Non-linear evolution of tidally forced inertial waves in rotating fluid bodies

Favier, Benjamin; Barker, Adrian J.; Baruteau, Clément; Ogilvie, Gordon I.

doi:10.1093/mnras/stu003

Cited by 90 publications

(108 citation statements)

References 56 publications

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“…Other mechanisms that may be important include inertial waves excited in the presence of a core (e.g. Ogilvie & Lin 2004;Goodman & Lackner 2009;Ogilvie 2013;Favier et al 2014), dissipation in the core itself (Remus et al 2012;, as well as the elliptical instability (e.g. Barker 2016).…”

Section: Discussionmentioning

confidence: 99%

On turbulence driven by axial precession and tidal evolution of the spin–orbit angle of close-in giant planets

Barker

2016

Mon. Not. R. Astron. Soc.

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The spin axis of a rotationally deformed planet is forced to precess about its orbital angular momentum vector, due to the tidal gravity of its host star, if these directions are misaligned. This induces internal fluid motions inside the planet that are subject to a hydrodynamic instability. We study the turbulent damping of precessional fluid motions, as a result of this instability, in the simplest local computational model of a giant planet (or star), with and without a weak internal magnetic field. Our aim is to determine the outcome of this instability, and its importance in driving tidal evolution of the spin-orbit angle in precessing planets (and stars). We find that this instability produces turbulent dissipation that is sufficiently strong that it could drive significant tidal evolution of the spin-orbit angle for hot Jupiters with orbital periods shorter than about 10-18 days. If this mechanism acts in isolation, this evolution would be towards alignment or anti-alignment, depending on the initial angle, but the ultimate evolution (if other tidal mechanisms also contribute) is expected to be towards alignment. The turbulent dissipation is proportional to the cube of the precession frequency, so it leads to much slower damping of stellar spin-orbit angles, implying that this instability is unlikely to drive evolution of the spin-orbit angle in stars (either in planetary or close binary systems). We also find that the instability-driven flow can act as a system-scale dynamo, which may play a role in producing magnetic fields in short-period planets.

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Section: Discussionmentioning

confidence: 99%

On turbulence driven by axial precession and tidal evolution of the spin–orbit angle of close-in giant planets

Barker

2016

Mon. Not. R. Astron. Soc.

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“…In previous experiments and simulations in spherical or ellipsoidal geometries, the geostrophic modes resulting from the nonlinear interactions of inertial waves manifest themselves as zonal flows, i.e., mean steady axisymmetric flows pervading the fluid interior [16,17,[51][52][53] (see [54], however). Their amplitudes tend to be proportional to β 2 E −α , with α ranging from 0 to 2 [52,55,56], depending on the excitation frequency. Since the amplitude of the rms velocity scales like β [19,53], the ratio of the geostrophic zonal flows to the 3D modes is, therefore, proportional to βE −α .…”

Section: -2mentioning

confidence: 99%

Inertial Wave Turbulence Driven by Elliptical Instability

et al. 2017

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The combination of elliptical deformation of streamlines and vorticity can lead to the destabilization of any rotating flow via the elliptical instability. Such a mechanism has been invoked as a possible source of turbulence in planetary cores subject to tidal deformations. The saturation of the elliptical instability has been shown to generate turbulence composed of nonlinearly interacting waves and strong columnar vortices with varying respective amplitudes, depending on the control parameters and geometry. In this Letter, we present a suite of numerical simulations to investigate the saturation and the transition from vortex-dominated to wave-dominated regimes. This is achieved by simulating the growth and saturation of the elliptical instability in an idealized triply periodic domain, adding a frictional damping to the geostrophic component only, to mimic its interaction with boundaries. We reproduce several experimental observations within one idealized local model and complement them by reaching more extreme flow parameters. In particular, a wave-dominated regime that exhibits many signatures of inertial wave turbulence is characterized for the first time. This regime is expected in planetary interiors.

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“…Recent work on tidal theory suggests that excitation and dissipation of inertial waves play an important role in stellar spin and orbital evolution (e.g., Ogilvie 2005;Favier et al 2014). Lai (2012) recognized that inertial waves offer a possible means for a planet to realign its host star without being ingested.…”

Section: Tidal Re-alignmentmentioning

confidence: 99%

Are Tidal Effects Responsible for Exoplanetary Spin–orbit Alignment?

Winn

2016

ApJ

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The obliquities of planet-hosting stars are clues about the formation of planetary systems. Previous observations led to the hypothesis that for close-in giant planets, spin-orbit alignment is enforced by tidal interactions. Here, we examine two problems with this hypothesis. First, Mazeh and coworkers recently used a new technique-based on the amplitude of starspot-induced photometric variability-to conclude that spin-orbit alignment is common even for relatively long-period planets, which would not be expected if tides were responsible. We re-examine the data and find a statistically significant correlation between photometric variability and planetary orbital period that is qualitatively consistent with tidal interactions. However it is still difficult to explain quantitatively, as it would require tides to be effective for periods as long as tens of days. Second, Rogers and Lin argued against a particular theory for tidal re-alignment by showing that initially retrograde systems would fail to be re-aligned, in contradiction with the observed prevalence of prograde systems. We investigate a simple model that overcomes this problem by taking into account the dissipation of inertial waves and the equilibrium tide, as well as magnetic braking. We identify a region of parameter space where re-alignment can be achieved, but it only works for closein giant planets, and requires some fine tuning. Thus, while we find both problems to be more nuanced than they first appeared, the tidal model still has serious shortcomings.

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Non-linear evolution of tidally forced inertial waves in rotating fluid bodies

Cited by 90 publications

References 56 publications

On turbulence driven by axial precession and tidal evolution of the spin–orbit angle of close-in giant planets

On turbulence driven by axial precession and tidal evolution of the spin–orbit angle of close-in giant planets

Inertial Wave Turbulence Driven by Elliptical Instability

Are Tidal Effects Responsible for Exoplanetary Spin–orbit Alignment?

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