  We argue that the recently reported Kolmogorov-like magnetic turbulence
spectrum in the cool core of the Hydra A galaxy cluster can be understood by
kinetic energy injection by active galaxies that drives a turbulent non-helical
magnetic dynamo into its saturated state. Although dramatic differences exist
between small-scale dynamo scenarios, their saturated state is expected to be
similar, as we show for three scenarios: the flux rope dynamo, the fluctuation
dynamo, and the explosive dynamo. Based on those scenarios, we develop an
analytical model of the hydrodynamic and magnetic turbulence in cool cores. The
model implies magnetic field strengths that fit well with Faraday rotation
measurements and minimum energy estimates for the sample of cool core clusters
having such data available. Predictions for magnetic fields in clusters for
which the appropriate observational information is still missing, and for yet
unobserved quantities like the hydrodynamical turbulence velocity and
characteristic length-scale are provided. The underlying dynamo models suggest
magnetic intermittency and possibly a large-scale hydrodynamic viscosity. We
conclude that the success of the model to explain the field strength in cool
core clusters indicates that in general cluster magnetic fields directly
reflect hydrodynamical turbulence, also in clusters without cool cores.
