Barker, AJ orcid.org/0000-0003-4397-7332, Jones, CA and Tobias, SM (2019) Angular momentum transport by the GSF instability: non-linear simulations at the equator. Monthly Notices of the Royal Astronomical Society, 487 (2). pp. 1777-1794. ISSN 0035-8711
Abstract
We present an investigation into the non-linear evolution of the Goldreich–Schubert–Fricke (GSF) instability using axisymmetric and 3D simulations near the equator of a differentially rotating radiation zone. This instability may provide an important contribution to angular momentum transport in stars and planets. We adopt a local Boussinesq Cartesian shearing box model, which represents a small patch of a differentially rotating stellar radiation zone. Complementary simulations are also performed with stress-free, impenetrable boundaries in the local radial direction. The linear and non-linear evolution of the equatorial axisymmetric instability is formally equivalent to the salt fingering instability. This is no longer the case in 3D, but we find that the instability behaves non-linearly in a similar way to salt fingering. Axisymmetric simulations – and those in 3D with short dimensions along the local azimuthal direction – quickly develop strong jets along the rotation axis, which inhibit the instability and lead to predator-prey-like temporal dynamics. In 3D, the instability initially produces homogeneous turbulence and enhanced momentum transport, though in some cases jets form on a much longer time-scale. We propose and validate numerically a simple theory for non-linear saturation of the GSF instability and its resulting angular momentum transport. This theory is straightforward to implement in stellar evolution codes incorporating rotation. We estimate that the GSF instability could contribute towards explaining the missing angular momentum transport required in red giant stars, and play a role in the long-term evolution of the solar tachocline.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society. ©: 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. |
Keywords: | hydrodynamics; instabilities; waves; Sun: rotation; stars: rotation |
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 Science & Technology Facilities Council (STFC) ST/S000275/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 May 2019 13:07 |
Last Modified: | 27 Jun 2019 15:18 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stz1386 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:146375 |