Turbulent Viscosity Acting on the Equilibrium Tidal Flow in Convective Stars

Vidal, Jérémie; Barker, Adrian J.

doi:10.3847/2041-8213/ab6219

Cited by 36 publications

(36 citation statements)

References 55 publications

(95 reference statements)

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“…The two laws were first recovered in separate studies, which support either the linear scaling (Penev et al 2007(Penev et al , 2009 or the quadratic suppression (Ogilvie & Lesur 2012;Braviner 2016;Duguid et al 2020). The coexistence of the two scaling laws has however been found subsequently, using an idealized turbulence model (Goldman 2008) and in our previous global DNS (Vidal & Barker 2020). These recent results have the potential to reconcile the previous theoretical and numerical findings.…”

Section: Introductionsupporting

confidence: 62%

“…Moreover, the recent numerical findings have shed light on the fact that the two scaling laws may be appropriate for different reasons than those originally suggested. On the one hand, the quadratic suppression has been convincingly found for high frequencies |ω t | ω cv , particularly those outside the turbulent cascade (Ogilvie & Lesur 2012;Braviner 2016;Duguid et al 2020;Vidal & Barker 2020). On the other hand, the linear reduction, which has been only observed in an intermediate-frequency range (with |ω t | ∼ ω cv ), may be correlated with the frequency spectrum of the (unperturbed) convection.…”

Section: Introductionmentioning

confidence: 84%

“…On the other hand, the linear reduction, which has been only observed in an intermediate-frequency range (with |ω t | ∼ ω cv ), may be correlated with the frequency spectrum of the (unperturbed) convection. Indeed, the convective frequency spectrum is expected to be flatter than the Kolmogorov frequency spectrum in that range, as reported for Boussinesq (Vidal & Barker 2020) or compressible (e.g. Penev et al 2011;Horst et al 2020) convection, such that predictions (1)-(2) may not be generic.…”

Section: Introductionmentioning

confidence: 84%

“…We employ dimensionless quantities for the simulations, adopting R as the length scale, the viscous time-scale R 2 /ν as the timescale, and (νQ T R 2 )/(6κ 2 ) as the unit of temperature (as in Vidal & Barker 2020). The dimensionless Boussinesq equations for the fluctuations [u, Θ] in the rotating frame are ∂ u ∂t…”

Section: Convection Modelmentioning

confidence: 99%

“…Owing to the importance of this problem to understand tidal evolution, we continue our numerical investigation (Vidal & Barker 2020) using global DNS of convection in the presence of the equilibrium tidal flow to gain robust physical insights into the efficiency of tidal dissipation in slowly rotating convective stars or planets. Our global model complements the previous local studies in Cartesian geometry (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Vidal

Barker

2020

Monthly Notices of the Royal Astronomical Society

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Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency |ωt| exceeds the turnover frequency ωcv of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equilibrium tidal flow, to measure the effective viscosity νE acting on the tidal flow when |ωt|/ωcv ≳ 1. We demonstrate that the frequency reduction of νE is correlated with the frequency spectrum of the (unperturbed) convection. For intermediate frequencies below those in the turbulent cascade (|ωt|/ωcv ∼ 1 − 5), the frequency spectrum displays an anomalous 1/ωα power law that is responsible for the frequency-reduction νE∝1/|ωt|α, where α < 1 depends on the model parameters. We then get |νE|∝1/|ωt|δ with δ > 1 for higher frequencies, and δ = 2 is obtained for a Kolmogorov turbulent cascade. A generic |νE|∝1/|ωt|2 suppression is next found for higher frequencies within the dissipation range of the convection (but with negative values). Our results indicate that a better knowledge of the frequency spectrum of convection is necessary to accurately predict the efficiency of tidal dissipation in stars and planets resulting from this mechanism.

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Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 84%

Section: Convection Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Vidal

Barker

2020

Monthly Notices of the Royal Astronomical Society

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Tidal Dissipation in Giant Planets

Fuller,

Guillot,

Mathis

et al. 2024

Space Sci Rev

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Tidal interactions between moons and planets can have major effects on the orbits, spins, and thermal evolution of the moons. In the Saturn system, tidal dissipation in the planet transfers angular momentum from Saturn to the moons, causing them to migrate outwards. The rate of migration is determined by the mechanism of dissipation within the planet, which is closely tied to the planet’s uncertain structure. We review current knowledge of giant planet internal structure and evolution, which has improved thanks to data from the Juno and Cassini missions. We discuss general principles of tidal dissipation, describing both equilibrium and dynamical tides, and how dissipation can occur in a solid core or a fluid envelope. Finally, we discuss the possibility of resonance locking, whereby a moon can lock into resonance with a planetary oscillation mode, producing enhanced tidal migration relative to classical theories, and possibly explaining recent measurements of moon migration rates.

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How tidal waves interact with convective vortices in rapidly rotating planets and stars

Dandoy¹,

Park²,

Augustson³

et al. 2023

A&A

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Context. The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star-planet and planet-moon systems. This dissipation is particularly efficient for young low-mass stars and gaseous giant planets, which are rapid rotators. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is commonly modeled as an effective eddy viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of the tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices such as those observed at the poles of Jupiter and Saturn. The large-scale vortices are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. Aims. We investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. Methods. We used a quasi-geostrophic semi-analytical model of a convective columnar vortex, which is validated by numerical simulations. First, we carried out linear stability analysis using both numerical and asymptotic Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) methods. We then conducted linear numerical simulations of the interactions between a convective columnar vortex and an incoming tidal inertial wave.Results. The vortex we consider is found to be centrifugally stable in the range −Ω p ≤ Ω 0 ≤ 3.62Ω p and unstable outside this range, where Ω 0 is the local rotation rate of the vortex at its center and Ω p is the global planetary (stellar) rotation rate. From the linear stability analysis, we find that this vortex is prone to centrifugal instability with perturbations with azimuthal wavenumbers m = {0, 1, 2}, which potentially correspond to eccentricity, obliquity, and asynchronous tides, respectively. The modes with m > 2 are found to be neutral or stable. The WKBJ analysis provides analytic expressions of the dispersion relations for neutral and unstable modes when the axial (vertical) wavenumber is sufficiently large. We verify that in the unstable regime, an incoming tidal inertial wave triggers the growth of the most unstable mode of the vortex. This would lead to turbulent dissipation. For stable convective columns, the wave-vortex interaction leads to the mixing of momentum for tidal inertial waves while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size (radius) of the vortex. Incoming tidal waves can also experience complex angular momentum exchanges locally at critical ...

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Turbulent Viscosity Acting on the Equilibrium Tidal Flow in Convective Stars

Cited by 36 publications

References 55 publications

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Tidal Dissipation in Giant Planets

How tidal waves interact with convective vortices in rapidly rotating planets and stars

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