Skip to main content
Earth, Planets and Space
Download PDF

Volume 59 Supplement 7

Special Issue: Perspectives of Geomagnetism: Geodynamo, Paleomagnetism, and Rock magnetism—Tribute to Prof. Masaru Kono

Gravitational energy release in an evolving Earth model

Earth, Planets and Space volume 59, pages 651–659 (2007)Cite this article

Abstract

The energy budget of the Earth’s core balances the heat lost through cooling with the sum of gravitational, latent heat and radioactive sources (if any). The gravitational and latent heat sources are due to the freezing of core mix onto the surface of the inner core. Gravitational energy is released because the light components of core mix that are released during freezing are buoyant, and rise as they rejoin the fluid core. This source of energy can be regarded as part of the total gravitational energy released as the entire Earth cools and contracts. The main purpose of this paper is to present a new method of evaluating the total energy release. The method is applied to two Earth models. Both show that the gravitational source that stirs the fluid core is less than 30% of the total gravitational energy released through the contraction of the Earth as it cools.

References

  • Alfè, D., M. J. Gillan, and G. D. Price, Composition and temperature of the Earth’s core constrained by combining ab initio calculations with seismic data, Earth Planet. Sci. Lett., 195, 91–98, 2002a.

    Article  Google Scholar 

  • Alfè, D., G. D. Price, and M. J. Gillan, Iron under Earth’s core conditions. Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations, Phys. Rev. B, 65, 165118, 2002b.

    Article  Google Scholar 

  • Braginsky, S. I., Structure of the F layer and reasons for convection in the Earth’s core, Soviet Phys. Dokl., 149, 8–10, 1963.

    Google Scholar 

  • Braginsky, S. I. and P. H. Roberts, Equations governing convection in Earth’s core and the Geodynamo, Geophys. Astrophys. Fluid Dynam., 79, 1–97, 1995.

    Article  Google Scholar 

  • Braginsky, S. I. and P. H. Roberts, On the theory of convection in the Earth’s core, pp. 60–82 in Advances in Nonlinear Dynamos, edited by Ferris Mas, A. and M. Núñez, Taylor and Francis, London, 2005.

    Google Scholar 

  • Braginsky, S. I. and P. H. Roberts, The anelastic and Boussinesq approximations, in Encyclopedia of Geomagnetism & Paleomagnetism, eds. D. Gubbins and E. Herrero-Bervera, Springer, 2007.

    Google Scholar 

  • Calderwood, A. R., The absolute and relative magnitudes of the power sources that drive the geomagnetic dynamo re-evaluated with a self-consistent geochemical model, EOS Trans. AGU, 81 (48), p.F354, Fall Meeting Suppl., Abstract T21A-0862, American Geophysical Union, December 2000.

    Google Scholar 

  • Calderwood, A. R., The thermal conductivity profile of the lower mantle and the present day net core heat flux, EOS Trans. AGU, 82 (47), p.F1132, Fall Meeting Suppl., Abstract T21A-0862, American Geophysical Union, December 2001.

    Google Scholar 

  • Dziewonski, A. M. and D. L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter, 25, 297–356, 1981.

    Article  Google Scholar 

  • Eddington, A. S., The internal Constitution of the Stars, University Press, Cambridge UK, 1926.

    Google Scholar 

  • Gessmann, C. K. and B. J. Wood, Potassium in the core?, Earth Planet. Sci. Lett., 200, 63–78, 2002.

    Article  Google Scholar 

  • Glatzmaier, G. A. and P. H. Roberts, An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection, Physica D, 97, 81–94, 1996.

    Article  Google Scholar 

  • Glatzmaier, G. A. and P. H. Roberts, Simulating the geodynamo, Contemp. Phys., 38, 269–288, 1997.

    Article  Google Scholar 

  • Gubbins, D., D. Alfè, G. Masters, D. Price, and M. J. Gillan, Can the Earth’s dynamo run on heat alone?, Geophys. J. Int., 155, 609–622, 2003.

    Article  Google Scholar 

  • Gubbins, D., D. Alfè, G. Masters, D. Price, and M. Gillan, Gross thermodynamics of two-component convection, Geophys. J. Int., 157, 1407–1414, 2004.

    Article  Google Scholar 

  • Labrosse, S., Thermal and magnetic evolution of Earth’s core, Phys. Earth Planet. Inter., 140, 127–143, 2003.

    Article  Google Scholar 

  • Labrosse, S., J.-P. Poirier, and J.-L. Le Mouël, On the cooling of the inner core, Phys. Earth Planet. Inter., 99, 1–17, 1997.

    Article  Google Scholar 

  • Labrosse, S., J.-P. Poirier, and J.-L. Le Mouël, The age of the inner core, Earth Planet. Sci. Lett., 190, 111–123, 2001.

    Article  Google Scholar 

  • Lay, T., J. Hernlund, E. J. Garnero, and M. S. Thorne, A post-perovskite lens and D″ heat flux beneath the central Pacific, Science, 314, 1272–1276, 2006.

    Article  Google Scholar 

  • Masters, G. and D. Gubbins, On the resolution of density within the Earth, Phys. Earth Planet. Inter., 140, 159–167, 2003.

    Article  Google Scholar 

  • Murthy, V. R., W. van Westrenen, and Y. Fei, Radioactive heat sources in planetary cores; experimental evidence for potassium, Nature, 423, 163–165, 2003.

    Article  Google Scholar 

  • Nayfeh, A. H., Perturbation Methods, Wiley, New York, 1973.

    Google Scholar 

  • Nimmo, F, G. D. Price, J. Brodholt, and D. Gubbins, The influence of potassium on core and geodynamo, Geophys. J. Int., 156, 363–376, 2004.

    Article  Google Scholar 

  • Poirier, J.-P., Introduction to the Physics of the Earth’s Interior, University Press, Cambridge U.K., 1991.

    Google Scholar 

  • Roberts, P. H., C. A. Jones, and A. R. Calderwood, Energy fluxes and ohmic dissipation in the earth’s core, pp. 100–129 in Earth’s Core and Lower Mantle, edited by Jones, C.A., A. M. Soward, and K. Zhang, Taylor and Francis, London, 2003.

    Google Scholar 

  • Schubert, G., D. L. Turcotte, and P. Olson, Mantle Convection in the Earth and Planets, University Press, Cambridge U.K., 2001.

    Book  Google Scholar 

  • Stacey, F D., Physics of the Earth, 2nd Edition, Wiley, New York, 1977.

    Google Scholar 

  • Stacey, F D., Physics of the Earth, 3rd Edition, Brookfield Press, Brisbane, 1992.

    Google Scholar 

  • Stacey, F D., High pressure equations of state and planetary interiors, Repts. Prog. Phys., 68, 341–383, 2005.

    Article  Google Scholar 

  • Stacey, F D. and O. L. Anderson, Electrical and thermal conductivities of Fe-Ni-Si alloy under core conditions, Phys. Earth Planet. Inter, 124, 153–162, 2001.

    Article  Google Scholar 

  • Stacey, F D. and P. M. Davis, High pressure equations of state with applications to the lower mantle and core, Phys. Earth Planet. Inter, 142, 137–184, 2004.

    Article  Google Scholar 

  • Stacey, F D. and C. H. B. Stacey, Gravitational energy of core evolution: implications for thermal history and geodynamo power, Phys. Earth Planet. Inter, 110, 83–93, 1999.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA, 90095, USA

    Paul H. Roberts

  2. Global Edge Institute, Tokyo Institute of Technology, Meguro-ku, Tokyo, 152-8551, Japan

    Masaru Kono

Authors
  1. Paul H. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masaru Kono
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masaru Kono.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Roberts, P.H., Kono, M. Gravitational energy release in an evolving Earth model. Earth Planet Sp 59, 651–659 (2007). https://doi.org/10.1186/BF03352727

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03352727

Key words