Hillier, A, Barker, A orcid.org/0000-0003-4397-7332, Arregui, I et al. (1 more author) (2019) On Kelvin–Helmholtz and parametric instabilities driven by coronal waves. Monthly Notices of the Royal Astronomical Society, 482 (1). pp. 1143-1153. ISSN 0035-8711
Abstract
The Kelvin–Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the oscillatory shear flow associated with an MHD wave. We investigate the linear stability of a discontinuous oscillatory shear flow in the presence of a horizontal magnetic field within a Cartesian framework that captures the essential features of MHD oscillations in flux tubes. We derive a Mathieu equation for the Lagrangian displacement of the interface and analyse its properties, identifying two different instabilities: a Kelvin–Helmholtz instability and a parametric instability involving resonance between the oscillatory shear flow and two surface Alfvén waves. The latter occurs when the system is Kelvin–Helmholtz stable, thus favouring modes that vary along the flux tube, and as a consequence provides an important and additional mechanism to extract energy. When applied to flows with the characteristic properties of kink waves in the solar corona, both instabilities can grow, with the parametric instability capable of generating smaller scale disturbances along the magnetic field than possible via the Kelvin–Helmholtz instability. The characteristic time-scale for these instabilities is ∼ 100 s, for wavelengths of 200 km. The parametric instability is more likely to occur for smaller density contrasts and larger velocity shears, making its development more likely on coronal loops than on prominence threads.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | instabilities, waves, Sun: corona, Sun: filaments, prominences, Sun: magnetic fields |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number Leverhulme Trust ECF-2014-216 Science & Technology Facilities Council (STFC) ST/R00059X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Oct 2018 11:23 |
Last Modified: | 06 Jan 2019 09:18 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/sty2742 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:136851 |