TITLE

# On spontaneous formation of current sheets: Untwisted magnetic fields

AUTHOR(S)
Bhattacharyya, R.; Low, B. C.; Smolarkiewicz, P. K.
PUB. DATE
November 2010
SOURCE
Physics of Plasmas;Nov2010, Vol. 17 Issue 11, p112901
SOURCE TYPE
DOC. TYPE
Article
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., 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 frozen-in 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 current-sheet formation and dissipation in the solar corona.
ACCESSION #
55509536

## Related Articles

• GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR 2-DIMENSIONAL NAVIER-STOKES EQUATIONS ON EXTERIOR DOMAINS WITH GROWING DATA AT INFINITY. CAMPITI, MICHELE; GALDI, GIOVANNI P.; HIEBER, MATTHIAS // Communications on Pure & Applied Analysis;Jul2014, Vol. 13 Issue 4, p1613

It is proved the existence of a unique, global strong solution to the two-dimensional Navier-Stokes initial-value problem in exterior domains in the case where the velocity field tends, at large spatial distance, to a prescribed velocity field that is allowed to grow linearly.

• Wang's shrinking cylinder problem with suction near a stagnation point. Lok, Y. Y.; Pop, I. // Physics of Fluids;Aug2011, Vol. 23 Issue 8, p083102

In this paper, the steady axisymmetric stagnation point flow of a viscous and incompressible fluid over a shrinking circular cylinder with mass transfer (suction) is studied. The flow is induced by a cylinder shrinking with a linear velocity distribution from the stagnation line. The fluid flow...

• Numerical investigation of flow through porous media using lattice Boltzmann method. Noorazizi, M. S.; Nor Azwadi, C. S. // AIP Conference Proceedings;6/30/2012, Vol. 1440 Issue 1, p863

This work presents a simulation of incompressible viscous flow within a two-dimensional square cavity filled with porous medium. This study aims to analyze the flow in a lid-driven cavity flow with different Reynolds number and porosity values. The Brinkmann-Forcheimer equation was coupled with...

• Dynamic response and stability of a flapping foil in a dense and viscous fluid. Chae, Eun Jung; Akcabay, Deniz Tolga; Young, Yin Lu // Physics of Fluids;Oct2013, Vol. 25 Issue 10, p104106

It is important to understand and accurately predict the static and dynamic response and stability of flexible hydro/aero lifting bodies to ensure their structural safety, to facilitate the design/optimization of new/existing concepts, and to test the feasibility of using advanced materials. The...

• A Multi-Fluid Compressible System as the Limit of Weak Solutions of the Isentropic Compressible Navier-Stokes Equations. Bresch, D.; Huang, X. // Archive for Rational Mechanics & Analysis;Aug2011, Vol. 201 Issue 2, p647

This paper mainly concerns the mathematical justification of a viscous compressible multi-fluid model linked to the Baer-Nunziato model used by engineers, see for instance I shii (Thermo-fluid dynamic theory of two-phase flow, Eyrolles, Paris, ), under a 'stratification' assumption. More...

• On the Domain Dependence of Solutions to the Compressible Navier-Stokes Equations of an Isothermal Fluid. Hlaváčová, Nikola // Acta Applicandae Mathematica;Apr2013, Vol. 124 Issue 1, p187

The aim of this paper is to study the behaviour of the variational solutions to the Navier-Stokes equations describing viscous compressible isothermal fluids with nonlinear stress tensors in a sequence of domains $\{\varOmega_{n}\} _{n=1}^{\infty}$. The sequence converges in sense of the...

• On the strong solutions of one-dimensional Navier-Stokes-Poisson equations for compressible non-Newtonian fluids. Song, Yukun; Yuan, Hongjun; Chen, Yang // Journal of Mathematical Physics;May2013, Vol. 54 Issue 5, p051502

We study the strong solutions of 1D Navier-Stokes-Poisson equations for compressible non-Newtonian fluids in bounded intervals. The model is raised from the viscous isentropic gas flow under considering an external force and the non-Newtonian gravitational force term. By using the iterative...

• Uniformly valid asymptotic flow analysis in curved channels. Zagzoule, M.; Cathalifaud, P.; Cousteix, J.; Mauss, J. // Physics of Fluids;Jan2012, Vol. 24 Issue 1, p013601

The laminar incompressible flow in a two-dimensional curved channel having at its upstream and downstream extremities two tangent straight channels is considered. A global interactive boundary layer (GIBL) model is developed using the approach of the successive complementary expansions method...

• On Plane-Parallel Separated Flows of an Incompressible Fluid near Flat Boundaries. Shmyglevskii, Yu. D.; Shcheprov, A.V. // Fluid Dynamics;Sep2002, Vol. 37 Issue 5, p674

On the basis of Stokes separated flows, examples of separated flows described by the Navier-Stokes equations of a viscous incompressible fluid are constructed. These flows are represented by series convergent in a certain non-zero neighborhood of a flat contour immersed in the flow. In this...

Share