Duguid, CD orcid.org/0000-0003-1199-3469, Barker, AJ orcid.org/0000-0003-4397-7332 and Jones, CA orcid.org/0000-0002-1105-3920 (2020) Tidal flows with convection: frequency dependence of the effective viscosity and evidence for antidissipation. Monthly Notices of the Royal Astronomical Society, 491 (1). pp. 923-943. ISSN 0035-8711
Abstract
Tidal interactions are important in driving spin and orbital evolution in planetary and stellar binary systems, but the fluid dynamical mechanisms responsible remain incompletely understood. One key mechanism is the interaction between tidal flows and convection. Turbulent convection is thought to act as an effective viscosity in damping large-scale tidal flows, but there is a long-standing controversy over the efficiency of this mechanism when the tidal frequency exceeds the turnover frequency of the dominant convective eddies. This high frequency regime is relevant for many applications, such as for tides in stars hosting hot Jupiters. We explore the interaction between tidal flows and convection using hydrodynamical simulations within a local Cartesian model of a small patch of a convection zone of a star or planet. We adopt the Boussinesq approximation and simulate Rayleigh-Bénard convection, modelling the tidal flow as a background oscillatory shear flow. We demonstrate that the effective viscosity of both laminar and turbulent convection is approximately frequency-independent for low frequencies. When the forcing frequency exceeds the dominant convective frequency, the effective viscosity scales inversely with the square of the tidal frequency. We also show that negative effective viscosities are possible, particularly for high frequency tidal forcing, suggesting the surprising possibility of tidal anti-dissipation. These results are supported by a complementary high-frequency asymptotic analysis that extends prior work by Ogilvie & Lesur. We discuss the implications of these results for interpreting the orbital decay of hot Jupiters, and for several other astrophysical problems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Authors. This is an author produced version of a paper accepted for publication in Monthly Notices of the Royal Astronomical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | hydrodynamics; convection; binaries: close; planet-star interactions; 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 Computing (Leeds) 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: | 14 Oct 2019 09:35 |
Last Modified: | 03 Feb 2020 05:27 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/mnras/stz2899 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:152070 |