Two-dimensional gyrokinetic turbulence
Two-dimensional gyrokinetic turbulence
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二维回旋湍流
DOI：
10.1017/s002211201000371x
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发表时间：
2009
影响因子：
3.7
通讯作者：
T. Tatsuno
中科院分区：
文献类型：
--
作者：
G. Plunk;S. Cowley;A. Schekochihin;T. Tatsuno
二维回旋动力学是研究动能磁化等离子体湍流的简单范例。在本文中，我们为这种湍流提出了一个全面的理论框架。我们研究由均匀和各向同性随机强迫驱动的逆级联和直接级联（“双级联”）。回旋动力学的关键特征长度，即拉莫尔半径，将尺度划分为两个物理上不同的范围。对于大于拉莫尔半径的尺度，我们从回旋运动系统中推导出熟悉的查尼-长谷川-美马方程，并解释其与回旋运动的关系。在小于拉莫尔半径的尺度上，通过非线性相混合过程在相空间（位置空间中的二维加上速度空间中的一维）中发生双级联。我们证明，在这些亚拉莫尔尺度上，湍流是自相似的，并且在位置和速度空间中表现出幂律谱。我们提出了汉克尔变换形式来表征速度空间谱。我们推导出三阶结构函数的精确关系，类似于柯尔莫哥洛夫的五分之四定律和亚格洛姆的三分之四定律，并且在长波长和短波长下都有效。我们展示了一般回旋不变量如何与控制长波长和短波长限制中的双级联的特定不变量相关。我们描述了从流体到全动力学范围的全范围级联。
Two-dimensional gyrokinetics is a simple paradigm for the study of kinetic magnetised plasma turbulence. In this paper, we present a comprehensive theoretical framework for this turbulence. We study both the inverse and direct cascades (the ‘dual cascade’), driven by a homogeneous and isotropic random forcing. The key characteristic length of gyrokinetics, the Larmor radius, divides scales into two physically distinct ranges. For scales larger than the Larmor radius, we derive the familiar Charney–Hasegawa–Mima equation from the gyrokinetic system, and explain its relationship to gyrokinetics. At scales smaller than the Larmor radius, a dual cascade occurs in phase space (two dimensions in position space plus one dimension in velocity space) via a nonlinear phase-mixing process. We show that at these sub-Larmor scales, the turbulence is self-similar and exhibits power-law spectra in position and velocity space. We propose a Hankel-transform formalism to characterise velocity-space spectra. We derive the exact relations for third-order structure functions, analogous to Kolmogorov's four-fifths and Yaglom's four-thirds laws and valid at both long and short wavelengths. We show how the general gyrokinetic invariants are related to the particular invariants that control the dual cascade in the long- and short-wavelength limits. We describe the full range of cascades from the fluid to the fully kinetic range.
影响因子：
2.2
作者：
I. Abel;Michael Barnes;S. Cowley;W. Dorland;A. Schekochihin
通讯作者：
I. Abel;Michael Barnes;S. Cowley;W. Dorland;A. Schekochihin