A number of studies do not fall into the main areas discussed below, but have been concerned with exploring various aspects of the underlying dynamics. The ability of multiple phase transitions to produce diapiric structures which may explain episodic hotspot volcanism was shown by Liu et al. [1991], who also considered the effect of a triple point in the phase diagram, as discussed in detail later. Weinstein [1993] showed how a combination of high Rayleigh number and strong internal heating with two phase transitions can lead to very strong variations in root mean square velocity and heat flux associated with episodic breakdown of layering.
In most studies, the dynamics are dominated by downwellings, due to the asymmetry introduced by internal heating and the close proximity of the transition zone to the upper boundary. However, the catastrophic downwelling avalanches do have important consequences for upwelling plume dynamics. When an avalanche occurs, the cold material spreading above the core-mantle boundary sweeps the hot lower boundary layer aside, triggering upwelling plumes [ Honda et al., 1993a; Tackley et al., 1993], an effect which Honda et al. [1993a] suggest may be the cause of ``superplumes'' (i.e., huge hot upwellings proposed by Larsen, [1991] to explain pulses of widespread volcanism in the Pacific Ocean). However, superplumes may not require upwelling all the way from the core-mantle boundary, particularly in an internally-heated mantle. During periods of mantle layering, a strong boundary layer develops at 660 km depth, such that the midmantle below this depth is much hotter than the upper mantle. During an avalanche, this hot midmantle material upwells into the upper mantle, resulting in a pulse of strongly elevated heat flow and volcanism, which may be the cause of superplume volcanism [ Weinstein, 1993]. A similar mechanism was observed by Steinbach et al. [1993], with Steinbach and Yuen [1994a] showing how temperature-dependent viscosity and latent heat amplifies the hot thermal anomalies in the upper mantle.
It is clearly desirable to develop a theoretical understanding of the effects observed in numerical simulations, and three groups have addressed this issue. Bercovici et al. [1993] examined the interaction of high-viscosity, planar or axisymmetric downwellings with an endothermic phase transition, using an analytical approach based on gravity currents, and found that cylindrical downwellings penetrate the phase transition more easily that linear downflows, as observed in the three-dimensional numerical simulations discussed in the next section. Solheim and Peltier [1994] applied a local boundary layer analysis to the internal boundary layer at 660 km depth in their numerical simulations, and determined that the boundary layer grew until some critical Rayleigh number was reached, at which breakdown of layering occurred. Tackley [1994] examined the interaction of idealized up- and downwellings with an endothermic phase transition, finding that the thickness of the up/downwelling was the dominant factor in determining its penetrative ability, and that most of the trends observed in numerical simulations could be explained in terms of geometry alone.