Fluid motion in a triaxial ellipsoidal cavity driven by libration

Abstract

Deformed by tidal forces and rotational e ects, the cavity of a planetary uid core is usually in the shape of non-spherical geometry. Gravitational interaction between a planet and its parent star or moon exerts a torque on the planet and forces its latitudinal libration which drives uid motion in non-spherical planetary cores via viscous and topographic coupling between the planetary mantle and uid core. We shall present an asymptotic theory { a mathematical solution of the Navior-Stokes solution in spheroidal geometry with small viscosity { describing the uid motion driven by latitudinal libration. We shall also present an e cient nite element method for simulating nonlinear ows in latitudinally librating, triaxial ellipsoidal cavities with stability properties and error estimates of the time-dependent nite element solution.