Convection in three dimensions with surface plates: Generation of toroidal flow

This work presents numerical calculations of mantle convection that incorporate some of the basic observational constraints imposed by plate tectonics. The model is three-dimensional and includes surface plates; it allows plate velocity to change dynamically according to the forces which result from convection. We show that plates are an effective means of introducing a toroidal component into the flow field. After initial transients the plate motion is nearly parallel to transform faults and in the direction that tends to minimizes the toroidal flow field. The toroidal field decays with depth from its value at the surface; the poloidal field is relatively constant throughout the layer but falls off slightly at the top and bottom boundaries. Layered viscosity increasing with depth causes the toroidal field to decay more rapidly, effectively confining it to the upper, low-viscosity layer. The effect of viscosity layering on the poloidal field is relatively small, which we attribute to its generation by temperature variations distributed throughout the system. The generation of toroidal flow by surface plates would seem to account for the observed nearly equal energy of toroidal and poloidal fields of plate motions on the Earth. A low-viscosity region in the upper mantle will cause the toroidal flow to decay significantly before reaching the lower mantle. The resulting concentration of toroidal flow in the upper mantle may result in more thorough mixing there and account for some of the geochemical and isotopic differences proposed to exist between the upper and lower mantles.