Multi-scale turbulence in the inner solar wind

Spacecraft measurements made in the solar wind show velocity and magnetic fluctuations over a broad range of frequencies. These fluctuations possess many properties expected of fully developed turbulence. In this paper, a brief overview is given on turbulence in the inner (< 1UA) solar wind at low (< 1Hz) and high (> 1Hz) frequencies for which non linear dispersive effects dominate. Then, a discussion is given about recent theoretical results on anisotropy in magnetohydrodynamic (MHD) turbulence and their relevance for understanding the data at low frequency. Finally, I show that incompressible Hall MHD may give a multi-scale description of inner solar wind turbulence; in particular, the non-linear dispersive effects lead to a steepening of the magnetic fluctuation power law spectrum similar to what is observed at high frequency.