Barker, AJ (2016) Non-linear tides in a homogeneous rotating planet or star: global simulations of the elliptical instability. Monthly Notices of the Royal Astronomical Society, 459 (1). pp. 939-956. ISSN 0035-8711
Abstract
I present results from the first global hydrodynamical simulations of the elliptical instability in a tidally deformed gaseous planet (or star) with a free surface. The elliptical instability is potentially important for tidal evolution of the shortest-period hot Jupiters. I model the planet as a spin–orbit aligned or anti-aligned, and non-synchronously rotating, tidally deformed, homogeneous fluid body. A companion paper presented an analysis of the global modes and instabilities of such a planet. Here I focus on the non-linear evolution of the elliptical instability. This is observed to produce bursts of turbulence that drive the planet towards synchronism with its orbit in an erratic manner. If the planetary spin is initially anti-aligned, the elliptical instability also drives spin–orbit alignment on a similar time-scale as the spin synchronization. The instability generates differential rotation inside the planet in the form of zonal flows, which play an important role in the saturation of the instability, and in producing the observed burstiness. These results are broadly consistent with the picture obtained using a local Cartesian model (where columnar vortices played the role of zonal flows). I also simulate the instability in a container that is rigid (but stress-free) rather than free, finding broad quantitative agreement. The dissipation resulting from the elliptical instability could explain why the shortest-period hot Jupiters tend to have circular orbits inside about 2–3 d, and predicts spin synchronization (and spin–orbit alignment) out to about 10–15 d. However, other mechanisms must be invoked to explain tidal circularization for longer orbital periods.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2016 The Author. 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 (2016) Non-linear tides in a homogeneous rotating planet or star: global simulations of the elliptical instability. Monthly Notices of the Royal Astronomical Society, 459 (1). pp. 939-956. is available online at: https://doi.org/10.1093/mnras/stw702 |
Keywords: | hydrodynamics; instabilities; waves; binaries: close; planetary systems; stars: rotation |
Dates: |
|
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 11:52 |
Last Modified: | 17 Jan 2018 13:34 |
Published Version: | https://doi.org/10.1093/mnras/stw702 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stw702 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108969 |