Mixing in numerical models of mantle convection incorporating plate kinematics

The process by which subducted lithosphere is mixed by mantle convection is investigated in numerical calculations. The results show that the observed isotopic heterogeneity of mantle sources and their ancient (1-2 b.y.) apparent ages are consistent with convective mixing. Passive tracers, which are introduced below "trenches," are efficiently dispersed, but nonetheless, heterogeneities in tracer density with a large range of length scales are observed to persist for 40 or more transit times (one transit time is the time to travel the fluid depth with the boundary velocity). In particular, there is a strong tendency to form high-density folds of the tracer strings, which persist much longer than simple shearing indicates. The folds persist because there is a strong tendency for material that enters the flow at the margins of cells to be transferred to adjacent cells, where it is "unmixed." When the simulations are scaled to the whole mantle, the tight clumps (folds) of tracers are shown to persist for up to 1-2 b .y. There is also a tendency for large-scale convection cells to remain isolated from recycled material for 1-2 b.y. These results are consistent with the significant chemical heterogeneity of the mantle as revealed by isotopic studies of oceanic basalts. Despite the spatial heterogeneity in tracer density, the average time tracers remain in the box from subduction at trenches to sampling at ridges (i.e., the residence time) is well constrained and within 20% of the mean residence time expected from an analytic model in which tracers are assumed to be sampled randomly. Model ages of the mantle that explicitly incorporate increased convection rates in the past and assume random sampling of heterogeneities bracket the - 2 b.y. apparent Pb-Pb and Rb-Sr isochrons of midocean ridge basalts and oceanic island basalts. The conclusion of persistent spatial heterogeneity is different from the conclusions drawn from other studies. The different conclusions result, primarily, from our emphasis on the details of spatial variations as opposed to some average of the mixing, from a difference in flow unsteadiness, and from the different ways tracers have been introduced into the flow