Two-dimensional correlation functions for density and magnetic field fluctuations in magnetosheath turbulence measured by the Cluster spacecraft

Knowledge of multidimensional correlation functions is crucial for understanding the anisotropy of turbulence. The two-dimensional (2-D) spatial correlation functions (SCFs) obtained in previous studies of space plasma turbulence were restricted to large-length scales and covered a limited angular domain of the two-point separation vector with respect to the mean magnetic field. Here we aim to derive 2-D SCFs with smaller-length scale and nearly full angular distribution for the fluctuations of the number density and magnetic field in magnetosheath turbulence. We use the Cluster four-spacecraft measurements of the fluctuations with respect to a temporally and spatially varying background magnetic field to construct the 2-D SCFs. We find that the correlation function of the density fluctuations shows a pattern similar to that of the magnetic field fluctuations, both of which appear to be composed of two populations, whereby the major population extends along the coordinate parallel to mean magnetic field (S∥) and the minor one deviates toward the perpendicular coordinate (S⊥). This pattern of 2-D SCFs implies that the energy of magnetosheath turbulence seems to cascade, in the inertial range close to the ion scale, mostly transverse to the background magnetic field and meanwhile partly along the field (i.e., k ⊥ >> k∥).