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Titel |
Mantle Convection in a Spherical Shell: The problems of using Frank-Kamenetskii Approximation for the viscosity law |
VerfasserIn |
Ana-Catalina Plesa, Christian Huettig, Doris Breuer |
Konferenz |
EGU General Assembly 2010
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Medientyp |
Artikel
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Sprache |
Englisch
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 12 (2010) |
Datensatznummer |
250037130
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Zusammenfassung |
Mantle convection in terrestrial planets is strongly influenced by the temperature dependence
of its viscosity. Considering this property, the mantle convection is basically divided into
three different regimes depending on the viscosity contrast: stagnant lid, sluggish and mobile
lid regime [1]. In the first regime the mantle is divided into two parts an active
part which is convecting and another one on top which is immobile. In the last
two regimes the surface material can move and is incorporated into the mantle
convection.
The temperature dependence of the mantle viscosity can be modeled using the so
called Arrhenius Law. In the Arrhenius formulation the temperature dependence of
the viscosity for a silicate mantle is given by the activation energy. Using realistic
values for the activation energy in the Arrhenius formulation will result in large
viscosity contrasts (~ 1040) which cannot be handled very well by the numeric.
Therefore, an approximation of the viscosity is commonly used to model the mantle
convection, i.e., the Frank-Kamenetskii approximation. This approximation linearises the
Arrhenius law, suggesting a viscosity which is many orders of magnitude smaller
at the surface. Although the approximation has been shown to represent only the
stagnant lid regime correctly, it is widely used in the literature also for the other
regimes.
We present a comparison of the mantle convection for stagnant lid cases using either the
Arrhenius law or the Frank-Kamenetskii approximation with a 3D spherical code, GAIA
[2,3].The results confirm earlier studies that the Frank-Kamenetskii approximation can be
used in the stagnant lid regime for a fixed Rayleigh number and a sufficiently thick stagnant
lid. However, several problems arise when using this approximation in numerical
simulations for a cooling mantle or for convection with a thin stagnant lid. A systematic
study is presented highlighting the differences in various control parameters of
mantle convection, e.g. degree of convection, Nusselt number, and stagnant lid
thickness.
References:
[1]. Solomatov, V.S.., Moresi, L.-N., Geophys. Research Letters, Vol. 24, No. 15, Pages
1907-1910, August 1, 1997
[2]. Huettig, C., Stemmer, K., Geochem. Geophys. Geosyst. (2008) doi: 10.1029/2007
GC001581
[3]. Huettig, C., Stemmer, K., Phys. Earth Planet Interiors (2008), doi: 10.1016/j.pepi.2008.07.007 |
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