Fundamental scales in the kinematic phase of the turbulent dynamo. Issue 2 (9th April 2022) - Kriel, Neco; Beattie, James R; Seta, Amit; Federrath, Christoph
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_ν = (0.025^+0.005_-0.006) k_turb Re^3/4 and k_η = (0.88^+0.21_-0.23) k_ν 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_η, 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.