Understanding the level of Turbulence by Asymmetric Distributions: a motivation for measurements in Space Plasmas

Abstract

In this article, on the basis of the Langevin equation applied to velocity fluctuations, we numerically model the Partial Variance of Increments, which is a useful tool to measure time and spatial correlations in space plasmas. We consider a Coupled Map Lattice model to relate the spatial scale of fluctuations, $k$, to some macro parameters of the systems, as the Reynolds number, $R_\lambda$, the $\kappa$ parameter of Kappa distributions, and a skewness parameter, $\delta$. To do so, we compute the Velocity Probability Density Function (PDF) for each spatial scale and different values of Reynolds number in the simulations. We fit the PDF with a Skew-Kappa distribution, and we obtain a numerical relationship between the level of turbulence of the plasma and the skewness of obtained distributions; namely $\langle \delta \rangle \sim R_\lambda^{-1/2}$. We expect the results exposed in this paper to be useful as a tool to characterize the turbulence in the context of space plasma and other environments.