Waves in the Earth’s core. 2: Diffusive Magneto-Coriolis waves.

Various types of waves exist in the Earth’s core. Waves associated with the magnetic field can leave a signature in the observed geomagnetic field, which may allow one to infer properties of the core. Among those, a balance of magnetic, Coriolis and pressure forces forms a type of waves known as Magneto-Coriolis (MC) waves. Previous studies of MC wave have mostly been focused on the ideal limit (without magnetic diffusion and viscous dissipation) with a columnar ansatz for the flow field. In this study, we investigate this problem by retaining the magnetic diffusion and three-dimensional flows in a full sphere. With several choices of axisymmetric background magnetic field, we analyse various branches of normal modes. The dependence of the normal mode's structure on the background field is clearly seen. A westward propagating branch with perfect columnar flows is found for some background B. We have also found eastward propagating modes constituted by flows with weaker columnarity. With the choice of Elsasser number Λ=1 (Coriolis and magnetic forces of similar magnitude), for axisymmetric background fields we find most of the MC modes have decay rates comparable or larger than their frequencies.