The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity field, the compressible Alfvén velocity and the scalar density, instead of the Elsässer variables used in previous works. The theoretical results show four different types of terms that are involved in the nonlinear cascade of the total energy in the inertial range. Each category is examined in detail, in particular those that can be written either as source or flux terms. Finally, the role of the background magnetic field $B_0$ is highlighted and comparison with the incompressible MHD (IMHD) model is discussed. This point is particularly important when testing the exact law on numerical simulations and in situ observations in space plasmas.
The zeroth law is one of the oldest conjecture in turbulence that is still unproven. Here, we consider weak solutions of one-dimensional compressible magnetohydrodynamics and demonstrate that the lack of smoothness of the fields introduces a new dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is positive and equal on average to the mean viscou…
We study the existence and property of Fast magnetosonic modes in 3D compressible MHD turbulence by carrying out a number of simulations with compressible and incompressible driving conditions. We use two approaches to determine the presence of Fast modes: mode decomposition based on spatial variations only and spatio-temporal 4D-FFT analysis of all fluctuations. The latter method enables us to quantify fluctuations that satisfy the dispersion relation of Fast modes with finite frequency. Overall, we find that the fraction of Fast modes identified via spatio-temporal 4D FFT approach in total f…
The role of the different helical components of the magnetic and velocity fields in the inverse spectral transfer of magnetic helicity is investigated through Fourier shell-to-shell transfer analysis. Both magnetic helicity and energetic transfer analysis are performed on chosen data from direct numerical simulations of homogeneous isothermal compressible magnetohydrodynamic turbulence, subject to both a large-scale mechanical forcing and a small-scale helical electromotive driving. The root mean square Mach number of the hydrodynamic turbulent steady-state taken as initial condition varies fr…
The inverse transfer of magnetic helicity is investigated through direct numerical simulations of large-scale-mechanically-driven turbulent flows in the isothermal ideal magnetohydrodynamics (MHD) framework. The mechanical forcing is either purely solenoidal or purely compressive and the turbulent steady-states considered exhibit root mean square (RMS) Mach numbers 0.1 $\lesssim$ M $\lesssim$ 11. A continuous small-scale electromotive forcing injects magnetic helical fluctuations, which lead to the build-up of ever larger magnetic structures. Spectral scaling exponents are observed which, for …
We derive two new forms of the Kármán-Howarth-Monin equation for decaying compressible Hall magnetohydrodynamic (MHD) turbulence. We test them on results of a weakly-compressible, two-dimensional, moderate-Reynolds-number Hall MHD simulation and compare them with an isotropic spectral transfer (ST) equation. The KHM and ST equations are automatically satisfied during the whole simulation owing to the periodic boundary conditions and have complementary cumulative behavior. They are used here to analyze the onset of turbulence and its properties when it is fully developed. These approaches give …
We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to…
Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory
利用磁层多尺度（MMS）航天器观测数据和最近导出的{ \it可压缩} Hall MHD湍流的精确定律，首次完整地估算了地球磁鞘中磁流体动力学（MHD）和亚离子尺度下的可压缩能量级联率$|\varepsilon_\text{C}|$.采用多航天器技术计算速度梯度和磁场梯度，然后计算出所有的关联函数。结果表明，当密度涨落相对较小时，$|\varepsilon_\text{C}|$在MHD尺度下与不可压缩类似物$|\varepsilon_\text{I}|$很好地一致，但在亚离子尺度下比$|\varepsilon_\text{I}|$大得多。对于较大的密度波动，在每个尺度上，$|\varepsilon_\text{C}|$都大于$|\varepsilon_\text{I}|$，并且其值显着高于较小的密度波动。我们的研究还表明，对于小的和大的密度波动，非通量项始终保持相对于通量项可以忽略不计，并且在亚离子尺度下对$|\varepsilon_\text{C}|$的主要贡献来自可压缩的霍尔通量。
In this paper, an energy-consistent finite difference scheme for the compressible hydrodynamic and magnetohydrodynamic (MHD) equations is introduced. For the compressible magnetohydrodynamics, an energy-consistent finite difference formulation is derived using the product rule for the spatial difference. The conservation properties of the internal, kinetic, and magnetic energy equations can be satisfied in the discrete level without explicitly solving the total energy equation. The shock waves and discontinuities in the numerical solution are stabilized by nonlinear filtering schemes. An energ…
We report analysis of sub-Alfvénic magnetohydrodynamic (MHD) perturbations in the low-\b{eta} radial-field solar wind using the Parker Solar Probe spacecraft data from 31 October to 12 November 2018. We calculate wave vectors using the singular value decomposition method and separate the MHD perturbations into three types of linear eigenmodes (Alfvén, fast, and slow modes) to explore the properties of the sub-Alfvénic perturbations and the role of compressible perturbations in solar wind heating. The MHD perturbations there show a high degree of Alfvénicity in the radial-field solar wind, with…
Spatiotemporal Properties of Compressible Magnetohydrodynamic Turbulence from Space Plasma
Institut für Physik und Astronomie, Universität Potsdam（波茨坦大学物理与天文学研究所）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）；Institute of Science and Technology for Deep Space Exploration, Nanjing University（南京大学深空探测科学与技术研究院）；Shandong Key Laboratory of Space Environment and Exploration Technology, Institute of Space Sciences, School of Space Science and Technology, Shandong University（山东大学空间科学与技术学院空间科学研究所空间环境与探测技术山东省重点实验室）；Universität Potsdam（波茨坦大学）
Various forms of exact laws governing magnetohydrodynamic (MHD) turbulence have been derived either in the incompressibility limit, or for isothermal compressible flows. Here we propose a more general method that allows us to obtain such laws for any turbulent isentropic flow (i.e., constant entropy). We demonstrate that the known MHD exact laws (incompressible and isothermal) and the new (polytropic) one can be obtained as specific cases of the general law when the corresponding closure equation is stated. We also recover all known exact laws of hydrodynamic (HD) turbulence (incompressible, i…
Effects of Alfvénicity on the Compressible Energy Cascade in Magnetohydrodynamic Solar Wind Turbulence: Evidence from Parker Solar Probe, Solar Orbiter, and WIND observations
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales（布宜诺斯艾利斯大学，理学院）；CONICET – Universidad de Buenos Aires, Instituto de Física Interdisciplinaria y Aplicada (INFINA)（阿根廷国家科学研究委员会–布宜诺斯艾利斯大学，交叉与应用物理研究所）；Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校，物理系）；Department of Astronomy, University of Maryland, College Park（马里兰大学帕克分校，天文学系）；Planetary Magnetospheres Laboratory, NASA Goddard Space Flight Center（NASA戈达德太空飞行中心，行星磁层实验室）
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 o…
We present the first estimation of the energy cascade rate in Jupiter's magnetosheath (MS). We use in-situ observations from the Jovian Auroral Distributions Experiment (JADE) and the magnetometer investigation (MAG) instruments onboard the Juno spacecraft, in concert with two recent compressible models to investigate the cascade rate in the magnetohydrodynamic (MHD) scales. While a high level of compressible density fluctuations is observed in the Jovian MS, a constant energy flux exists in the MHD inertial range. The compressible isothermal and polytropic energy cascade rates increase in the…
The pseudospectral method is a highly accurate numerical scheme suitable for turbulence simulations. We have developed an open-source pseudospectral code, \textsc{\textsf{Calliope}}, which adopts the P3DFFT library \citep{Pekurovsky2012} to perform a fast Fourier transform with the two-dimensional (pencil) decomposition of numerical grids. \textsc{\textsf{Calliope}} can solve incompressible magnetohydrodynamics (MHD), isothermal compressible MHD, and rotational reduced MHD with parallel computation using very large numbers of cores ($> 10^5$ cores for $2048^3$ grids). The code can also solve f…
