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arXiv 2201.10819physics.plasm-ph
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可压缩霍尔磁流体力学精确定律的深入数值研究turbulence

An in-depth numerical study of exact laws for compressible Hall magnetohydrodynamic turbulence

R. Ferrand, F. Sahraoui, S. Galtier, N. Andrés, P. Mininni, P. Dmitruk

摘要:

近年来,可压缩磁流体动力学(MHD)和霍尔磁流体动力学(CHMHD)湍流的各种精确定律被推导出来。除了它们的基本理论兴趣之外,这些定律通常用于估计航天器观测的能量耗散率,以解决各种相关问题,例如,到太阳风(SW)和磁层等离子体的加热。在这里,我们使用各种$1024^3$直接数值模拟(DNS)数据的自由衰减等温CHMHD湍流获得的GHOST代码(地球物理高阶套件湍流)来分析两个最近导出的精确的法律。模拟结果反映了不同的初始马赫数和背景磁场强度。分析表明,在惯性范围内的两个法律的等效性和相关的霍尔效应的强度的级联率在亚离子尺度的幅度。当以其一般形式(即,不限于惯性范围),讨论了关于定态假设的有效性或模拟中强迫的缺乏的一些微妙之处。我们发现,湍流的自由衰减性质引起了从大尺度强迫向存在一个尺度相关的能量库的级联或耗散加油的转变。精确定律的简化形式(在惯性范围内有效)最终成立,即使平稳性假设没有得到充分验证。

英文摘要:

Various exact laws governing compressible magnetohydrodynamic (MHD) and Hall-MHD (CHMHD) turbulence have been derived in recent years. Other than their fundamental theoretical interest, these laws are generally used to estimate the energy dissipation rate from spacecraft observations in order to address diverse problems related, e.g., to heating of the solar wind (SW) and magnetospheric plasmas. Here we use various $1024^3$ direct numerical simulation (DNS) data of free-decay isothermal CHMHD turbulence obtained with the GHOST code (Geophysical High-Order Suite for Turbulence) to analyze two of the recently derived exact laws. The simulations reflect different intensities of the initial Mach number and the background magnetic field. The analysis demonstrates the equivalence of the two laws in the inertial range and relates the strength of the Hall effect to the amplitude of the cascade rate at sub-ion scales. When taken in their general form (i.e., not limited to the inertial range) some subtleties regarding the validity of the stationarity assumption or the absence of the forcing in the simulations are discussed. We show that the free-decay nature of the turbulence induces a shift from a large scale forcing towards the presence of a scale-dependent reservoir of energy fueling the cascade or dissipation. The reduced form of the exact laws (valid in the inertial range) ultimately holds even if the stationarity assumption is not fully verified.

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