding the geometry of the latter, except in the derivation of an approximate thermal diffusion operator. To test the new PG implementation, we calculated the critical parameters for onset of thermal convection in a spherical domain. We found that the PG model prediction is in better agreement with unapproximated, 3-D calculations in rapidly rotating regimes, compared to another state-of-the-art columnar-flow model.