  Galaxy clusters are potentially powerful probes of the large-scale velocity
field in the Universe because their peculiar velocity can be estimated directly
via the kinematic Sunyaev-Zeldovich effect (kSZ). Using high-resolution
cosmological simulations of an evolving cluster of galaxies, we evaluate how
well the average velocity obtained via a kSZ measurement reflects the actual
cluster peculiar velocity. We find that the internal velocities in the
intracluster gas are comparable to the overall cluster peculiar velocity, 20 to
30% of the sound speed even when a cluster is relatively relaxed. Nevertheless,
the velocity averaged over the kSZ map inside a circular aperture matched to
the cluster virial region provides an unbiased estimate of a cluster's radial
peculiar velocity with a dispersion of 50 to 100 km/s, depending on the line of
sight and dynamical state of the cluster. This dispersion puts a lower limit on
the accuracy with which cluster peculiar velocity can be measured. Although the
dispersion of the average is relatively small, the velocity distribution is
broad; regions of low signal must be treated with care to avoid bias. We
discuss the extent to which systematic errors might be modelled, and the
resulting limitations on using galaxy clusters as cosmological velocity
tracers.
