Nonaxisymmetric anisotropy of solar wind turbulence as a direct test for models of magnetohydrodynamic turbulence

Single point spacecraft observations of the turbulent solar wind flow exhibit a characteristic nonaxisymmetric anisotropy that depends sensitively on the perpendicular power spectral exponent. We use this nonaxisymmetric anisotropy as a function of wave vector direction to test models of MHD turbulence. Using Ulysses magnetic field observations in the fast, quiet polar solar wind we find that the Goldreich-Sridhar model of MHD turbulence is not consistent with the observed anisotropy, whereas the observations are well reproduced by the "slab+2D" model. The Goldreich-Sridhar model alone cannot account for the observations unless an additional component is also present.     

Magnetic discontinuities in magnetohydrodynamic turbulence and in the solar wind

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Δθ, across fixed spatial increments Δx in direct numerical simulations of MHD turbulence with an imposed uniform guide field B(0). A large region of the probability density function (pdf) for Δθ is found to follow an exponential decay, proportional to exp(-Δθ/θ(*)), with characteristic angle θ(*)≈(14°)(b(rms)/B(0))(0.65) for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b(rms)/B(0). We also observe an excess of small angular discontinuities when Δx becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.     

An observational picture of solar-wind MHD turbulence

Summary A review of the available information on the MHD fluctuations in the solar wind is given. The most general properties of the picture which derives from the satellite measurements are discussed. The very important result which seems to appear is the fact that the low-frequency MHD fluctuations are characteristic of a turbulent state. Clearly this state cannot be represented by the usual models based on the hypothesis of the presence of simple waves in the solar wind. It is then rather natural to suppose that these observational data should be usefully analysed only through the theoretical methods developed to study the strong MHD turbulence. Moreover, this analysis is rather stimulating since the solar wind offers us one of the rare possibilities to have observational tests of the theoretical models of strong MHD turbulence.     

Self-similar signature of the active solar corona within the inertial range of solar-wind turbulence

We quantify the scaling of magnetic energy density in the inertial range of solar-wind turbulence seen in situ at 1 AU with respect to solar activity. At solar maximum, when the coronal magnetic field is dynamic and topologically complex, we find self-similar scaling in the solar wind, whereas at solar minimum, when the coronal fields are more ordered, we find multifractality. This quantifies the solar-wind signature that is of direct coronal origin and distinguishes it from that of local MHD turbulence, with quantitative implications for coronal heating of the solar wind.     

On Yaglom’s Law for the Interplanetary Proton Density and Temperature Fluctuations in Solar Wind Turbulence

In the past decades, there has been an increasing literature on the presence of an inertial energy cascade in interplanetary space plasma, being interpreted as the signature of Magnetohydrodynamic turbulence (MHD) for both fields and passive scalars. Here, we investigate the passive scalar nature of the solar wind proton density and temperature by looking for scaling features in the mixed-scalar third-order structure functions using measurements on-board the Ulysses spacecraft during two different periods, i.e., an equatorial slow solar wind and a high-latitude fast solar wind, respectively. We find a linear scaling of the mixed third-order structure function as predicted by Yaglom’s law for passive scalars in the case of slow solar wind, while the results for fast solar wind suggest that the mixed fourth-order structure function displays a linear scaling. A simple empirical explanation of the observed difference is proposed and discussed.     

Nonaxisymmetric anisotropy of solar wind turbulence

A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent solar wind are observed to be ordered with respect to the bulk macroscopic flow as well as the background magnetic field. Here, nonaxisymmetry across the inertial and dissipation ranges is quantified using in situ observations from Cluster. The observed inertial range nonaxisymmetry is reproduced by a "fly through" sampling of a direct numerical simulation of MHD turbulence. Furthermore, fly through sampling of a linear superposition of transverse waves with axisymmetric fluctuations generates the trend in nonaxisymmetry with power spectral exponent. The observed nonaxisymmetric anisotropy may thus simply arise as a sampling effect related to Taylor's hypothesis and is not related to the plasma dynamics itself.     

Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wave number ranges in a Beta > or approximately = 1 plasma. The k(-5/3) inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfvén speed. At smaller wavelengths krho(i) > or = 1 the electric spectrum is enhanced and is consistent with the expected dispersion relation of short-wavelength kinetic Alfvén waves. Kinetic Alfvén waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluidlike nature of the solar wind.     

Collisionless magnetohydrodynamic turbulence in two dimensions

In this paper we give a formulation of two-dimensional (2D) collisionless magnetohydrodynamic (MHD) turbulence that includes the effects of both electron inertia and electron pressure (or parallel electron compressibility) and is applicable to strongly magnetized collisionless plasmas. We place particular emphasis on the departures from the 2D classical MHD turbulence results produced by the collisionless MHD effects. We investigate the fractal/multi-fractal aspects of spatial intermittency. The fractal model for intermittent collisionless MHD turbulence appears to be able to describe the observed k⁻¹ spectrum in the solar wind. Multi-fractal scaling behaviors in the inertial range are first deduced, and are then extrapolated down to the dissipative microscales. We then consider a parabolic-profile model for the singularity spectrum f (α), as an explicit example of a multi-fractal scenario. These considerations provide considerable insights into the basic mechanisms underlying spatial intermittency in 2D fully developed collisionless MHD turbulence.     

Anisotropy of imbalanced Alfvénic turbulence in fast solar wind

We present the first measurement of the scale-dependent power anisotropy of Elsasser variables in imbalanced fast solar wind turbulence. The dominant Elsasser mode is isotropic at lower spacecraft frequencies but becomes increasingly anisotropic at higher frequencies. The subdominant mode is anisotropic throughout. There are two distinct subranges exhibiting different scalings within what is normally considered the inertial range. The low Alfvén ratio and the different scaling of the Elsasser modes suggests an interpretation of the observed discrepancy between the velocity and magnetic field scalings, the total energy is dominated by the latter. These results do not appear to be fully explained by any of the current theories of incompressible imbalanced MHD turbulence.     

Anomalous flow deflection at earth's low-Alfvén-Mach-Number bow shock

Earth's magnetosphere is an obstacle to the supersonic solar wind and the bow shock is formed in the front side of it. In ordinary hydrodynamics, the flow decelerated at the shock is diverted around the obstacle symmetrically about the Earth-Sun line, which is indeed observed in the magnetosheath most of the time. Here we show a case under a very low-density solar wind in which duskward flow was observed in the dawnside magnetosheath. A Rankine-Hugoniot test shows that the magnetic effect is crucial for this "wrong flow" to appear. A full three-dimensional magnetohydrodynamics (MHD) simulation of the situation confirming this interpretation and earlier simulations is also performed. It is illustrated that in addition to the "wrong flow" feature, various peculiar characteristics appear in the global picture of the MHD flow interaction with the obstacle.     

Compressibility in solar wind plasma turbulence

Incompressible magnetohydrodynamics is often assumed to describe solar wind turbulence. We use extended self-similarity to reveal scaling in the structure functions of density fluctuations in the solar wind. The obtained scaling is then compared with that found in the inertial range of quantities identified as passive scalars in other turbulent systems. We find that these are not coincident. This implies that either solar wind turbulence is compressible or that straightforward comparison of structure functions does not adequately capture its inertial range properties.     

Anisotropic third-moment estimates of the energy cascade in solar wind turbulence using multispacecraft data

The first direct determination of the inertial range energy cascade rate, using an anisotropic form of Yaglom's law for magnetohydrodynamic turbulence, is obtained in the solar wind with multispacecraft measurements. The two-point mixed third-order structure functions of Els?sser fluctuations are integrated over a sphere in magnetic field-aligned coordinates, and the result is consistent with a linear scaling. Therefore, volume integrated heating and cascade rates are obtained that, unlike previous studies, make only limited assumptions about the underlying spectral geometry of solar wind turbulence. These results confirm the turbulent nature of magnetic and velocity field fluctuations in the low frequency limit, and could supply the energy necessary to account for the nonadiabatic heating of the solar wind.     

Spectral slope and Kolmogorov constant of MHD turbulence

The spectral slope of strong MHD turbulence has recently been a matter of controversy. While the Goldreich-Sridhar model predicts a -5/3 slope, shallower slopes have been observed in numerics. We argue that earlier numerics were affected by driving due to a diffuse locality of energy transfer. Our highest-resolution simulation (3072(2)×1024) exhibited the asymptotic -5/3 scaling. We also discover that the dynamic alignment, proposed in models with -3/2 slope, saturates and cannot modify the asymptotic, high Reynolds number slope. From the observed -5/3 scaling we measure the Kolmogorov constant C(KA)=3.27±0.07 for Alfvénic turbulence and C(K)=4.2±0.2 for full MHD turbulence, which is higher than the hydrodynamic value of 1.64. This larger C(K) indicates inefficient energy transfer in MHD turbulence, which is in agreement with diffuse locality.     

Weak compressible magnetohydrodynamic turbulence in the solar corona

This Letter presents a calculation of the power spectra of weakly turbulent Alfvén waves and fast magnetosonic waves ("fast waves") in low- plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfvén waves. High-frequency waves produced by MHD turbulence are a promising explanation for the anisotropic heating of minor ions in the solar corona.     

On the temporal power spectra of scintillations by propagation through a moving random medium with wave turbulence

The formation of the temporal spectrum of scintillations is considered for electromagnetic waves propagating in a moving continuous random medium with wave turbulence. The relative contributions of the motion of the medium and turbulent wave propagation to the transformation of the spatial spectrum into a temporal one are discussed. Some results obtained from radio occultation by solar wind plasma at small solar elongations are used for choosing a suitable model for wave turbulence.     

Gyrokinetic simulations of solar wind turbulence from ion to electron scales

A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.     

磁流体力学湍流的一些规律

本文从处理湍流场的普遍方法──“任一物理量都可分解成平均值与涨落值之和”出发，利用量纲估计和磁流体力学湍流近似对磁流体力学基本方程进行讨论，得出有关磁流体力学湍流场的一些结论．这些结论对研究目前阶段的磁流体力学湍流理论是很有用的。     

Kinetic simulations of magnetized turbulence in astrophysical plasmas

This Letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic- and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfvén waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfvén waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.     

Numerical Simulation of the 12 May 1997 CME Event

Our newly developed CESE MHD model is used to simulate sun-earth connection event with the well-studied 12 May 1997 CME event as an example. The main features and approximations of our numerical model are as follows： （1） The modifed conservation element and solution element （CESE） numerical scheme in spherical geometry is implemented in our code. （2） The background solar wind is derived from a 3D time-dependent numerical MHD model by input measured photospheric magnetic fields. （3） Transient disturbances are derived from solar surface by introducing a mass flow of hot plasma. The numerical simulation has enabled us to predict the arrival of the interplanetary shock and provided us with a relatively satisfactory comparison with the WIND spacecraft observations.