Elliptical instability of the flow in a rotating shell

Lacaze, Laurent; Gal, Patrice Le; Dizès, Stéphane Le

doi:10.1016/j.pepi.2005.03.005

Cited by 35 publications

(29 citation statements)

References 40 publications

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“…As shown in figure 5, the growth rate decreases as Λ/4, following the analytical result given by (6). Also shown are the theoretical dashed curves for = 0.095 and = 0.105 representing the uncertainty in .…”

Section: Methodssupporting

confidence: 69%

“…It has for instance been observed in wakes [1], [2], in elliptically deformed containers, [3], [4], [5], [6], and more generally in the transition to turbulence of strained vortices [7]. Since its discovery in the mid-1970s, it has received considerable attention, theoretically, experimentally and numerically (see for instance the review by Kerswell [8]).…”

Section: Introductionmentioning

confidence: 99%

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On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids

2009

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International audienceThe effects of an imposed magnetic field on the development of the elliptical instability in a rotating spheroid filled with a conducting fluid are considered. Theoretical and experimental studies of the spin-over mode, as well as a more general short-wavelength Lagrangian approach, demonstrate that the linear growth rate of the instability and the square amplitude of the induced magnetic field fall down linearly with the square of the imposed magnetic field. Application of the results to the Galilean moon Io confirms the fundamental role played by the elliptical instability at the planetary scale

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Section: Methodssupporting

confidence: 69%

Section: Introductionmentioning

confidence: 99%

On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids

2009

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“…where is the ellipticity, NV and V are functions of the inner to outer spheres ratio ( NV ¼ 0.5 and V ¼ 2.62 for ¼ 0, NV ¼ 0.5 and V ¼ 1.8 for ¼ 1/3) (see Lacaze et al 2005). …”

Section: The Elliptical Instabilitymentioning

confidence: 99%

Magnetic field induced by elliptical instability in a rotating spheroid

Lacaze

Herreman

Bars

et al. 2006

Geophysical & Astrophysical Fluid Dynamics

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The tidal or the elliptical instability of the rotating fluid flows is generated by the resonant interaction of the inertial waves. In a slightly elliptically deformed rotating sphere, the most unstable linear mode is called the spin-over mode, and is a solid body rotation versus an axis aligned with the maximum strain direction. In the non-viscous case, this instability corresponds to the median moment of the inertial instability of the solid rotating bodies. This analogy is furthermore illustrated by an elliptical top experiment, which shows the expected inviscid heteroclinic behaviour. In geophysics, the elliptical instability may appear in the molten liquid cores of the rotating planets, which are slightly deformed by the tidal gravitational effects of the close bodies. It may then participate in the general outer core dynamics and possibly the geodynamo process. In this context, Kerswell and Malkus (Kerswell, R.R. and Malkus, W.V.R., Tidal instability as the source for Io's magnetic signature. Geophys. Res. Lett., 1998, 25, 603-606) showed that the puzzling magnetic field of the Jovian satellite Io may indeed be induced by the elliptically unstable motions of its liquid core that deflect the Jupiter's magnetic field. Our magnetohydrodynamics (MHD) experiment is a toy-experiment of this geophysical situation and demonstrates for the first time the possibility of an induction of a magnetic field by the flow motions due to the elliptical instability. A full analytical calculation of the magnetic dipole induced by the spin-over is presented. Finally, exponential growths of this induced magnetic field in a slightly deformed rotating sphere filled with galinstan liquid metal are measured for different rotating rates. Their growth rates compare well with the theoretical predictions in the limit of a vanishing Lorentz force.

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“…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].…”

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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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Elliptical instability of the flow in a rotating shell

Cited by 35 publications

References 40 publications

On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids

On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids

Magnetic field induced by elliptical instability in a rotating spheroid

Inertial Wave Turbulence Driven by Elliptical Instability

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