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Geodynamics 4: Mixing

Geodynamics 4: Mixing. Louise Kellogg University of California, Davis. Outline:. Why care about mixing? Physics of mixing Mixing in the mantle. Global scale: mantle contains both well-mixed regions and heterogeneity. Fine-scale variations in the Galapagos. Fine scale heterogeneity.

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Geodynamics 4: Mixing

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  1. Geodynamics 4: Mixing • Louise Kellogg • University of California, Davis

  2. Outline: • Why care about mixing? • Physics of mixing • Mixing in the mantle

  3. Global scale: mantle contains both well-mixed regions and heterogeneity Fine-scale variations in the Galapagos Fine scale heterogeneity Galapagos Islands (from Harpp and White, 2001, G-cubed)

  4. Scales of heterogeneity in an exposed peridotite Allègre and Turcotte, Nature (1986)

  5. The scale of heterogeneity led Allègre and Turcotte (1986) to propose a ‘marble cake’ structure to the mantle Image from epicurious.com

  6. Allègre and Turcotte 1986 A. Levander et al. Tectonophysics 416 (2006) 167–185

  7. Starting point (figure from Ottino) Stretching and folding Molecular diffusion Breakup Stretching and folding Stretching and folding

  8. Dynamics of mixing in a simplified mantle model 300,000 particles Starting position

  9. Some mixing scales 1020 Astrophysics interiors of stars turbulent Mechanical Engineering combustion 1010 Atmospheric dispersion Oceanography • Chemical engineering • chemical reactors Reynolds Number 100 Physiology blood vessels Bioengineering aeration in bioreactors 10-10 Food engineering blending additives Polymer Engineering Geophysics mantle convection laminar 10-20 10-6 100 106 1012 Length scale (meters)

  10. clip from fluid dynamics film series - 13:09

  11. Starting point (figure from Ottino) Stretching and folding Molecular diffusion Breakup Stretching and folding Stretching and folding

  12. Kellogg and Turcotte, 1987 EPSL What about chemical diffusion?

  13. Allègre and Turcotte, Nature (1986) looked at timescales as a way of figuring out the scales of heterogeneity

  14. Some ways to analyze mixingin models of the mantle • Dispersal of heterogeneities (visually or using statistical methods) • Computing derived isotopic signatures

  15. Convective mixing and the fine structure of mantle heterogeneity, Peter Olson, David A. Yuen and Derick BalsigerPhysics of the Earth and Planetary Interiors, 36 (1984) 291—304

  16. “Underresolved sampling leads to apparent homogeneity” - From Olson et al. 1984

  17. Convective mixing and the fine structure of mantle heterogeneity, Peter Olson, David A. Yuen and Derick BalsigerPhysics of the Earth and Planetary Interiors, 36 (1984) 291—304

  18. 0 km 670 km Depth 2900 km 10 100 1 Normalized viscosity Hunt and Kellogg 2000 Mixing in 2-D with particles •Added at subduction zones •Removed at mid-ocean ridges

  19. 1 10 100 Hunt & Kellogg - effect of viscosity on mixing Constant viscosity viscosity 10 1 100 Pressure-dependent viscosity: smooth increase 1 10 100 Transition zone viscosity: Jump at 670 km

  20. Initial location of particles(Hunt and Kellogg model)

  21. Similar to the kinematic mixing shown by Ottino

  22. Badro et al. (Science, 2003,2004) show that Fe2+ in the two major phases in the deep lower mantle undergoes a transition from a high-spin to a low-spin state. Lower mantle phases: Perovskite: (Fe,Mg)SiO3 Magnesiowüstite:(Fe,Mg)O

  23. Possible effects of this transition? • Thermal conductivity INCREASES (because low-spin Fe2+ is nearly translucent to thermal radiation.) • Viscosity INCREASES (relating to a rise in the melting temperature of perovskite with increasing Mg content.) • Hypothesis: Changes in these properties may inhibit thermal convection, creating a stagnant layer or layered regime in the lower mantle (Badro et al. (2003,2004)).

  24. f = 1 (reference model) Movie1p

  25. f = 50 Movie3p.mov

  26. f = 100 4pi.mov

  27. Mixing in a 3D spherical model of present-day mantle convection Peter van Keken and Shijie Zhong

  28. Ferrachat & Ricard, Mixing in 3-D plate driven flowsChaotic trajectories occur even in steady-state flows

  29. 50 Poincare sections - Ferrachat & Ricard 2001

  30. Lyapunov exponents estimated by tracking tracers: Both chaotic and laminar mixing are observed Ferrachat & Ricard 2001

  31. Computing isotopic signaturesEvolution of U-Pb and Sm-Nd systems in numerical models of mantle convection and plate tectonicsShunxing Xie and Paul J. Tackley, J. Geophys. Research, 109, B11204, 2004 1 By 2 By 3 By T 206/204 Pb

  32. The role of viscosity contrasts Mixing of heterogeneities in the mantle: Effect of viscosity differences Michael Manga GEOPHYSICAL RESEARCH LETTERS VOL. 23, NO. 4, PAGES 403-406, FEBRUARY 15, 1996 More viscous Less viscous Isoviscous

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