Simulations of the Small‐Scale Turbulent Dynamo

We report the results of an extensive numerical study of the small-scale turbulent dynamo. The focus is on large magnetic Prandtl numbers, which are relevant for hot low-density astrophysical plasmas. A Pr parameter scan is given for the model case of low-Reynolds-number turbulence. The main results are (i) the folded structure of the field (direction reversals at the resistive scale, field lines straight up to the flow scale) persists from the kinematic to the nonlinear regime, (ii) the field distribution is lognormal and self-similar during the kinematic stage of the dynamo and exponential in the saturated state; (iii) the bulk of the magnetic energy is at the resistive scale in the kinematic regime and remains there in saturation, although the magnetic-energy spectrum becomes much shallower. We propose an analytical model of the dynamo saturation based on the idea of partial two-dimensionalization of the velocity field with respect to the local direction of the magnetic folds. The saturated spectra resulting from the model are in excellent agreement with numerical results. Comparisons with large-Re, moderate-Pr runs are carried out to confirm the relevance of the above results and to test heuristic scenarios of dynamo saturation. New features at large Re include elongation of the folds in the nonlinear regime from the viscous scale to the box scale and the presence of an intermediate nonlinear regime of slower-than-exponential magnetic-energy growth. Numerical results for the saturated state do not support scale-by-scale equipartition between magnetic and kinetic energies, with a definite excess of magnetic energy at small scales. A physical picture of the saturated state is proposed.