Formation of magnetic discontinuities through viscous relaxation

Abstract

According to Parker's magnetostatic theorem, tangential discontinuities in magnetic field, or current sheets (CSs), are generally unavoidable in an equilibrium magnetofluid with infinite electrical conductivity and complex magnetic topology. These CSs are due to a failure of a magnetic field in achieving force-balance everywhere and preserving its topology while remaining in a spatially continuous state. A recent work [Kumar, Bhattacharyya, and Smolarkiewicz, Phys. Plasmas 20, 112903 (2013)] demonstrated this CS formation utilizing numerical simulations in terms of the vector magnetic field. The magnetohydrodynamic simulations presented here complement the above work by demonstrating CS formation by employing a novel approach of describing the magnetofluid evolution in terms of magnetic flux surfaces instead of the vector magnetic field. The magnetic flux surfaces being the possible sites on which CSs develop, this approach provides a direct visualization of the CS formation, helpful in understanding the governing dynamics. The simulations confirm development of tangential discontinuities through a favorable contortion of magnetic flux surfaces, as the magnetofluid undergoes a topologypreserving viscous relaxation from an initial non-equilibrium state with twisted magnetic field. A crucial finding of this work is in its demonstration of CS formation at spatial locations away from the magnetic nulls. V C 2014 AIP Publishing LLC. [http://dx.

On the Role of Repetitive Magnetic Reconnections in Evolution of Magnetic Flux Ropes in Solar Corona

“…As demonstrated by recent numerical simulations (Kumar et al 2014(Kumar et al , 2015b, such coevolution spontaneously develop current sheets (CSs); i.e., two dimensional surfaces of intense volume current density across which the MFLs flip sign. These simulations attribute the appearance of CSs to favorable contortions of MFSs, generic to the high-S magnetofluids dynamics.…”

“…The terminal state is then expected to be static where the pressure gradient is balanced by the Lorentz force as MFLs cannot get diffused because of the flux-freezing. In simulations however, only a quasi-steady state is achieved, maintained by a partial balance of Lorentz force, pressure gradient and viscous drag; details of the energetics can be found in (Bhattacharyya et al 2010;Kumar et al 2014Kumar et al , 2015a.…”

“…These two requirements are achieved through the following numerical scheme. Viscous relaxation (Bhattacharyya et al 2010;Kumar et al 2014Kumar et al , 2015a of a thermally homogeneous, incompressible magnetofluid with infinite electrical conductivity is employed to evolve the fluid under the flux-freezing till CSs develop. To focus on the idea, the relevant Navier-Stokes MHD equations are…”

Simulated evolution of three-dimensional magnetic nulls leading to generation of cylindrically-shaped current sheets

“…Notably, the surfaces are elongated along z and are situated away from the 3D nulls, indicating the development of the elongated CSs away from the nulls. Such development of CSs can be because of favorable contortions of contributing magnetic flux surfaces 14,15 .…”

“…Importantly, B 2 is known to have 3D nulls 14 . With B 1 lacking any nulls, B is expected to has the identical skeletal topology as B 2 and additionally, a non-zero Lorentz force.…”