Properties of current sheets in two-dimensional tearing-mediated magnetohydrodynamic turbulence

TL;DR

This work analyzes current sheets in a high-resolution 2D tearing-mediated MHD turbulence simulation, focusing on their geometry, dynamics, and relation to scale-dependent dynamic alignment (SDDA). By automating current-sheet identification and applying PCA-based geometry, the authors find that sheet aspect ratios follow a Sweet-Parker-like scaling $a/L\sim S_L^{-1/2}$, while the length–thickness relation shows strong correlations with Sweet-Parker or ideal-tearing expectations rather than SDDA predictions. Although SDDA signatures appear in alignment statistics, there is no direct causal link between current-sheet geometry and SDDA, suggesting that SDDA-based models may need revision to accurately capture reconnection-dominated dissipation in turbulence. These findings have implications for interpreting dissipation processes in solar wind turbulence and for developing reconnection-focused theories of MHD turbulence.

Abstract

It is well known that the nonlinear evolution of magnetohydrodynamic (MHD) turbulence generates intermittent current sheets. In the solar wind turbulence, current sheets are frequently observed and they are believed to be an important pathway for the turbulence energy to dissipate and heat the plasma. In this study, we perform a comprehensive analysis of current sheets in a high-resolution two-dimensional simulation of balanced, incompressible MHD turbulence. The simulation parameters are selected such that tearing mode instability is triggered and plasmoids are generated throughout the simulation domain. We develop an automated method to identify current sheets and accurately quantify their key parameters including thickness ($a$), length ($L$), and Lundquist number ($S$). Before the triggering of tearing instability, the current sheet lengths are mostly comparable to the energy injection scale. After the tearing mode onsets, smaller current sheets with lower Lundquist numbers are generated. We find that the aspect ratio ($a/L$) of the current sheets scales approximately as $S^{-1/2}$, i.e. the Sweet-Parker scaling. While a power-law scaling between $L$ and $a$ is observed, no clear correlation is found between the upstream magnetic field strength and thickness $a$. Finally, although the turbulence energy shows anisotropy between the directions parallel and perpendicular to the local magnetic field increment, we do not observe a direct correspondence between the shape of the current sheets and that of the turbulence "eddies." These results suggest that one needs to be cautious when applying the scale-dependent dynamic alignment model to the analysis of current sheets in MHD turbulence.

Figures (11)

• Figure 1: Time evolution of (a) $\sigma_c$ (blue) and $\sigma_r$ (orange); (b) kinetic energy (blue), magnetic energy (orange), and energies of $\bm{z^+}$ (green) and $\bm{z^-}$ (red); (c) averaged $J^2$ (blue), $\omega^2$ (orange), and $2 \bm{J} \cdot \bm{\omega}$ (green).
• Figure 2: Power spectra of (a) magnetic field, (b) velocity, (c) $\bm{z^+}$, and (d) $\bm{z^-}$ calculated along $x$. In each panel, different solid curves correspond to spectra at different time moments. Blue dotted-dashed lines are linear-fitting of the spectra at $t=0.6$ using $\frac{1}{128}\leq k \leq \frac{1}{16}$. The black dashed lines show $\propto k^{-5/3}$ for reference. The yellow shade in each panel marks $\frac{1}{16} \leq k \leq \frac{1}{8}$ that correspond to the initial fluctuations.
• Figure 3: Evolution of $J_z$ in the subdomain $x \in [0.2,0.7]$, $y\in [0,0.5]$. In Panel (c), the green box marks the current sheet analyzed in detail in Section \ref{['sec:results_case']} and Figure \ref{['fig:evolution_single_CS']}.
• Figure 4: Scale-dependent Kurtosis of magnetic field at different time moments. The yellow shade marks the wavelength-range of the initial fluctuations.
• Figure 5: (a) Same as Panel (c) of Figure \ref{['fig:evolution_Jz_2D']} with identified current sheets marked by yellow ($J_z>0$) and green ($J_z<0$). (b) Probability distribution function (PDF) of $J_z$ at $t=0.3$. Blue bars are all the data points and orange bars are data points with identified current sheets removed. (c) Time evolution of filling factor (blue), i.e. area of current sheets divided by the total area of the domain, and number of current sheets (orange). (d) $\int J_z^2$ inside the current sheets over $\int J_z^2$ throughout the simulation domain.