Varying the forcing scale in low Prandtl number dynamos

TL;DR

This study investigates how the scale of turbulent forcing affects small-scale dynamo action in low Prandtl number fluids, finding that the dynamo's excitation conditions are independent of the forcing scale.

Contribution

It demonstrates that small-scale dynamo excitation does not depend on the forcing wavenumber, clarifying the role of spectral bottleneck effects in turbulence.

Findings

Dynamo excitation is independent of forcing scale.

Spectral bottleneck effects are invariant under forcing wavenumber changes.

Effective forcing wavenumber is about twice the minimum wavenumber at low forcing.

Abstract

Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumber, that the small-scale dynamo does not depend on the scale-separation between the size of the simulation domain and the integral scale of the turbulence, i.e., the forcing scale. Moreover, the spectral bottleneck in turbulence, which has been implied as being responsible for raising the excitation conditions of small-scale dynamos, is found to be invariant under changing the forcing wavenumber. However, when forcing at the lowest few wavenumbers, the effective forcing wavenumber that enters in the definition of the magnetic Reynolds number is found to be about twice the minimum wavenumber of the domain. Our work is relevant to future studies of small-scale dynamos, of which several applications are being discussed.