Waves in the Earth’s core. IV. The structure of inviscid torsional oscillations in a spherical shell

We study the properties of cylindrical oscillations of electrically conducting fluid in the presence of a magnetic field, a phenomenon known in geomagnetism as torsional oscillations (TOs) since their discovery by J. B. Taylor and S. I. Braginsky. The chosen geometry is a spherical shell, consistent with Earth’s present-day geometry. We concentrate on the scenario where fluid viscosity is absent in our calculations, but magnetic diffusivity is retained, appropriate to the geophysical conditions in Earth’s fluid outer core. Two axisymmetric background magnetic fields that provide the restoring torques to the motions are considered, one of dipole parity and the other of quadrupole parity. The anticipated class of equatorially symmetric (ES) azimuthal motions is joined by an antisymmetric class that exists in the shell geometry but is absent in the full sphere. Compared to previous studies in a full sphere, our results reveal that computing the eigenmodes of TOs in a spherical shell under the inviscid limit is considerably more computationally challenging. Only one large-scale eigenmode exists (filling the whole shell), while many modes with higher frequencies tend to be concentrated inside the tangent cylinder. We complement our inviscid calculations with calculations in which viscosity is retained, and find convergence (with decreasing viscous diffusion) towards the inviscid results.