Skip to content

On spontaneous formation of current sheets: Untwisted magnetic fields


Citation:Bhattacharyya, R., B.C. Low, and P. Smolarkiewicz, 2010: On spontaneous formation of current sheets: Untwisted magnetic fields. Physics of Plasmas, 17, 17 pp, DOI: 10.1063/1.3496379.
UCAR/NCAR/UCP Authors:
UCAR Affiliations: Atmospheric Chemistry Division (ACD), High Altitude Observatory (HAO), Mesoscale and Microscale Meteorology Division (MMM), NCAR Earth System Laboratory (NESL)
Abstract:This is a study of the spontaneous formation of electric current sheets in an incompressible viscous fluid with perfect electrical conductivity, governed by the magnetohydrodynamic Navier–Stokes equations. Numerical solutions to two initial value problems are presented for a three-dimensional, periodic, untwisted magnetic field evolving, with no change in magnetic topology under the frozen-in condition and at characteristic fluid Reynolds numbers of the order of 500, from a nonequilibrium initial state with the fluid at rest. The evolution converts magnetic free energy into kinetic energy to be all dissipated away by viscosity so that the field settles into a minimum-energy, static equilibrium. The solutions demonstrate that, as a consequence of the frozen-in condition, current sheets must form during the evolution despite the geometric simplicity of the prescribed initial fields. In addition to the current sheets associated with magnetic neutral points and field reversal layers, other sheets not associated with such magnetic features are also in evidence. These current sheets form on magnetic flux surfaces. This property is used to achieve a high degree of the frozen-in condition in the simulations, by describing the magnetic field entirely in terms of the advection of its flux surfaces and integrating the resulting governing equations with a customized version of a general-purpose high-resolution (viz., nonoscillatory) hydrodynamical simulation code EULAG [ J. M. Prusa et al. View More
Keywords:Electrohydrodynamics, Flow simulation, Laminar flow, Magnetohydrodynamics, Navier-Stokes equations, Numerical analysis, Viscosity
Classification:Refereed
Resource Type:Article
Date Published
Relations:
Published Version:10.1063/1.3496379
Copyright Notice:Copyright 2010 American Institute of Physics.
Citable URL: