Three-dimensional spatial structures of solar wind turbulence from 10 000-km to 100-km scales

Using the four Cluster spacecraft, we have determined the three-dimensional wave-vector spectra of fluctuating magnetic fields in the solar wind. Three different solar wind intervals of Cluster data are investigated for this purpose, representing three different spatial scales: 10 000 km, 1000 km, and 100 km. The spectra are determined using the wave telescope technique (k-filtering technique) without assuming the validity of Taylor's frozen-in-flow hypothesis nor are any assumptions made as to the symmetry properties of the fluctuations. We find that the spectra are anisotropic on all the three scales and the power is extended primarily in the directions perpendicular to the mean magnetic field, as might be expected of two-dimensional turbulence, however, the analyzed fluctuations are not axisymmetric. The lack of axisymmetry invalidates some earlier techniques using single spacecraft observations that were used to estimate the percentage of magnetic energy residing in quasi-two-dimensional power. However, the dominance of two-dimensional turbulence is consistent with the relatively long mean free paths of cosmic rays in observed in the heliosphere. On the other hand, the spectra also exhibit secondary extended structures oblique from the mean magnetic field direction. We discuss possible origins of anisotropy and asymmetry of solar wind turbulence spectra.