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 haloes 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 haloes to clusters with disturbed X-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 haloes 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 per cent 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 Gyr 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 LX–P1.4 GHz relation. However, our result may be consistent with the observed bimodality, as here we are not including a full treatment of cosmic ray sources and magnetic fields.