The Influence of a Homogeneous Magnetic Field on the Ekman and Stewartson Layers

This contribution is aimed at a comparison of two different methods of how to deal with the solid inner core in geodynamo models. The first method, based on a direct application of the non-slip boundary conditions, was frequently used in the past. The second one, developed by the authors of the present paper, is based on an advanced analytical solution within the boundary layers and consequent formulation of new boundary conditions on the flow in the volume of the outer core. As an example we have used the results obtained by Hollerbach (1997) in the study of the influence of an imposed axial magnetic field on the fluid flow in a differentially rotating spherical shell. In the case of a weak imposed magnetic field, our solutions are very similar to those of Hollerbach. This non-trivial correspondence confirms the correctness of both methods, which are different not only in the formulation of boundary conditions, but also in the numerical methods: whereas Hollerbach used spectral methods, our computer code is based on finite differences. The influence of the conductivity of the inner core on the fluid flow was also studied.