Spectral Evolution and Current Sheet Analysis as Probes of Reconnection-Mediated Decay in Magnetically Dominated Turbulence

TL;DR

This work tests a reconnection-mediated decay model for magnetically dominated MHD turbulence across 2D, 2.5D, and 3D setups with both helicity regimes. It shows that magnetic-energy decay follows a Sweet-Parker-like scaling, $\tau_{\rm decay} \propto S^{1/2}$, and that anastrophy acts as the robust conserved quantity constraining nonhelical turbulence, with spectral evolution captured by a broken power-law model linking sub-inertial and inertial ranges. The study reveals that reconnection occurs in localized current sheets whose local Lundquist numbers are substantially smaller than the global value, explaining why global decay laws are insensitive to current-sheet resolution and only converge to SP predictions at high resolution. These findings unify the dimensionality and helicity regimes under a reconnection-centric picture, with direct implications for the decay of primordial magnetic fields and their observational constraints in astrophysical and cosmological contexts.

Abstract

The decay of magnetically dominated turbulence exhibits robust inverse transfer of magnetic energy even in the absence of net magnetic helicity, challenging traditional cascade-based phenomenology. While recent studies suggest that magnetic reconnection governs the evolution of such systems, a comprehensive understanding has been lacking. Here we test a reconnection-mediated model for decaying magnetic turbulence in two-dimensional (strict-2D), 2.5D, and three-dimensional (3D) systems with both helical and nonhelical initial conditions. We show that the magnetic-energy decay timescale scales with the Lundquist number in a manner consistent with Sweet-Parker-type reconnection rather than Alfvenic or purely resistive timescales. We develop a broken power-law model for the magnetic energy spectra and provide analytic predictions for the temporal evolution of energy across both sub-inertial and inertial ranges, which are confirmed by high-resolution simulations. In nonhelical turbulence, these results favor anastrophy as the dominant constraint over helicity fluctuations. Using Minkowski functionals to analyze reconnecting current sheets in real space, we find that the structures controlling the decay are substantially smaller than the global magnetic correlation scale, implying local Lundquist numbers well below the system-scale value. This explains the weak sensitivity of global decay laws to current-sheet resolution and that the current-sheet aspect ratios converge toward Sweet-Parker predictions only at sufficiently high resolution. Together, these results establish magnetic reconnection as the organizing principle underlying inverse transfer, spectral evolution, and decay in magnetically dominated turbulence, providing a unified picture applicable across dimensionality and helicity regimes with direct implications for astrophysical plasmas.

Figures (20)

• Figure 1: Scaling of the decay time with the Lundquist number: From top to bottom, rows correspond to strict 2D , 2.5D nonhelical, and 3D nonhelical simulations. The left column shows the temporal evolution of magnetic energy; dash--dotted curves indicate fits using Eq. (\ref{['fit']}), and vertical solid lines mark the corresponding $1/C$. The middle column shows the evolution of $C_M(t)$, defined in Eq. (\ref{['cm']}), for simulations with increasing initial Lundquist numbers $S$. The right column shows the average $C_M$ as a function of the initial Lundquist number. Best-fit scalings and associated uncertainties are indicated in the legends and are consistent with SP--type reconnection.
• Figure 2: Temporal evolution of the rising (top) and decaying (bottom) spectral modes in a strict 2D $2048^2$ simulation with initial $S \simeq 1000$ and $k_p = 60$. The measured scalings are consistent with the reconnection timescale and with anastrophy conservation.
• Figure 3: Same as Fig. \ref{['fig:2D S1000 spec evol']}, but for the 2.5D nonhelical case.
• Figure 4: Same as Fig. \ref{['fig:2D S1000 spec evol']}, but for the 3D nonhelical case with initial $S\approx2300$. Run from Brandenburg_Kahniashvili_2017
• Figure 5: Same as Fig. \ref{['fig:2D S1000 spec evol']}, but for the 2.5D helical case. The measured scalings are consistent with the reconnection timescale and helicity conservation.