Mean zonal flows induced by weak mechanical forcings in rotating spheroids

Cébron, David; Vidal, Jérémie; Schaeffer, Nathanaël; Borderies, Antonin; Sauret, Alban

doi:10.1017/jfm.2021.220

“…The Ekman number scalings we have observed are very different from the zonal flows generated by tidal forcing in a full sphere in the experiments (with a deformable no-slip boundary) of, for example, Morize et al (2010), where the zonal velocity scales as 2 E −3/10 , or for those produced by inertial waves, as studied in Cébron al. (2021) and Lin & Noir (2021), where it instead scales 2 E 0 or 2 E −1/10 , respectively (though these also result from self-interaction, so the zonal velocity also scales as 2 ).…”

Section: Scaling Laws For Tidally-generated Differential Rotation: Ef...contrasting

confidence: 79%

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

Astoul

¹

,

Barker

²

2022

Monthly Notices of the Royal Astronomical Society

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In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long timescales. 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 nonlinear 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 nonlinear hydrodynamical simulations in adiabatic and incompressible convective shells, we investigate how the addition of nonlinear 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 nonlinear 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.

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“…The Ekman number scalings we have observed are very different from the zonal flows generated by tidal forcing in a full sphere in the experiments (with a deformable no-slip boundary) of, for example, Morize et al (2010), where the zonal velocity scales as 𝜖 2 E −3/10 , or for those produced by libration-driven inertial waves, as studied in Cébron et al (2021) and Lin & Noir (2021), where it instead scales as 𝜖 2 E 0 or 𝜖 2 E −1/10 , respectively (though these also result from self-interaction, so the zonal velocity also scales as 𝜖 2 ). We underline that the best fitting laws here seem quite different from the ones emerging in Paper I in E −3/2 and E −1/2 , presumably because of the non-wavelike nonlinearities involved in their work.…”

Section: Scaling Laws For Tidally-generated Differential Rotation: Ef...contrasting

confidence: 74%

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

Astoul¹,

Barker²

2022

Preprint

0

View full text Add to dashboard Cite

In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long timescales. 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 nonlinear 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 nonlinear hydrodynamical simulations in adiabatic and incompressible convective shells, we investigate how the addition of nonlinear 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 nonlinear 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.

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“…is worth noting that the mean geostrophic flow ω(2) z has an amplitude that is independent of E in the vanishing regime E → 0, which is somehow similar to the mean geostrophic flows driven by nonlinear boundary-layer interactions for NS-BC (e.g. Cébron et al 2021).…”

Section: Laminar Forced Flowsmentioning

confidence: 61%

“…Busse 1968; Cébron et al. 2021) or in the bulk through the action of the Reynolds stresses (e.g. Zhang & Liao 2004; Livermore et al.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Precession-driven flows in stress-free ellipsoids

Vidal

¹

,

Cébron

²

2022

Self Cite

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Motivated by modelling rotating turbulence in planetary fluid layers, we investigate precession-driven flows in ellipsoids subject to stress-free boundary conditions (SF-BC). The SF-BC could indeed unlock numerical constraints associated with the no-slip boundary conditions (NS-BC), but are also relevant for some astrophysical applications. Although SF-BC have been employed in the pioneering work of Lorenzani & Tilgner (J. Fluid Mech., vol. 492, 2003, pp. 363–379), they have scarcely been used due to the discovery of some specific mathematical issues associated with angular momentum conservation. We revisit the problem using asymptotic analysis in the low-viscosity regime, which is validated with numerical simulations. First, we extend the reduced model of uniform-vorticity flows in ellipsoids to account for SF-BC. We show that the long-term evolution of angular momentum is affected by viscosity in triaxial geometries, but also in axisymmetric ellipsoids when the mean rotation axis of the fluid is not the symmetry axis. In a regime relevant to planets, we analytically obtain the primary forced flow in triaxial geometries, which exhibits a second inviscid resonance. Then, we investigate the bulk instabilities existing in precessing ellipsoids. We show that using SF-BC would be useful to explore the non-viscous instabilities (e.g. Kerswell, Geophys. Astrophys. Fluid Dyn., vol. 72, 1993, pp. 107–144), which are presumably relevant for planetary applications but are often hampered in experiments or simulations with NS-BC.

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Mean zonal flows induced by weak mechanical forcings in rotating spheroids

Abstract: Abstract

Cited by 15 publications

References 81 publications

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

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

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

Precession-driven flows in stress-free ellipsoids

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