Convection-driven hydromagnetic waves in planetary fluid cores

We study hydromagnetic waves driven by thermal convection in a self-gravitating, rapidly rotating fluid spherical shell permeated by both poloidal and toroidal axisymmetric magnetic fields. The imposed magnetic fields satisfy electrically insulating boundary conditions at both surfaces of the shell and have an equatorial dipolar symmetry. The system is a model of the cores of the Earth and other planets, where magnetic fields are generated. We focus on the effect of poloidal magnetic fields at an asymptotically small Ekman number E = 10−6. We find two new modes for convection-driven hydromagnetic waves. When the poloidal field is larger than the toroidal field, the waves propagate rapidly eastwards and concentrate just outside the “tangent cylinder”, which has axis parallel to the rotation axis and just encloses the inner sphere. When the poloidal field is comparable to the toroidal field the waves also propagate eastwards but concentrate inside the tangent cylinder. When the toroidal field is larger than the poloidal field the waves propagate slowly either eastwards or westwards and concentrate on lower to middle latitudes. In all the three cases, the flow approximately satisfies the two-dimensional Proudman-Taylor constraint, even though the theorem does not strictly apply because the magnetic forces are strong.