  Azimuthal accelerations of cylindrical surfaces co-axial with the rotation
axis have been inferred to exist in Earth's fluid core on the basis of magnetic
field observations and changes in the length-of-day. These accelerations have a
typical timescale of decades. However, the physical mechanism causing the
accelerations is not well understood. Scaling arguments suggest that the
leading order torque averaged over cylindrical surfaces should arise from the
Lorentz force. Decadal fluctuations in the magnetic field inside the core,
driven by convective flows, could then force decadal changes in the Lorentz
torque and generate zonal accelerations. We test this hypothesis by
constructing a quasi-geostrophic model of magnetoconvection, with
thermally-driven flows perturbing a steady, imposed background magnetic field.
We show that when the Alfv\'{e}n number in our model is similar to that in
Earth's fluid core, temporal fluctuations in the torque balance are dominated
by the Lorentz torque, with the latter generating mean zonal accelerations. Our
model reproduces both fast, free Alfv\'{e}n waves and slow, forced
accelerations, with ratios of relative strength and relative timescale similar
to those inferred for the Earth's core. The temporal changes in the magnetic
field which drive the time-varying Lorentz torque are produced by the
underlying convective flows, shearing and advecting the magnetic field on a
timescale associated with convective eddies. Our results support the hypothesis
that temporal changes in the magnetic field deep inside Earth's fluid core
drive the observed decadal zonal accelerations of cylindrical surfaces through
the Lorentz torque.
