MHD turbulence in the solar wind: self-similarity, intermittency and coherent structures

High-resolution numerical simulations on the one hand and solar wind data analysis on the other hand have allowed for much progress in our understanding of magnetohydrodynamic (MHD) turbulence. In particular the high resolution of solar wind measurements has allowed us to characterize the intermittency observed on small scales. In this paper we will give a schematic view of the main properties of solar wind MHD turbulence and discuss some recent results obtained from the analysis of velocity and magnetic field data measured during the space experiments Helios and ISEE. In particular, we will show that applying Haar wavelets technique to about one year of data taken every minute during the ISEE space experiment, it is possible to calculate spectra and structure functions of the turbulence; moreover the definition of conditioned structure function allows: (a) for the elimination of intermittency effects in spectra and thus for a clear identification of which kind of phenomenology of nonlinear cascade between Kolmogorov and Kraichnan is taking place in the solar wind turbulence; (b) for the identification of the most intermittent structures which turn out to be either shock waves or one-dimensional current sheets, at variance with ordinary fluid intermittency, where the most intermittent structures are found to be two-dimensional vortices.