We present a numerical scheme for modelling unresolved turbulence in cosmological adaptive mesh refinement codes. As a first application, we study the evolution of turbulence in the intra-cluster medium and in the core of a galaxy cluster. Simulations with and without subgrid scale model are compared in detail. Since the flow in the ICM is subsonic, the global turbulent energy contribution at the unresolved length scales is smaller than 1% of the internal energy. We find that the production of turbulence is closely correlated with merger events occurring in the cluster environment, and its dissipation locally affects the cluster energy budget. Because of this additional source of dissipation, the core temperature is larger and the density is smaller in the presence of subgrid scale turbulence than in the standard adiabatic run, resulting in a higher entropy core value.

We performed a set of cosmological simulations of major mergers in galaxy clusters, in order to study the evolution of merger shocks and the subsequent injection of turbulence in the post-shock region and in the intra-cluster medium (ICM). The computations have been performed with the grid-based, adaptive mesh refinement (AMR) hydrodynamical code Enzo, using a refinement criterion especially designed for refining turbulent flows in the vicinity of shocks. When a major merger event occurs, a substantial amount of turbulence energy is injected in the ICM of the newly formed cluster. Our simulations show that the shock launched after a major merger develops an ellipsoidal shape and gets broken by the interaction with the filamentary cosmic web around the merging cluster. The size of the post-shock region along the direction of shock propagation is of the order of 300 kpc h −1 , and the turbulent velocity dispersion in this region is larger than 100 km s −1 . We performed a scaling analysis of the turbulence energy within our cluster sample. The best fit for the scaling of the turbulence energy with the cluster mass is consistent with M 5/3 , which is also the scaling law for the thermal energy in the self-similar cluster model. This clearly indicates the close relation between virialization and injection of turbulence in the cluster evolution. As for the turbulence in the cluster core, we found that within 2 Gyr after the major merger (the timescale for the shock propagation in the ICM), the ratio of the turbulent to total pressure is larger than 10%, and after about 4 Gyr it is still larger than 5%, a typical value for nearly relaxed clusters. Turbulence at the cluster center is thus sustained for several Gigayears, which is substantially longer than typically assumed in the turbulent re-acceleration models, invoked for explaining the statistics of observed radio halos. Striking similarities in the morphology and other physical parameters between our simulations and the 'symmetrical radio relics' found at the periphery of the merging cluster Abell 3376 are finally discussed. In particular, the interaction between the merger shock and the filaments surrounding the cluster could explain the presence of 'notch-like' features at the edges of the double relics.

The injection and evolution of turbulence in the intergalactic medium is studied by means of mesh‐based hydrodynamical simulations, including a subgrid‐scale (SGS) model for small‐scale unresolved turbulence. The simulations show that the production of turbulence has a different redshift dependence in the intracluster medium (ICM) and the warm‐hot intergalactic medium (WHIM). We show that the turbulence in the ICM is produced chiefly by merger‐induced shear flows, whereas the production in the WHIM is dominated by shock interactions. Secondly, the effect of dynamical pressure support on the gravitational contraction has been studied. This turbulent support is stronger in the WHIM gas at baryon overdensities 1 ≲δ≲ 100 and less relevant for the ICM. Although the relative mass fraction of the gas with large vorticity is considerable (52 per cent in the ICM), we find that for only about 10 per cent in mass this is dynamically relevant, namely not associated with an equally large thermal pressure support. According to this result, a significant non‐thermal pressure support counteracting the gravitational contraction is a localized characteristic in the cosmic flow, rather than a widespread feature.

The development of turbulent gas flows in the intra‐cluster medium and in the core of a galaxy cluster is studied by means of adaptive mesh refinement (AMR) cosmological simulations. A series of six runs was performed, employing identical simulation parameters but different criteria for triggering the mesh refinement. In particular, two different AMR strategies were followed, based on the regional variability of control variables of the flow and on the overdensity of subclumps, respectively. We show that both approaches, albeit with different results, are useful to get an improved resolution of the turbulent flow in the ICM. The vorticity is used as a diagnostic for turbulence, showing that the turbulent flow is not highly volume filling but has a large area‐covering factor, in agreement with previous theoretical expectations. The measured turbulent velocity in the cluster core is larger than 200 km s−1, and the level of turbulent pressure contribution to the cluster hydrostatic equilibrium is increased by using the improved AMR criteria.

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