The influences of the depth-dependent thermal expansivity and viscosity on mantle flows have been investigated with an axisymmetric spherical-shell model and a comparison has been made with Cartesian results. This comparison between the Cartesian and spherical-shell geometries shows that there are present in both geometries large thermal plumes while the downwellings are stronger in the Cartesian geometry. Spherical models with a small core, as perhaps in the case of Mars, produce huge megaplumes with large heads, which can extend several tens of degrees on the planetary surface. We have also investigated the influence of the Rayleigh number, internal heating and depth-dependent properties on the time-dependent phase-space trajectories of the dynamically induced moments of inertia and the surface Nusselt number. The magnitudes of perturbed moment of inertia range between 10-6 and 10-7 of the principal moments of inertia. There are substantial temporal variations in the moment of inertia due to the plume-plume collisional dynamics. Large, homoclinic-like, excursions in the phase-space trajectories can occur occasionally in the depth-dependent models. The time-scales associated with changes of the surface Nusselt number are faster than those associated with variations in the moment of inertia.