Imposing a magnetic field across a nonaxisymmetric shear layer in a rotating spherical shell

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Abstract
In the context of the generation of the Earth’s magnetic field, nonaxisymmetric solutions of the forced momentum equation in a rotating spherical shell are considered in the inertia-less, inviscid limit. It has previously been pointed out that, in general, such solutions are singular, with all three flow components discontinuous across the cylinder tangent to the inner core and parallel to the axis of rotation. An integral constraint on the forcing was derived, which must be satisfied if the inviscid solution is to be nonsingular, and it was suggested that in the presence of a magnetic field the Lorentz force would adjust to satisfy this constraint, thereby eliminating the need for the viscous shear layer, which otherwise resolves the singularity. In this work an axisymmetric field is imposed across this shear layer, and it is demonstrated that for a sufficiently strong field this adjustment does indeed occur.

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