Dissipation in dynamos at low and high magnetic Prandtl numbers

TL;DR

This study uses simulations to show how energy dissipation in dynamos varies with magnetic Prandtl number, revealing a power-law relationship and implications for astrophysical phenomena like quasar accretion.

Contribution

It extends understanding of magnetic Prandtl number effects on dynamo dissipation from small to large values, highlighting the dominance of viscous dissipation at high Prandtl numbers.

Findings

Dissipation ratio scales with magnetic Prandtl number as a power law with exponent ~0.6.

Large-scale alpha-squared dynamo action sustains magnetic fields across six orders of magnitude.

Most energy is viscously dissipated at high magnetic Prandtl numbers, affecting simulation regimes.

Abstract

Using simulations of helically driven turbulence, it is shown that the ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number in power law fashion with an exponent of approximately 0.6. Over six orders of magnitude in the magnetic Prandtl number the magnetic field is found to be sustained by large-scale dynamo action of alpha-squared type. This work extends a similar finding for small magnetic Prandtl numbers to the regime of large magnetic Prandtl numbers. At large magnetic Prandtl numbers, most of the energy is dissipated viscously, lowering thus the amount of magnetic energy dissipation, which means that simulations can be performed at magnetic Reynolds numbers that are large compared to the usual limits imposed by a given resolution. This is analogous to an earlier finding that at small magnetic Prandtl numbers, most of the energy is dissipated resistively, lowering the amount of kinetic energy dissipation, so simulations can then be performed at much larger fluid Reynolds numbers than otherwise. The decrease in magnetic energy dissipation at large magnetic Prandtl numbers is discussed in the context of underluminous accretion found in some quasars.