Eyink Gregory L
Department of Applied Mathematics & Statistics, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Oct;82(4 Pt 2):046314. doi: 10.1103/PhysRevE.82.046314. Epub 2010 Oct 27.
We study the Lagrangian mechanism of the fluctuation dynamo at zero Prandtl number and infinite magnetic Reynolds number, in the Kazantsev-Kraichnan model of white-noise advection. With a rough velocity field corresponding to a turbulent inertial range, flux freezing holds only in a stochastic sense. We show that field lines arriving to the same point which were initially separated by many resistive lengths are important to the dynamo. Magnetic vectors of the seed field that point parallel to the initial separation vector arrive anticorrelated and produce an "antidynamo" effect. We also study the problem of "magnetic induction" of a spatially uniform seed field. We find no essential distinction between this process and fluctuation dynamo, both producing the same growth rates and small-scale magnetic correlations. In the regime of very rough velocity fields where fluctuation dynamo fails, we obtain the induced magnetic energy spectra. We use these results to evaluate theories proposed for magnetic spectra in laboratory experiments of turbulent induction.
在白噪声平流的卡赞采夫 - 克莱奇南模型中，我们研究了零普朗特数和无限磁雷诺数下波动发电机的拉格朗日机制。对于对应于湍流惯性范围的粗糙速度场，通量冻结仅在随机意义上成立。我们表明，最初被许多电阻长度分隔的到达同一点的场线对发电机很重要。与初始分离向量平行的种子场磁矢量反相关到达并产生“反发电机”效应。我们还研究了空间均匀种子场的“磁感应”问题。我们发现这个过程与波动发电机之间没有本质区别，两者产生相同的增长率和小尺度磁相关性。在波动发电机失效的非常粗糙速度场 regime 中，我们得到了感应磁能谱。我们利用这些结果来评估在湍流感应实验室实验中提出的磁谱理论。
