A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid

D. Cébron (1) , M. Le Bars (1) , J. Leontini (2) , P. Maubert (1) , P. Le Gal (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 Department of Mechanical and Aerospace Engineering [Victoria]]

The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing some known analytical results. This model is then used to address open questions that were up to now inaccessible using theoretical and experimental approaches. Growth rates and mode selection of the instability are systematically studied as a function of the aspect ratio of the ellipsoid and as a function of the inclination of the rotation axis compared to the deformation plane. We also quantify the saturation amplitude of the flow driven by the instability and calculate the viscous dissipation that it causes. This tidal dissipation can be of major importance for some geophysical situations and we thus derive general scaling laws which are applied to typical planetary cores.

Mots clés: Tides; tidal/elliptical instability; planetary cores; finite element

Domaines: Sciences de la Terre

D. Cébron, M. Le Bars, J. Leontini, P. Maubert, P. Le Gal. A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid. Physics of the Earth and Planetary Interiors, 2010, 182 (1-2), pp.119. ⟨10.1016/j.pepi.2010.07.003⟩. ⟨hal-00675798⟩