Magnetic Prandtl number dependence of kinetic to magnetic dissipation ratio

TL;DR

This study uses numerical simulations to show that the ratio of kinetic to magnetic energy dissipation in hydromagnetic turbulence increases with the magnetic Prandtl number, with different scaling laws for helical and non-helical turbulence.

Contribution

It demonstrates the Prandtl number dependence of energy dissipation ratios and explores this behavior through turbulence shell models and scalar models.

Findings

Dissipation ratio increases with Prandtl number, following a power law.

Exponent of the power law varies between 1/3 and 2/3 depending on turbulence helicity.

Energy conversion efficiency depends on microphysical dissipation processes.

Abstract

Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfven kinks.