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:   Bhattacharyya, R. , NCAR Earth System Laboratory (NESL), Atmospheric Chemistry Division (ACD)
 Low, B.C. , High Altitude Observatory (HAO)
 Smolarkiewicz, P. , NCAR Earth System Laboratory (NESL), Mesoscale and Microscale Meteorology Division (MMM)


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 Navierâ€“Stokes equations. Numerical solutions to two initial value problems are presented for a threedimensional, periodic, untwisted magnetic field evolving, with no change in magnetic topology under the frozenin 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 minimumenergy, static equilibrium. The solutions demonstrate that, as a consequence of the frozenin 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 frozenin 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 generalpurpose highresolution (viz., nonoscillatory) hydrodynamical simulation code EULAG [ J. M. Prusa et al., , Comput. Fluids 37, 1193 (2008) ]. Incompressibility imposes the additional global constraint that the flux surfaces must evolve with no change in the spatial volumes they enclose. In this approach, current sheet formation is demonstrated graphically by the progressive pressing together of suitably selected flux surfaces until their separation has diminished below the minimal resolved distance on a fixed grid. The frozenin condition then fails in the simulation as the field reconnects through an effecting numerical resistivity. The principal results are related to the Parker theory of currentsheet formation and dissipation in the solar corona. View More 

Keywords:  Electrohydrodynamics, Flow simulation, Laminar flow, Magnetohydrodynamics, NavierStokes equations, Numerical analysis, Viscosity 

Classification:  Refereed 

Resource Type:  Article 

Date Published  November 01, 2010 

Relations:  

Published Version:  10.1063/1.3496379 

Copyright Notice:  Copyright 2010 American Institute of Physics. 

Citable URL:  http://nldr.library.ucar.edu/repository/collections/OSGC000000001433 
