Jurčišinová E, Jurčišin M, Remecký R
Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 2):046311. doi: 10.1103/PhysRevE.84.046311. Epub 2011 Oct 14.
The turbulent magnetic Prandtl number in the framework of the kinematic magnetohydrodynamic (MHD) turbulence, where the magnetic field behaves as a passive vector field advected by the stochastic Navier-Stokes equation, is calculated by the field theoretic renormalization group technique in the two-loop approximation. It is shown that the two-loop corrections to the turbulent magnetic Prandtl number in the kinematic MHD turbulence are less than 2% of its leading order value (the one-loop value) and, at the same time, the two-loop turbulent magnetic Prandtl number is the same as the two-loop turbulent Prandtl number obtained in the corresponding model of a passively advected scalar field. The dependence of the turbulent magnetic Prandtl number on the spatial dimension d is investigated and the source of the smallness of the two-loop corrections for spatial dimension d=3 is identified and analyzed.
在运动磁流体动力学（MHD）湍流框架下，磁场表现为由随机纳维 - 斯托克斯方程平流的无源矢量场，通过场论重整化群技术在两圈近似下计算湍流磁普朗特数。结果表明，运动MHD湍流中湍流磁普朗特数的两圈修正小于其主导阶值（一圈值）的2%，同时，两圈湍流磁普朗特数与在相应的被动平流标量场模型中得到的两圈湍流普朗特数相同。研究了湍流磁普朗特数对空间维度d的依赖性，并确定和分析了空间维度d = 3时两圈修正较小的原因。
