A parameterized model for the evolution of isotopic heterogeneities in a convecting system

It is experimentally shown that, although steady convective flows are efficient means to heterogeneity within a single cell, they do not produce a dispersal of heterogeneous material over scales that are large by comparison to their depth, which requires that the flow be time-dependent on a time scale comparable to the overturn time. Convection in an internally heated layer does possess this property, and numerical solutions are presently used to study the way in which it disperses a set of neutrally bouyant particles initially confined to a small space. The derived concept of effective diffusivity is applied to the isotopic evolution of the Sm-Nd and Rb-Sr systems, with spatial variations generated by horizontal variations in degree of melting 1.8 billion years ago.