# Mean-field dynamo due to spatiotemporal fluctuations of the turbulent kinetic energy

## TL;DR

This paper demonstrates that fluctuations in turbulent kinetic energy can generate large-scale magnetic fields through a mean-field dynamo mechanism, even without kinetic helicity, by analyzing the effects of these fluctuations on turbulent diffusivity.

## Contribution

It introduces a novel analytical framework showing how mesoscale turbulent kinetic energy fluctuations can drive dynamo action independently of kinetic helicity.

## Key findings

- Mesoscale kinetic energy fluctuations can induce dynamo growth.
- Fluctuations reduce turbulent diffusion and introduce drift effects.
- Turbulent diamagnetism can sustain mean fields without $ ext{η}$-fluctuations.

## Abstract

In systems where the standard $\alpha$ effect is inoperative, one often explains the existence of mean magnetic fields by invoking the `incoherent $\alpha$ effect', which appeals to fluctuations of the mean kinetic helicity at a mesoscale. Most previous studies, while considering fluctuations in the mean kinetic helicity, treated the mean turbulent kinetic energy at the mesoscale as a constant, despite the fact that both these quantities involve second-order velocity correlations. The mean turbulent kinetic energy affects the mean magnetic field through both turbulent diffusion and turbulent diamagnetism. In this work, we use a double-averaging procedure to analytically show that fluctuations of the mean turbulent kinetic energy at the mesoscale (giving rise to $\eta$-fluctuations at the mesoscale, where the scalar $\eta$ is the turbulent diffusivity) can lead to the growth of a large-scale magnetic field even when the kinetic helicity is zero pointwise. Constraints on the operation of such a dynamo are expressed in terms of dynamo numbers that depend on the correlation length, correlation time, and strength of these fluctuations. In the white-noise limit, we find that these fluctuations reduce the overall turbulent diffusion, while also contributing a drift term which does not affect the growth of the field. We also study the effects of nonzero correlation time and anisotropy. Turbulent diamagnetism, which arises due to inhomogeneities in the turbulent kinetic energy, leads to growing mean field solutions even when the $\eta$-fluctuations are statistically isotropic.