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

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 the 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.

Automated summary

We investigate the kinematic evolution of a magnetic field transported by turbulent hydrodynamic flow and extend the Kazantsev-Kraichnan model to study time irreversible flows. Our results show that the spectrum of the magnetic field in the viscous range follows a power law with a flatter slope compared to the predictions of the Kazantsev model, in agreement with numerical simulations. The rate of magnetic energy growth is slower in this non-time symmetric case. Additionally, we find that the formation of a power-law spectrum in high magnetic Prandtl turbulent plasma takes a very long time and may not occur due to nonlinearity, proposing an alternative viewpoint for describing the spectrum shape at finite time.