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

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

3. 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)

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

5. 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

6. A. Levander et al. Tectonophysics 416 (2006) 167–185
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 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)

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?
Kellogg and Turcotte, 1987 EPSL

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

14. Some ways to analyze mixing in 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 Balsiger Physics 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 Balsiger Physics of the Earth and Planetary Interiors, 36 (1984) 291—304

18. 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

19. 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

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)).

25. f = 1
(reference model)
Movie1p

26. f = 50
Movie3p.mov

27. f = 100
4pi.mov

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

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

32. 50 Poincare sections - Ferrachat & Ricard 2001

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

34. 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

35. 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 , FEBRUARY 15, 1996
More viscous
Isoviscous
Less viscous

36. 36