A parameterized model for the evolution of isotopic heterogeneities in a convecting system |
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| Authors: | Frank M Richter Stephen F Daly Henri-Claude Nataf |
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| Institution: | 1. Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637U.S.A.;2. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109U.S.A.;3. Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125U.S.A. |
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| Abstract: | Laboratory experiments are used to illustrate how steady convective flows, while efficient at stirring an initial heterogeneity within a single cell, do not produce dispersal of heterogeneous material over scales large compared to the depth. Long-range dispersal requires that the flow be time dependent on a time scale comparable to the overturn time. Convection in an internally heated layer has this property and numerical solutions are used to study the way in which it disperses a set of neutrally buoyant particles that were initially confined to a small space. The horizontal dispersal of these particles is reasonably well represented by an effective diffusivity of 0.3 cm2/s for a Rayleigh number of 106. The concept of an effective diffusivity is then applied to the isotopic evolution of the Sm-Nd and Rb-Sr systems with spatial variations generated by horizontal variations in degree of melting 1.8×109 years ago. The present-day average ε value one would measure in such a system depends on the average degree of melting, the amplitude and length scale of variations in partial melt, and the effective diffusivity assumed. Especially in the case of Nd the differences in average ε value between a uniform and a spatially variable (but with the same average) melting case can be significant. The range of ε values about the average is controlled by the competing effects of generation by the differences in enrichment factor and decay due to the effective diffusivity. |
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