Barker, AJ and Latter, HN (2015) On the vertical-shear instability in astrophysical discs. Monthly Notices of the Royal Astronomical Society, 450 (1). pp. 21-37. ISSN 0035-8711
Abstract
We explore the linear stability of astrophysical discs exhibiting vertical shear, which arises when there is a radial variation in the temperature or entropy. Such discs are subject to a ‘vertical-shear instability’, which recent non-linear simulations have shown to drive hydrodynamic activity in the MRI-stable regions of protoplanetary discs. We first revisit locally isothermal discs using the quasi-global reduced model derived by Nelson et al. This analysis is then extended to global axisymmetric perturbations in a cylindrical domain. We also derive and study a reduced model describing discs with power-law radial entropy profiles (‘locally polytropic discs’), which are somewhat more realistic in that they possess physical (as opposed to numerical) surfaces. The fastest growing modes have very short wavelengths and are localized at the disc surfaces (if present), where the vertical shear is maximal. An additional class of modestly growing vertically global body modes is excited, corresponding to destabilized classical inertial waves (‘r modes’). We discuss the properties of both types of modes, and stress that those that grow fastest occur on the shortest available length-scales (determined either by the numerical grid or the physical viscous length). This ill-posedness makes simulations of the instability difficult to interpret. We end with some brief speculation on the non-linear saturation and resulting angular momentum transport.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | accretion, accretion discs, hydrodynamics, instabilities, waves, planetary systems |
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 |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Apr 2017 11:55 |
Last Modified: | 23 Jun 2023 22:18 |
Published Version: | https://doi.org/10.1093/mnras/stv640 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stv640 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108972 |