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Elasticity of tangled magnetic fields

Published online by Cambridge University Press:  15 October 2020

D. N. Hosking*
Affiliation:
Oxford Astrophysics, Denys Wilkinson Building, Keble Road, OxfordOX1 3RH, UK Merton College, Merton Street, OxfordOX1 4JD, UK
A. A. Schekochihin
Affiliation:
Merton College, Merton Street, OxfordOX1 4JD, UK Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, OxfordOX1 3PU, UK
S. A. Balbus
Affiliation:
Oxford Astrophysics, Denys Wilkinson Building, Keble Road, OxfordOX1 3RH, UK New College, Holywell Street, OxfordOX1 3BN, UK
*
Email address for correspondence: david.hosking@physics.ox.ac.uk

Abstract

The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of ‘magnetoelastic waves’, the isotropic analogue of Alfvén waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.

Type
Research Article
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

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