Mantle mixing revisited:
The influence of viscosity and implications for chemical geodynamics

Kellogg, L H - Department of Geology, University of California, Davis, 1 Shields Avenue, Davis, CA 95616, United States
Turcotte, D L - Department of Geology, University of California, Davis, 1 Shields Avenue, Davis, CA 95616, United States

The introduction of the term chemical geodynamics was accompanied by an interest in the processes by which mantle convection disperses heterogeneities. The rate and efficacy of mantle mixing constrains the origin and fate of the isotopic heterogeneity seen in mid-ocean ridges and oceanic islands. Heterogeneity is introduced into the mantle by processes associated with melting, alteration, and subduction, while heterogeneity is destroyed by the stirring action of convection, the stretching and folding common to all kinematic mixing processes. Mantle mixing is affected by a variety of factors, including time-varying flow, plate motion, viscosity variations, and phase transitions. Chaotic mixing can be observed in calculations of time-varying 2-D flows; this is confirmed by calculating the deformation of strain markers to obtain an estimate of the Lyapunov exponent. Chaotic mixing can be countered to some extent by increases in mantle viscosity at depth and by high-pressure solid-state phase transitions that influence the pattern of convection. Stirring may be rapid on a regional scale (resulting in fairly uniform mid-ocean ridge basalts on length-scales up to thousands of km) while heterogeneities at the global scale of the Dupal anomaly are retained for billions of years because of isolation across long-wavelength cells. In numerical calculations of the paths of passive tracers in convection, extreme changes of viscosity and thermal conductivity in the lower mantle slow the rate of flow in the lower mantle, but this does not much inhibit the overall rate of dispersal of heterogeneities. Essentially, the regions that exhibit high rates of stretching and thinning have the most important influence on mixing, and packets of material that are stirred rapidly in regions of high strain rate are carried wholesale into regions of more sluggish convection. The analysis of mixing is complicated by the fact that structures created by passive tracers in 3D exhibit different characteristics than structures observed in 2D models. Nevertheless, it remains difficult to account for mantle isotope systematics and for the Earth's overall heat flow budget without invoking some barriers to flow in the mantle's interior, such as would be provided by mantle layering.