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 ¢ B t () whose time stationarity is fulfilled by our criterion f<10°(f is the angle between the two averaged magnetic fields after cutting ¢ B t () into two halves). We find for the first time the isotropic scaling feature of the magnetic-trace structure functions with scaling indices- 0.63 0.08 and 0.70 0.04, 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- 0.47 0.10 and 0.51 0.09. We also find that with increasing f 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.
Energy supply sources for the heating process in the slow solar wind remain unknown. The Parker Solar Probe (PSP) mission provides a good opportunity to study this issue. Recently, PSP observations have found that the slow solar wind experiences stronger heating inside 0.24 au. Here for the first time we measure in the slow solar wind the radial gradient of the low-frequency breaks on the magnetic trace power spectra and evaluate the associated energy supply rate. We find that the energy supply rate is consistent with the observed perpendicular heating rate calculated based on the gradient of the magnetic moment. Based on this finding, one could explain why the slow solar wind is strongly heated inside 0.25 au but expands nearly adiabatically outside 0.25 au. This finding supports the concept that the energy added from the energy-containing range is transferred by an energy cascade process to the dissipation range, and then dissipates to heat the slow solar wind. The related issues for further study are discussed.
Magnetic-field directional turning (MFDT) and magnetic-velocity alignment structure (MVAS) are two typical types of structures in the solar wind. However, their fluctuation amplitudes in different turbulence states have not been studied before. Here, we present the amplitude distributions of MFDTs and MVASs in the plane, where is the correlation coefficient between magnetic-field and velocity fluctuations multiplied by the sign of the x component of the mean field in geocentric solar ecliptic coordinates, and σ r is normalized residual energy. Measurements from the WIND spacecraft in the slow solar wind during 2005–2009 are used for the analysis. The data are cut into intervals with duration of 6 minutes, and the intervals that are nearly incompressible are selected for analysis. We find that for the fluctuations with and −1 < σ r < −0.6, which are considered to be associated with MFDTs, the level contours of the pixel average amplitude of magnetic-field fluctuations in the plane show a horizontal-stripe feature with approximately km s−1 in Alfvén units. For the fluctuations with and −0.9 < σ r < −0.2, which are considered to be associated with MVASs, the level contours of the pixel average amplitude of velocity fluctuations show a vertical stripe feature with approximately km s−1. Consequently, the level contours of the pixel average amplitudes of Elsässer variables show “U” and “W” shapes, respectively. These results will help us to understand the nature of the fluctuations in the solar wind.
The von Kármán-Howarth equations give a starting basis for the classical turbulence theory. The formula for the magnetohydrodynamics von Kármán decay rate represents an energy source in many solar wind models with turbulence as the driver. However, it still lacks the radial trend comparison between the von Kármán decay rate, the energy supply rate, and the perpendicular heating rate based on direct observations of the solar wind. Here we carry out this kind of comparison for the first time using Parker Solar Probe measurements from its first three orbits. We find that the radial variation of the von Kármán decay rate is consistent with that of both the energy supply rate and the heating rate in the slow solar wind. These results support the idea that the von Kármán decay law is an active process responsible for solar wind heating. These results also suggest a new idea that both the von Kármán decay law and the low-frequency break sweeping may be controlled by the same nonlinear process. Some limitations of the present study are also addressed.
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