The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

Astoul, Aurélie; Barker, Adrian J.

doi:10.1093/mnras/stac2117

Cited by 10 publications

(12 citation statements)

References 125 publications

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“…The results obtained with the convective column model proposed by Grooms et al (2010) can also be applied to other vortices triggered by rotating double-diffusive convection (Moll & Garaud 2017) or by the nonlinear interactions of tidal inertial waves (Astoul & Barker 2022). The inertial wave-vortex interaction is also crucial in other configurations.…”

Section: Towards a Complete Nonlinear Picturementioning

confidence: 88%

“…Depending on the boundary conditions and other internal properties, such as wave frequency, wavenumbers, or the shear Rossby number, the inertial waves may experience either damping, over-reflection, or over-transmission. The latter can ultimately lead to shear instability if the waves interfere constructively and sustain their growth as successive overreflection (or over-transmission) of the waves occurs (Lindzen 1988;Harnik & Heifetz 2007;Astoul & Barker 2022).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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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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Section: Towards a Complete Nonlinear Picturementioning

confidence: 88%

Section: Conclusion and Discussionmentioning

confidence: 99%

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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“…We introduce several quantities to analyze our simulations. The energy in the differential rotation E dr triggered by nonlinear IW interactions, integrated over the volume V of the shell, is defined as (see also Tilgner 2007;Favier et al 2014;Astoul & Barker 2022)…”

Section: Modeling Nonlinear Tidal Inertial Wavesmentioning

confidence: 99%

“…However, some close-in planets (such as Hot Jupiters) and stars in close binary systems may have sufficiently large tidal amplitudes for important nonlinear effects that could considerably alter tidal dissipation rates. We have therefore started to explore in detail the nonlinear evolution of tidally excited IWs in convective envelopes of stars and giant planets in Astoul & Barker (2022;hereafter AB22), building upon Favier et al (2014) and Barker (2016).…”

Section: Introductionmentioning

confidence: 99%

Tidally Excited Inertial Waves in Stars and Planets: Exploring the Frequency-dependent and Averaged Dissipation with Nonlinear Simulations

Astoul,

Barker

2023

ApJL

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We simulate the nonlinear hydrodynamical evolution of tidally excited inertial waves in convective envelopes of rotating stars and giant planets modeled as spherical shells containing incompressible, viscous, and adiabatically stratified fluid. This model is relevant for studying tidal interactions between close-in planets and their stars, as well as close low-mass star binaries. We explore in detail the frequency-dependent tidal dissipation rates obtained from an extensive suite of numerical simulations, which we compare with linear theory, including with the widely employed frequency-averaged formalism to represent inertial wave dissipation. We demonstrate that the frequency-averaged predictions appear to be quite robust and are approximately reproduced in our nonlinear simulations spanning the frequency range of inertial waves as we vary the convective envelope thickness, tidal amplitude, and Ekman number. Yet, we find nonlinear simulations can produce significant differences with linear theory for a given tidal frequency (potentially by orders of magnitude), largely due to tidal generation of differential rotation and its effects on the waves. Since the dissipation in a given system can be very different both in linear and nonlinear simulations, the frequency-averaged formalism should be used with caution. Despite its robustness, it is also unclear how accurately it represents tidal evolution in real (frequency-dependent) systems.

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“…This collapse to turbulence either occurs via weak inertial wave "turbulence" 4,6,9,10 , or rotating turbulence involving largescale geostrophic vortices or zonal flows 5,[7][8][9][10][11] . The inertial wave "turbulence" (involving a sea of weakly interacting inertial waves) may occur when the forcing amplitude is weak 10,12 , or when geostrophic modes are suppressed, either by artificial frictional damping 9 or via an external process such as the imposition of a magnetic field 6 .…”

Section: Introductionmentioning

confidence: 99%

The interactions of the elliptical instability and convection

Vries¹,

Barker²,

Hollerbach³

2023

Preprint

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The elliptical instability is an instability of elliptical streamlines, which can be excited by large-scale tidal flows in rotating fluid bodies, and excites inertial waves if the dimensionless tidal amplitude (ε) is sufficiently large. It operates in convection zones but its interactions with turbulent convection have not been studied in this context. We perform an extensive suite of Cartesian hydrodynamical simulations in wide boxes to explore the interactions of the elliptical instability and Rayleigh-Bénard convection. We find that geostrophic vortices generated by the elliptical instability dominate the flow, with energies far exceeding those of the inertial waves. Furthermore, we find that the elliptical instability can operate with convection, but it is suppressed for sufficiently strong convection, primarily by convectivelydriven large-scale vortices. We examine the flow in Fourier space, allowing us to determine the energetically dominant frequencies and wavenumbers. We find that power primarily concentrates in geostrophic vortices, in wavenumbers that are convectively unstable, and along the inertial wave dispersion relation, even in non-elliptically deformed convective flows. Examining linear growth rates on a convective background, we find that convective large-scale vortices suppress the elliptical instability in the same way as the geostrophic vortices created by the elliptical instability itself. Finally, convective motions act as an effective viscosity on large-scale tidal flows, providing a sustained energy transfer (scaling as ε 2 ). Furthermore, we find that the energy transfer resulting from bursts of elliptical instability, when it operates, is consistent with the ε 3 scaling found in prior work.

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The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

Cited by 10 publications

References 125 publications

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

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

Tidally Excited Inertial Waves in Stars and Planets: Exploring the Frequency-dependent and Averaged Dissipation with Nonlinear Simulations

The interactions of the elliptical instability and convection

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