On magnetostrophic inertia-less waves in quasi-geostrophic models of planetary cores

We investigate quasi-geostrophic waves in a rotating spherical shell permeated by an imposed magnetic field (B) over bar. A projection of the momentum equation onto a well chosen class of velocity fields results in a quasi-geostrophic reduced model where, in contrast with previous such models, the evolution of the velocity is not prescribed by an equation for the axial vorticity. We consider fields (B) over bar that may be longitudinally dependent. Increasing the angular rotation frequency, we find that the non-axisymmetric Alfven waves that are present at low rotation morph into inertial waves, torsional Alfven waves and low frequency magnetostrophic waves that satisfy Taylor's constraint (i.e. vanishing acceleration of the geostrophic cylinders by the magnetic forces).