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The slow wind anisotropy is observed by Dasso et al. as elongation along the magnetic field direction in the magnetic self-correlation contours calculated from data sets of two-day-long data and averaged for five years in 1998–2002, which is consistent with prediction by the “critical balance cascade theory.” More pronounced elongation at smaller scales than at larger scales has also been predicted by this theory. However, this prediction has not yet been checked by observations. Here, we present a check of the variation trend of the anisotropy with scales by presenting level contours of magnetic field and velocity self-correlations using intervals with durations varying from two days to one hour as observed by the Advanced Composition Explorer during 1998–2002 in the slow wind. We find that the level contours elongate along the magnetic field direction at durations of two days and one day. But they become isotropic for shorter intervals from about 10 hours to 1 hour. We also find that in the fast wind, the variation of the anisotropy with the scale has the same trend as in the slow wind. The 2D isotropic feature of the solar wind fluctuations shown by these statistical results is not consistent with the existing theory and will open a new avenue for studying solar wind turbulence. [ABSTRACT FROM AUTHOR]

The power spectrum of magnetic fluctuations has a break at the high-frequency end of the inertial range. Beyond this break, the spectrum becomes steeper than the Kolmogorov law f−5/3. The break frequency was found to be associated with plasma beta (β). However, the full-range β dependence of the ion-scale spectral break has not been presented before in observational studies. Here we show the continuous variation of the break frequency on full-range β in the solar wind turbulence. By using measurements from the WIND and Ulysses spacecraft, we show the break frequency (fb) normalized, respectively, by the frequencies corresponding to ion inertial length (fdi), ion gyroradius (), and cyclotron resonance scale (fri) as a function of β for 1306 intervals. Their β values spread from 0.005 to 20, which nearly covers the full β range of the observed solar wind turbulence. It is found that () generally decreases (increases) with β, while is nearly a constant. We perform a linear fit on the statistical result, and obtain the empirical formulas , , and to describe the relation between fb and β. We also compare our observations with a numerical simulation and the prediction by ion cyclotron resonance theory. Our result favors the idea that the cyclotron resonance is an important mechanism for energy dissipation at the spectral break. When β ≪ 1 and β ≫ 1, the break at fdi and may also be associated with other processes. [ABSTRACT FROM AUTHOR]

Turbulence in the solar wind was recently reported to be anisotropic, with the average power spectral index close to −2 when sampling parallel to the local mean magnetic field and close to −5/3 when sampling perpendicular to the local . This result was widely considered to be observational evidence for the critical balance theory (CBT), which is derived by making the assumption that the turbulence strength is close to one. However, this basic assumption has not yet been checked carefully with observational data. Here we present for the first time the scale-dependent magnetic-field fluctuation amplitude, which is normalized by the local and evaluated for both parallel and perpendicular sampling directions, using two 30-day intervals of Ulysses data. From our results, the turbulence strength is evaluated as much less than one at small scales in the parallel direction. An even stricter criterion is imposed when selecting the wavelet coefficients for a given sampling direction, so that the time stationarity of the local is better ensured during the local sampling interval. The spectral index for the parallel direction is then found to be −1.75, whereas the spectral index in the perpendicular direction remains close to −1.65. These two new results, namely that the value of the turbulence strength is much less than one in the parallel direction and that the angle dependence of the spectral index is weak, cannot be explained by existing turbulence theories, like CBT, and thus will require new theoretical considerations and promote further observations of solar-wind turbulence. [ABSTRACT FROM AUTHOR]

The scaling anisotropy is crucial to interpret the nonlinear interactions in solar wind turbulence. Previous observations provide diverse results and the structure function analyses are also reported to be an approach to investigate the scaling anisotropy based on a local magnetic field. However, the determination of the sampling angle with respect to the local background magnetic field requires that the observed time series for the average are time stationary. Whether or not this required time stationarity is compatible with the measurements has not been investigated. Here we utilize the second-order structure function method to study the scaling anisotropy with a time-stationary background field. We analyze 88 fast solar wind intervals each with time durations ≥ 2 days measured by WIND spacecraft in the period 2005–2018. We calculate the local magnetic field as the average of the time series whose time stationarity is fulfilled by our criterion ϕ < 10° (ϕ is the angle between the two averaged magnetic fields after cutting into two halves). We find for the first time the isotropic scaling feature of the magnetic-trace structure functions with scaling indices and , respectively, with the local magnetic field parallel and perpendicular to the solar wind velocity directions. The scaling for the velocity-trace structure functions is also isotropic and the indices are and . We also find that with increasing ϕ threshold to 90°, the scaling index of the magnetic-trace structure function in the parallel direction decreases to −0.81, while the rms of the instantaneous angle between magnetic field and solar wind velocity increases up to 45° at the timescale 150 s, indicating a mix of perpendicular measurements into parallel ones at large scales. [ABSTRACT FROM AUTHOR]

The self-correlation level contours at 1010 cm scale reveal a 2D isotropic feature in both the slow solar wind fluctuations and the fast solar wind fluctuations. However, this 2D isotropic feature is obtained based on the assumption of axisymmetry with respect to the mean magnetic field. Whether the self-correlation level contours are still 3D isotropic remains unknown. Here we perform for the first time a 3D self-correlation level contours analysis on the solar wind turbulence. We construct a 3D coordinate system based on the mean magnetic field direction and the maximum fluctuation direction identified by the minimum-variance analysis method. We use data with 1 hr intervals observed by WIND spacecraft from 2005 to 2018. We find, on one hand, in the slow solar wind, the self-correlation level contour surfaces for both the magnetic field and the velocity field are almost spherical, which indicates a 3D isotropic feature. On the other hand, there is a weak elongation in one of the perpendicular directions in the fast solar wind fluctuations. The 3D feature of the self-correlation level contours surfaces cannot be explained by the existing theory. [ABSTRACT FROM AUTHOR]

The compressible component of solar wind turbulence displays a slow-mode feature. However, the nature of the slow-mode fluctuations remain open. In this work, based on numerical simulations of the driven compressible magnetohydrodynamic (MHD) turbulence with a uniform mean magnetic field, we use polarization of the MHD modes to decompose turbulent velocity and magnetic fields into Alfvén modes, slow modes, and fast modes. The numerical results with different cross-helicity, plasma beta β, and Alfvén Mach number note that fast modes are a marginal component among the three decomposed modes, and the compressible component of the MHD turbulence behaves mainly as the slow modes. Both of the decomposed slow modes and Alfvén modes exhibit a Kolmogorov-like power-law spectrum and evident anisotropy, with wavevectors mainly distributing around the directions perpendicular to the uniform mean field. For the first time, it is found that the propagating slow magnetosonic waves as well as the non-propagating slow-mode structures are combined to contribute to the compressible fluctuations, and the propagating Alfvén waves as well as the non-propagating Alfvén-mode structures coexist for the non-compressible fluctuations. However, there is unlikely a one-to-one match between the identified slow waves and Alfvén waves, or between the identified slow-mode structures and Alfvén-mode structures. These findings provide a new perspective on our understanding of the compressible and non-compressible fluctuations. [ABSTRACT FROM AUTHOR]

Multi-order structure functions in the solar wind are reported to display a monofractal scaling when sampled parallel to the local magnetic field and a multifractal scaling when measured perpendicularly. Whether and to what extent will the scaling anisotropy be weakened by the enhancement of turbulence amplitude relative to the background magnetic strength? In this study, based on two runs of the magnetohydrodynamic (MHD) turbulence simulation with different relative levels of turbulence amplitude, we investigate and compare the scaling of multi-order magnetic structure functions and magnetic probability distribution functions (PDFs) as well as their dependence on the direction of the local field. The numerical results show that for the case of large-amplitude MHD turbulence, the multi-order structure functions display a multifractal scaling at all angles to the local magnetic field, with PDFs deviating significantly from the Gaussian distribution and a flatness larger than 3 at all angles. In contrast, for the case of small-amplitude MHD turbulence, the multi-order structure functions and PDFs have different features in the quasi-parallel and quasi-perpendicular directions: a monofractal scaling and Gaussian-like distribution in the former, and a conversion of a monofractal scaling and Gaussian-like distribution into a multifractal scaling and non-Gaussian tail distribution in the latter. These results hint that when intermittencies are abundant and intense, the multifractal scaling in the structure functions can appear even if it is in the quasi-parallel direction; otherwise, the monofractal scaling in the structure functions remains even if it is in the quasi-perpendicular direction. [ABSTRACT FROM AUTHOR]

Solar wind fluctuations reveal the ubiquity of intermittency, which is believed to affect the spectral signatures of turbulence. In this work, based on simulation of driven compressible MHD turbulence, we apply the wavelet technique to the magnetic field and velocity to identify intermittency, and we analyze the influence of the intermittency on the quasi-perpendicular scaling in the inertial range. The numerical results show that the original magnetic and velocity fluctuations are anisotropic, and have a power anisotropy with a spectral index approaching the Iroshnikov–Kraichnan scaling in the direction quasi-perpendicular to the local mean magnetic field. As in observations of the solar wind fluctuations, as the scale decreases in the simulation, the calculated probability distribution functions (pdfs) of the wavelet coefficients become extended on both tails of the non-Gaussian distribution, with a rapid increase in flatness. After intermittency has been removed from the driven turbulence, at each scale, the pdfs approach a Gaussian distribution, with the flatness being ∼3. Meanwhile, the quasi-perpendicular scaling for both fluctuations becomes steeper and close to a Kolmogorov scaling, which may be a result of the stronger intermittency in the quasi-perpendicular direction and at the smaller scales. These results suggest that there is intermittency superposed on the “background” turbulence that seems to have the Kolmogorov scaling, whereby the overall slope is getting flatter with the involvement of intermittency. [ABSTRACT FROM AUTHOR]