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Cited by 71High-pressure geophysics and materialsGeomagnetism and Paleomagnetism StudiesGeophysics and Gravity Measurements

The influence of the boundary conditions and rotation on convection in the Earth's mantle

Open access
McKenzie, D. P.·1968·Geophysical Journal International
DOI 10.1111/j.1365-246x.1968.tb00203.x
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Abstract

The external nonhydrostatic gravity field must be maintained by flow within the mantle. An analysis of axisymmetric poloidal circulation in a rotating compressible sphere shows it to be more important than was previously believed. However, such flow is probably unable to produce the observed nonhydrostatic equatorial bulge. The basic equations are nonlinear, but can be solved if the viscosity is sufficiently large. The conditions which must be satisfied before this approximation is valid are examined in some detail because of their relevance to convection in the mantle. The horizontal temperature differences between oceans and continents must also drive convection currents, though such flow can only be of local importance at present. Two-dimensional convection driven by horizontal temperature variations can successfully account for most of the phenomena which are believed to be the surface expressions of flow in the mantle. The only exception is the gravity anomaly over the rising current, which is positive in the model. Though this linear theory is not self consistent, it does show that convection of heat is the only important nonlinear term. Further understanding of the problem will require numerical analysis.

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Crossref · 10.1111/j.1365-246x.1968.tb00203.x

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  • In the combined convective-elastic plate model, the gravity anomaly over the rising current becomes negative at dimensionless wavenumber k' = 0.43.

    “Gravity becomes negative over the rising current when k' = 0.43.”

    From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as McKenzie (1968)

    In the Introduction and Section 3, McKenzie says the calculated gravity anomaly is positive over the rising limb, not negative. The paper suggests that internal heating or convective heat transport might reverse the sign, but it does not report a negative anomaly at k′ = 0.43 or a result for the specified combined convective-elastic plate model. (LLM, conf=0.85)

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  • In a convecting fluid with imposed horizontal temperature variation, constant viscosity, and a free surface, the surface gravity anomaly is positive over rising fluid.

    “McKenzie (1968) obtained the surface gravity field of a convecting fluid driven by an imposed horizontal temperature variation, and showed that if the viscosity was constant and the surface free, the gravity anomaly was positive over the rising fluid.”

    From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as McKenzie (1968)

  • For a surface plate with nonzero shear modulus, convection cells much wider than the plate thickness behave as if the plate were absent, so the gravity-deformation relation is that of McKenzie (1968); cells much narrower than the plate thickness do not deform the surface and give negative gravity over a rising region.

    “It is then obvious that convection cells whose width is large compared to the plate thickness will behave as if the plate were absent and hence the relation between gravity and surface deformation will be that given by McKenzie (1968), but if the scale is small compared to the thickness, the surface will not deform and the gravity anomaly will be negative over a rising region.”

    From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as McKenzie (1968)

  • In the same setting, if the surface cannot deform, the gravity anomaly over rising fluid is negative.

    “If, however, the surface was not allowed to deform, the gravity anomaly was negative.”

    From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as McKenzie (1968)

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Cites

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Research works printed but not linked: 6

  1. by S . K. Runcorn. Academic Press, New York.
  2. Jeffreys, H., 1959. The Earth, Cambridge University Press.
  3. Lamb, H., 1932. Hydrodynamics, Cambridge University Press, reprinted by Dover, New York.
  4. Landau, L. D. & Liftshitz, E. M., 1959. Fluid Mechanics, Pergamon, Oxford.
  5. Munk, W. H. & MacDonald, G. J. F., 1960a. The Rotation of the Earth, Cam- bridge University Press.
  6. McKenzie, D. P., 1968. The geophysical importance of high temperature creep, in Proceedings of the NASA Conference on the History of the Earth's Crust, Princeton University Press, in press.

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Authors
McKenzie, D. P.
Corresponding author
McKenzie, D. P.
ORCID
McKenzie, D. P.
Venue
Geophysical Journal International
Publisher
Oxford University Press (OUP)
Published
1968-08
Volume
15
Issue
5
Pages
457-500
ISSN
  • 0956-540X (ISSN-L)
  • 1365-246X
DOI
10.1111/j.1365-246x.1968.tb00203.x
OpenAlex
W2031869231
Cited by
71
References
49
Citations by year
2024: 4 · 2023: 11 · 2022: 1 · 2021: 3 · 2017: 2 · 2016: 1 · 2015: 1
FWCI
4.20
Type
journal article
Language
en
Open access
Locations
Geophysical Journal International (publishedVersion)
Funders
  • California Institute of Technology
  • King's College London
Topics
  • Physical Sciences › Earth and Planetary Sciences › Geophysics › High-pressure geophysics and materials
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Geomagnetism and Paleomagnetism Studies
  • Physical Sciences › Earth and Planetary Sciences › Oceanography › Geophysics and Gravity Measurements
Keywords
mantle convection, Earth's mantle, boundary conditions, rotation, equatorial bulge, two-dimensional convection, gravity anomalies, heat transport

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