The kinetic helicity needed to drive large-scale dynamos

TL;DR

This paper investigates the conditions under which large-scale magnetic fields are generated by turbulent flows, showing that a critical level of kinetic helicity relative to the domain size is necessary for dynamo action.

Contribution

The study demonstrates through simulations that large-scale dynamo energy scales linearly with normalized helicity and domain-to-eddy scale ratio, establishing a critical helicity threshold for dynamo onset.

Findings

Large-scale magnetic energy increases linearly with normalized helicity and scale ratio.

Dynamo action begins when normalized helicity exceeds the inverse of the scale ratio.

Small-scale dynamo action does not significantly affect large-scale dynamo development.

Abstract

Magnetic field generation on scales large compared with the scale of the turbulent eddies is known to be possible via the so-called $\alpha$ effect when the turbulence is helical and if the domain is large enough for the $\alpha$ effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. (2012, Phys. Rev. E85, 066406) of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC-flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos.