Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Effects from equation of state and rheology in dissipative heating in compressible mantle convection


The thermal profile in the Earth's interior is influenced by many factors. One of the least understood and studied processes is that resulting from adiabatic heating and viscous dissipation. With the exception of the work by Jarvis and McKenzie1 very little has been done on the effects of compressibility on mantle circulation. It is quite common for geophysicists to add the adiabatic temperature gradient a posteriori2 to temperature profiles derived from Boussinesq (incompressible) equations. Recently it has been shown3 with the mean-field method4 that there exists a strong coupling between the Theological parameters, such as the activation volume, and the thermodynamic constants governing adiabatic heating. Here we point out the important consequences brought about by incorporating the effects of equations of state and rheology in the dissipative heating term of the energy equation. We demonstrate explicitly the ways in which compression may raise the interior mantle temperature and illustrate how this effect can, in turn, be used for constraining some of the intrinsic parameters associated with the equation of state in the mantle.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout


  1. Jarvis, G. T. & McKenzie, D. P. J. Fluid Mech. 96, 515–583 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  2. Jeanloz, R. & Morris, S. A. Rev. Earth planet. Sci. 14, 377–416 (1986).

    Article  ADS  Google Scholar 

  3. Quareni, F., Yuen, D. A. & Saari, M. R. Geophys. Res. Lett. 13, 38–41 (1986).

    Article  ADS  Google Scholar 

  4. Gough, D. O., Spiegel, E. A. & Toomre, J. J. Fluid Mech. 68, 695–719 (1975).

    Article  ADS  Google Scholar 

  5. Yuen, D. A. & Fleitout, L. M. Nature 313, 125–128 (1985).

    Article  ADS  Google Scholar 

  6. Spera, F. J., Yuen, D. A., Clark, S. & Hong, H. J. Geophys. Res. Lett. 86, 153–156 (1986).

    Article  ADS  Google Scholar 

  7. Roberts, P. H. J. Fluid Mech. 30, 33–49 (1967).

    Article  ADS  Google Scholar 

  8. Sammis, C. G., Smith, J. C., Schubert, G. & Yuen, D. A. J. geophys. Res. 82, 3747–3761 (1977).

    Article  ADS  CAS  Google Scholar 

  9. Boehler, R. J. geophys. Res. 86, 7159–7162 (1981).

    Article  ADS  CAS  Google Scholar 

  10. Knittle, E., Jeanloz, R. & Smith, G. L. Nature 319, 214–216 (1986).

    Article  ADS  CAS  Google Scholar 

  11. Zebib, A. F., Schubert, G. & Straus, J. M. J. Fluid Mech. 97, 257–277 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  12. Olson, P. L. J. geophys. Res. 86, 4881–4890 (1981).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yuen, D., Quareni, F. & Hong, HJ. Effects from equation of state and rheology in dissipative heating in compressible mantle convection. Nature 326, 67–69 (1987).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing