Stretching and mixing of viscous blobs in Earth's mantle

Abstract

The stretching and mixing of blobs more viscous than the surrounding mantle is an important issue: The subducted lithospheric material at depth might be more viscous than the surrounding mantle, and its ability to mix affects its properties as a geochemical reservoir. In order to study the effect of the viscosity ratio λ (viscosity of the blob to the viscosity of the surrounding mantle) on the deformation we perform three types of two‐dimensional numerical simulations: a pure shear simulation, a simulation of steady state convection, and a simulation of time‐dependent convection. In a pure shear flow the inverse of the rate of deformation of a viscous blob is, to a first approximation, a linear function of the ratio λ/ A R , where A R is the aspect ratio of the blob. For a viscous blob in a steady convection cell a periodic deformation is superimposed on the long‐term deformation. The period corresponds to an overturn time along the streamline followed by the blob. The strains of this periodic deformation obey the laws found for pure shear. In a time‐dependent flow, more representative of the mantle flow, we find that the average distance a * between two tracers situated within a viscous blob obeys the relationship ln( a */ a 0 )= At /(1+λ) 2 and that it is independent of the aspect ratio of the blob. These two results are well explained by a simple model of successive strains in arbitrary directions. The viscosity contrast controls the mixing efficiency, and it has an effect much larger than predicted by earlier studies. Blobs of matter more viscous than the average mantle can therefore persist unmixed in the mantle over Earth's history.