Testing for Markovian character of transfer of fluctuations in solar wind turbulence on kinetic scales

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Dariusz Wójcik, Wiesław M. Macek
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Abstract

We apply statistical analysis to search for processes responsible for turbulence in physical systems. In our previous studies, we have shown that solar wind turbulence in the inertial range of large magnetohydrodynamic scales exhibits Markov properties. We have recently extended this approach on much smaller kinetic scales. Here we are testing for the Markovian character of stochastic processes in a kinetic regime based on magnetic field and velocity fluctuations in the solar wind, measured onboard the Magnetospheric Multiscale (MMS) mission: behind the bow shock, inside the magnetosheath, and near the magnetopause. We have verified that the Chapman-Kolmogorov necessary conditions for Markov processes is satisfied for local transfer of energy between the magnetic and velocity fields also on kinetic scales. We have confirmed that for magnetic fluctuations, the first Kramers-Moyal coefficient is linear, while the second term is quadratic, corresponding to drift and diffusion processes in the resulting Fokker-Planck equation. It means that magnetic self-similar turbulence is described by generalized Ornstein-Uhlenbeck processes. We show that for the magnetic case, the Fokker-Planck equation leads to the probability density functions of the kappa distributions, which exhibit global universal scale invariance with a linear scaling and lack of intermittency. On the contrary, for velocity fluctuations, higher order Kramers-Moyal coefficients should be taken into account and hence scale invariance is not observed. However, the nonextensity parameter in Tsallis entropy provides a robust measure of the departure of the system from equilibrium. The obtained results are important for a better understanding of the physical mechanism governing turbulent systems in space and laboratory.

Abstract Image

测试太阳风湍流波动在动力学尺度上的马尔可夫转移特性
我们运用统计分析来寻找物理系统中的湍流过程。在之前的研究中,我们已经证明太阳风湍流在大磁流体动力尺度的惯性范围内表现出马尔可夫特性。最近,我们将这一方法扩展到了更小的动力学尺度上。在这里,我们根据磁层多尺度(MMS)任务测量到的太阳风中的磁场和速度波动,测试随机过程在一个动力学机制中的马尔可夫特性:弓形冲击后、磁鞘内和磁绝点附近。我们验证了马尔可夫过程的 Chapman-Kolmogorov 必要条件在磁场和速度场之间的局部能量转移以及动力学尺度上都得到了满足。我们证实,对于磁波动,第一项克拉默-莫亚系数是线性的,而第二项是二次的,与由此产生的福克-普朗克方程中的漂移和扩散过程相对应。这意味着磁性自相似湍流是由广义的奥恩斯坦-乌伦贝克过程描述的。我们的研究表明,在磁性情况下,福克-普朗克方程可以得到卡帕分布的概率密度函数,它具有线性缩放和无间歇性的全局普遍尺度不变性。相反,对于速度波动,需要考虑更高阶的克拉默-莫亚系数,因此无法观察到尺度不变性。然而,Tsallis 熵中的非密度参数为系统偏离平衡提供了一个稳健的衡量标准。所获得的结果对于更好地理解空间和实验室湍流系统的物理机制非常重要。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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