Magnetic dynamo action in random flows with zero and finite correlation times

TL;DR

This paper compares the Kazantsev dynamo model, which assumes instantaneously correlated flow, with simulated flows having finite correlation times, revealing differences in magnetic growth rates and spectra that can be reconciled through filtering techniques.

Contribution

The study demonstrates how finite correlation times in flows affect dynamo properties and proposes a method to align model predictions with simulated results.

Findings

Kazantsev model predicts higher magnetic growth rates.

Magnetic spectra peak at smaller scales in the Kazantsev model.

Filtering diffusivity spectra can reconcile differences between models and simulations.

Abstract

Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible, non-helical, homogeneous and isotropic flow. In the Kazantsev dynamo model the statistics of the driving flow are assumed to be instantaneously correlated in time. Here we compare the results of the model with the dynamo properties of a simulated flow that has equivalent spatial characteristics as the Kazantsev flow but different temporal statistics. In particular, the simulated flow is a solution of the forced Navier-Stokes equations and hence has a finite correlation time. We find that the Kazantsev model typically predicts a larger magnetic growth rate and a magnetic spectrum that peaks at smaller scales. However, we show that by filtering the diffusivity spectrum at small scales it is possible to bring the growth rates into agreement and simultaneously align the magnetic spectra.