  The predominant force balance in rapidly rotating planetary cores is between
Coriolis, pressure, buoyancy and Lorentz forces. This magnetostrophic balance
leads to a Taylor state where the spatially averaged azimuthal Lorentz force is
compelled to vanish on cylinders aligned with the rotation axis. Any deviation
from this state leads to a torsional oscillation, signatures of which have been
observed in the Earth's secular variation and are thought to influence length
of day variations via angular momentum conservation. In order to investigate
the dynamics of torsional oscillations, we perform several three-dimensional
dynamo simulations in a spherical shell. We find torsional oscillations,
identified by their propagation at the correct Alfv\'{e}n speed, in many of our
simulations. We find that the frequency, location and direction of propagation
of the waves are influenced by the choice of parameters. Torsional waves are
observed within the tangent cylinder and also have the ability to pass through
it. Several of our simulations display waves with core travel times of 4 to 6
years. We calculate the driving terms for these waves and find that both the
Reynolds force and ageostrophic convection acting through the Lorentz force are
important in driving torsional oscillations.
