The whole heliosphere is permeated by the solar wind (SW), a supersonic plasma flow of solar origin which continuously expands into space. During its expansion, the SW develops a strong turbulent character, which evolves towards a state that resembles the well known hydrodynamic turbulence described by Kolmogorov. Because of a strong carried magnetic field, low-frequency fluctuations in the SW are usually described within a magnetohydrodynamic (MHD) framework. The presence of magnetic field has non trivial effects on the turbulent dynamics and allows for interesting analogies between MHD turbulence and fluid turbulence with rotation and/or stratification. Common features for these systems are in fact the presence of waves interacting with turbulent eddies, and anisotropy.
In recent years the occurrence of an MHD turbulent cascade has been validated in the SW through the systematic observation of an exact scaling law for the mixed third order moment of the velocity and magnetic field, or their combination using the Elsässer variables, known as the Politano & Pouquet (P&P) law or Yaglom law for the MHD. Observations of the P&P law also provided for the first time a direct estimation of the transfer rate of the turbulent energy, which is thought to contribute to the “in situ” heating of the wind. SW plasma is in fact known to cool down more slowly than expected for an adiabatic spherical expansion while it is blowing away from the Sun.
After a review of the main results obtained in this framework, I will show that the occurrence of the MHD cascade in the fast SW measured by the spacecraft Ulysses over the Sun’s poles is related with local properties of the velocity and magnetic field fluctuations. These are the reduction of the correlation between velocity and magnetic field (weak cross-helicity); the presence of large-scale velocity shears; the steepening and extension down to low frequencies of the turbulent spectra. Dependence of the energy cascade rate with radial distance, latitude and solar activity is presented, corroborating the importance of local alignment of velocity and magnetic fields, and confirming the non universal character of solar wind MHD turbulence. The role of direct numerical simulations will also be stressed that can complement the observations and data analysis, with a specific example concerning the role of kinetic helicity in an anisotropic fluid systems in comparison with the role of the cross-helicity in MHD. Indeed numerical modelling appears to be of fundamental importance to have a global view on the basic mechanisms governing turbulence, and decipher the complex and poorly accessible phenomena characterizing heliospheric plasmas.