Skip to main content

Thank you for visiting nature.com. 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.

Power requirement of the geodynamo from ohmic losses in numerical and laboratory dynamos

Abstract

In the Earth's fluid outer core, a dynamo process converts thermal and gravitational energy into magnetic energy. The power needed to sustain the geomagnetic field is set by the ohmic losses (dissipation due to electrical resistance)1. Recent estimates of ohmic losses cover a wide range, from 0.1 to 3.5 TW, or roughly 0.3–10% of the Earth's surface heat flow1,2,3,4. The energy requirement of the dynamo puts constraints on the thermal budget and evolution of the core through Earth's history1,2,3,4,5. Here we use a set of numerical dynamo models to derive scaling relations between the core's characteristic dissipation time and the core's magnetic and hydrodynamic Reynolds numbers—dimensionless numbers that measure the ratio of advective transport to magnetic and viscous diffusion, respectively. The ohmic dissipation of the Karlsruhe dynamo experiment6 supports a simple dependence on the magnetic Reynolds number alone, indicating that flow turbulence in the experiment and in the Earth's core has little influence on its characteristic dissipation time. We use these results to predict moderate ohmic dissipation in the range of 0.2–0.5 TW, which removes the need for strong radioactive heating in the core7 and allows the age of the solid inner core to exceed 2.5 billion years.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Scaling of magnetic dissipation time.
Figure 2: Pressure drop versus flow rate in the Karlsruhe dynamo experiment.
Figure 3: Secular variation time scaling.

References

  1. 1

    Buffett, B. A. Estimates of heat flow in the deep mantle based on the power requirements of the geodynamo. Geophys. Res. Lett. 29, doi:1.1029/2001GL014649 (2002)

  2. 2

    Roberts, P. H., Jones, C. A. & Calderwood, A. R. in Earth's Core and Lower Mantle (eds Jones, C. A., Soward, A. M. & Zhang, K.) 100–129 (Taylor & Francis, London, 2003)

    Google Scholar 

  3. 3

    Labrosse, S. Thermal and magnetic evolution of the Earth's core. Phys. Earth Planet. Inter. 140, 127–143 (2003)

    ADS  Article  Google Scholar 

  4. 4

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

    ADS  Article  Google Scholar 

  5. 5

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

    ADS  CAS  Article  Google Scholar 

  6. 6

    Stieglitz, R. & Müller, U. Experimental demonstration of the homogeneous two-scale dynamo. Phys. Fluids 13, 561–564 (2001)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Gessmann, C. K. & Wood, B. J. Potassium in the Earth's core? Earth Planet. Sci. Lett. 200, 63–78 (2002)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Langel, R. A. & Estes, R. H. A geomagnetic field spectrum. Geophys. Res. Lett. 9, 250–253 (1982)

    ADS  Article  Google Scholar 

  9. 9

    Kuang, W. & Bloxham, J. An Earth-like numerical dynamo model. Nature 389, 371–374 (1997)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Roberts, P. H. & Glatzmaier, G. A. A test of the frozen-flux approximation using a new geodynamo model. Phil. Trans. R. Soc. Lond. A 358, 1109–1121 (2000)

    ADS  Article  Google Scholar 

  11. 11

    Christensen, U., Olson, P. & Glatzmaier, G. A. Numerical modeling of the geodynamo: a systematic parameter study. Geophys. J. Int. 138, 393–409 (1999)

    ADS  Article  Google Scholar 

  12. 12

    Kutzner, C. & Christensen, U. R. From stable dipolar to reversing numerical dynamos. Phys. Earth Planet. Inter. 131, 29–45 (2002)

    ADS  Article  Google Scholar 

  13. 13

    Müller, U. & Stieglitz, R. The Karlsruhe dynamo experiment. Nonlin. Proc. Geophys. 9, 165–170 (2002)

    ADS  Article  Google Scholar 

  14. 14

    Tilgner, A. Numerical simulation of the onset of dynamo action in an experimental two-scale dynamo. Phys. Fluids 14, 4092–4094 (2002)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Hulot, G. & LeMouël, J. L. A statistical approach to the Earth's main magnetic field. Phys. Earth Planet. Inter. 82, 167–183 (1994)

    ADS  Article  Google Scholar 

  16. 16

    Bloxham, J. & Jackson, A. Time-dependent mapping of the magnetic field at the core-mantle boundary. J. Geophys. Res. 97, 19537–19563 (1992)

    ADS  Article  Google Scholar 

  17. 17

    Buffett, B. A. The thermal state of the Earth's core. Science 299, 1675–1676 (2003)

    CAS  Article  Google Scholar 

  18. 18

    Rama Murthy, V., van Westrenen, W. & Fei, Y. Experimental evidence that potassium is a substantial radioactive heat source in planetary cores. Nature 423, 163–165 (2003)

    ADS  Article  Google Scholar 

  19. 19

    McElhinny, M. W. & Senanayake, W. E. Paleomagnetic evidence for the existence of the geomagnetic field 3.5 Ga ago. J. Geophys. Res. 85, 3523–3528 (1980)

    ADS  Article  Google Scholar 

  20. 20

    Secco, R. A. & Schloessin, H. H. The electrical resistivity of solid and liquid Fe at pressures up to 7 GPa. J. Geophys. Res. 94, 5887–5894 (1989)

    ADS  Article  Google Scholar 

  21. 21

    Bloxham, J., Gubbins, D. & Jackson, A. Geomagnetic secular variations. Phil. Trans. R. Soc. Lond. A 329, 415–502 (1989)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank U. Müller for the permission to use unpublished results from the laboratory dynamo experiment. This work was supported by the priority programme “Geomagnetic secular variations” of the Deutsche Forschungsgemeinschaft.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ulrich R. Christensen.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Christensen, U., Tilgner, A. Power requirement of the geodynamo from ohmic losses in numerical and laboratory dynamos. Nature 429, 169–171 (2004). https://doi.org/10.1038/nature02508

Download citation

Further reading

Comments

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.

Search

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