Nonlinear flow within a triaxial ellipsoidal planet driven by combined longitudinal and latitudinal libration

Deformed by tidal forces, the cavity of a planetary fluid core may be in the shape of a triaxial ellipsoid x 2 / a 2 + y 2 / b 2 + z 2 / c 2 = 1 , where a, b and c are different semi-axes and z is in the direction of rotation. Longitudinal libration of the planet is a periodic oscillation of its rotation rate around its rotating axis while latitudinal libration is the inclination of axis of rotation to the normal of the planetary orbital plane. The motion of a homogeneous fluid confined in a triaxial ellipsoidal cavity, which undergoes both latitudinal and longitudinal libration, is investigated via direct numerical simulation using an EBE (Element-By-Element) finite element method. It is shown that latitudinal libration leads to the resonance with spheroidal inertial modes while longitudinal libration has no contribution. On the other hand, longitudinal libration modifies the flow structure in dramatically different ways in the prograde phase (when the planet’s rotation speeds up) and retrograde phase (when the planet slows down). Implications of the result for planetary evolution are also discussed.