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| Titel |
Comparison of isoviscous and viscously stratified spherical shell and plane-layer convection calculations |
| VerfasserIn |
Keely A. O'Farrell, Julian P. Lowman, Hans-Peter Bunge |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250049376
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| Zusammenfassung |
| Plane-layer geometry convection models remain a useful tool for investigating planetary
mantle dynamics but yield significantly warmer geotherms than spherical shell systems with a
small inner to outer radius ratio, f. For example, in a uniform property spherical shell with
the same radius ratio, f, as the Earth’s mantle; a bottom heating Rayleigh number, Ra, of 107
and a nondimensional internal heating rate, H, of 23 (arguably Earth-like values) are
insufficient to heat the mean temperature, θ, 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 θ, 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 mean temperature, θ, of a spherical system
described by f. 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 the
Earth and 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 a lower mantle that
gradually increases in viscosity by a factor of 30 relative to the upper mantle. In
this case the cooling required to match plane-layer convection temperatures with
spherical shell temperatures is less than in isoviscous convection but still substantial. |
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