We report on results of recent, high resolution hydrodynamic simulations of the formation and evolution of X-ray clusters of galaxies carried out within a cosmological framework. We employ the highly accurate piecewise parabolic method (PPM) on fixed and adaptive meshes which allow us to resolve the flow field in the intracluster gas. The excellent shock capturing and low numerical viscosity of PPM represent a substantial advance over previous studies using SPH. We find that in flat, hierarchical cosmological models, the ICM is in a turbulent state long after turbulence generated by the last major merger should have decayed away. Turbulent velocites are found to vary slowly with cluster radius, being $\sim 25%$ of $σ_{vir}$ in the core, increasing to $\sim 60%$ at the virial radius. We argue that more frequent minor mergers maintain the high level of turbulence found in the core where dynamical times are short. Turbulent pressure support is thus significant throughout the cluster, and results in a somewhat cooler cluster ($T/T_{vir} \sim .8$) for its mass. Some implications of cluster turbulence are discussed.

10 pages, 4 figures, to appear in Ringberg Workshop on M87, eds. K. Meisenheimer and H-J. Roeser, Springer Verlag. Additional color images available at http://zeus.ncsa.uiuc.edu:8080/Xray/clusters.html