A&A 539, A78 (2012) Astronomy DOI: 10.1051/0004-6361/201117741 & c ESO 2012 Astrophysics Elliptical instability in terrestrial planets and moons D. Cebron1,M.LeBars1, C. Moutou2,andP.LeGal1 1 Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 6594, CNRS and Aix-Marseille Université, 49 rue F. Joliot-Curie, BP 146, 13384 Marseille Cedex 13, France e-mail:
[email protected] 2 Observatoire Astronomique de Marseille-Provence, Laboratoire d’Astrophysique de Marseille, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France Received 21 July 2011 / Accepted 16 January 2012 ABSTRACT Context. 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. Aims. 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. Methods. Previous studies and theoretical results for the elliptical instability are re-evaluated and extended to cope with an astro- physical 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.