Astoul, A orcid.org/0000-0002-8561-0769 and Barker, AJ orcid.org/0000-0003-4397-7332 (2022) The effects of nonlinearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems. Monthly Notices of the Royal Astronomical Society, 516 (2). pp. 2913-2935. ISSN 0035-8711
Abstract
In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long time-scales. Tidally forced inertial waves (restored by the Coriolis acceleration) in the convective envelopes of low-mass stars and giant gaseous planets contribute greatly to the tidal dissipation when they are excited and subsequently damped (e.g. through viscous friction), especially early in the life of a system. These waves are known to be subject to non-linear effects, including triggering differential rotation in the form of zonal flows. In this study, we use a realistic tidal body forcing to excite inertial waves through the residual action of the equilibrium tide in the momentum equation for the waves. By performing 3D non-linear hydrodynamical simulations in adiabatic and incompressible convective shells, we investigate how the addition of non-linear terms affects the tidal flow properties, and the energy and angular momentum redistribution. In particular, we identify and justify the removal of terms responsible for unphysical angular momentum evolution observed in a previous numerical study. Within our new set-up, we observe the establishment of strong cylindrically sheared zonal flows, which modify the tidal dissipation rates from prior linear theoretical predictions. We demonstrate that the effects of this differential rotation on the waves neatly explains the discrepancies between linear and non-linear dissipation rates in many of our simulations. We also highlight the major role of both corotation resonances and parametric instabilities of inertial waves, which are observed for sufficiently high tidal forcing amplitudes or low viscosities, in affecting the tidal flow response.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Authors. This is an author produced version of an article published in Monthly Notices of the Royal Astronomical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | planet-star interactions, hydrodynamics, stars: low-mass, planets and satellites: gaseous planets, waves, instabilities |
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 STFC (Science and Technology Facilities Council) ST/S000275/1 STFC (Science and Technology Facilities Council) ST/W000873/1 STFC (Science and Technology Facilities Council) ST/R00059X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 Jul 2022 12:57 |
Last Modified: | 06 Feb 2023 13:42 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stac2117 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:189449 |