## Dynamical influences of depth-dependent properties on mantle
upwellings and temporal variations of the moment of inertia

**J. Moser , **
**David A. Yuen** ** , **
**T. B. Larsen & **
**Ctirad Matyska**
### Summary

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.

Phys. Earth Planet. Inter., **102**(1997), 153-170.