DYNAMICAL INFLUENCES OF DEPTH-DEPENDENT PROPERTIES ON MANTLE UPWELLINGS AND TEMPORAL VARIATIONS OF THE MOMENT OF INERTIA

The influences of the depth-dependent thermal expansivity and viscosit y on mantle flows have been investigated with an axisymmetric spherica l-shell model and a comparison has been made with Cartesian box result s. This comparison between the Cartesian and spherical-shell geometrie s shows that there are present in both configurations large thermal pl umes, while the downwellings are stronger in the Cartesian geometry. S pherical models with a small core, as perhaps in the case of Mars, pro duce huge megaplumes with large heads, which can extend several tens o f degrees on the planetary surface. We have also investigated the infl uence of the Rayleigh number, internal heating and depth-dependent pro perties on the time-dependent phase-space trajectories of the dynamica lly induced moments of inertia and the surface Nusselt number. Large, homoclinic-like, excursions in the phase-space trajectories can occur occasionally in the depth-dependent models and are due to the time-dep endent nature of the plume dynamics. The time-scales associated with c hanges of the surface Nusselt number are faster than those associated with variations in the moment of inertia for earth-like Raleigh number s. There are substantial temporal variations in the moment of inertia due to the plume-plume collisional dynamics. In the case of Earth, the magnitudes of perturbed moment of inertia may reach as large as 10(-5 ) of the principal moments of inertia. Such a possibility points to a fundamentally important role played by the lower mantle dynamics in po lar wander over geological time scales. (C) 1997 Elsevier Science B.V.