Nonlinear small-scale dynamos at low magnetic Prandtl numbers

TL;DR

This study investigates small-scale dynamo behavior at low magnetic Prandtl numbers, revealing how energy dissipation and magnetic field strength depend on Pm, with implications for understanding turbulence and magnetic field generation.

Contribution

It provides the first detailed analysis of saturated small-scale dynamos at Pm as low as 0.01, highlighting energy dissipation mechanisms and spectral features.

Findings

Most energy dissipated via Joule heat at low Pm

Kinetic energy dissipation scales as Pm^{1/2} for Pm<0.1

Magnetic field strength weakly depends on Pm, decreasing by a factor of 2 from Pm=1 to 0.01

Abstract

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.