Magnetic spherical Couette flow in linear combinations of axial and dipolar fields

We present axisymmetric numerical calculations of the fluid flow induced in a spherical shell with inner sphere rotating and outer sphere stationary. A magnetic field is also imposed, consisting of particular linear combinations of axial and dipolar fields, chosen to make $B_r=0$ at either the outer sphere, or the inner, or in between. This leads to the formation of Shercliff shear layers at these particular locations. We then consider the effect of increasingly large inertial effects, and show that an outer Shercliff layer is eventually de-stabilized, an inner Shercliff layer appears to remain stable, and an in-between Shercliff layer is almost completely disrupted even before the onset of time-dependence, which does eventually occur though

On obliquely magnetized and differentially rotating stars

We investigate the interaction of differential rotation and a misaligned magnetic field. The incompressible magnetohydrodynamic equations are solved numerically for a free-decay problem. In the kinematic limit, differential rotation annihilates the non-axisymmetric field on a timescale proportional to the cube root of magnetic Reynolds number ($Rm$), as predicted by R\"adler. Nonlinearly, the outcome depends upon the initial energy in the non-axisymmetric part of the field. Sufficiently weak fields approach axisymmetry as in the kinematic limit; some differential rotation survives across magnetic surfaces, at least on intermediate timescales. Stronger fields enforce uniform rotation and remain non-axisymmetric. The initial field strength that divides these two regimes does not follow the scaling $Rm^{-1/3}$ predicted by quasi-kinematic arguments, perhaps because our $Rm$ is never sufficiently large or because of reconnection. We discuss the possible relevance of these results to tidal synchronization and tidal heating of close binary stars, particularly double white dwarfs