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Abstract

The main tools by which we can study the dynamics of Earth’s fluid core are direct numerical simulations (DNS). In spite of their success, their high computational cost prevents DNS from reaching Earth-like parameters regimes. Previous studies support the idea that the vast majority of the kinetic energy in the core is contained in columnar, vertically invariant structures. Columnar flow models capitalise on this observation and transform the original, 3D governing equations in a simplified, 2D set. These models have proven their potential in simulating the dynamics of Earth’s fluid core in extreme parameter regimes. However, current approaches are not capable of treating the magnetic field within the same 2D framework. Plesio-geostrophy (PG) was developed to overcome this limitation. Our PG model describes fluid flows, magnetic field and temperature via 2D variables. We tested our novel PG methodology on a set of linear problems of relevance to the dynamics of Earth’s fluid core: inertial and magneto-hydrodynamics waves propagation, and onset of thermal convection. All diffusivities are taken into account. The effect of viscous boundary layers is parameterised via a novel, fully spectral numerical methodology that does not require special treatments of the critical latitudes. We successfully benchmarked the PG model results against both 3D and other columnar flow models and calculated solutions at geophysically relevant parameter regimes.