Letter | Published:

The effect of compressible flow on anti-dynamo theorems

Abstract

The ‘anti-dynamo’ theorems (ADTs) impose restrictions on the symmetry properties of the velocity and magnetic fields associated with sustained dynamo action in an electrically conducting body of fluid, such as the Earth's core. However, several of these ADTs depend on the assumption that the fluid flow is incompressible, and we show here that their validity is queried when compressible flow is considered. In particular, non-stationary axisymmetric dynamos may no longer be prohibited by Cowling's theorem. The high degree of axisymmetry of Saturn's magnetic dipole, revealed by the recent Pioneer 11 flyby, may be related to the planet's large compressibility.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1

    Cowling, T. G. Mon. Not. R. astr. Soc. 94, 39–48 (1933).

  2. 2

    Backus, G. & Chandrasekhar, S. Proc. natn Acad. Sci. U.S.A. 42, 105–109 (1956).

  3. 3

    Cowling, T. G. Q. J. Mech. appl. Math. 10, 129–136 (1957).

  4. 4

    Braginskii, S. I. Sov. Phys. JETP 20, 726–735 (1964).

  5. 5

    Lortz, D. Phys. Fluids 11, 913–915 (1968).

  6. 6

    Elasser, W. M. Phys. Rev. 69, 106–116 (1946).

  7. 7

    Bullard, E. C. & Gellman, H. Phil. Trans. R. Soc. A247, 213–278 (1954).

  8. 8

    Backus, G. Ann. Phys. 4, 372–447 (1958).

  9. 9

    Moffatt, H. K. Magnetic Field Generation in Electrically Conducting Fluids, 121–122 (Cambridge University Press, 1978).

  10. 10

    Childress, S. Théorie Magnétohydrodynamique de l'Effet Dynamo (Institut Henri Poincaré, Paris, 1968).

  11. 11

    Namikawa, T. & Matsushita, S. Geophys. J. R. astr. Soc. 19, 395–415 (1970).

  12. 12

    Krause, F. & Roberts, P. H. Mathematika 20, 24–33 (1973).

  13. 13

    Smylie, D. E. & Rochester, M. G. Eos 60, 753 (1979).

  14. 14

    Moffatt, H. K. Magnetic Field Generation in Electrically Conducting Fluids, 113–122 (Cambridge University Press, 1978).

  15. 15

    Smith, E. J. et al. Eos 60, 865 (1979).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

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.