  The outskirts of galaxy clusters are characterised by the interplay of gas
accretion and dynamical evolution involving turbulence, shocks, magnetic fields
and diffuse radio emission. The density and velocity structure of the gas in
the outskirts provide an effective pressure support and affect all processes
listed above. Therefore it is important to resolve and properly model the
turbulent flow in these mildly overdense and relatively large cluster regions;
this is a challenging task for hydrodynamical codes. In this work, grid-based
simulations of a galaxy cluster are presented. The simulations are performed
using adaptive mesh refinement (AMR) based on the regional variability of
vorticity, and they include a subgrid scale model (SGS) for unresolved
turbulence. The implemented AMR strategy is more effective in resolving the
turbulent flow in the cluster outskirts than any previously used criterion
based on overdensity. We study a cluster undergoing a major merger, which
drives turbulence in the medium. The merger dominates the cluster energy budget
out to a few virial radii from the centre. In these regions the shocked
intra-cluster medium is resolved and the SGS turbulence is modelled, and
compared with diagnostics on larger length scale. The volume-filling factor of
the flow with large vorticity is about 60% at low redshift in the cluster
outskirts, and thus smaller than in the cluster core. In the framework of
modelling radio relics, this point suggests that upstream flow inhomogeneities
might affect pre-existing cosmic-ray population and magnetic fields, and the
resulting radio emission.
