NONLINEAR SMALL-SCALE DYNAMOS AT LOW MAGNETIC PRANDTL NUMBERS

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