Magnetic energy spectrum produced by turbulent dynamo: effect of time irreversibility

TL;DR

This paper investigates how time irreversibility in turbulent flows affects the magnetic energy spectrum during the dynamo process, revealing slower growth rates and flatter spectra than classical models predict, with implications for high Prandtl number plasmas.

Contribution

It extends the Kazantsev-Kraichnan model to include time irreversibility, showing its impact on magnetic spectrum shape and growth rate in turbulent dynamos.

Findings

Power-law spectrum in viscous range is flatter than Kazantsev prediction.

Magnetic energy growth rate is slower with time irreversibility.

Spectrum formation at high Prandtl numbers may be very slow or incomplete.

Abstract

We consider the kinematic stage of evolution of magnetic field advected by turbulent hydrodynamic flow. We use a generalization of the Kazantsev-Kraichnan model to investigate time irreversible flows. In the viscous range of scales, the infinite-time limit of the spectrum is a power law but its slope is more flat than that predicted by Kazantsev model. This result agrees with numerical simulations. The rate of magnetic energy growth is slower than that in the time-symmetric case. We show that for high magnetic Prandtl turbulent plasma, the formation of the power-law spectrum shape takes very long time and may never happen because of the nonlinearity. We propose another ansatz to describe the spectrum shape at finite time.