Erfahrungsbericht NEMO-Netzwerk „Netzwerk für Innovative Logistik (NIL)“ 16.06.2010 Uwe Pfeil
Modul BWP12 16.06.2010 Zustandsgleichungen (III): dynamische Eigenschaften.
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Transcript of Modul BWP12 16.06.2010 Zustandsgleichungen (III): dynamische Eigenschaften.
Modul BWP1216.06.2010
Zustandsgleichungen (III):Zustandsgleichungen (III):dynamische Eigenschaftendynamische Eigenschaften
Modul BWP1216.06.2010
Antriebskraft: thermische Konvektion
Rayleigh Zahl „Ra“
Ra =0Tgd3
Thermischer Auftrieb (Energiequelle)
Schicht-dicke
Viskosität(behindernd)
Thermische Dissipation
(behindernd)
- thermischer Ausdehnungskoeffizient
g - Schwerebeschleunigung
0 - Dichte
Modul BWP1216.06.2010
Übergang zu einerÜbergang zu einer
kontinuumsmechanischen kontinuumsmechanischen BeschreibungBeschreibung
Modul BWP1216.06.2010
zu lösendeszu lösendes
Gl.-System !Gl.-System !
- thermischer Ausdehnungskoeffizient
0 - Dichte - thermische Leitfähigkeit - dynamische Viskositätcp - spezifische Wärmekapazität
g - Schwerebeschleunigung
Erhaltungssatz für die Masse Erhaltungssatz für die Masse **
Erhaltungssatz für die Energie Erhaltungssatz für die Energie **
ErhaltungssatzErhaltungssatzfür den Impuls für den Impuls **
(Kräftebilanz)(Kräftebilanz)
* D/Dt /t + vi/xi (substanzielle Ableitung)
Modul BWP1216.06.2010
Zur Bestimmung der Zur Bestimmung der
dynamischen Eigenschaftendynamischen Eigenschaften
im Erdinnern benötigt man die im Erdinnern benötigt man die
Kenntnis der MaterialparameterKenntnis der Materialparameter
, , ccpp
als Funktion der Tiefe !als Funktion der Tiefe !(d.h. insbesondere in Abhängigkeit (d.h. insbesondere in Abhängigkeit
von Druck und Temperatur etc.)von Druck und Temperatur etc.)
Modul BWP1216.06.2010
Numerische LösungNumerische Lösung
des denkbar einfachsten Falls:des denkbar einfachsten Falls:
alle Materialparameter alle Materialparameter konstantkonstant
Modul BWP1216.06.2010
numerische Lösung für Ra = 104
(finite element solver „citcom“)
Raum-zeitliche Entwicklung der Temperatur TRaum-zeitliche Entwicklung der Temperatur T
Modul BWP1216.06.2010
numerische Lösung für Ra = 105
(finite element solver „citcom“)
Raum-zeitliche Entwicklung der Temperatur TRaum-zeitliche Entwicklung der Temperatur T
Modul BWP1216.06.2010
numerische Lösung für Ra = 106
(finite element solver „citcom“)
Raum-zeitliche Entwicklung der Temperatur TRaum-zeitliche Entwicklung der Temperatur T
Modul BWP1216.06.2010
Stabilitätsanalyse für denStabilitätsanalyse für den
WärmetransportWärmetransport
in diesem Fallin diesem Fall
Modul BWP1216.06.2010
kritischeRayleigh-Zahl
Racr= 658
Modul BWP1216.06.2010
Modul BWP1216.06.2010
Modul BWP1216.06.2010
Thermal modeling gives a driving force for subduction due to the integrated negative
buoyancy (sinking) of cold dense slab from density contrast between it and the warmer and
less dense material at same depth outside. Negative buoyancy is associated with the cold downgoing limb of mantle convection pattern.
Since the driving force depends on thermal density contrast, it increases for
(i) Higher v, faster subducting & hence colder plate
(ii) Higher L, thicker and older & hence colder plate
Expression is similar to that for “ridge push” since both forces are thermal buoyancy forces
““SLAB PULL” plate driving forceSLAB PULL” plate driving force
Modul BWP1216.06.2010
Abschätzung von tektonischen Kräften
„ridge-push“ vs. „slab-pull“
~ 1012 Nm-1 ~ 1013 Nm-1
Modul BWP1216.06.2010
Coldest portion reaches only ~ half mantle temperature in about 10 Myr, about the time required for the slab to reach 660 km.
Thus restriction of seismicity to depths < 660 km does not indicate that the slab is no longer a discrete thermal and mechanical entity.
From thermal standpoint, there is no reason for slabs not to penetrate into lower mantle.
When a slab descends through lower mantle at the same rate (it probably slows due to the more viscous lower mantle), it retains a significant thermal anomaly at the core-mantle boundary, consistent with models of that region
Slabs are not thermally equilibrated with mantleSlabs are not thermally equilibrated with mantle
Stein & Stein, 1996
Modul BWP1216.06.2010
Was passiert,wenn die Viskosität
in der Erdenicht konstant ist,d.h. mit der Tiefe
abnimmt ?
Modul BWP1216.06.2010
„Lithosphäre“
„stagnant lid“
Modul BWP1216.06.2010
Plattentektonik
3 Typen von Plattengrenzen
Ozeane Kontinente
Modul BWP1216.06.2010
simple scaling viewL
W
D
FR
FB
vplate T
density after expansion
t)1/2
cooling thickness time t
- bouyancy forceFR - resistance force
Modul BWP1216.06.2010
density size gravity
mass acceleration*
„bouyancy force“
stress
area„resistance force“
because of
Plate tectonics: scaling view (I)
FB = DW ) g
FR = v/LDW )
and = = vL
Modul BWP1216.06.2010
FB FR
~ Ra 2/3
Plate tectonics: scaling view (II)
Modul BWP1216.06.2010
T = 1400 K temperature difference
= 3 ·10-6 m2/s thermal expansion
= 1022 Pa s viscosity
= 10-6 m2/s thermal diffusivity
= 3 ·103 kg/m3 density
g = 10 m/s2 grav. acceleration
L = 3 ·106 m layer thickness
plate velocity ~ 14 cm/yr !
Modul BWP1216.06.2010Stein & Wysession, Blackwell 2003
Different stresses result if weight of column of material supported in
different ways
similar to what seismic focal mechanisms show !
Forces within subducting platesForces within subducting plates
Modul BWP1216.06.2010
Clapeyron slope describes how mineral phase Clapeyron slope describes how mineral phase changes occur at different depths in cold slabschanges occur at different depths in cold slabs
use thermal model to find dT, phase
relations to find and thus dP
convert to convert to depth change depth change
dzdz
Modul BWP1216.06.2010
Opposite deflection of mineral phase boundariesOpposite deflection of mineral phase boundaries
Upward deflection of the 410 km and downward deflection of the 660 km discontinuities have been observed in travel time studies.
In contrast, the ringwoodite ( spinel phase) to perovoskite plus magnesiowustite transition, thought to
give rise to the 660 km discontinuity, is endothermic (absorbs heat) so H > 0. Because this is a
transformation to denser phases (V < 0), Clapeyron slope is negative, and the 660 km discontinuity should be
deeper in slabs than outside
Because spinel is denser than olivine, V < 0. This reaction is exothermic (gives off heat) so H < 0 is also negative, causing a positive Clapeyron slope. The slab is
colder than the ambient mantle (T<0 ), so this phase change occurs at a lower pressure (P<0), corresponding
to shallower depth
Modul BWP1216.06.2010
Kirby et al., Rev. Geophys. 1996
Metastable delay of mineral phase transformationsMetastable delay of mineral phase transformations
Modul BWP1216.06.2010
Predicted mineral phase boundaries and resulting buoyancy forces in slab with
and without metastable olivine wedge
For equilibrium mineralogy cold slab has negative thermal buoyancy, negative
compositional buoyancy from elevated 410 km discontinuity, and positive
compositional buoyancy from depressed 660 km discontinuity
Metastable wedge gives positive compositional buoyancy and decreases
force driving subduction
Stein & Rubie, Science 1999
negative buoyancy favours subduction, whereas positive buoyancy opposes it.
Metastable delay of mineral phase transformationsMetastable delay of mineral phase transformations
Modul BWP1216.06.2010
Deep earthquakes from metastable olivine ?Deep earthquakes from metastable olivine ?
Kirby et al., Rev. Geophys. 1996
Modul BWP1216.06.2010
Intermediate depth earthquakes (I)Intermediate depth earthquakes (I)
Under equilibrium conditions, eclogite
should form by the time slab reaches ~70 km
depth. However, travel time studies in some slabs
find low-velocity waveguide interpreted as
subducting crust extending to deeper
depths. Hence eclogite-forming reaction may be
slowed in cold downgoing slabs,
allowing gabbro to persist metastably.
Oceanic crust should undergo two important mineralogic transitions as it subducts. Hydrous (water-bearing) minerals formed at fractures and faults
warm up and dehydrate. Gabbro transforms to eclogite, rock of same composition composed of denser minerals.
Kirby et al., Rev. Geophys. 1996
Modul BWP1216.06.2010
Intermediate depth earthquakes (II)Intermediate depth earthquakes (II)
Support for this model comes from the fact that
the intermediateearthquakes occur below the island arc volcanoes,
which are thought to result when water released from the
subducting slab causes partial melting in the
overlying asthenosphere.
In this model intermediate earthquakes occur by slip on faults, but phase changes favor faulting. The extensional focal mechanisms may also reflect the phase change, which would
produce extension in the subducting crust.
Kirby et al., Rev. Geophys. 1996
Modul BWP1216.06.2010
various kineticprocesses during
subduction
P. van Keken, 2004
Modul BWP1216.06.2010
Deep subduction process is a chemical reactor that brings cold
shallow minerals into temperature and pressure
conditions of mantle transition zone where these
phases are no longer thermodynamically stable.
Because there is no direct way of studying what is happening and what comes out, one seeks to
understandthe system by studying
earthquakes that somehow reflect what is happening.
Kirby et al., 1996
Complex thermal structure, mineralogy & geometry of Complex thermal structure, mineralogy & geometry of subducted slabs in the mantle transition zonesubducted slabs in the mantle transition zone