Elliptical instability in terrestrial planets and moons

Abstract

The presence of celestial companions means that any planet may be subject to three kinds of harmonic mechanical forcing: tides, precession/nutation, and libration. These forcings can generate flows in internal fluid layers, such as fluid cores and subsurface oceans, whose dynamics then significantly differ from solid body rotation. In particular, tides in non-synchronized bodies and libration in synchronized ones are known to be capable of exciting the so-called elliptical instability, i.e. a generic instability corresponding to the destabilization of two-dimensional flows with elliptical streamlines, leading to three-dimensional turbulence. We aim here at confirming the relevance of such an elliptical instability in terrestrial bodies by determining its growth rate, as well as its consequences on energy dissipation, on magnetic field induction, and on heat flux fluctuations on planetary scales. Previous studies and theoretical results for the elliptical instability are re-evaluated and extended to cope with an astrophysical context. In particular, generic analytical expressions of the elliptical instability growth rate are obtained using a local WKB approach, simultaneously considering for the first time (i) a local temperature gradient due to an imposed temperature contrast across the considered layer or to the presence of a volumic heat source and (ii) an imposed magnetic field along the rotation axis, coming from an external source. The theoretical results are applied to the telluric planets and moons of the solar system as well as to three Super-Earths: 55 CnC e, CoRoT-7b, and GJ 1214b. For the tide-driven elliptical instability in non-synchronized bodies, only the Early Earth core is shown to be clearly unstable. For the libration-driven elliptical instability in synchronized bodies, the core of Io is shown to be stable, contrary to previously thoughts, whereas Europa, 55 CnC e, CoRoT-7b and GJ 1214b cores can be unstable. The subsurface ocean of Europa is slightly unstable}. However, these present states do not preclude more unstable situations in the past.

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Cited by in corpus (25)

• Magnetically Controlled Circulation on Hot Extrasolar Planets
• CoRoT: harvest of the exoplanet program
• Intertial wave turbulence driven by elliptical instability
• Ocean Circulation on Enceladus With a High Versus Low Salinity Ocean
• Tidally driven dynamos in a rotating sphere
• Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores
• Experimental study of the non-linear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence
• Scaling laws to understand tidal dissipation in fluid planetary regions and stars I - Rotation, stratification and thermal diffusivity
• Magnetic fields driven by tidal mixing in radiative stars
• Libration driven elliptical instability
• Fossil field decay due to nonlinear tides in massive binaries
• Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits
• Parametric instability and wave turbulence driven by tidal excitation of internal waves
• Nonlinear tides in a homogeneous rotating planet or star: global modes and elliptical instability
• Latitudinal libration driven flows in triaxial ellipsoids
• Mean zonal flows induced by weak mechanical forcings in rotating spheroids
• Libration driven multipolar instabilities
• Applications of a finite-volume algorithm for incompressible MHD problems
• Elliptical instability of compressible flow in ellipsoids
• Rotational dynamics of planetary cores: instabilities driven by precession, libration and tides
• Acoustic and inertial modes in planetary-like rotating ellipsoids
• The rotation of Io predicted by the Poincaré-Hough model
• The interactions of the elliptical instability and convection
• Did lunar tides sustain the early Earth's dynamo?
• New insights on Titan's interior from its obliquity