Braginskii magnetohydrodynamics for arbitrary magnetic topologies: coronal applications

MacTaggart, D. , Vergori, L. and Quinn, J. (2017) Braginskii magnetohydrodynamics for arbitrary magnetic topologies: coronal applications. Journal of Fluid Mechanics, 826, pp. 615-635. (doi:10.1017/jfm.2017.463)

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Abstract

We investigate single-fluid magnetohydrodynamics (MHD) with anisotropic viscosity, often referred to as Braginskii MHD, with a particular eye to solar coronal applications. First, we examine the full Braginskii viscous tensor in the single-fluid limit. We pay particular attention to how the Braginskii tensor behaves as the magnetic field strength vanishes. The solar corona contains a magnetic field with a complex and evolving topology, so the viscosity must revert to its isotropic form when the field strength is zero, e.g. at null points. We highlight that the standard form in which the Braginskii tensor is written is not suitable for inclusion in simulations as singularities in the individual terms can develop. Instead, an altered form, where the parallel and perpendicular tensors are combined, provides the required asymptotic behaviour in the weak-field limit. We implement this combined form of the tensor into the Lare3D code, which is widely used for coronal simulations. Since our main focus is the viscous heating of the solar corona, we drop the drift terms of the Braginskii tensor. In a stressed null point simulation, we discover that small-scale structures, which develop very close to the null, lead to anisotropic viscous heating at the null itself (that is, heating due to the anisotropic terms in the viscosity tensor). The null point simulation we present has a much higher resolution than many other simulations containing null points so this excess heating is a practical concern in coronal simulations. To remedy this unwanted heating at the null point, we develop a model for the viscosity tensor that captures the most important physics of viscosity in the corona: parallel viscosity for strong field and isotropic viscosity at null points. We derive a continuum model of viscosity where momentum transport, described by this viscosity model, has the magnetic field as its preferred orientation. When the field strength is zero, there is no preferred direction for momentum transport and viscosity reverts to the standard isotropic form. The most general viscous stress tensor of a (single-fluid) plasma satisfying these conditions is found. It is shown that the Braginskii model, without the drift terms, is a specialization of the general model. Performing the stressed null point simulation with this simplified model of viscosity reveals very similar heating profiles compared to the full Braginskii model. The new model, however, does not produce anisotropic heating at the null point, as required. Since the vast majority of coronal simulations use only isotropic viscosity, we perform the stressed null point simulation with isotropic viscosity and compare the heating profiles to those of the anisotropic models. It is shown than the fully isotropic viscosity can over-estimate the viscous heating by an order of magnitude.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Quinn, Mr Jamie and Mactaggart, Dr David and Vergori, Dr Luigi
Authors: MacTaggart, D., Vergori, L., and Quinn, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Fluid Mechanics
Publisher:Cambridge University Press
ISSN:0022-1120
ISSN (Online):1469-7645
Published Online:09 August 2017
Copyright Holders:Copyright © 2017 Cambridge University Press
First Published:First published in Journal of Fluid Mechanics 826:615-635
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
716211The evolution of magnetic helicity in the dynamic solar atmosphereDavid MactaggartThe Carnegie Trust for the Universities of Scotland (CARNEGTR)70323M&S - MATHEMATICS