Two-time energy spectrum of weak magnetohydrodynamic turbulence
Two-time energy spectrum of weak magnetohydrodynamic turbulence
复制标题
DOI：
10.1103/physrevresearch.2.023189
复制
发表时间：
2020-04
期刊：
影响因子：
--
通讯作者：
J. C. Perez;Augustus A. Azelis;S. Bourouaine
中科院分区：
文献类型：
--
作者：
J. C. Perez;Augustus A. Azelis;S. Bourouaine
本文利用弱湍流封闭，从描述弱磁流体动力学的非线性方程组出发，确定了弱磁流体动力学湍流的二次功率谱结构。二次能谱是湍流理论中的一个基本量，它可以导出均匀湍流系统的大多数统计特性。通过空间傅里叶变换获得的一个密切相关的量是两点两时间相关函数，描述了湍流波动的基本动力学所产生的时空相关性。这两个量在基本湍流理论以及湍流实验和模拟分析中都是核心。然而，这些数量的第一性原理推导仍然难以捉摸，由于统计封闭问题，其中动力学方程的相关性在命令$n$依赖于相关性的命令$n+1$。最近发射的帕克太阳探测器（PSP）将探索太阳风产生的近太阳区域，重新引起了科学界对了解时空相关性的结构和可能的普遍性质的兴趣。弱MHD湍流制度，我们认为在这项工作中允许自然渐近封闭的两个时间的频谱，这可能适用于其他弱湍流制度中发现的流体和等离子体。对于不可压缩的Alfvenic涨落，导出了一个与尺度相关的时间相关函数的积分-微分方程，其非线性动力学由约化的MHD方程描述。
In this work a weak-turbulence closure is used to determine the structure of the two-time power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. The two-time energy spectrum is a fundamental quantity in turbulence theory from which most statistical properties of a homogeneous turbulent system can be derived. A closely related quantity, obtained via a spatial Fourier transform, is the two-point two-time correlation function describing the space-time correlations arising from the underlying dynamics of the turbulent fluctuations. Both quantities are central in fundamental turbulence theories as well as in the analysis of turbulence experiments and simulations. However, a first-principles derivation of these quantities has remained elusive due to the statistical closure problem, in which dynamical equations for correlations at order $n$ depend on correlations of order $n+1$. The recent launch of the Parker Solar Probe (PSP), which will explore the near-Sun region where the solar wind is born, has renewed the interest in the scientific community to understand the structure, and possible universal properties of space-time correlations. The weak MHD turbulence regime that we consider in this work allows for a natural asymptotic closure of the two-time spectrum, which may be applicable to other weak turbulence regimes found in fluids and plasmas. An integro-differential equation for the scale-dependent temporal correlation function is derived for incompressible Alfvenic fluctuations whose nonlinear dynamics is described by the reduced MHD equations.