Kinematic considerations for mantle mixing

Abstract. Recent experimental and computational studies tal and computational mixing studies in highly controlled show that"islands"(u~mixedrcgions that donot interactwith flows show that even seemingly inconsequential errors in the surrounding regions) are ubiquitous features in chaotically computed velocity field of 3-D or time-dependent flows can advecting fluids. Such is~ands~~uitenaturall ~ account for the geochemically inferred coexistence of apparently distinct, long-lived geochemical heterogeneity with relatively homo-geneous regions of an actively convecting mantle. These results also indicate that mixing patterns-the set of islands and folds characterizing the large-scale material advection-are sensitive to small variations in the rheology of the fluid. Therefore, interpretation of numerical simulations of mantle transport and mixing is less straightforward than currently supposed. Computational studies of analytic flow solutions with systematically introduced and controlled errors indi-cate that mantle simulations are unlikely to accurately com-pute individual trajectories for even moderate time, but that tmjectory ensembles can be accuntely computed for long time. Significantly, computations also indicate that mixing and transport resultsmay not evolve smoothly with increased rheological realism