Deformation of tracers in isoviscous 3D flows with applications to mantle mixing
Conjeepuram, N - University of California Davis, Geology Dept, One Shields Avenue, Davis, CA 95616 United States
Kellogg, L H - University of California Davis, Geology Dept, One Shields Avenue, Davis, CA 95616 United States
A long-standing problem in mantle dynamics is the mechanism by which the different distribution of geochemical signatures of mid-ocean ridge basalts (MORB) and ocean island basalts (OIB) evolved. The geochemical signatures require preservation of heterogenities for billions of years. Several mechanisms have been proposed, including layering and long-lived blobs or veins in the mantle. To assess the various proposed models requires understanding the inherent differences in the rate of mixing between different types of flows. Extensive study in 2-D models showed that mixing achieved through stretching and thinning is exponential in chaotic flows and linear in steady flows. In three dimension, relatively simple model geometries can produce both chaotic and non-chaotic stream lines under steady conditions. Quantitative methods used to assess mixing include examining the distribution of passive tracers, attaching time-evolution information to simulate decay of radioactive isotopes, and calculating the Lyapunov exponent, which characterizes whether two nearby particles diverge at an exponential rate. Here we assess mixing of tracer particles in a model of mantle flow with a geometry that includes plate-driven flow, building on earlier work by Ferrachat and Ricard (1998). We use CitcomCU, a mantle convection code in 3D cartesian geometry, with suitable velocity boundary conditions to simulate a spreading center geometry. We treat these passive tracers as infinitesimal strain markers and compute the stretching and thinning of the resulting ellipsoids along the particle trajectory. Calculating the full 3D strain marker evolution allows us to assess the mixing in a method similar to the Lyapunov exponent, while also allowing us to investigate the development of fabrics associated with the system.