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Tidal flows with convection: frequency dependence of the effective viscosity and evidence for antidissipation

Lookup NU author(s): Dr Craig Duguid

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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 antidissipation. 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.

Publication metadata

Author(s): Duguid CD, Barker AJ, Jones CA

Publication type: Article

Publication status: Published

Journal: Monthly Notices of the Royal Astronomical Society

Year: 2020

Volume: 491

Issue: 1

Pages: 923–943

Print publication date: 01/01/2020

Online publication date: 23/10/2019

Acceptance date: 11/10/2019

ISSN (print): 0035-8711

ISSN (electronic): 1365-2966

Publisher: Oxford University Press

URL: https://doi.org/10.1093/mnras/stz2899

DOI: 10.1093/mnras/stz2899

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