Fundamental scales in the kinematic phase of the turbulent dynamo. Issue 2 (9th April 2022)

• Record Type: Journal Article
• Authors: Kriel, Neco; Beattie, James R; Seta, Amit; Federrath, Christoph
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 513:Issue 2(2022)
• Page Start: 2457
• Page End: 2470
• Publication Date: 2022-04-09
• Subjects: dynamo -- magnetic fields -- MHD -- turbulence; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stac969
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, k p, do magnetic fields become most concentrated? There has been some disagreement about whether k p is controlled by the viscous scale, k ν (where turbulent kinetic energy dissipates), or the resistive scale, k η (where magnetic fields dissipate). Here, we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run 104-simulations with hydrodynamic Reynolds numbers of 10 ≤ Re ≤ 3600, and magnetic Reynolds numbers of 270 ≤ Rm ≤ 4000, to explore the dependence of k p on k ν and k η . Using physically motivated models for the kinetic and magnetic energy spectra, we measure k ν, k η, and k p, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_\nu = (0.025^{+0.005}_{-0.006})\, k_\text{turb}\, \mbox{Re}^{3/4}$ and $k_\eta = (0.88^{+0.21}_{-0.23})\, k_\nu \, \mbox{Pm}^{1/2}$, where k turb is the turbulence driving wavenumber and Pm = Rm/Re is the magnetic Prandtl number. We demonstrate that the principle dependence of k p is on k η . For plasmas, where Re ≳ 100, we find that $k_p= (1.2_{-0.2}^{+0.2})\, k_\eta$, with the proportionality constant related to the power-law 'Kazantsev' exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where Re > 100, compared to Re < 100. We report a minimum critical hydrodynamic Reynolds number, Recrit = 100 for bonafide turbulent dynamo action.