HR: 16:45h
AN: V44B-04    [Abstracts]
TI: Stretching of passive tracers and implications for mantle mixing
AU: * Conjeepuram, N
EM: natarajan@geology.ucdavis.edu
AF: Dept. of Geology U.C Davis, University of California One Shields Avenue, Davis, CA 95616-8605, United States
AU: Kellogg, L H
EM: kellogg@geology.ucdavis.edu
AF: Dept. of Geology U.C Davis, University of California One Shields Avenue, Davis, CA 95616-8605, United States
AB: Mid ocean ridge basalts(MORB) and ocean island basalts(OIB) have fundamentally different geochemical signatures. Understanding this difference requires a fundamental knowledge of the mixing processes that led to their formation. Quantitative methods used to assess mixing include examining the distribution of passive tracers, attaching time-evolution information to simulate decay of radioactive isotopes, and, for chaotic flows, calculating the Lyapunov exponent, which characterizes whether two nearby particles diverge at an exponential rate. Although effective, these methods are indirect measures of the two fundamental processes associated with mixing namely, stretching and folding. Building on work done by Kellogg and Turcotte, we present a method to compute the stretching and thinning of a passive, ellipsoidal tracer in three orthogonal directions in isoviscous, incompressible three dimensional flows. We also compute the Lyapunov exponents associated with the given system based on the quantitative measures of stretching and thinning. We test our method with two analytical and three numerical flow fields which exhibit Lagrangian turbulence. The ABC and STF class of analytical flows are a three and two parameter class of flows respectively and have been well studied for fast dynamo action. Since they generate both periodic and chaotic particle paths depending either on the starting point or on the choice of the parameters, they provide a good foundation to understand mixing. The numerical flow fields are similar to the geometries used by Ferrachat and Ricard (1998) and emulate a ridge - transform system. We also compute the stable and unstable manifolds associated with the numerical flow fields to illustrate the directions of rapid and slow mixing. We find that stretching in chaotic flow fields is significantly more effective than regular or periodic flow fields. Consequently, chaotic mixing is far more efficient than regular mixing. We also find that in the numerical flow field, there is a fundamental topological difference in the regions exhibiting slow or regular mixing for different model geometries.
DE: 1025 Composition of the mantle
DE: 1213 Earth's interior: dynamics (1507, 7207, 7208, 8115, 8120)
DE: 7208 Mantle (1212, 1213, 8124)
DE: 8124 Earth's interior: composition and state (1212, 7207, 7208, 8105)
SC: Volcanology, Geochemistry, Petrology [V]
MN: 2007 Fall Meeting