  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.
