Magnetohydrodynamic Turbulence
Magnetohydrodynamic Turbulence
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DOI：
10.1017/cbo9780511535222.002
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发表时间：
2003
影响因子：
2.2
通讯作者：
D. Biskamp
中科院分区：
文献类型：
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作者：
D. Biskamp
流体动力学湍流是物理学研究的一个主要课题已经有世纪之久，但等离子体中的湍流在日常生活中甚至在实验室条件下都是不寻常的，它的相关性只是随着天体物理学的发展才变得明显。对于宏观过程，磁流体动力学的描述通常是足够的，它的应用，以现实的现象开始与工作巴彻勒在1950年的发电机问题。太阳耀斑、太阳风、地球发电机和恒星吸积盘，仅举几个例子，后来被添加到适合MHD描述的现象列表中：自然，关于这样一个庞大主题的文献是巨大的，但到目前为止，还没有一本参考书提供主要概念和结果的最新说明。Dieter Biskamp的专著很适合填补这一空白。MHD方程在许多方面与Navier-Stokes方程相似，并且平行性扩展到理解湍流的几个关键概念，例如自组织、级联和闭合方法。也许最强的一部分，这本书从教学的观点是这种平行的方式被利用，以突出的相似性和差异与流体动力学湍流，和形式的关键现象排除MHD，如阿尔文效应或流动各向异性，修改经典的结果。在对基本的MHD方程、理想不变量和线性波进行了清晰简洁的介绍之后，这本书描述了一些导致湍流的经典不稳定性，例如开尔文-亥姆霍兹不稳定性。其次是不可压缩湍流的统计理论。正如作者所断言的，20世纪80年代开创的动力系统方法未能产生新的物理见解，不是因为任何内在的缺陷，而是因为湍流流体和等离子体中存在大量的自由度（用数学术语来说，本质上是吸引子的维度）。因此，我们必须处理三个基本的方法：现象学的缩放参数的精神Kolmogorov的K41理论;封闭理论，通过截断在某个点的层次的时刻方程;并验证这些方法的可扩展性，数值模拟的原始动力学方程。Biskamp是一位数学大师，这本书用图形很好地说明了这些理论的优点和缺点。两个特定的MHD不变量（磁螺旋度和交叉螺旋度）在叶栅方向的关键作用是非常清楚的解释，以及适用范围的柯尔莫哥洛夫和Iroshnikov-Kraichnan统计，其中有一些争论，直到最近。可压缩湍流和湍流对流是解决下，和专着结束了三个具体的天体物理学主题的研究：太阳风，吸积盘和星际湍流。在这里，文本必然变得更具描述性和经验性，因为现象的复杂性与我们对它们的详细知识成反比。尽管如此，一些更容易处理的过程，如某些几何形状的不稳定性，是相当详细的，总的来说，一个人得到的感觉理解的基本问题。很少有批评可以瞄准这本专著，他们中的大多数人都回答了需要保持其长度范围内。因此，湍流发电机和湍流重联几乎完全被省略，而其他学科，如平均场电动力学和衰变定律，比作者承认的更具争议性。此外，虽然Biskamp对仅仅从动力学方程中获得关于不稳定性的许多知识持怀疑态度，但从Constantin和Febrmann（1994）的工作开始，一些关于标度指数的有用估计已经得到了严格的证明。这当然不会减损从这本书中获得的极好的全球印象，这本书无疑属于每一个MHD湍流学生的书架。穆努涅斯
While hydrodynamic turbulence has been a major subject of physical research for more than a century, turbulence in plasmas is unusual in daily life or even laboratory conditions, and its relevance only became apparent with the development of astrophysics. For macroscopic processes, the magnetohydrodynamic description is usually adequate, and its application to realistic phenomena started with the work of Batchelor in 1950 on the dynamo problem. Solar flares, the solar wind, the geodynamo and stellar accretion disks, to name only a few, were added later to the list of phenomena amenable to a MHD description: naturally the literature on such a vast subject is immense, but so far there was not a reference book providing an up-to-date account of the main concepts and results. The monograph by Dieter Biskamp is well suited to fill this void. The MHD equations are similar in many ways to the Navier-Stokes ones, and the parallelism extends to several key concepts in the understanding of turbulence, such as self-organization, cascades and closure methods. Perhaps the strongest part of the book from a didactic viewpoint is the way this parallelism is exploited to highlight the similarities and differences with hydrodynamic turbulence, and the form that key phenomena exclusive of MHD, such as the Alfvén effect or flow anisotropy, modify the classical results. After a clear and concise introduction to the basic MHD equations, ideal invariants and linear waves, the book describes some classical instabilities leading to turbulence, such as the Kelvin--Helmholtz instability. This is followed by the statistical theory of incompressible turbulence. As the author asserts, the dynamical systems approach pioneered in the nineteen eighties has failed to produce new physical insights, not because of any intrinsic flaw, but because of the large number of degrees of freedom (in mathematical parlance, essentially the dimension of the attractor) present in turbulent fluids and plasmas. We must therefore handle three essential methods: phenomenological scaling arguments in the spirit of Kolmogorov's K41 theory; closure theories, obtained by truncating at some point the hierarchy of moment equations; and to verify the plausibility of these approaches, numerical simulations of the original dynamic equations. Biskamp is a master of numerics and the book is well-illustrated with graphics pointing out the strengths and shortcomings of these theories. The key role of two specific MHD invariants (the magnetic helicity and the cross-helicity) in the cascades direction is very clearly explained, as well as the ranges of applicability of the Kolmogorov and the Iroshnikov-Kraichnan statistics, about which there was some polemic until recently. Compressible turbulence and turbulent convection is tackled next, and the monograph ends with studies of three specific astrophysical topics: the solar wind, accretion disks and interstellar turbulence. Here the text becomes of necessity more descriptive and empirical, as the complexity of the phenomena grows in inverse proportion to our detailed knowledge of them. Nevertheless some of the more amenable processes, such as the instabilities of certain geometries, are reasonably detailed and on the whole one gets the feeling of understanding the basics of the problems. Few criticisms can be levelled at this monograph, and most of them are answered by the need to keep its length within bounds. Thus, turbulent dynamos and turbulent reconnection are almost entirely omitted, and other subjects, such as mean-field electrodynamics and decay laws, are more controversial than the author admits. Also, while Biskamp is probably right in being skeptical about deriving much knowledge on intermittency from the dynamic equations alone, some useful estimates on scaling exponents have been rigorously proved, beginning with the work of Constantin and Fefferman (1994). This certainly does not detract from the excellent global impression obtained from this book, which undoubtedly belongs on the shelves of every student of MHD turbulence. M Núñez