University of California, Davis Geodynamics 4: Mixing Louise Kellogg University of California, Davis

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

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

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

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

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

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

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

Some mixing scales 1020 1010 Reynolds Number 100 10-10 10-20 10-6 100 turbulent Astrophysics interiors of stars 1010 Mechanical Engineering combustion 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 10-20 laminar 10-6 100 106 1012 Length scale (meters)

clip from fluid dynamics film series - 13:09

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

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

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

Some ways to analyze mixing in models of the mantle Dispersal of heterogeneities (visually or using statistical methods) Computing derived isotopic signatures

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

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

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

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

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

Initial location of particles (Hunt and Kellogg model)

Similar to the kinematic mixing shown by Ottino

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

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)).

f = 1 (reference model) Movie1p

f = 50 Movie3p.mov

f = 100 4pi.mov

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

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

50 Poincare sections - Ferrachat & Ricard 2001

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

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

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 Isoviscous Less viscous

36