The study of velocity fields of the hot gas in galaxy clusters can help to unravel details of microphysics on small-scales and to decipher the nature of feedback by active galactic nuclei (AGN). Likewise, magnetic fields as traced by Faraday rotation measurements (RMs) inform about their impact on gas dynamics as well as on cosmic ray production and transport. We investigate the inherent relationship between large-scale gas kinematics and magnetic fields through non-radiative magnetohydrodynamical simulations of the creation, evolution and disruption of AGN jet-inflated lobes in an isolated Perseus-like galaxy cluster, with and without pre-existing turbulence. In particular, we connect cluster velocity measurements with mock RM maps to highlight their underlying physical connection, which opens up the possibility of comparing turbulence levels in two different observables. For single jet outbursts, we find only a local impact on the velocity field, i.e. the associated increase in velocity dispersion is not volume-filling. Furthermore, in a setup with pre-existing turbulence, this increase in velocity dispersion is largely hidden. We use mock X-ray observations to show that at arcmin resolution, the velocity dispersion is therefore dominated by existing large-scale turbulence and is only minimally altered by the presence of a jet. For the velocity structure of central gas uplifted by buoyantly rising lobes, we find fast, coherent outflows with low velocity dispersion. Our results highlight that projected velocity distributions show complex structures which pose challenges for the interpretation of observations.
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