  We track the histories of massive clusters of galaxies formed within a
cosmological hydrodynamic simulation. Specifically, we track the time evolution
of the energy in random bulk motions of the intracluster medium and X-ray
measures of cluster structure and their relationship to cluster mergers. We aim
to assess the viability of the turbulent re-acceleration model for the
generation of giant radio halos by comparing the level of turbulent kinetic
energy in simulated clusters with the observed properties of radio halo
clusters, giving particular attention to the association of radio halos to
clusters with disturbedX-ray structures. The evolution of X-ray cluster
structure and turbulence kinetic energy, k, in simulations can then inform us
about the expected lifetime of radio halos and the fraction of clusters as a
function of redshift expected to host them. We find strong statistical
correlation of disturbed structure measures and the presence of enhancements in
k. Specifically, quantitatively "disturbed", radio halo-like X-ray morphology
in our sample indicates a 92% chance of the cluster in question having k
elevated to more than twice its minimum value over the cluster's life. The
typical lifetime of episodes of elevated turbulence is on the order of 1 Gyr,
though these periods can last 5 Gyrs or more. This variation reflects the wide
range of cluster histories; while some clusters undergo complex and repeated
mergers spending a majority of their time in elevated k states, other clusters
are relaxed over nearly their entire history. We do not find a bimodal
relationship between cluster X-ray luminosity and the total energy in
turbulence that might account directly for a bimodal L_X-P_{1.4 GHz} relation.
However, our result may be consistent with the observed bimodality, as here we
are not including a full treatment of cosmic rays sources and magnetic fields.
