Elliptical instability in rotating spherical fluid shells: application to Earth’s fluid core

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

doi:10.1016/j.pepi.2004.01.001

Cited by 16 publications

(17 citation statements)

References 24 publications

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“…Thus it is reasonable to expect this mode to be also the most unstable in the shell. The experiment of Seyed-Mahmoud et al (2004) and our own experimental observations presented in the next section confirm this expectation. Moreover, as in Lacaze et al (2004), the inner shear layers induced by the boundary layer eruptions at the critical latitude (Hollerbach and Kerswell, 1995) are expected not to significantly modify our results and will not be considered in the following.…”

Section: Inviscid Theorysupporting

confidence: 77%

“…Elsewhere, −R i < z < R i , and contrary to the model used in Seyed-Mahmoud et al (2004), the inner sphere influences the main flow by inducing a potential flow of same order as the imposed deformation. This main flow defined by Eq.…”

Section: Inviscid Theorymentioning

confidence: 93%

“…Another example can be found in Aldridge and Toomre (1969) where some of the eigenmodes of a rotating sphere were excited by applying a resonant modulation on the rotating velocity. Later, using an inner deformable body placed inside a rotating sphere, Aldridge et al (1997) and Seyed-Mahmoud et al (2004) described some of the inertial waves of the shell with different frequencies and spatial structures. In this last experiment, some features of the elliptical instability were also detected.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Inviscid Theorysupporting

confidence: 77%

Section: Inviscid Theorymentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Elliptical instability of the flow in a rotating shell

Lacaze¹,

Gal²,

Dizès³

2005

Physics of the Earth and Planetary Interiors

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“…Thus, the outcome of tidal instability in shells should be considered. The tidal (elliptical) instability does exist in shells, as confirmed experimentally and numerically for homogeneous fluids (Aldridge et al 1997;Seyed-Mahmoud et al 2000;Lacaze et al 2005;Seyed-Mahmoud et al 2004;Lemasquerier et al 2017). Indeed, the local stability theory we have presented remains formally valid in shells.…”

Section: Perspectivessupporting

confidence: 70%

Fossil field decay due to nonlinear tides in massive binaries

Vidal

Cébron

ud‐Doula

et al. 2019

A&A

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Context. Surface magnetic fields have been detected in 5 to 10% of isolated massive stars, hosting outer radiative envelopes. They are often thought to have a fossil origin, resulting from the stellar formation phase. Yet, magnetic massive stars are scarcer in (close) short-period binaries, as reported by the BinaMIcS (Binarity and Magnetic Interaction in various classes of Stars) collaboration. Aims. Different physical conditions in the molecular clouds giving birth to isolated stars and binaries are commonly invoked. In addition, we propose that the observed lower magnetic incidence in close binaries may be due to nonlinear tides. Indeed, close binaries are probably prone to tidal instability, a fluid instability growing upon the equilibrium tidal flow via nonlinear effects. Yet, stratified effects have hitherto been largely overlooked. Methods. We theoretically and numerically investigate tidal instability in rapidly rotating, stably stratified fluids permeated by magnetic fields. We use the short-wavelength stability method to propose a comprehensive (local) theory of tidal instability at the linear onset, discussing damping effects. Then, we propose a mixing-length theory for the mixing generated by tidal instability in the nonlinear regime. We successfully assess our theoretical predictions against proofof-concept, direct numerical simulations. Finally, we compare our predictions with the observations of short-period, double-lined spectroscopic binary systems. Results. Using new analytical results, cross-validated by a direct integration of the stability equations, we show that tidal instability can be generated by nonlinear couplings of inertia-gravity waves with the equilibrium tidal flow in short-period massive binaries, even against the Joule diffusion. In the nonlinear regime, a fossil magnetic field can be dissipated by the turbulent magnetic diffusion induced by the saturated tidal flows. Conclusions. We predict that the turbulent Joule diffusion of fossil fields would occur in a few million years for several short-period massive binaries. Therefore, turbulent tidal flows could explain the observed dearth of some short-period magnetic binaries.

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“…Libration, precession and tidal instabilities have been the subject of numerous studies focusing on their threshold and linear growth (Le Bars et al, 2015, and references therein), and more recently on their nonlinear saturation (e.g., Barker & Lithwick, 2013a;Le Reun et al, 2017;Lin et al, 2015), combining theoretical, experimental, and numerical approaches. The relevance of those alternative sources of core turbulence for terrestrial bodies has also been the subject of several studies (e.g., Grannan et al, 2016;Lemasquerier et al, 2017;Seyed-Mahmoud et al, 2004) and has given birth to unconventional scenarios to explain past or existing dynamos: for example, on Io (Kerswell & Malkus, 1998), on Mars (Arkani-Hamed et al, 2008, on the Moon (Dwyer et al, 2011;Le Bars et al, 2011), and on the early Earth (Andrault et al, 2016). However, studies of the dynamo capability of the flows resulting from libration, precession, and tides have been up to now sparse and limited to idealized or simplified configurations: that is, laminar dynamos from the precession base flow (Ernst-Hullermann et al, 2013), dynamos for tidal instability with ad hoc bulk forcing in a spherical domain (Cébron & Hollerbach, 2014;Vidal et al, 2017), laminar dynamos in a spheroidal domain for precession and libration instabilities (Wu & Roberts, 2009 (but see also Guermond et al, 2013), and turbulent dynamos in a spherical domain for precession (Kida & Shimizu, 2011;Lin et al, 2016;Tilgner, 2005Tilgner, , 2007.…”

Section: Introductionmentioning

confidence: 99%

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

Reddy

Favier

Bars

2018

Geophysical Research Letters

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Dynamo action in planetary cores has been extensively studied in the context of convectively driven flows. We show in this letter that mechanical forcings, namely, tides, libration, and precession, are also able to kinematically sustain a magnetic field against ohmic diffusion. Previous attempts published in the literature focused on the laminar response or considered idealized spherical configurations. In contrast, we focus here on the developed turbulent regime and we self‐consistently solve the magnetohydrodynamic equations in an ellipsoidal container. Our results open new avenues of research in dynamo theory where both convection and mechanical forcing can play a role, independently or simultaneously.

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Elliptical instability in rotating spherical fluid shells: application to Earth’s fluid core

Cited by 16 publications

References 24 publications

Elliptical instability of the flow in a rotating shell

Elliptical instability of the flow in a rotating shell

Fossil field decay due to nonlinear tides in massive binaries

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

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