THE EVOLUTION OF MHD TURBULENCE IN THE SOLAR WIND

Abstract

Based on the previous work by Marsch and Tu /1/ and Tu and Marsch /2,3/, an extended theoretical model is presented in this paper in order to explain the radial evolution of the solar wind fluctuations. The idea is to combine systematically in a single model the three basic observed features: Alfvén waves, turbulence and convective structures. Part of the small-scale variations are Alfvén waves that are believed to be created near the coronal base and to propagate outward along the magnetic field lines. The large-scale variations along the magnetic field lines may be considered as convective structures that are static during the solar wind expansion time. The variations perpendicular to the convected magnetic field lines can also have small scales and contribute considerably to the solar wind fluctuations when the data sampling conditions are favourable. Nonlinear interactions will take place between inward and outward propagating Alfvén waves, between the cross-field variations themselves (2-D-turbulence) and between the cross-field fluctuations and the Alfvén waves. These nonlinear interactions then make the fluctuations to be turbulent in nature. With this idea some empirical trends of the radial evolution of solar wind turbulence can easily be explained. An increase of the relative amount of convective magnetic fluctuations against propagating Alfvén waves in the sampled data will result in a decrease of the cross-helicity, σc, and Alfvén ratio rA. Under some reasonable assumptions, the spectral transfer equations for the fluctuations composed of propagating Alfvén waves and convective structures can be derived. For a very simple model an analytical solution of these transfer equations is given and found to be in qualitative agreement with the observations.