Mixing and the distribution of heterogeneities in a chaotically convecting mantle

Chemical heterogeneities are introduced into the mantle by subduction of oceanic lithosphere and possibly by subduction of sediments and delamination of the continental lithosphere. These heterogeneities are blended into the mantle by convective mixing. Chemically distinct heterogeneities are stirred into the surrounding mantle matrix by convective shear, which deforms them, increasing the area of contact between an heterogeneity and the matrix. Final homogenization is accomplished by diffusion, which brings centimetersized heterogeneities into chemical equilibrium with the matrix. Numerical models of mantle convection suggest that it is chaotic. To study the effect of a chaotic flow on mixing, we have generated a space-filling, two-dimensional flow using the Lorenz equations in the chaotic regime as a driver. We specify a two-mode expansion of the stream function, resulting in a flow which oscillates smoothly between one and two cells. Particle paths are chaotic in time and space. Mixing is very rapid; the mixing time for heterogeneities with an initial size of 6 km is 240 m.y. for layered mantle convection; the corresponding mixing time for whole mantle convection is 960 m.y. The source region for mid-ocean ridge basalts has a "marble cake" structure; it is made up of material which has been processed through ridges, subducted, stretched, and thinned and is either partially or wholly homogenized. The incompletely mixed subducted oceanic crust forms bands of eclogite in the peridotite matrix. These bands range in scale from 6 km to a few centimeters.