Studying the properties of reconnection-driven turbulence

TL;DR

The paper investigates statistical properties of reconnection-driven turbulence within the self-driven reconnection framework using 3D resistive MHD simulations (AMUN). It finds a Kolmogorov-like velocity spectrum $E_v \propto k^{-5/3}$ and a steeper magnetic spectrum $E_b \propto k^{-8/3}$ along the current-sheet normal, with most cases showing scale-dependent anisotropy ($\ell_{\parallel} \propto \ell_{\perp}^{2/3}$) that becomes isotropic in the presence of a guide field. The turbulence is quasi-incompressible in adiabatic runs, with energy largely in the velocity solenoidal component, and velocity intermittency is stronger than magnetic intermittency. These results offer spectral and directional fingerprints for reconnection-driven turbulence and bolster the self-driven reconnection framework's applicability to astrophysical plasmas.

Abstract

Magnetic reconnection, often accompanied by turbulence interaction, is a ubiquitous phenomenon in astrophysical environments. However, the current understanding of the nature of turbulent magnetic reconnection remains insufficient. We investigate the statistical properties of reconnection turbulence in the framework of the self-driven reconnection. Using the open-source software package AMUN, we first perform numerical simulations of turbulent magnetic reconnection. We then obtain the statistical results of reconnection turbulence by traditional statistical methods such as the power spectrum and structure function. Our numerical results demonstrate: (1) the velocity spectrum of reconnection turbulence follows the classical Kolmogorov type of $E\propto k^{-5/3}$, while the magnetic field spectrum is steeper than the Kolmogorov spectrum, which are independent of limited resistivity, guide field, and isothermal or adiabatic fluid states; (2) most of the simulations show the anisotropy cascade, except that the presence of a guide field leads to an isotropic cascade; (3) reconnection turbulence is incompressible in the adiabatic state, with energy distribution dominated by the velocity solenoidal component; (4) different from pure magnetohydrodynamic (MHD) turbulence, the intermittency of the velocity field is stronger than that of the magnetic field in reconnection turbulence. The steep magnetic field spectrum, together with the velocity spectrum of Kolmogorov type, can characterize the feature of the reconnection turbulence. In the case of the presence of the guide field, the isotropy of the reconnection turbulence cascade is also different from the cascade mode of pure MHD turbulence. Our experimental results provide new insights into the properties of reconnection turbulence, which will contribute to advancing the self-driven reconnection theory.

Figures (6)

• Figure 1: 3D view of turbulent reconnection structure at $t=4t_{\rm A}$ and $20t_{\rm A}$. The solid lines represent the magnetic field lines colored with the field strength, filled in the 3D current isosurface with $|J|\ge 0.01$. This 3D view is based on SD2 listed in Table \ref{['tab:parameters']}.
• Figure 2: The mean (panel (a)) and fluctuation (panel (b)) magnetic energies, kinetic energy (panel (c)), and dissipated energy (panel (d)) as a function of the evolution time. The black solid line in panel (d) represents the internal energy growth of SD6.
• Figure 3: Spectral distributions of magnetic (left column) and velocity (right column) fields. Upper row: spectral distributions in the three axis directions at $t=20t_{\rm A}$. Lower row: spectral evolutions in the process of turbulence development, where the color bar shows the simulation time in units of Alfvén time $t_{\rm A}$. These results are based on high resolution simulations of SD1.
• Figure 4: Power spectral distributions of magnetic (panel (a)) and velocity (panel (b)) fields normalized in their mean power at $t=20t_{\rm A}$ for all models SD1 to SD6 listed in Table \ref{['tab:parameters']} .
• Figure 5: Distributions of magnetic and kinetic energies compare with distributions of internal energies (panel (a)), as well as the solenoidal and compressive components of kinetic energies (panel (b)). Simulations are from the adiabatic state (SD6 listed in Table \ref{['tab:parameters']}) at $t=20t_{\rm A}$.