Tidal instability in stellar and planetary binary systems

Bars, Michaël Le; Lacaze, Laurent; Dizès, Stéphane Le; Gal, Patrice Le; Rieutord, M.

doi:10.1016/j.pepi.2009.07.005

Cited by 61 publications

(63 citation statements)

References 18 publications

(32 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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 . As the elliptical instability grows, provided β > E 1=2 [5], we conclude that for α < 1=2, there exists a regime where inertial wave turbulence is expected at low β and E-see right panel of Fig. 4.…”

Section: -2mentioning

confidence: 68%

“…More generally, it has been proposed as a general process to transfer energy to smaller scales in turbulence (see [2] and references within). It is important for geophysical fluid dynamics because it can drive flows in planetary cores subjected to tidal deformations [3][4][5][6]. It has been invoked to explain the magnetic field of the early Moon [7] and Earth [8].…”

mentioning

confidence: 99%

“…This instability develops in rotating fluids when the streamlines are deformed into ellipses. Its linear growth, due to the resonance of two inertial waves with the elliptical basic flow, is well described both theoretically [2,[9][10][11] and experimentally [3][4][5]12]. The nonlinear saturation of the elliptical instability remains poorly understood, but it is the relevant regime to describe vortex core breakdown [13], as well as dissipation and magnetic field generation in planetary cores [14].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Inertial Wave Turbulence Driven by Elliptical Instability

et al. 2017

View full text Add to dashboard Cite

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.

show abstract

Section: -2mentioning

confidence: 68%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Inertial Wave Turbulence Driven by Elliptical Instability

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Note that spheroidal or ellipsoidal geometry has frequently been employed by many authors to study fluid motion in geophysical and astrophysical contexts (see e.g. Vanyo et al 1995;Lorenzani & Tilgner 2001;Noir et al 2003;Wu & Roberts 2009;Le Bars et al 2010).…”

Section: Introduction and Formulationmentioning

confidence: 99%

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

2012

View full text Add to dashboard Cite

We consider a homogeneous fluid of viscosity ν confined within an oblate spheroidal cavity, x 2 /a 2 + y 2 /a 2 + z 2 /(a 2 (1 − E 2 )) = 1, with eccentricity 0 < E < 1. The spheroidal container rotates rapidly with an angular velocity Ω 0 , which is fixed in an inertial frame and defines a small Ekman number E = ν/(a 2 |Ω 0 |), and undergoes weak latitudinal libration with frequencyω|Ω 0 | and amplitude Po|Ω 0 |, where Po is the Poincaré number quantifying the strength of Poincaré force resulting from latitudinal libration. We investigate, via both asymptotic and numerical analysis, fluid motion in the spheroidal cavity driven by latitudinal libration. When |ω − 2/(2 − E 2 )| O(E 1/2 ), an asymptotic solution for E 1 and Po 1 in oblate spheroidal coordinates satisfying the no-slip boundary condition is derived for a spheroidal cavity of arbitrary eccentricity without making any prior assumptions about the spatial-temporal structure of the librating flow. In this case, the librationally driven flow is nonaxisymmetric with amplitude O(Po), and the role of the viscous boundary layer is primarily passive such that the flow satisfies the no-slip boundary condition. When |ω − 2/(2 − E 2 )| O(E 1/2 ), the librationally driven flow is also non-axisymmetric but latitudinal libration resonates with a spheroidal inertial mode that is in the form of an azimuthally travelling wave in the retrograde direction. The amplitude of the flow becomes O(Po/E 1/2 ) at E 1 and the role of the viscous boundary layer becomes active in determining the key property of the flow. An asymptotic solution for E 1 describing the librationally resonant flow is also derived for an oblate spheroidal cavity of arbitrary eccentricity. Three-dimensional direct numerical simulation in an oblate spheroidal cavity is performed to demonstrate that, in both the non-resonant and resonant cases, a satisfactory agreement is achieved between the asymptotic solution and numerical simulation at E 1.

show abstract

“…However, in natural systems, both the rotation and the gravitational tides deform the celestial body into a triaxial ellipsoid, where the so-called elliptical (or tidal) instability may take place (see [21][22][23][24][25] for details on this instability and its geo-and astro-physical applications). The elliptical instability takes place in any rotating fluid whose streamlines are elliptically deformed (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Tilt-over mode in a precessing triaxial ellipsoid

2010

Self Cite

View full text Add to dashboard Cite

The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincaré [Bull. Astr. 27, 321 (1910)] and Busse [J. Fluid Mech., 33, 739 (1968)] are extended to this more complex geometry, which corresponds to a tidally deformed spinning astrophysical body. As confirmed by three-dimensional numerical simulations, the proposed analytical model provides an accurate description of the stationary flow in an arbitrary triaxial ellipsoid, until the appearance at more vigorous forcing of time dependent flows driven by tidal and/or precessional instabilities.

show abstract

Tidal instability in stellar and planetary binary systems

Cited by 61 publications

References 18 publications

Inertial Wave Turbulence Driven by Elliptical Instability

Inertial Wave Turbulence Driven by Elliptical Instability

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

Tilt-over mode in a precessing triaxial ellipsoid

Contact Info

Product

Resources

About