Scaling-laws and high-order statistics in strong Alfvenic turbulence

The bulk of the fluctuation energy in the solar wind is observed to be the form of incompressible fluctuations of the plasma velocity and magnetic field, consistent with strong Alfvenic turbulence. Over the last few decades, significant progress has been made in theory and numerical simulations of Alfvenic turbulence allowing for direct comparisons with solar wind observations. A large part of this progress has been devoted to explain scaling laws in the power spectrum of velocity and magnetic field fluctuations, turbulence anisotropy and turbulent dissipation, which are inextricably related to the second and third order statistics of the underlying turbulence. More recently there has been increased interest in understanding high-order statistics (or intermittency), at and beyond third order, due to its intimate relation to the fundamental properties of small-scale structures in which the turbulence is ultimately dissipated. Understanding the nature of these small-scale structures generated by the turbulence has profound implications in a number of practical applications, such as turbulent heating in the solar wind and cosmic-ray acceleration. In this work we present an extensive analysis of scaling-laws governing the structure of high-order statistics in steady-state strong Alfven turbulence from high-resolution numerical simulations. High Reynolds number numerical simulations with up to 2048^3 grid points are used to construct three dimensional probability distribution functions, using over one-billion samples per distribution, allowing for measurements of structure functions and scaling law exponents with unprecedented accuracy. The results are discussed in the context of recent models and simulations of anisotropy and intermittency as well as solar wind observations. We will also discuss the limits and uncertainties associated with the estimation of high-order moments from a finite-number of samples, which are unavoidable in numerical simulations.