Flows driven by libration, precession, and tides in planetary cores

Bars, Michaël Le

doi:10.1103/physrevfluids.1.060505

Cited by 12 publications

(8 citation statements)

References 70 publications

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“…For all cases, we start with a purely hydrodynamic simulation until it reaches a quasi-steady turbulent state, checked to be consistent with the results previously obtained with a single fluid domain only. The details of the mechanism responsible for the turbulent motions have been discussed in details in previous papers [see Le Le Bars, 2016, and references therein] and we focus here on the magnetohydrodynamic properties of these flows. We then restart the simulation at a fixed magnetic Prandtl number and solve simultaneously for the magnetic potential including an initial magnetic perturbation in the form of an axial dipole in the fluid part of the domain.…”

Section: Resultsmentioning

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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Section: Resultsmentioning

confidence: 99%

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

Reddy

Favier

Bars

2018

Geophysical Research Letters

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“…The vector u contains the value of the amplitudes of the spherical harmonic expansions at the internal collocation nodes. The linear part L depends on the three nondimensional parameters (4). It has a diagonal block of dimension N − 1 for 0 0 , followed by a block-tridiagonal part of L rows of blocks of dimension 3(N − 1) for the rest of amplitudes, due to the structure of the operator Q.…”

Section: Formulation and Numerical Methodsmentioning

confidence: 99%

“…The ellipsoidal shapes are substituted by perfect spheres when the rotation is relatively low, although there are exceptions (see, for instance, Refs. [3,4]). The momentum, energy, and concentration equations can be integrated in time to obtain information from the simulations, or particular invariant objects such as equilibria, waves, or other periodic regimes can be computed with adapted numerical nonlinear solvers.…”

Section: Introductionmentioning

confidence: 99%

Torsional solutions of convection in rotating fluid spheres

Umbría

Net

2019

Phys. Rev. Fluids

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A numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres is presented. Their dependence on the Rayleigh number has been found for two pairs of Ekman (E) and small Prandtl (Pr) numbers in the region of parameters where, according to Zhang et al. [J. Fluid Mech. 813, R2 (2017)], the linear stability of the conduction state predicts that they can be preferred at the onset of convection. The bifurcation to periodic torsional solutions is supercritical for sufficiently small Pr. They are not rotating waves, unlike the nonaxisymmetric case. Therefore they have been computed by using continuation methods for periodic orbits. Their stability with respect to axisymmetric perturbations and physical characteristics have been analyzed. It was found that the time-and space-averaged equatorially antisymmetric part of the kinetic energy of the stable orbits splits into equal poloidal and toroidal parts, while the symmetric part is much smaller. Direct numerical simulations for E = 10 −4 at higher Rayleigh numbers (Ra) show that this trend is also valid for the nonperiodic flows and that the mean values of the energies remain almost constant with Ra. However, the modulated oscillations bifurcated from the quasiperiodic torsional solutions reach a high amplitude, compared with that of the periodic, increasing slowly and decaying very fast. This repeated behavior is interpreted as trajectories near heteroclinic chains connecting unstable periodic solutions. The torsional flows give rise to a meridional propagation of the kinetic energy near the outer surface and an axial oscillation of the hot nucleus of the metallic fluid sphere.

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“…Chandrasekhar 1969), which disturb their rotational dynamics. It bears the name of mechanical or harmonic forcing (Le Le Bars 2016), such as tides, librations or precession. Librations are oscillations of the figure axes of a synchronised body with respect to a given mean rotation axis.…”

Section: Physical Contextmentioning

confidence: 99%

Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits

Vidal

Cébron

2017

J. Fluid Mech.

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We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical problem is the stability of Roche-Riemann ellipsoids moving on circular Kepler orbits. However previous stability studies have to be reassessed. Indeed they only consider global perturbations of large wavelength or local perturbations of short wavelength. Moreover many planets and stars undergo orbital motions on eccentric Kepler orbits, implying time-dependent ellipsoidal semi-axes. This time dependence has never been taken into account in hydrodynamic stability studies. In this work we overcome these stringent assumptions. We extend the hydrodynamic stability analysis of rotating ellipsoids to the case of eccentric orbits. We have developed two open source and versatile numerical codes to perform global and local inviscid stability analyses. They give sufficient conditions for instability. The global method, based on an exact and closed Galerkin basis, handles rigorously global ellipsoidal perturbations of unprecedented complexity. Tidally driven and libration-driven elliptical instabilities are first recovered and unified within a single framework. Then we show that new global fluid instabilities can be triggered in ellipsoids by tidal effects due to eccentric Kepler orbits. Their existence is confirmed by a local analysis and direct numerical simulations of the fully nonlinear and viscous problem. Thus a non-zero orbital eccentricity may have a strong destabilising effect in celestial fluid bodies, which may lead to space-filling turbulence in most of the parameters range.

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Flows driven by libration, precession, and tides in planetary cores

Cited by 12 publications

References 70 publications

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

Torsional solutions of convection in rotating fluid spheres

Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits

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