Barker, AJ, Braviner, HJ and Ogilvie, GI (2016) Non-linear tides in a homogeneous rotating planet or star: global modes and elliptical instability. Monthly Notices of the Royal Astronomical Society, 459 (1). pp. 924-938. ISSN 0035-8711
Abstract
We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders ℓ ≤ 5, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when nΩ ≲−1 nΩ≲−1 , where n and Ω are the orbital and spin angular frequencies, respectively) if the tidal amplitude is sufficiently large. We also explore the instability in a rigid ellipsoidal container, which is found to be quantitatively similar to that with a realistic free surface. Finally, we study the effect of rotation and tidal deformation on mode frequencies. We find that larger rotation rates and larger tidal deformations both decrease the frequencies of the prograde sectoral surface gravity modes. This increases the prospect of their tidal excitation, potentially enhancing the tidal response over expectations from linear theory. In a companion paper, we use our results to interpret global simulations of the elliptical instability.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The version of record Barker, AJ, Braviner, HJ and Ogilvie, GI (2016) Non-linear tides in a homogeneous rotating planet or star: global modes and elliptical instability. Monthly Notices of the Royal Astronomical Society, 459 (1). pp. 924-938 is available online at: https://doi.org/10.1093/mnras/stw701 |
Keywords: | hydrodynamics; instabilities; waves; binaries: close; planetary systems; 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 |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Dec 2016 12:06 |
Last Modified: | 16 Jan 2018 04:11 |
Published Version: | https://doi.org/10.1093/mnras/stw701 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stw701 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108970 |