Flows Driven by Libration, Precession, and Tides

Bars, Michaël Le; Cébron, David; Gal, Patrice Le

doi:10.1146/annurev-fluid-010814-014556

Cited by 151 publications

(127 citation statements)

References 140 publications

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“…1), most of the energy is localized on the dispersion relation at the frequencies AEγ=Ω [ Fig. 2(a)], as expected from the temporal resonance condition with the base flow frequency 2γ [2,6]. In the early times of the saturated phase (t ¼ 50 to t ¼ 105 in Fig.…”

Section: -2mentioning

confidence: 78%

“…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].…”

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confidence: 99%

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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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Inertial Wave Turbulence Driven by Elliptical Instability

et al. 2017

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“…10 The aspects of the mechanically forced flows, described above, are thoroughly reviewed in Ref. 33.…”

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confidence: 99%

Experimental study of global-scale turbulence in a librating ellipsoid

et al. 2014

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We present laboratory experimental results demonstrating that librational forcing of an ellipsoidal container of water can produce intense motions through the mechanism of a libration driven elliptical instability (LDEI). These libration studies are conducted using an ellipsoidal acrylic container filled with water. A particle image velocimetry method is used to measure the 2D velocity field in the equatorial plane over hundreds libration cycles for a fixed Ekman number, E = 2 × 10 −5 . In doing so, we recover the libration induced base flow and a time averaged zonal flow. Further, we show that LDEI in non-axisymmetric container geometries is capable of driving both intermittent and saturated turbulent motions in the bulk fluid. Additionally, we measure the growth rate and amplitude of the LDEI induced excited flow in a fully ellipsoidal container at more extreme parameters than previously studied [Noir

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“…In the ocean, they are mostly generated by tide and winds and are expected to provide the missing contribution to the global energy budget of the ocean (Munk & Wunsch 1998). In planets and stars, they are excited by gravitational effects (Le Bars, Cébron & Le Gal 2015) or convection (Rogers & Glatzmaier 2005) and could play a role in the generation of zonal flows (Tilgner 2007) and in dissipative † Email address for correspondence: ledizes@irphe.univ-mrs.fr processes (Ogilvie & Lin 2004). In the present work, we are considering the simple configuration of a librating disk in a stratified and rotating fluid, for which an exact solution can be obtained to provide some general information on the structure of the wave field and its associated mean flow correction.…”

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“…Such a forcing is present in most planets (Comstock & Bills 2003) due to their gravitational interaction with other surrounding massive objects. It corresponds to one of the possible mechanical forcings associated with gravitation, the others being tides and precession (see Le Bars et al 2015). In the ocean, tide corresponds to the dominant harmonic forcing.…”

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Wave field and zonal flow of a librating disk

Dizès

2015

J. Fluid Mech.

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In this work, we provide a viscous solution of the wave field generated by librating a disk (harmonic oscillation of the rotation rate) in a stably stratified rotating fluid. The zonal flow (mean flow correction) generated by the nonlinear interaction of the wave field is also calculated in the weakly nonlinear framework. We focus on the low dissipative limit relevant for geophysical applications and for which the wave field and the zonal flow exhibit generic features (Ekman scaling, universal structures, etc.). General expressions are obtained which depend on the disk radius a * , the libration frequency ω * , the rotation rate Ω * of the frame, the buoyancy frequency N * of the fluid, its kinematic diffusion ν * and its thermal diffusivity κ * . When the libration frequency is in the inertia-gravity frequency interval (min(Ω * , N * ) < ω * < max(Ω * , N * )), the presence of conical internal shear layers is observed in which the spatial structures of the harmonic response and of the mean flow correction are provided. At the point of focus of these internal shear layers on the rotation axis, the largest amplitudes are obtained: the angular velocity of the harmonic response and the mean flow correction are found to be O(εE −1/3 ) and (ε 2 E −2/3 ) respectively, where ε is the libration amplitude and E = ν * /(Ω * a * 2 ) is the Ekman number. We show that the solution in the internal shear layers and in the focus region is at leading order the same as that generated by an oscillating source of axial flow localized at the edge of the disk (oscillating Dirac ring source).

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Flows Driven by Libration, Precession, and Tides

Cited by 151 publications

References 140 publications

Inertial Wave Turbulence Driven by Elliptical Instability

Inertial Wave Turbulence Driven by Elliptical Instability

Experimental study of global-scale turbulence in a librating ellipsoid

Wave field and zonal flow of a librating disk

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