http://arxiv.org/abs/2204.00828
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, $\kp$, do magnetic fields become most concentrated? There has been some disagreement about whether $\kp$ is controlled by the viscous scale, $\knu$ (where turbulent kinetic energy dissipates), or the resistive scale, $\keta$ (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 \mbox{$10 \leq \Reyk \leq 3600$}, and magnetic Reynolds numbers of \mbox{$270 \leq \Reym \leq 4000$}, to explore the dependence of $\kp$ on $\knu$ and $\keta$. Using physically motivated models for the kinetic and magnetic energy spectra, we measure $\knu$, $\keta$ and $\kp$, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations \mbox{$\knu = (0.025^{+0.005}{-0.006})\, k\turb\, \Reyk^{3/4}$} and \mbox{$\keta = (0.88^{+0.21}{-0.23})\, \knu\, \Pranm^{1/2}$}, where $k\turb$ is the turbulence driving wavenumber and $\Pranm=\Reym/\Reyk$ is the magnetic Prandtl number. We demonstrate that the principle dependence of $\kp$ is on $\keta$. For plasmas where $\Reyk \gtrsim 100$, we find that \mbox{$\kp = (1.2_{-0.2}^{+0.2})\, \keta$}, 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 $\Reyk > 100$, compared to $\Reyk < 100$. We report a minimum critical hydrodynamic Reynolds number, $\Reyk_\crit = 100$ for bonafide turbulent dynamo action.
N. Kriel, J. Beattie, A. Seta, et. al.
Tue, 5 Apr 22
40/83
Comments: 15 pages, 10 figures
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