Most of the modeling so far discussed assumed that the viscosity is constant, or depth-dependent, whereas the viscosity of the Earth is strongly dependent on temperature. The dominant features in mantle convection are the high-viscosity, downwelling lithospheric slabs, and low-viscosity upwelling plumes, and thus one modeling approach has been to isolate these features, performing detailed local calculations to study the interaction of these features with phase transitions.
Early work on slabs [ Christensen and Yuen, 1984] modeled the interaction of a high viscosity slab (but with non-linear rheology at high stress levels) with a combined phase transition and chemical discontinuity in a unit aspect ratio box, and comparison of the results with similar constant viscosity results [ Christensen and Yuen, 1985] indicated that the critical Clapeyron slope required to stop the slab penetrating did not depend greatly on viscosity contrast. This style of modeling was recently revived by Zhong and Gurnis [1994], who modeled a high viscosity oceanic plate with purely Newtonian rheology (i.e., linear, with stress proportional to strain rate) subducting as a slab at the end of a two-dimensional box, with the 660 km phase transition included. They found that a high viscosity slab penetrated the phase transition more easily than a constant viscosity slab, and that longer plate length (aspect ratio), resulted in easier slab penetration. King and Ita [1994] found that high slab viscosity moderated the ``catastrophic'' effects of avalanches found in constant-viscosity calculations. Phase transitions in a cold descending slab may also be delayed by kinetic effects, which cause minerals to metastably overshoot the equilibrium phase boundary and transform at a higher pressure [ Daessler and Yuen, 1993; Solomatov and Stevenson, 1994].
Recently, numerical studies of low-viscosity plumes interacting with the 660 km
discontinuity have been performed. Nakakuki et al., [1994] modeled the interaction of
a plume with a combined phase and chemical boundary, and found that a low viscosity
plume has more difficulty penetrating the phase transition than a constant viscosity plume, a
conclusion also reached by Davies [1994]. Another study (G. Schubert, C. Anderson,
and P. Goldman, Mantle plume interaction with an endothermic phase change, submitted to
J. Geophys. Res., 1994) noted that the latent heat released by a penetrating plume is
significant, increasing the plume temperature in the upper mantle relative to what it would
be without the phase transition, thus increasing the ability of the plume to thermally thin the
lithosphere and cause melting and volcanism. In both studies, a Clapeyron slope of -3 or -4
MPa K
was necessary to prevent the plume from penetrating the upper mantle.
Some global models (i.e., not focusing on particular features) of convection with variable viscosity and phase changes have also been presented [ Yuen et al., 1992; Steinbach and Yuen, 1993; Zhong and Gurnis, 1994]. These indicate that a purely temperature-dependent viscosity greatly enhances the propensity to layering. However, realistic slabs are not obtained, and the local slab models discussed earlier show that high viscosity should enhance the penetrative ability. Thus, it seems critical to for models to obtain realistic subduction, in order for conclusions about slab penetration to be accurate.