Statistical properties of three-dimensional Hall magnetohydrodynamics turbulence

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 di, we have carried out detailed pseudospectral DNSs of the 3D HMHD equations and their counterparts for 3D MHD (di=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.

Topology of Magnetic and Velocity Fields at Kinetic Scales in Incompressible Plasma Turbulence

“…A clear correlation between these three geometric invariants is identified, with the correlation coefficients 0.962, 0.839, and 0.939, respectively. These strong spatial correlations between these two invariants are analogous to the numerical results of hydrodynamic turbulence (e.g., Blackburn et al, 1996), reduced MHD turbulence (e.g., Dallas & Alexakis, 2013), Hall MHD turbulence (e.g., Yadav et al, 2022), and plasma Particle-In-Cell turbulence (e.g., Yang et al, 2017). Moreover, the present results are compatible with previous observational studies of compressible magnetosheath turbulence (Bandyopadhyay et al, 2020).…”

“…In hydrodynamics turbulence, 𝐴𝐴 𝐴𝐴(𝑄𝑄𝐴𝐴, 𝑅𝑅𝐴𝐴) has a prominent tendency to develop a skewed teardrop shape aligning with the second and fourth quadrants (e.g., Blackburn et al, 1996;Martín et al, 1998;Meneveau, 2011), thus indicating a preference of turbulence to develop vortex stretching and sheet-like structures. This common feature has also been identified in the simulations of decaying MHD turbulence (Dallas & Alexakis, 2013) and Hall MHD turbulence (e.g., Yadav et al, 2022). Consolini et al (2015) also observed this inclined shape of 𝐴𝐴 (𝑄𝑄𝐴𝐴, 𝑅𝑅𝐴𝐴) maps above the characteristic ion scale by in one-hour measurements from the Cluster satellite.…”

Efficient kinetic Lattice Boltzmann simulation of three-dimensional Hall-MHD turbulence

“…2010; Meyrand & Galtier 2012; Ferrand et al. 2022; Yadav, Miura & Pandit 2022), which integrate of course the dynamical equations in the Fourier space. Interestingly, Mahajan & Krishan (2005) derived an analytical solution for the non-dissipative Hall-MHD equations, then extended by Xia & Yang (2015) with the inclusion of dissipative effects.…”

“…Due to their high computational cost, the availability in the literature of plasma simulations reproducing the Hall-MHD range of scales (in three dimensions) is much less than for the MHD case. Moreover, Hall-MHD simulations are in general performed using pseudo-spectral codes (Gómez et al 2010;Meyrand & Galtier 2012;Ferrand et al 2022;Yadav, Miura & Pandit 2022), which integrate of course the dynamical equations in the Fourier space. Interestingly, Mahajan & Krishan (2005) derived an analytical solution for the non-dissipative Hall-MHD equations, then extended by Xia & Yang (2015) with the inclusion of dissipative effects.…”