Most studies have been performed in two dimensions (2-D). The influence of three-dimensionality (3-D) on these effects has been explored by two groups, in spherical geometry by Tackley et al. [1993, 1994] (illustrated in Figure 1), and in Cartesian geometry by Honda et al. [1993a&b], Reuteler et al. [1994] (which includes a video depicting avalanches), and Yuen et al. [1994] (illustrated in Figure 2). Although the basic avalanche mechanism is qualitatively similar to two-dimensional (2-D) results, there are significant differences, both quantitative and qualitative, between the two geometries, which arise because the correct morphology and planform cannot be obtained in 2-D. In particular, 3-D avalanches occur as cylindrical downwelling plumes, a geometry which is not possible in 2-D geometry, except at the symmetry axis in axisymmetric models.
The planform observed in 3-D spherical geometry [ Tackley et al., 1993, 1994] is
illustrated in Figure 1, and can be summarized as follows: In the upper mantle, an
interconnected network of linear downwelling sheets, which do not penetrate the phase
transition, is observed. At the intersections of these sheets, pools of cold material
accumulate in the transition zone. These break through intermittently into the midmantle in
the form of broad cylindrical avalanches, and in the deep mantle, large pools of cold
material form above the core-mantle boundary, an effect which is accentuated by spherical
geometry. Upwelling plume activity is weak, although broad hot structures are visible in
the upper mantle and deep mantle. The cylindrical avalanches overlap in time, and thus, the
time-dependence of globally-averaged quantities, such as mass flux across the 660, is
much weaker than that in comparable axisymmetric spherical models. Figure 2 shows a
sequence of 3-D simulations in Cartesian geometry from Yuen et al. [1994], in which
the surface Rayleigh number is increased from 2x10
to 4x10
. These are
discussed in more detail in a later section. These 3-D simulations lack surface plates and
temperature-dependent viscosity, both of which are thought to strongly influence the style
of convection, and thus it is not clear whether the observed features, such as cylindrical
lower-mantle downwellings, are truly representative of those in the real Earth. Future
calculations will resolve such issues.