Statistical Properties of three-dimensional Hall Magnetohydrodynamics Turbulence

TL;DR

This study conducts detailed numerical simulations to analyze the statistical properties of three-dimensional Hall magnetohydrodynamics (HMHD) turbulence, comparing it with standard MHD to understand the effects of the ion-inertial scale and Reynolds number.

Contribution

It provides comprehensive statistical analysis of 3D HMHD turbulence through high-resolution DNS, exploring its dependence on key physical parameters and comparing it with 3D MHD turbulence.

Findings

Differences in energy spectra between HMHD and MHD turbulence.

Distinct intermittency measures in HMHD versus MHD.

Variation of energy dissipation rates with Reynolds number and ion-inertial scale.

Abstract

The three-dimensional (3D) Hall magnetohydrodynamics (HMHD) equations are often used to study turbulence in the solar wind. Some earlier studies have investigated the statistical properties of 3D HMHD turbulence by using simple shell models or pseudospectral direct numerical simulations (DNSs) of the 3D HMHD equations; these DNSs have been restricted to modest spatial resolutions and have covered a limited parameter range. To explore the dependence of 3D HMHD turbulence on the Reynolds number $Re$ and the ion-inertial scale $d_{i}$, we have carried out detailed pseudospectral DNSs of the 3D HMHD equations and their counterparts for 3D MHD ($d_{i} = 0$). We present several statistical properties of 3D HMHD turbulence, which we compare with 3D MHD turbulence by calculating (a) the temporal evolution of the energy-dissipation rates and the energy, (b) the wave-number dependence of fluid and magnetic spectra, (c) the probability distribution functions (PDFs) of the cosines of the angles between various pairs of vectors, such as the velocity and the magnetic field, and (d) various measures of the intermittency in 3D HMHD and 3D MHD turbulence.