Other
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.p21a1587o&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #P21A-1587
Other
[5418] Planetary Sciences: Solid Surface Planets / Heat Flow, [5430] Planetary Sciences: Solid Surface Planets / Interiors, [6296] Planetary Sciences: Solar System Objects / Extra-Solar Planets
Scientific paper
In a uniform property spherical shell with the same inner to outer radius ratio, f, as the Earth's mantle; a bottom heating Rayleigh number, Ra, of 1e7 and a nondimensional internal heating rate, H, of 23 (arguably Earth-like values) are insufficient to heat the mean temperature, T, above the mean of the boundary value temperatures (non-dimensional value 0.5). To address this geometrical effect, we implement heat sinks as a method of lowering the mean temperature in 3D plane-layer convecting systems. We analyze the mean temperatures of over 100 convection models to derive a single equation relating T, Ra, H and f in spherical and plane-layer systems featuring free-slip surfaces. For a given Rayleigh number, the derived expression can be used to calculate an appropriate heating or cooling rate for a plane-layer convection model in order to obtain the T of a spherical system described by f. Encouragingly, we find that at a Rayleigh number consistent with estimates of the effective value of Ra for the Earth's mantle, geotherms are similar for an appropriately cooled plane-layer system and a spherical shell model featuring a value for H based on estimates of the present-day rate of terrestrial mantle internal heating. Our findings have important implications for plane-layer geometry numerical models of mantle convection when emulating spherical shell convection at higher Rayleigh numbers. For higher Rayleigh numbers, the case applicable to super-Earths, the mean temperature of a mixed heating mode spherical system decreases faster than a plane-layer system so that the difference in the thermal structure of the two geometries increases. Accordingly, the inclusion of cooling in plane-layer models grows in importance. We extend our comparisons of the differences in plane-layer geometry convection and convection in a spherical shell geometry with the Earth's f value by considering systems featuring stratified viscosities. Complexity is added to the comparisons by the fact that T is a function of aspect ratio in the plane-layer calculations.
Bunge H.
Lowman Julian P.
O'Farrell Keely A.
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