transition from pervasive to segregated fluid flow in ductile rocks james connolly and yuri...
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Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks
James Connolly and Yuri Podladchikov, ETH Zurich
A transition between “Darcy” and Stokes regimes
• Geological scenario• Review of steady flow instabilities => porosity waves
• Analysis of conditions for disaggregation
Lithosphere
Partia lly (3 vol % ) m oltenasthenosphere
Basalt d ikes
Basalt s ills
M assive D unites
R eplacive D unites
R eplacive D unites = reactive transport channeling instability?
Basalt d ikes = se lf propagating cracks?
Basalt s ills = segregation caused by m agica l perm eability barriers?
M assive D unites = rem obilized replacive dunite?
M id-O cean R idge
lithosphere
1D Flow Instability, Small (<<1) Formulation, Initial Conditions
-250 -200 -150 -100 -50 0
2
4
6
8t = 0
z
-250 -200 -150 -100 -50 0-1
-0.5
0
0.5
1
z
p
1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1
p =
d, disaggregation condition
1D Movie? (b1d)
1D Final
-350 -300 -250 -200 -150 -100 -50 0
1
2
3
4
5t = 70
z
-350 -300 -250 -200 -150 -100 -50 0-1
-0.5
0
0.5
1
z
p
1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1
p
• Solitary vs periodic solutions
• Solitary wave amplitude close to source amplitude
• Transient effects lead to mass loss
2D Instability
Birth of the Blob
• Stringent nucleation conditions
• Small amplification, low velocities
• Dissipative transient effects
Bad news for Blob fans:
Is the blob model stupid?
A differential compaction model
Dike Movie? (z2d)
The details of dike-like waves
Comparison movie (y2d2)
Final comparison
• Dike-like waves nucleate from essentially nothing
• They suck melt out of the matrix
• They are bigger and faster
• Spacing c, width d
But are they solitary waves?
Velocity and Amplitude
0 5 10 15 20 25 30 353.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
time /
Blob model
amplitudevelocity
0 0.5 1 1.5 2 2.5 3 3.50
5
10
15
20
25
30
35
40
time /
Dike model
amplitudevelocity
1D Quasi-Stationary State
4.5 5 5.5-10
-5
0
5
10
15
20
25
30
35
x/
Horizontal Section
-60 -40 -20 0-10
-5
0
5
10
15
20
25
30
35
y/
Vertical Section
0 10 20 30 40
-6
-4
-2
0
2
4
6
p
Phase Portrait
Pressure,Porosity
Pressure,Porosity
• Essentially 1D lateral pressure profile• Waves grow by sucking melt from the matrix
•The waves establish a new “background”” porosity• Not a true stationary state
1
1
So dike-like waves are the ultimate in porosity-wave fashion:
They nucleate out of essentially nothing They suck melt out of the matrix
They seem to grow inexorably toward disaggregation
But
Do they really grow inexorably, what about 1?
Can we predict the conditions (fluxes) for disaggregation?
Simple 1D analysis
Mathematical Formulation
• Incompressible viscous fluid and solid components
• Darcy’s law with k = f(), Eirik’s talk
• Viscous bulk rheology with
• 1D stationary states traveling with phase velocity
es
s
2 2q
11
d
1
q
mq
pv
f
f
es
s
pv
(geological formulations ala McKenzie have )
Balancing ball
gv h
t x
v p
x
t z
0 ,p
fz
xv
t
1( )s
pf
z
v g h
x v x
sp H
p
0h
vdv g dxx
0 s
Hpdp d
2
2
vE hg
2
2 sp
U H sg
Porosity WaveBalancing Ball
H(omega)
Phase diagram
Sensitivity to Constituitive Relationships
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