3-D feature of self-correlation level contours at $10^{10}\ \mathrm{cm}$ scale in solar wind turbulence

The self-correlation level contours at $10^{10}\ \mathrm{cm}$ scale reveal a 2-D isotropic feature in both the slow solar wind fluctuations and the fast solar wind fluctuations. However, this 2-D 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 3-D isotropic remains unknown. Here we perform for the first time a 3-D self-correlation level contours analysis on the solar wind turbulence. We construct a 3-D coordinate system based on the mean magnetic field direction and the maximum fluctuation direction identified by the minimum-variance analysis (MVA) method. We use data with 1-hour 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 3-D isotropic feature. On the other hand, there is a weak elongation in one of the perpendicular direction in the fast solar wind fluctuations. The 3-D feature of the self-correlation level contours surfaces cannot be explained by the existed theory.