  It has been shown that the gas velocities within the intracluster medium
(ICM) can be measured by applying novel XMM-Newton EPIC-pn energy scale
calibration, which uses instrumental Cu Ka as reference for the line emission.
Using this technique, we have measured the velocity distribution of the ICM for
clusters involving AGN feedback and sloshing of the plasma within the
gravitational well (Virgo and Centaurus) and a relaxed one (Ophiuchus). We
present a detailed study of the kinematics of the hot ICM for these systems.
First, we compute the velocity probability distribution functions (PDFs) from
the velocity maps. We find that for all sources the PDF follows a normal
distribution, with a hint for a multimodal distribution in the case of
Ophiuchus. Then, we compute the velocity structure function (VSF) for all
sources in order to study the variation with scale as well as the nature of
turbulence in the ICM. We measure a turbulence driving scale of 10-20 kpc for
the Virgo cluster, while the Ophiuchus cluster VSF reflects the absence of
strong interaction between the ICM and a powerful Active Galactic Nucleus (AGN)
at such spatial scales. For the former, we compute a dissipation time larger
than the jet activity cycle, thus indicating that a more efficient heating
process than turbulence is required to reach equilibrium. This is the first
time that the VSF of the hot ICM has been computed using direct velocity
measurements from X-ray astronomical observations.
