  The dynamics of the intracluster medium (ICM) is affected by turbulence
driven by several processes, such as mergers, accretion and feedback from
active galactic nuclei. X-ray surface brightness fluctuations have been used to
constrain turbulence in galaxy clusters. Here, we use simulations to further
investigate the relation between gas density and turbulent velocity
fluctuations, with a focus on the effect of the stratification of the ICM. In
this work, we studied the turbulence driven by hierarchical accretion by
analysing a sample of galaxy clusters simulated with the cosmological code
ENZO. We used a fixed scale filtering approach to disentangle laminar from
turbulent flows. In dynamically perturbed galaxy clusters, we found a relation
between the root mean square of density and velocity fluctuations, albeit with
a different slope than previously reported. The Richardson number is a
parameter that represents the ratio between turbulence and buoyancy, and we
found that this variable has a strong dependence on the filtering scale.
However, we could not detect any strong relation between the Richardson number
and the logarithmic density fluctuations, in contrast to results by recent and
more idealised simulations. In particular, we find a strong effect from radial
accretion, which appears to be the main driver for the gas fluctuations. The
ubiquitous radial bias in the dynamics of the ICM suggests that homogeneity and
isotropy are not always valid assumptions, even if the turbulent spectra follow
Kolmogorov's scaling. Finally, we find that the slope of the velocity and
density spectra are independent of cluster-centric radii.
