Mak, J, Griffiths, SD orcid.org/0000-0002-4654-2636 and Hughes, DW orcid.org/0000-0002-8004-8631 (2016) Shear flow instabilities in shallow-water magnetohydrodynamics. Journal of Fluid Mechanics, 788. pp. 767-796. ISSN 0022-1120
Abstract
Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as Høiland’s growth-rate bound and Howard’s semi-circle theorem, are extended to this shallow-water system for quite general flow and field profiles. In the limit of long-wavelength disturbances, a generalisation of the asymptotic analysis of Drazin & Howard (J. Fluid Mech., vol. 14, 1962, pp. 257–283) is performed, establishing that flows can be distinguished as either shear layers or jets. These possess contrasting instabilities, which are shown to be analogous to those of certain piecewise-constant velocity profiles (the vortex sheet and the rectangular jet). In both cases it is found that the magnetic field and stratification (as measured by the Froude number) are generally each stabilising, but weak instabilities can be found at arbitrarily large Froude number. With this distinction between shear layers and jets in mind, the results are extended numerically to finite wavenumber for two particular flows: the hyperbolic-tangent shear layer and the Bickley jet. For the shear layer, the instability mechanism is interpreted in terms of counter-propagating Rossby waves, thereby allowing an explication of the stabilising effects of the magnetic field and stratification. For the jet, the competition between even and odd modes is discussed, together with the existence at large Froude number of multiple modes of instability.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2016, CUP. This is an author produced version of a paper published in Journal of Fluid Mechanics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | instability;; magnetohydrodynamics; shallow water flows |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Jan 2016 10:21 |
Last Modified: | 15 Apr 2021 12:40 |
Published Version: | http://dx.doi.org/10.1017/jfm.2015.718 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jfm.2015.718 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94122 |