论文标题
湍流发电机运动阶段的基本尺度
Fundamental scales in the kinematic phase of the turbulent dynamo
论文作者
论文摘要
湍流发电机是一种强大的机制，可将湍流动能转换为磁能。关于通过湍流扩增磁场的一个关键问题是，在什么规模上，$ k _ {\ rm p} $，磁场是否变得最集中？关于$ k _ {\ rm p} $是由粘性量表，$k_ν$（湍流动能消散）还是电阻刻度，$k_η$（在磁场消散的情况下），存在一些分歧。在这里，我们使用磁流体动力湍流的直接数值模拟来测量湍流发电机运动相的特征尺度。我们运行$ 104 $ - 示例，具有$ 10 \ leq {\ rm re} \ leq 3600 $的$ 10 \ leq {\ rm req 3600 $，以及磁性雷诺数为$ 270 \ leq {\ rm rm rm} \ rm rm} \ leq 4000 $，以探索$ k__ $ k_的依赖$ k_ p p \ k_使用动力动机的动力模型和磁能谱，我们测量$k_ν$，$k_η$和$ k _ {\ rm p} $，确保获得所获得的量表是数值收敛的。我们确定总体耗散量表关系$k_ν=（0.025^{+0.005} _ { - 0.006}）\，k _ {\ rm turb} \，{\ rm re}^{3/4} {3/4} $ and $ k_ =（ {\ rm pm}^{1/2} $，其中$ k _ {\ rm turb} $是湍流驱动waveNumber，$ {\ rm pm} = {\ rm rm rm}/{\ rm rm}/{\ rm re t} $是磁性prandtl number。我们证明了$ k _ {\ rm p} $的原理依赖性在$k_η$上。对于等离子体，其中$ {\ rm re} \ gtrsim 100 $，我们发现$ k _ {\ rm p} =（1.2 _ { - 0.2}^{+0.2}）\，k_η$，其比例性是与peasteragrage o lapecterage opectional ovelage permaint opectional opectional ovelage。在整个研究中，我们在发电机的基本特性中发现了二分法，其中$ {\ rm re}> 100 $，而$ {\ rm re} <100 $。我们报告了一个最小关键的流体动力雷诺数，$ {\ rm re} _ {\ rm crit} = 100 $，用于thrafide turbulent dynamo动作。
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, $k_{\rm p}$, do magnetic fields become most concentrated? There has been some disagreement about whether $k_{\rm p}$ 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 $10 \leq {\rm Re} \leq 3600$, and magnetic Reynolds numbers of $270 \leq {\rm Rm} \leq 4000$, to explore the dependence of $k_{\rm p}$ on $k_ν$ and $k_η$. Using physically motivated models for the kinetic and magnetic energy spectra, we measure $k_ν$, $k_η$ and $k_{\rm p}$, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_ν= (0.025^{+0.005}_{-0.006})\, k_{\rm turb}\, {\rm Re}^{3/4}$ and $k_η= (0.88^{+0.21}_{-0.23})\, k_ν\, {\rm Pm}^{1/2}$, where $k_{\rm turb}$ is the turbulence driving wavenumber and ${\rm Pm}={\rm Rm}/{\rm Re}$ is the magnetic Prandtl number. We demonstrate that the principle dependence of $k_{\rm p}$ is on $k_η$. For plasmas where ${\rm Re} \gtrsim 100$, we find that $k_{\rm p} = (1.2_{-0.2}^{+0.2})\, k_η$, 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 ${\rm Re} > 100$, compared to ${\rm Re} < 100$. We report a minimum critical hydrodynamic Reynolds number, ${\rm Re}_{\rm crit} = 100$ for bonafide turbulent dynamo action.
