## Comparison between Newtonian and
non-Newtonian flow driven by internal loads

**Ondrej Cadek** ** , **
**Y. Ricard** ** , **
**Zdenek Martinec** ** & **
**Ctirad Matyska**
### Summary

The interpretation of long wavelength geoid and plate motions
on the basis of dynamic Earth models has usually been done assuming
linear viscous rheologies in
the mantle. In this paper, we develop spherical three-dimensional models
of mantle circulation using power-law creep rheologies with an
exponent *n*=3. In the
steady state limit, the stress-dependent rheologies only modify
the amplitude of the topography supported by an internal load by a few
percents with respect to the linear predictions. The geoid anomalies induced
by internal loads can be affected by around 20%. These changes
are also occurring at degrees and orders different from those of the mass
anomaly itself. As the geoid spectrum is strongly decreasing with
degree, the dynamic topography induced at high degrees can be contaminated
in a non-negligible way by the low degree
loads. The main contamination occurs at a harmonic triple of
that of the most important load. The flow structure is much more dependent
on the form of the constitutive law than the dynamic topography and the
geoid. On the contrary to linear rheology, a power-law creep
is able to sustain a toroidal velocity field. However, this toroidal
component only carries a few percents of the kinetic energy and thus, the
non linear creep with *n*=3 cannot by itself explain the observed
quasi-equipartition of plate tectonic energy between toroidal and poloidal
components.

Geophys. J. Int., **102** (1993), 103-114.