Shell models of magnetohydrodynamic turbulence
Shell models of magnetohydrodynamic turbulence
复制标题
磁流体动力湍流的壳模型
DOI：
10.1016/j.physrep.2012.09.001
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
P. Frick
中科院分区：
文献类型：
--
作者：
F. Plunian;R. Stepanov;P. Frick
流体动力学湍流的壳模型起源于七十年代。他们的主要目的是用一组简单的常微分方程来描述谱空间中均匀和各向同性湍流的统计。在八十年代，磁流体动力学（MHD）湍流的壳模型出现的基础上相同的原则，作为他们的流体动力学对应部分，但也纳入磁场和速度场之间的相互作用。近年来，已经取得了重大进展，如列入非本地相互作用和适当的定义螺旋度。虽然壳模型不能解释MHD湍流的空间复杂性，但它们的动力学并没有过度简化，并且确实反映了真实的MHD湍流的动力学，包括大尺度模式的不稳定性或混沌反转。此外，这些模型使用无量纲参数的实际值（高动力学和磁雷诺数，低或高磁普朗特数），允许扩展的惯性范围和准确的耗散率。使用现代计算机，直接数值模拟很难达到30年的惯性范围，而使用壳模型则可能达到8年。在这篇综述中，我们建立了一个通用的数学框架，允许任何MHD壳模型的描述。介绍了后者的种类及其优缺点。最后，我们考虑了一些应用，处理自由衰减MHD湍流，发电机行动，阿尔文波和霍尔效应。
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models. In this review we set up a general mathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decaying MHD turbulence, dynamo action, Alfvén waves and the Hall effect.
DOI：
10.1140/epjb/e2010-00003-0
发表时间：
2010
期刊：
The European Physical Journal B
影响因子：
--
作者：
S. Chakraborty;M. H. Jensen;A. Sarkar
通讯作者：
A. Sarkar