Abstract. 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 ¤ux rope dynamo, the ¤uctuation 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 £eld strengths that £t well with Faraday rotation measurements and minimum energy estimates for the sample of cool core clusters having such data available. Predictions for magnetic £elds 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 largescale hydrodynamic viscosity. We conclude that the success of the model to explain the £eld strength in cool core clusters indicates that in general cluster magnetic £elds directly re¤ect hydrodynamical turbulence, also in clusters without cool cores.