Beyond the Maltese Cross: Geometry of Turbulence between 0.2 and 1 AU

The spectral anisotropy of turbulent structures has been measured in the solar wind since 1990, relying on the assumption of axisymmetry around the mean magnetic field. However, early and recent works indicate that this hypothesis might be partially wrong, thus raising two questions: (i) is it correct to interpret measurements at 1 AU (the so-called maltese cross) in term of a sum of slab and 2D turbulence? (ii) what information is really contained in the maltese cross? We solve direct numerical simulations of the MHD equations including the transverse stretching exerted by the mean solar wind flow and study the genuine 3D anisotropy of turbulence as well as that one resulting from the assumption of axisymmetry around the mean field, B0. We show that the a slab component results from the axisymmetry assumption when the real anisotropy is ruled by the radial axis. This strongly depends on the initial state of fluctuations (at 0.2 AU in our simulations): a spectrum axisymmetric around B0 roughly conserves its symmetry, thus resisting the stretching in directions perpendicular to the radial; an isotropic spectrum instead becomes essentially axisymmetric with respect to the radial direction, even at inertial-range scales. We suggest that close to the Sun, slow-wind turbulence has a spectrum that is axisymmetric around B0 and the measured 2D component at 1 AU describes the real shape of turbulent structures. On the contrary, fast-wind turbulence has a more isotropic spectrum at the source and becomes radially symmetric at 1 AU. Such structure is hidden by the symmetrization applied to the data that instead returns a slab geometry. We conlcude by discussing the cascade rates associated to fast and slow wind.