Turbulent dissipation in 1D and 3D simulations of thin solar wind flux tube

Turbulence is likely to be the main source of heating of the solar corona and solar wind. The turbulent cascade transfers energy from large scale motions down to ion and electron scales, where the plasma is heated. Self-consistent simulations of the turbulent solar wind heating are however very hard to achieve as the cascade spans many scales and physical, fluid and kinetic, processes. In this talk, we focus on the inertial range of the cascade, which may be modeled with MHD. Using a 1D profile along a solar wind flux tube, we show that we can power a solar wind solution through a compressible cascade triggered by a non-linear parametric instability. The dissipation process of this simulation is, however, unlikely to be similar to 3D realistic configurations. Hence, we compare this simulation with an extremely high resolution 3D simulation of a thin flux tube, allowed by the new GPU accelerated MHD code Idefix. We compare the Politano-Pouquet law in its classical and weak formulation to assess the means of the dissipation in both simulations.