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

The columnar -flow appro ximation allows the development of computationally efficient nu- merical 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 deri v ation of an ap- proximate 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.