On the Statistics of Elsasser Increments in Solar Wind and Magnetohydrodynamic Turbulence

TL;DR

This study compares the scale-dependent probability distributions of Elsasser increments in solar wind data and MHD simulations, revealing potentially universal scaling laws and offering new methods for high-order statistical analysis.

Contribution

It provides a comprehensive comparison of Elsasser increment PDFs from solar wind observations and MHD simulations, highlighting exponential tail behavior and proposing a novel approach for high-order statistics.

Findings

PDF tails exhibit exponential decay with scale-dependent power-law behavior

Observed and simulated PDFs show different decay exponents, indicating different turbulence regimes

Extrapolated tail behavior suggests universal high-order statistical properties

Abstract

We investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets of WIND data (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous Reduced MHD turbulence on a $2048^3$ rectangular mesh. A large statistical sample of Alfv\'enic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power-laws of the form $\alpha_l\propto l^{-\mu}$, where $l$ the scale size, with $\mu$ around 0.2 for observations and 0.4 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results points to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative methodology to investigate high-order statistics in solar wind observations.