Nonlinear small-scale dynamos at low magnetic Prandtl numbers

Axel Brandenburg

Published 2011-06-28, updated 2011-09-28Version 2

Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers Pm down to 0.01. For Pm < 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 Pm^{1/2} 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 Pm and decreases by about a factor of 2 as Pm is decreased from 1 to 0.01. The possibility of dynamo action at Pm=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.