Cosmological constraints from X-ray and microwave observations of galaxy clusters are subjected to sys-tematic uncertainties. Non-thermal pressure support due to internal gas motions in galaxy clusters is one of the major sources of astrophysical uncertainties. Using a mass-limited sample of galaxy clusters from a high-resolution hydrodynamical cosmological simulation, we characterize the non-thermal pressure fraction profile and study its dependence on redshift, mass, and mass accretion rate. We find that the non-thermal pressure frac-tion profile is universal across redshift when galaxy cluster radii are defined with respect to the mean matter density of the universe instead of the commonly used critical density. We also find that the non...