University of Illinois Urbana-Champaign

Does the earth's nonuniform gravitational field affect its mantle convection?

Hsui, Albert T.; Riahi, Daniel N.; ICTAM

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https://hdl.handle.net/2142/112659

Description

Title
Does the earth's nonuniform gravitational field affect its mantle convection?
Author(s)
  • Hsui, Albert T.
  • Riahi, Daniel N.
  • ICTAM
Issue Date
2000-07
Keyword(s)
  • Vertical Flow
  • Heat Transfer
  • Conference Guide
Abstract
The gravity field of the Earth's mantle has been modeled previously by other investigators based on constraints derived from seismic studies as well as the bulk mass and the moment of inertia factor of the Earth. It shows a rather peculiar form that has a local minimum and a local maximum. It is strikingly different from the constant gravity or the linearly varying gravity that commonly used for mantle dynamic investigations. To evaluate if this peculiar gravity structure plays any role in the determination of the vertical flow structure or the heat transfer in the mantle, two theoretical studies have been carried out. Our stability analysis shows that the critical Rayleigh number for the onset of instability can be modified by the curvature of the gravity profile. Qualitatively, gravity with a local maximum tends to enhance flow intensity, whereas gravity with a local minimum shows the opposite effect. An examination of the eigenvectors of the stability analysis suggests that dynamic layering may be possible for flow fields with local gravity extremums, or at least mathematically. However, a closer examination indicates that dynamic layering can only occur if gravity changes sign within the flow field, which is impossible to realize for the mantle. Consequently, it is concluded that gravity extremums alone cannot produce dynamic layering within Earth's mantle. A boundary layer model has also been developed to study the effects of a variable gravity field to the heat transfer within the mantle. This study is able to quantify the qualitative conclusion described earlier based on the critical Rayleigh number consideration. Our result shows that even for a gravity variation as large as the reference gravity itself, surface Nusselt number is not expected to change by more than a few percent. On the basis of these studies, it appears that the peculiar gravity profile within the Earth's mantle will play no important role in the determination of the mantle flow structure, nor will it affect the total heat transport by very much.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 949
  • 2000-6024
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112659
Copyright and License Information
Copyright 2000 Board of Trustees of the University of Illinois

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