Jurčišinová E, Jurčišin M, Menkyna M, Remecký R
Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.
Department of Medical and Clinical Biophysics, Faculty of Medicine, P. J. Šafárik University in Košice, Trieda SNP 1, 040 11 Košice, Slovakia.
Phys Rev E. 2021 Jul;104(1-2):015101. doi: 10.1103/PhysRevE.104.015101.
Using the field-theoretic renormalization group approach and the operator product expansion technique in the second order of the corresponding perturbative expansion, the influence of finite-time correlations of the turbulent velocity field on the scaling properties of the magnetic field correlation functions as well as on the anisotropy persistence deep inside the inertial range are investigated in the framework of the generalized Kazantsev-Kraichnan model of kinematic magnetohydrodynamic turbulence. Explicit two-loop expressions for the scaling exponents of the single-time two-point correlation functions of the magnetic field are derived and it is shown that the presence of the finite-time velocity correlations has a nontrivial impact on their inertial-range behavior and can lead, in general, to significantly more pronounced anomalous scaling of the magnetic field correlation functions in comparison to the rapid-change limit of the model, especially for the most interesting three-dimensional case. Moreover, by analyzing the asymptotic behavior of appropriate dimensionless ratios of the magnetic field correlation functions, it is also shown that the presence of finite-time correlations of the turbulent velocity field has a strong impact on the large-scale anisotropy persistence deep inside the inertial interval. Namely, it leads to a significant enhancement of the anisotropy persistence, again, especially in three spatial dimensions.
利用场论重整化群方法以及在相应微扰展开二阶的算符乘积展开技术，在运动磁流体动力学湍流的广义卡赞采夫 - 克莱奇南模型框架下，研究了湍流速度场的有限时间关联对磁场关联函数标度性质以及惯性范围深处各向异性持续性的影响。推导了磁场单次两点关联函数标度指数的显式双圈表达式，结果表明有限时间速度关联的存在对其惯性范围行为有非平凡影响，并且一般而言，与模型的快速变化极限相比，会导致磁场关联函数的反常标度明显更显著，特别是对于最有趣的三维情况。此外，通过分析磁场关联函数适当无量纲比的渐近行为，还表明湍流速度场的有限时间关联的存在对惯性区间深处的大尺度各向异性持续性有强烈影响。也就是说，它导致各向异性持续性显著增强，同样，特别是在三个空间维度中。
