Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
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低磁普朗特数下的脉动发电机和湍流感应
DOI：
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发表时间：
2007
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通讯作者：
T. A. Yousef
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作者：
A. Schekochihin;A. Schekochihin;A. Iskakov;S. Cowley;James C. McWilliams;M. R. E. Proctor;T. A. Yousef
本文是关于不可压缩非螺旋随机强迫磁流体动力学 (MHD) 湍流直接数值模拟程序的详细报告，该程序用于解决湍流发电机理论中长期存在的问题，并证明波动发电机存在于大磁雷诺数 Rm ≫ 1 和小磁普朗特数 Pm ≪ 1 的极限。发电机临界 Rmc 与 流体动力学雷诺数 Re 是在 1 ≲ Re ≲ 6700 时获得的。在极限 Pm ≫ 1 下，Rmc 最多比先前在大和中等普朗特数下完善的发电机大三倍：Re ≳ 6000 时的 Rmc ≲ 200 相比，Re ≳ 6000 时的 Rmc ∼ 60 。稳定性曲线 Rmc(Re)（以及发电机的性质）与平均流动的模拟和液态金属实验的情况有很大不同。目前还无法从数值上确定磁能的增长率是否处于极限 Re ≫ Rm ≫ 1 范围内（如果发电机由电阻尺度上的惯性范围运动驱动，则应该是这种情况），或者趋向于与外尺度运动的周转率相当的与 Rm 无关的值。低 Pm 状态下的磁能谱与 Pm ⩾ 1 情况有本质上的不同，并且似乎形成负谱斜率，尽管当前分辨率不足以确定其渐近形式。在 处，研究了由弱平均场的湍流缠结引起的磁波动，并检查了高于电阻标度的 k−1 谱的可能性。当 Rm < 1 较低时，准静态近似可以很好地描述引起的波动； k−11/3 谱首次在直接数值模拟中得到证实。讨论了湍流感应结果在理解从发电机产生的磁场到较小规模的磁波动的非局域能量转移中的应用。这里报告的结果对于理解宇宙等离子体中小尺度磁场的起源具有根本重要性。
This paper is a detailed report on a programme of direct numerical simulations of incompressible nonhelical randomly forced magnetohydrodynamic (MHD) turbulence that are used to settle a long-standing issue in the turbulent dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm ≫ 1 and small magnetic Prandtl number Pm ≪ 1. The dependence of the critical Rmc for dynamo versus the hydrodynamic Reynolds number Re is obtained for 1 ≲ Re ≲ 6700. In the limit Pm ≫ 1, Rmc is at most three times larger than for the previously well established dynamo at large and moderate Prandtl numbers: Rmc ≲ 200 for Re ≳ 6000 compared to Rmc ∼ 60 for . The stability curve Rmc(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate of the magnetic energy is in the limit Re ≫ Rm ≫ 1, as should be the case if the dynamo is driven by the inertial-range motions at the resistive scale, or tends to an Rm-independent value comparable to the turnover rate of the outer-scale motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm ⩾ 1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At , the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k−1 spectrum above the resistive scale is examined. At low Rm < 1, the induced fluctuations are well described by the quasistatic approximation; the k−11/3 spectrum is confirmed for the first time in direct numerical simulations. Applications of the results on turbulent induction to understanding the nonlocal energy transfer from the dynamo-generated magnetic field to smaller-scale magnetic fluctuations are discussed. The results reported here are of fundamental importance for understanding the genesis of small-scale magnetic fields in cosmic plasmas.