Energy transfers in dynamos with small magnetic Prandtl numbers

TL;DR

This paper presents high-resolution numerical simulations of small magnetic Prandtl number dynamos, revealing that magnetic energy mainly grows through large-scale energy transfers and remains significantly below kinetic energy levels.

Contribution

It provides detailed analysis of energy fluxes and shell-to-shell transfers in small Pm dynamos, contrasting with high Pm and decaying cases, advancing understanding of magnetic energy growth mechanisms.

Findings

Magnetic energy growth mainly from large-scale velocity to magnetic transfer

Magnetic flux is predominantly forward in energy transfer

Magnetic energy remains below kinetic energy near dynamo transition

Abstract

We perform numerical simulation of dynamo with magnetic Prandtl number $\mathrm{Pm} =0.2$ on $1024^3$ grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our results with those for dynamo with $\mathrm{Pm} =20$ and decaying dynamo.