Geodynamics 4: Mixing
description
Transcript of Geodynamics 4: Mixing
Geodynamics 4: MixingLouise Kellogg
University of California, Davis
Outline:
•Why care about mixing?
•Physics of mixing
•Mixing in the mantle
(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
4
Scales of heterogeneity in an exposed peridotite
Allègre and Turcotte, Nature (1986)
The scale of heterogeneity led Allègre and Turcotte (1986) to propose a ‘marble cake’
structure to the mantle
Image from epicurious.com
Allègre and Turcotte 1986
A. Levander et al. Tectonophysics 416 (2006) 167–185
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)
300,000 particlesStarting position
QuickTime™ and aSorenson Video decompressorare needed to see this picture.
Dynamics of mixing in a simplified mantle model
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
10
clip from fluid dynamics film series - 13:09
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)
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
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 •Removed at mid-ocean ridges
2900 km
670 km
Normalized viscosity
Dep
th
0 km
1 10 100
Hunt and Kellogg 2000
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
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
f=10
f=50
f=100
f=150
€
μl
/ μ0
25
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Movie1p
f = 1(reference model)
€
μl
/ μ0
26
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Movie3p.mov
f = 50
€
μl
/ μ0
27
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
4pi.mov
f = 100
€
μl
/ μ0
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↑
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
Mixing in a 3D spherical model of present-day mantle convectionPeter 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 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
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
3636