Physics
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002agufm.p22c0417z&link_type=abstract
American Geophysical Union, Fall Meeting 2002, abstract #P22C-0417
Physics
5430 Interiors (8147), 5455 Origin And Evolution, 5724 Interiors (8147), 5749 Origin And Evolution, 8147 Planetary Interiors (5430, 5724)
Scientific paper
Core formation is generally thought to have occurred concurrently with or soon after planet formation and, therefore, determines the initial conditions for thermal evolution models to a significant extent. A possible scenario for the formation of a planetary core calls for the settling of iron-rich melt diapirs in a solid matrix. Assuming that a planet in the late stage of accretion has a magma ocean, there soon will form a layer of molten iron at the bottom of the magma ocean. Since the iron has a higher density than the underlying planetary mantle, it may sink in a Rayleigh-Taylor instability. Because the viscosity contrast is essentially infinite, the sinking melt diapir will take the shape of a sphere. We have modelled the Stokes falling of an iron sphere through a silicate mantle with temperature dependent viscosity using a 2-D finite element program (FEATFLOW) written by S. Turek. We solve the incompressible Navier--Stokes equation coupled with the energy and mass conservation equations. From these models the effect of the temperature dependence of the silicate rock viscosity on the sinking rate can be estimated. Depending on the rate of change of viscosity with temperature and the contrast in the rock viscosity immediately at the diapir (ν 0 and far from the diapir (ν ∞ the drag force exerted on the diapir can easily be reduced by several orders of magnitude. Equating the drag force with the body force will allow the terminal velocity of the sinking diapir to be calculated. For a viscosity contrast of ν ∞ /ν 0 of 103 or more the terminal velocity can be increased by a factor of ten with respect to the isoviscous case with ν = ν ∞ . To further increase core formation rate it may help to include the stress dependence of the rock rheology.
Spohn Tilman
Ziethe Ruth
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