Turbulent dynamics of the Solar Wind

The aim of this thesis is the study of the development of turbulence in the solar wind between 0.2 and 1 astronomical unit (AU) from the Sun (i.e. Earth's orbit). The study is done by solving the magnetohydrodynamics equations (MHD) after subtracting the mean radial flow. The two aspects of turbulence that interest us are the 3D structure of the energy spectra and the heating of plasma that results from the turbulent dissipation of eddies and current layers transported by the wind. We want to determine which conditions of the plasma close to the Sun can result into what we observe at 1 AU. We have relatively detailed measurements of what happens between 0.3 and 1 AU. One important goal of this work is to determine if the physics present in the equations that are integrated (MHD) is sufficient to reproduce what is observed in this interval of distances. We introduce the context of our work in the first part. We give a summary of the physics concerning the solar wind and the solar corona, and the basic equations used to describe the solar wind plasma and an introduction to turbulence. Part 2 is dedicated to the study of anisotropy in the turbulent cascade, which characterizes 3D spectra. In the inertial range, in-situ measurements at 1 AU show complex figures for these spectra that we can interpret in several ways: numerical simulations allow to clear ambiguities. An important question is to know whether the Earth-Sun symmetry axis or the mean magnetic field axis is dominant. The third part focuses on turbulent heating in fast and slow winds. Between 0.3 and 1 AU, proton temperature decreases more slowly than expected, which requires a heating source. This source is supposed to be the continuous dissipation of eddies and current layers transported by the wind. To start with, we consider the simple case of Burgers equation, which is a one-dimensional model for shock formation. Thereupon, we switch to the 3-dimensional case, where we consider initial conditions appropriate for slow and fast winds. In the last part we expose our conclusions and propose the implementation of temperature anisotropy as future work. (author)