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Nusselt-Rayleigh number scaling for spherical shell Earth mantle simulation up to a Rayleigh number of 109109

Wolstencroft, M., Davies, John Huw ORCID: and Davies, David Rhodri ORCID: 2009. Nusselt-Rayleigh number scaling for spherical shell Earth mantle simulation up to a Rayleigh number of 109109. Physics of the Earth and Planetary Interiors 176 (1-2) , pp. 132-141. 10.1016/j.pepi.2009.05.002

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An investigation of the power law relationship between Nusselt number (Nu) and Rayleigh number (Ra) for Earth’s convecting mantle is presented. The Nu(Ra) relationship was calculated from the results of a model with three dimensional spherical geometry and free slip boundary conditions. Both basally and internally heated convection has been examined. For Nu(Ra)=aRaβ, β was found to be 0.294±0.004 for basally heated systems, which is lower than the value of 1/3 suggested by conventional boundary layer theory. The exponent β=0.337±0.009 for internally heated systems, when the internally heated Ra is converted to a basally heated equivalent for comparison. The influence of the method used to calculate β was also considered, with particular attention paid to high Ra. As an example of the significance of β=0.29 rather than 1/3, a Ra of 109 results in a surface heat flux which is ≈32% lower. Within the range of Ra used in this study, there is no evidence that β changes at high Ra. Therefore, that mechanism cannot be used to moderate mantle temperature when projecting back to early Earth conditions. The differing planform of basally and internally heated models was shown to result in different scaling relationships between root mean square surface velocity and Ra for the two modes of heating, in particular, a much lower surface velocity for internally heated cases relative to equivalent Ra basally heated cases.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Advanced Research Computing @ Cardiff (ARCCA)
Earth and Environmental Sciences
Subjects: Q Science > QE Geology
Uncontrolled Keywords: Planetary mantle; Rayleigh number; Nusselt number; Thermal evolution; Spherical geometry
Publisher: Elsevier
ISSN: 0031-9201
Last Modified: 18 Oct 2022 12:19

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