Mixing of passive heterogeneities by mantle convection

Abstract

The kinematic processes by which thermal convection can mix together large‐scale mantle heterogeneities are described theoretically and with a series of numerical experiments. We have analyzed the time evolution of a large‐scale passive, diffusive scalar anomaly subject to two models of mantle flow: (1) turbulent flow, in which material elements are elongated exponentially with time, and (2) laminar flow, in which material elements are elongated according to a power law function of time. Mixing time scales are computed for both models. They are found to depend on the initial volume of the heterogeneity, the sample volume (the volume of the mantle which is averaged in process of measuring the anomaly), and the Peclet number, the ratio of strain rate to diffusive transport rate. Predictions from the two models have been tested against numerical simulations of mixing in a cellular convective eddy, at high Peclet numbers. The transport equation was integrated using the Lagrangian method of tracking particles, with the particle density being proportional to the anomaly magnitude. Diffusion was included by adding Gaussian‐random displacements at each time step. Simulations were made with up to 40,000 particles. Mixing times from the numerical experiments agree most closely with predictions from the laminar theory. The theory and the numerical experiments indicate the following: (1) Mixing by creeping flow in the mantle is a cascade phenomenon. Individual Fourier components of an anomaly are transferred up the wave number spectrum at a rate proportional to the mean Lagrangian strain rate. Because of the cascade effect, the time scale for mixing thermal anomalies is short, in the range 75–200 m.y., depending on the initial scale of the anomaly. The time scale for mixing large‐scale compositional anomalies is far longer, approximately the age of the earth. (2) Mixing of compositional anomalies tends to produce a laminated upper mantle, in which ancient heterogeneity is stretched into thin subhorizontal layers.