On the properties of scale-dependent probability distribution functions of Elsasser increments in solar wind and MHD turbulence

In this work we investigate the properties of probability distribution functions (PDFs) of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs, and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics from a 23 years-long sample of WIND data near 1-AU, as well as high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a 2048^3 mesh, are used to construct the scale-dependent PDFs. We propose Normal Inverse Gaussian distributions to model the behavior of the PDFs from the outer scale to the dissipation scales, describing the evolution of increments from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. These distributions suggest some universal characteristics present in all three data sets.