Effects of magnetic–vortical interactions on magnetic splitting

We propose an analytical approach based on the Frenet–Serret (FL) frame field, where an FL frame and the corresponding curvature and torsion are defined at each point along magnetic field lines, to investigate the evolution of magnetic tubes and their interaction with vortex tubes in magnetohydrodynamics. Within this framework, simplified expressions for the Lorentz force, its curl, the dynamics of flux tubes and helicity are derived. We further perform direct numerical simulations on the linkage between the magnetic and vortex tubes and investigate the effect of the initial angle $\theta$ , ranging from $0^{\,\circ}$ to $45^{\,\circ}$ , on their evolution. Our results show that magnetic tubes with non-zero curvature generate Lorentz forces, which in turn produce dipole vortices. These dipole vortices lead to the splitting of the magnetic tubes into smaller structures, releasing magnetic energy. Both magnetic and vortex tubes exhibit quasi-Lagrangian behaviour, maintaining similar shapes during initial evolution and consistent relative positions over time. A vortex tube with strength comparable to that of the magnetic tube, where the kinetic energy induced by the vortex tube is of the same order as the magnetic energy in the magnetic tube, can inhibit magnetic tube splitting by disrupting the formation of vortex dipoles. Additionally, minor variations in the angular configuration of the vortex tubes significantly influence their interaction with the magnetic field and the evolution of large-scale flow structures.