Galaxy clusters are unique laboratories for studying astrophysical processes
and their impact on gas kinematics. Despite their importance, the full
complexity of gas motion within and around clusters remains poorly known. This
paper is part of a series presenting first results from the new TNG-Cluster
simulation, a suite of 352 massive clusters including the full cosmological
context, mergers, accretion, baryonic processes, feedback, and magnetic fields.
Studying the dynamics and coherence of gas flows, we find that gas motions in
cluster cores and intermediate regions are largely balanced between inflows and
outflows, exhibiting a Gaussian distribution centered at zero velocity. In the
outskirts, even the net velocity distribution becomes asymmetric, featuring a
double peak where the second peak reflects cosmic accretion. Across all cluster
regions, the resulting net flow distribution reveals complex gas dynamics.
These are strongly correlated with halo properties: at a given total cluster
mass, unrelaxed, late-forming halos with less massive black holes and lower
accretion rates exhibit a more dynamic behavior. Our analysis shows no clear
relationship between line-of-sight and radial gas velocities, suggesting that
line-of-sight velocity alone is insufficient to distinguish between inflowing
and outflowing gas. Additional properties, such as temperature, can help break
this degeneracy. A velocity structure function (VSF) analysis indicates more
coherent gas motion in the outskirts and more disturbed kinematics towards halo
centers. In all cluster regions, the VSF shows a slope close to the theoretical
models of Kolmogorov (1/3), except within 50 kpc of the cluster cores, where
the slope is significantly steeper. The outcome of TNG-Cluster broadly aligns
with observations of the VSF of multiphase gas across different scales in
galaxy clusters, ranging from 1 kpc to Megaparsec scales.Comment: Submitted to A&A. See the TNG-Cluster website at
https://www.tng-project.org/cluster