Mathematics – Metric Geometry
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufm.v11e..03s&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #V11E-03
Mathematics
Metric Geometry
8124 Earth'S Interior: Composition And State (1212, 7207, 7208, 8105), 8125 Evolution Of The Earth (0325), 8147 Planetary Interiors (5430, 5724, 6024)
Scientific paper
Core formation is the first major differentiation event that determines the initial conditions from which terrestrial planets have evolved until present. The separation of metal and silicates in terrestrial planets is likely to generate substantially large amounts of heat by conversion of potential energy into thermal energy via viscous heating. This gravitational heat release for an Earth or a Mars-like planet represents a temperature increase of few hundreds to few thousands Kelvin. While estimating the total amount of gravitational heating in a planet is relatively straightforward, determining its partitioning between the silicate and metallic part is not a trivial task. We thus investigate dynamically the heat partitioning between metal and silicate during core formation by negative diapirism. We model numerically the sinking of iron-rich diapirs through a viscous silicate mantle, in spherical axisymmetric geometry. We carried a parameter study in which shear heating as well as several viscous rheologies were considered and systematically varied. We developed a simple semi-analytical model that captures the essential physics and we subsequently use it to derive general scaling laws for the time evolution of heat distribution between the iron-diapirs and the silicate material. These scaling laws are then used to determine the heat distribution within terrestrial planets during their growth and early differentiation.
Samuel Henri
Tackley Paul J.
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