NONLINEAR small-scale dynamos at low magnetic prandtl numbers

Abstract

Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers PrM down to 0.01. For PrM < 0.1, most of the energy is dissipated via Joule heat and, in agreement with earlier results for helical large-scale dynamos, kinetic energy dissipation is shown to diminish proportional to Pr1/2M down to values of 0.1. In agreement with earlier work, there is, in addition to a short Golitsyn k -11/3 spectrum near the resistive scale, also some evidence for a short k -1 spectrum on larger scales. The rms magnetic field strength of the small-scale dynamo is found to depend only weakly on the value of PrM and decreases by about a factor of two as PrM is decreased from 1 to 0.01. The possibility of dynamo action at PrM = 0.1 in the nonlinear regime is argued to be a consequence of a suppression of the bottleneck seen in the kinetic energy spectrum in the absence of a dynamo and, more generally, a suppression of kinetic energy near the dissipation wavenumber. © 2011. The American Astronomical Society. All rights reserved.