Geodynamics 4: Mixing Louise Kellogg University of California, Davis.
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Transcript of Geodynamics 4: Mixing Louise Kellogg University of California, Davis.
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Geodynamics 4: MixingLouise Kellogg
University of California, Davis
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Outline:
•Why care about mixing?
•Physics of mixing
•Mixing in the mantle
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(from Harpp and White,2001, G-cubed)
Fine-scale variations in the Galapagos
Gal
apag
os I
slan
ds
Global scale: mantle contains both well-mixed regions and heterogeneity
Fine scale heterogeneity
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4
Scales of heterogeneity in an exposed peridotite
Allègre and Turcotte, Nature (1986)
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The scale of heterogeneity led Allègre and Turcotte (1986) to propose a ‘marble cake’
structure to the mantle
Image from epicurious.com
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Allègre and Turcotte 1986
A. Levander et al. Tectonophysics 416 (2006) 167–185
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QuickTime™ and a decompressor
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Stretching and folding
Molecular diffusion
Stretching and folding
Breakup
Stretching and folding
Starting point (figure from Ottino)
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300,000 particlesStarting position
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Dynamics of mixing in a simplified mantle model
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Some mixing scales
Length scale (meters)
Reyn
old
s N
um
ber
10-6 100 106 1012
10-20
10-10
1010
100
1020
turbulent
laminar
Astrophysicsinteriors of stars
Mechanical Engineeringcombustion
Atmosphericdispersion
OceanographyChemical engineering
chemical reactors
Physiologyblood vesselsBioengineering
aeration in bioreactors
Food engineeringblending additives
Polymer EngineeringGeophysicsmantle convection
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clip from fluid dynamics film series - 13:09
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QuickTime™ and a decompressor
are needed to see this picture.
Stretching and folding
Molecular diffusion
Stretching and folding
Breakup
Stretching and folding
Starting point (figure from Ottino)
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Kellogg and Turcotte, 1987 EPSL
What about chemical diffusion?
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Allègre and Turcotte, Nature (1986) looked at timescales as a way of figuring out the scales
of heterogeneity
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Some ways to analyze mixing
in models of the mantle
•Dispersal of heterogeneities (visually or using statistical methods)
•Computing derived isotopic signatures
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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
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“Underresolved sampling leads to apparent homogeneity” - From Olson et al. 1984
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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
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Mixing in 2-D with particles •Added at subduction zones •Removed at mid-ocean ridges
2900 km
670 km
Normalized viscosity
Dep
th
0 km
1 10 100
Hunt and Kellogg 2000
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Constant viscosity
Pressure-dependent viscosity: smooth increase
Transition zone viscosity: Jump at 670 km
Hunt & Kellogg - effect of viscosity on mixing
viscosity
1 10 100
1 10 100
1 10 100
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Initial location of particles
(Hunt and Kellogg model)
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Similar to the kinematic mixing shown by Ottino
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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
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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)).
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f=1
f=10
f=50
f=100
f=150
€
μl
/ μ0
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Movie1p
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4pi.mov
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Particle Distributions after 4 Ga
Starting particle distributionat steady-state conditions
f=50
f=10
f=1
f=100
f=150
40
1
0.5
~161,000 Particles Total
~40,250 in lower right quadrant↑
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Configurational Entropy
f=1
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
0 1 2 3 4 0 1 2 3 4
f=10 f=50
f=100 f=150
Calculating the configurational entropy of particles with starting positions above the increase in viscosity thermal conductivity - varies as function of the distribution of particles in space.
Method defined by Goltz and Bose (2004) and Turcotte (2001)
1
0.9
0.8
0.7
0.6
0.5
1
0.9
0.8
0.7
0.6
0.5
1
0.9
0.8
0.7
0.6
0.5
1
0.9
0.8
0.7
0.6
0.5
1
0.9
0.8
0.7
0.6
0.5
time (Ga) time (Ga) time (Ga)
time (Ga) time (Ga)
1 10 50 100 150f
.5
1
1.5
2
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Mixing in a 3D spherical model of present-day mantle convectionPeter van Keken and Shijie Zhong
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Ferrachat & Ricard, Mixing in 3-D plate driven flows
Chaotic trajectories occur even in steady-state flows
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50 Poincare sections - Ferrachat & Ricard 2001
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Lyapunov exponents estimated by tracking tracers: Both chaotic and laminar
mixing are observed Ferrachat & Ricard
2001
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Computing isotopic signaturesEvolution 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
T
1 By 2 By 3 By
206/204 Pb
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The role of viscosity contrasts
Mixing of heterogeneities in the mantle: Effect of viscosity differences
Michael Manga
GEOPHYSICAL RESEARCH LETTERSVOL. 23, NO. 4, PAGES 403-406, FEBRUARY 15, 1996
IsoviscousMore viscous
Less viscous
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3636