Quasi-two-dimensionality of three-dimensional, magnetically dominated, decaying turbulence

Abstract: Decaying magnetohydrodynamic (MHD) turbulence is important in various astrophysical contexts, including early universe magnetic fields, star formation, turbulence in galaxy clusters, magnetospheres and solar corona. Previously known in the nonhelical case of magnetically dominated decaying turbulence, we show that magnetic reconnection is important also in the fully helical case and is likely the agent responsible for the inverse transfer of energy. Again, in the fully helical case, we find that there is a similarity in power law decay exponents in both 2.5D and 3D simulations. To understand this intriguing similarity, we investigate the possible quasi-two-dimensionalization of the 3D system. We perform Minkowski functional analysis and find that the characteristic length scales of a typical magnetic structure in the system are widely different, suggesting the existence of local anisotropies. Finally, we provide a quasi-two-dimensional hierarchical merger model which recovers the relevant power law scalings. In the nonhelical case, we show that a helicity-based invariant cannot constrain the system, and the best candidate is still anastrophy or vector potential squared, which is consistent with the quasi-two-dimensionalization of the system.

• The paper demonstrates that magnetic reconnection drives inverse energy transfer in decaying MHD turbulence by collapsing evolution curves across different Lundquist numbers.
• It uses both helical and nonhelical simulations to show that quasi-two-dimensional scaling laws can effectively describe turbulent behavior when local anisotropies are present.
• The authors introduce a hierarchical merger model that leverages mass and helicity conservation to provide a novel framework for interpreting energy decay in astrophysical plasmas.

Quasi-Two-Dimensionality of Three-Dimensional, Magnetically Dominated, Decaying Turbulence

This paper focuses on the study of decaying magnetohydrodynamic (MHD) turbulence, a phenomenon with significant implications for various astrophysical and space plasma contexts. The authors explore the inverse transfer of energy in cases of helical and nonhelical three-dimensional turbulence and the role of magnetic reconnection in these processes. They propose a hierarchical quasi-two-dimensional model to understand the similarities between two-dimensional (2D) and three-dimensional (3D) cases.

The paper examines both helical and nonhelical cases to illustrate how magnetic reconnection is vital to the dynamics of these systems. It confirms that in magnetically dominated decaying turbulence, magnetic reconnection drives the turbulence and contributes to the inverse energy transfer process. This is evidenced by the collapse of evolution curves across different Lundquist numbers when using the reconnection timescale, indicating the reconnection timescale as the relevant dynamical timescale rather than the Alfvén timescale conventionally considered in MHD. This commonality across helical and nonhelical cases suggests that the 2D scaling laws effectively describe 3D turbulence, provided that the system exhibits quasi-two-dimensional behavior due to local anisotropies.

For the helical case, the authors demonstrate that magnetic helicity is a significant conserved quantity that constrains the system's evolution, leading to the observed power-law decay exponents in both 2.5D and 3D simulations. These simulations depict scaling laws consistent with the expectation of magnetic helicity conservation. The study introduces the Saffman helicity invariant but finds it less relevant than anastrophy in explaining the scaling laws.

In the nonhelical scenario, the authors challenge existing assertions about the conservation of the Saffman helicity invariant in constraining the decay of nonhelical turbulence. They propose that vector potential squared (anastrophy) is a more appropriate invariant that effectively constrains the decay process. This insight builds on previous studies showing a tendency for 3D nonhelical turbulence to mirror 2D behaviors, despite the absence of magnetic helicity.

The research underscores the significance of numerical simulations with high Lundquist numbers, which reveal the system's inverse transfer process more accurately. With regards to local anisotropy, the authors utilize Minkowski functional analysis to quantify the magnetic field structures, indicating that these fields exhibit prominent local anisotropy, consistent with quasi-two-dimensional behavior. This anisotropy is manifest as prolate spheroids, reflecting local magnetic structure anisotropies.

The authors introduce a quasi-2D hierarchical merger model (Q2DHM) that leverages the principles of mass conservation and either flux or helicity conservation. This model accounts for an inverse transfer of magnetic energy by considering mergers of magnetic structures in discrete stages, maintaining mass and a relevant magnetic flux or helicity.

In conclusion, the paper offers a detailed study of the mechanisms underpinning the inverse energy transfer in decaying MHD turbulence, providing a novel perspective on the observed power-law similarity between 2D and 3D systems. This research contributes to a deeper theoretical understanding of the dynamics in astrophysical plasma turbulence and aids in generalizing approaches to the study of turbulence in magnetized environments. Future developments could involve resolving high Lundquist number simulations, allowing more precise probing of reconnection physics and further refining the understanding of quasi-two-dimensional dynamics in turbulent systems.