Tidal instability in a rotating and differentially heated ellipsoidal shell

David Cébron (1) , Pierre Maubert (1) , Michael Le Bars (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

The stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo- and astrophysical contexts and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows.

Mots clés: Tides and planetary waves; Heat flow; Core; outer core and inner core

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

David Cébron, Pierre Maubert, Michael Le Bars. Tidal instability in a rotating and differentially heated ellipsoidal shell. Geophysical Journal International, 2010, 182 (3), pp.1311-1318. ⟨10.1111/j.1365-246X.2010.04712.x⟩. ⟨hal-00522051⟩