Vortex-magnetic competition and regime transitions in antiparallel flux tubes

TL;DR

This work addresses how vorticity and magnetic fields coevolve in MHD turbulence under competition between inertia and Lorentz forces. Using direct numerical simulations of antiparallel vortex and magnetic flux tubes in a triply periodic domain, with the interaction parameter $N_i$ spanning from $12.8$ to $32{,}000$ and identical tube thickness, the authors recover velocity via Biot–Savart and solve the incompressible MHD equations in the Elsasser form. They identify three regimes: (i) a vortex-dominated joint reconnection at low $N_i$ with a dynamo-like transfer of kinetic to magnetic energy, (ii) an instability-triggered cascade at moderate $N_i$ featuring partial reconnection and a $k^{-5/3}$ energy spectrum, and (iii) Lorentz-induced vortex disruption at high $N_i$ that suppresses reconnection and leads to dissipative decay. A flux-transport model explains residual flux and partial reconnection, showing good agreement with DNS. The results illuminate how inertial–Lorentz balance governs energy transfer and coherent structure formation in MHD turbulence, with implications for solar and astrophysical plasmas and guidance for future studies at higher Reynolds numbers and varying magnetic Prandtl numbers.

Abstract

Vortex-magnetic interactions shape magnetohydrodynamic (MHD) turbulence, influencing energy transfer in astrophysical, geophysical, and industrial systems. On the Sun, granular-scale vortex flows couple strongly with magnetic fields, channeling energy into the corona. At high Reynolds numbers, vorticity and magnetic fields are nearly frozen into the charged fluid, and MHD flows emerge from the Lorentz force mediated interactions between coherent vortex structures in matter and the field. To probe this competition in a controlled setting, we revisit the canonical problem of two antiparallel flux tubes. By varying the magnetic flux threading each tube--and thus sweeping the interaction parameter $N_i$, which gauges Lorentz-to-inertial force balance--we uncover three distinct regimes: vortex-dominated joint reconnection, instability-triggered cascade, and Lorentz-induced vortex disruption. At low $N_i$, classical vortex dynamics dominate, driving joint vortex-magnetic reconnection and amplifying magnetic energy via a dynamo effect. At moderate $N_i$, the system oscillates between vorticity-driven attraction and magnetic damping, triggering instabilities and nonlinear interactions that spawn secondary filaments and drive an energy cascade. At high $N_i$, Lorentz forces suppress vortex interactions, aligning the tubes axially while disrupting vortex cores and rapidly converting magnetic to kinetic energy. These findings reveal how the inertial-Lorentz balance governs energy transfer and coherent structure formation in MHD turbulence, offering insight into vortex-magnetic coevolution in astrophysical plasmas.

Figures (20)

• Figure 1: Schematic illustration of vortex flows in the solar atmosphere. Vortices extend from the convection zone through the photosphere and chromosphere into the corona. Blue lines represent magnetic field lines within the vortices, and red arrows indicate the direction of fluid motion.
• Figure 2: Initial configuration of antiparallel flux tubes. (a) Initial configuration of the centerlines of flux tubes, shown in perspective, side, top, and front views (ordered from left to right, top to bottom). (b) Initial vortex or magnetic surfaces of the antiparallel flux tubes. Some attached field lines (red) are integrated from points on these surfaces.
• Figure 3: Evolution of flow structures for (a) pure vortex reconnection at $N_i=12.8$ and (b) pure magnetic splitting at $N_i \rightarrow \infty$, visualized through volume rendering of (a) vorticity magnitude $|\boldsymbol{\omega}|$ and (b) magnetic induction magnitude $|\boldsymbol{b}|$.
• Figure 4: Flux transfer in (a) pure vortex reconnection and (b) magnetic splitting. Shown is the time evolution of (a) vorticity flux and (b) magnetic flux through half of the $x = 0$ (solid lines) and $y = 0$ (dashed lines) planes, normalized by the initial flux in the $x = 0$ plane.
• Figure 5: Evolution of flow structures for vortex–magnetic joint reconnection at $\Rey=R_m=2000$ and $N_i=12.8$, visualized through volume rendering of (a) vorticity magnitude $|\boldsymbol{\omega}|$ and (b) magnetic induction magnitude $|\boldsymbol{b}|$.