Quantifying Mixing and Scales of Heterogeneity in 2-D Numerical Models of Chaotic Mantle Mixing

Fundamental to our understanding of geochemical reservoirs within the Earth's mantle is the concept of the scale and distribution of heterogeneity. Although many studies approach this concept qualitatively few have attempted a quantitative assessment. Through a collaborative effort at the CIDER (Cooperative Institute for Deep Earth Research) 2006 summer workshop, we applied a 2-D/1-D power spectral and statistical analysis, respectively, to the temperature field and passive tracer distribution within a 2-D numerical model of mantle convection. The resultant data provides a means to objectively describe the scales of mixing and heterogeneity within various model scenarios. The dynamic models used had a 1x10 aspect ratio, included temperature- and pressure-dependent viscosity, had a Rayleigh number of 10^7, and had both internal and basal heating. One end member case includes a layered structure for viscosity and thermal conductivity, with a sharp increase in the mid-mantle. Spectral analysis of the temperature fields indicates that power near the upper and lower boundary layers is concentrated in long-wavelength structures while in the mid-mantle the spectrum is broader. Layering the viscosity structure enhances this dichotomy, but does not isolate the upper from the lower mantle and does not necessarily lead to decreased mixing rates or efficiency. Preliminary results demonstrate that the overall particle distribution, measured as a function of the distance between particles, is not necessarily unimodal. Furthermore, at a given time step this distribution may become multimodal.