Elliptical instability of the Earth's fluid core

Aldridge, K. D.; Seyed-Mahmoud, B.; Henderson, Gary; Wijngaarden, William van

doi:10.1016/s0031-9201(97)00065-4

Cited by 37 publications

(29 citation statements)

References 14 publications

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“…Indeed, we can now quantitatively estimate the presence of an elliptical instability in a planetary core given by > 0 (see equation (5)): as shown in figure 6, an elliptical instability is proved on the Io and possible on the Earth (see also Kerswell 1994). Besides, we can also quantitatively demonstrate that the typical timescale of the inertial instabilities (given by 1=) is much larger than the rotation rate (see also Aldridge et al 1997). Finally, the intermittency cycles and the phase reversals observed in the hydrodynamics at low Ekman numbers (see figure 1) could translate into the magnetic field excursions and the reversals in planets.…”

Section: The Elliptical Instability In Geophysicsmentioning

confidence: 58%

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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Section: The Elliptical Instability In Geophysicsmentioning

confidence: 58%

Magnetic field induced by elliptical instability in a rotating spheroid

Lacaze

Herreman

Bars

et al. 2006

Geophysical & Astrophysical Fluid Dynamics

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“…Recent measurements of magnetic fields around relatively small planets such as the Jovian moons Io and Ganymède (Kivelson et al, 1996a,b) may reinforce the interest in the study of inertial instabilities such as the elliptical or the precessional ones (Malkus, 1968;Busse, 1968;Noir et al, 2001;Kerswell, 1993;Lorenzani and Tilgner, 2003). Aldridge et al (1997), and Seyed-Mahmoud et al (2000 have performed computations and built as already mentioned, a rotating deformable shell where they observed the presence of the elliptical instability. Using the technique invented by Malkus in 1989(Malkus, 1989, and more recently used and extended to triangular distortions by Eloy et al (2003), we have applied an elliptical constraint to a deformable rotating sphere (Lacaze et al, 2004) and visualized the spin-over mode generated by the elliptical instability.…”

Section: Introductionmentioning

confidence: 89%

Elliptical instability of the flow in a rotating shell

Lacaze¹,

Gal²,

Dizès³

2005

Physics of the Earth and Planetary Interiors

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A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating cores of planets when deformed by tides coming from neighboring gravitational bodies. Theoretical estimations for the growth rates and for the non linear amplitude saturations of the unstable mode are obtained and compared to experimental data obtained from Laser Döppler anemometry measurements. Visualizations and descriptions of the various characteristics of the instability are given as functions of the flow parameters.

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“…Evaluation of P ell for the Earth is difficult because its core is just at the vicinity of the threshold for instability, where ω ell rapidly changes from 0 to 1 (Lacaze et al, 2006). Following Aldridge et al (1997), if we suppose that the growth rate of the instability is correctly approximated by the classical formula = 0.5ε − 2.62 √ E and that the typical growth rate of the instability in the Earth ranges between 10 3 and 10 6 years, the dissipation due to the (laminar) tidal instability ranges between P ell ∼ 10 9 W and P ell ∼ 2 × 10 5 W, respectively. It thus remains relatively small compared to the viscous dissipation by water tides on ocean floor (typically 2 × 10 12 W), which is supposed to be the dominant effect in the case of the Earth.…”

Section: Fig 5 Kalliroscope Visualization Of the Elliptical Instabimentioning

confidence: 99%

“…Its presence in planetary and stellar systems, elliptically deformed by gravitational tides, has been suggested for several years. It could for instance be responsible for the surprising existence of a mag-netic field in Io (Kerswell and Malkus, 1998;Lacaze et al, 2006;Herreman et al, 2009) and for fluctuations in the Earth's magnetic field on a typical timescale of 10,000 years (Aldridge et al, 1997). It may also have a significant influence on the evolution of binary stars (e.g.…”

Section: Introductionmentioning

confidence: 99%

Tidal instability in stellar and planetary binary systems

Bars

Lacaze

Dizès

et al. 2010

Physics of the Earth and Planetary Interiors

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a b s t r a c tIn this paper, we combine theoretical and experimental approaches to study the tidal instability in planetary liquid cores and stars. We demonstrate that numerous complex modes can be excited depending on the relative values of the orbital angular velocity˝o rbit and of the spinning angular velocity˝s pin , except in a stable range characterized by˝s pin /˝o rbit ∈ [−1;1/3]. Even if the tidal deformation is small, its subsequent instability -coming from a resonance process -may induce motions with large amplitude, which play a fundamental role at the planetary scale. This general conclusion is illustrated in the case of Jupiter's moon Io by a coupled model of synchronization, demonstrating the importance of energy dissipation by elliptical instability.

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Elliptical instability of the Earth's fluid core

Cited by 37 publications

References 14 publications

Magnetic field induced by elliptical instability in a rotating spheroid

Magnetic field induced by elliptical instability in a rotating spheroid

Elliptical instability of the flow in a rotating shell

Tidal instability in stellar and planetary binary systems

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