Simulations of fluid motion in spheroidal planetary cores driven by latitudinal libration

Abstract

The motion of a homogeneous viscous fluid confined in a latitudinally librating, oblate spheroidal cavity with arbitrary eccentricity γ is investigated via direct three-dimensional numerical simulation using an EBE (Element-By-Element) finite element method. When the spheroidal cavity has moderate or large eccentricity with topographic coupling being dominant, an inviscid analytical solution describing the fluid motion driven by latitudinal libration is derived for the purpose of illustrating the nature of the fluid motion. It suggests that, in contrast to the fluid motion driven by longitudinal libration in ellipsoidal cavities, resonance of a spheroidal inertial wave mode with azimuthal wavenumber m = 1 can occur when the non-dimensional frequency of forced latitudinal libration is close to ω resonance = 2/(2 − γ 2), as predicted by the inviscid analytical solution. Three-dimensional direct numerical simulation at non-resonant frequencies, which includes the full effect of viscosity and nonlinearity, is carried out, showing a satisfactory agreement between the inviscid analytical solution and the numerical simulation. Emphasis of the numerical simulation is then placed on the strongly nonlinear librating flow at the exact resonance. The simulation reveals the existence of strong retrograde mean zonal flow due to nonlinear effects in the viscous boundary layer and different profiles of the zonal flow dependent upon the size of the libration frequency. Implications of the result for planetary evolution are also discussed.