Skip to main content

On the Saturation of Astrophysical Dynamos: Numerical Experiments with the No-Cosines Flow


In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo’s mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate in the linear regime, the dynamo saturates at a level significantly higher than normal turbulent dynamos, namely at exact equipartition when the magnetic Prandtl number Prm∼ 1. Visualization of the magnetic and velocity fields at saturation will help us to understand some of the aspects of the non-linear dynamo problem.


  1. Archontis, V., Dorch, S. B. F., and Nordlund, Å.: 2003a, Astron. Astrophys. 397, 393.

    Article  ADS  Google Scholar 

  2. Archontis, V., Dorch, S. B. F., and Nordlund, Å.: 2003b, Astron. Astrophys. 410, 759.

    Article  ADS  Google Scholar 

  3. Cattaneo, F., Hughes, D. W., and Kim, E.: 1996, Phys. Rev. Lett. 76, 2057.

    Article  ADS  Google Scholar 

  4. Childress, S. and Gilbert, A. D.: 1995, Stretch, Twist, Fold: The Fast Dynamo, Springer-Verlag, Berlin, p. 52.

    Google Scholar 

  5. Choudhuri, A. R.: 2003, Solar Phys. 215, 31.

    Article  ADS  Google Scholar 

  6. Dorch, S. B. F.: 2000, Physica Scripta 61, 717.

    Article  ADS  Google Scholar 

  7. Galloway, D. and Proctor, M.: 1992, Nature 356, 691.

    Article  ADS  Google Scholar 

  8. Haugen, N. E. L., Brandenburg, A., and Dobler, W.: 2003, Astrophys. J. 597, L141.

    Article  ADS  Google Scholar 

  9. Moreno-Insertis, F., Caligari, P., and Schüssler, M.: 1994, Solar Phys. 153, 449.

    Article  ADS  Google Scholar 

  10. Nordlund, A., Brandenburg, A., Jennings, R. L., Rieutord, M., Roukolainen, J., Stein, R. F., and Tuominen, I.: 1992, Astrophys. J. 392, 647.

    Article  ADS  Google Scholar 

  11. Parker, E. N.: 1979, Cosmical Magnetic Fields, Clarendon, Oxford.

    Google Scholar 

  12. Safier, P. N.: 1999, Astrophys. J. 510, L127.

    Article  ADS  Google Scholar 

  13. Tanner, S. and Hughes, D.: 2003, Astrophys. J. 586, 585.

    Article  ADS  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to S. B. F. Dorch.

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Cite this article

Dorch, S.B.F., Archontis, V. On the Saturation of Astrophysical Dynamos: Numerical Experiments with the No-Cosines Flow. Sol Phys 224, 171–178 (2004).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:


  • Growth Rate
  • Numerical Experiment
  • Velocity Field
  • High Growth
  • Prandtl Number