We compare DNS calculations of homogeneous isotropic turbulence with the statistical properties of intra-cluster turbulence from the Matryoshka Run (Miniati 2014) and find remarkable similarities between their inertial ranges. This allowed us to use the time dependent statistical properties of intra-cluster turbulence to evaluate dynamo action in the intra-cluster medium, based on earlier results from numerically resolved nonlinear magneto-hydrodynamic turbulent dynamo (Beresnyak 2012). We argue that this approach is necessary (a) to properly normalize dynamo action to the available intra-cluster turbulent energy and (b) to overcome the limitations of low Re affecting current numerical models of the intra-cluster medium. We find that while the properties of intra-cluster magnetic field are largely insensitive to the value and origin of the seed field, the resulting values for the Alfven speed and the outer scale of the magnetic field are consistent with current observational estimates, basically confirming the idea that magnetic field in todays galaxy clusters is a record of its past turbulent activity.
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