  We have implemented an Adaptive Mesh Refinement criterion explicitly designed
to increase spatial resolution around discontinuities in the velocity field in
ENZO cosmological simulations. With this technique, shocks and turbulent eddies
developed during the hierarchical assembly of galaxy clusters are followed with
unprecedented spatial resolution, even at large distances from the clusters
center. By measuring the spectral properties of the gas velocity field, its
time evolution and the properties of shocks for a reference galaxy cluster, we
investigate the connection between accretion processes and the onset of chaotic
motions in the simulated Inter Galactic Medium over a wide range of scales
