Observations of Anisotropic Scaling of Solar Wind Turbulence

Abstract

Using high-speed solar wind data recorded by the Ulysses spacecraft, we investigate and estimate the anisotropic inertial range scaling of the interplanetary magnetic field. We apply the method of the magnetic structure function (MSF), Sⁿ (τ) = lang|b(t + τ) - b(t)| ⁿ rang vprop τ^ζ(n), to analyze the scaling of solar wind turbulence over the range from 1 s to 10⁴ s. By sorting the fluctuations according to the direction of the local mean magnetic field, we obtain a second-order structure function in (r, Θ) coordinates that reveals the scale-dependent anisotropy of the power spectrum. The scale-dependent anisotropy of the MSF indicates that the fluctuation energy tends to cascade toward the direction perpendicular to the local field. The dependence of the MSF scaling index ζ on the direction of the local field is found to be similar to that reported in Horbury et al. and Podesta, with ζ_bottom = 0.53 ± 0.18 and ζ_par = 1.00 ± 0.14. Furthermore, we estimate and find the scaling law between the perpendicular and parallel scales r _par vprop r ^0.614 _bottom, which implies the elongation along the parallel direction as the turbulence eddy evolves toward the small lengthscales. These results are in agreement with the predictions of magnetohydrodynamic turbulence theory.