  We present results from a large set of N-body/SPH hydrodynamical cluster
simulations aimed at studying the statistical properties of turbulence in the
ICM. The numerical hydrodynamical scheme employs a SPH formulation in which
gradient errors are strongly reduced by using an integral approach. We consider
both adiabatic and radiative simulations. We construct clusters subsamples
according to the cluster dynamical status or gas physical modeling, from which
we extract small-scale turbulent velocities obtained by applying to cluster
velocities different multiscale filtering methods. The velocity power spectra
of non-radiative relaxed clusters are mostly solenoidal and steeper than
Kolgomorov. Cooling runs are distinguished by much shallower spectra, a feature
which we interpret as the injection of turbulence at small scales due to the
interaction of compact cool gas cores with the ICM. Turbulence in galaxy
clusters is then characterized by multiple injection scales, with the small
scale driving source acting in addition to the large scale injection
mechanisms. Cooling runs of relaxed clusters exhibit enstrophy profiles with a
power-law behavior over more than two decades in radius, and a
turbulent-to-thermal energy ratio ~1 %. In accord with Hitomi observations, in
the core of a highly relaxed cluster we find low level of gas motions. In
addition, the estimated cluster radial profile of the sloshing oscillation
period exhibits an associated Froude number satisfying Fr ~ 0.1 within r /
r_{200} <~ 0.1. Our findings suggest that in cluster cores ICM turbulence
approaches a stratified anisotropic regime, with weak stirring motions
dominated by gravity buoyancy forces and strongly suppressed along the radial
direction. We conclude that turbulent heating cannot be considered the main
heating source in cluster cores.
