Stirring and mixing in the mantle by plate-scale flow: Large persistent blobs and long tendrils coexist

The stirring of a small, passive heterogeneity in an unsteady circulation is investigated by following the boundary of the heterogeneity; the circulation mimics features of plate-scale flow. After initial release, the heterogeneity is stirred and subsequently consists of at least one large "blob" connected to long, but thin tendrils. Tendrils exponentially lengthen and exponentially thin with time, as predicted by a turbulent mixing law, but the width of blobs decays about 100 times more slowly. The blobs mix slowly because they are smaller than the scale of flow and are sheared and occasionally unmixed by the laminar flow within the interiors of convection cells. The decay time of 1 to 100 km sized heterogeneities is on the order of billions of years for whole-mantle convection and thus is in accord with isotopic observations which indicate the mantle has chemical heterogeneities persisting for billions of years