A dynamo model in a spherical shell

Authors

  • M. Reshetnyak
  • B. Steffen

Keywords:

метод контрольных объемов
магнитное поле
внутреннее ядро
инверсии
геодинамо
стратификация
планеты-гиганты

Abstract

For the convection-driven dynamo in the Boussinesq approximation in a rotating spherical shell, we study various regimes of thermal convection which may occur in the planetary cores. Our dynamo model is based on the control volume method, which is well suited for parallel computers using message passing. We consider different boundary conditions at the surface of the shell and mimic a regime with stratification, which is typical for compositional convection. The influence of the inner solid conductive core on reversals is considered. Applications of our modeling to the two different planetary geometries mdash; the Earth and Giant planets mdash; are discussed.

New computational technologies

Downloads

Published

2005-01-18

Issue

Vol. 6 (2005): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

M. Reshetnyak

Schmidt Institute of Physics of the Earth of RAS (IPE RAS)

B. Steffen

Central Institute for Applied Mathematics (ZAM) of Fofshungszentrum Jülich
Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

References

  1. Zeldovich Ya.B., Ruzmaikin A.A., Sokoloff D.D. Magnetic fields in astrophysics. New York: Gordon and Breach. 1983.
  2. Geomagnetism. Ed. by Jacobs J.A. Vol. 2, 3. New York: Academic Press. 1988.
  3. Jones C.A. Convection-driven geodynamo models // Phil. Trans. R. Soc. London. 2000. T. A 358. 873-897.
  4. Kono M., Roberts P. Recent geodynamo simulations and observations of the geomagnetic field // Reviews of Geophysics. 2002. 40, N 10. B1-B41.
  5. Hejda P., Reshetnyak M. Control volume method for the dynamo problem in a sphere with the free rotating inner core // Studia geoph. et. geod. 2003. 47. 147-159.
  6. Hejda P., Reshetnyak M. Control volume method for the thermal convection problem in a rotating spherical shell: test on the benchmark solution // Studia geoph. et. geod. 2004. 48. 741-746.
  7. Hollerbach R., Jones C. Influence of the Earth’s inner core on geomagnetic fluctuations and reversals // Nature. 1993. 365. 541-543.
  8. Wicht J. Inner-core conductivity in numerical dynamo simulations // Phys. Earth Planet. Inter. 2002. 132. 281-302.
  9. Christensen U.R., Aubert J., Cardin P., Dormy E, Gibbons S., Glatzmaier G.A., Grote E., Honkura Y., Jones C., Kono M., Matsushima M., Sakuraba A., Takahashi F., Tilgner A., Wicht J., Zhang K. A numerical dynamo benchmark // Phys. Earth Planet. Inter. 2001. 128. 25-34.
  10. Krause F., Rädler K.-H. Mean field magnetohydrodynamics and dynamo theory. Berlin: Akademie-Verlag, 1980.
  11. Patankar S.V. Numerical heat transfer and fluid flow. New York: Taylor & Francis, 1980.
  12. Sarson G.R., Jones C.A., Longbottom A.W. The influence of the boundary region on the geodynamo // Phys. Earth Planet. Inter. 1997. 101. 13-32.
  13. Glatzmaier G.A., Coe R.S., Hongre L., Roberts P. The role of the Earth’s mantle in controlling the frequency of geomagnetic reversals // Nature. 1999. 401. 885-890.
  14. Glatzmaier G.A., Roberts P.H. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle // Phys. Earth Planet. Inter. 1995. 91. 63-75.
  15. Wicht J., Olson P. A detailed study of the polarity reversal mechanism in a numerical dynamo model // Geochemistry, Geophysics, Geosystems. 2004. 5, N 3. 1-23.
  16. Kutzner C., Cristensen U.R. From stable dipolar towards reversing numerical dynamos // Phys. Earth Planet. Inter. 2002. 131. 29-45.
  17. Simitev R. Ph.D. Thesis: Convection and magnetic field generation in rotating spherical fluid shells. Bayreuth: University of Bayreuth, 2004. http://www.phy.uni-bayreuth.de/theo/tp4/members/simitev.html
  18. Jacobs J.A. Reversals of the Earth’s magnetic field. 2nd edition. Cambridge: Cambridge University Press, 2004.
  19. Braginsky S.I., Roberts P.H. Equations governing convection in the Earth’s core and the geodynamo // Geophys. Astrophys. Fluid Dynamics. 1995. 79. 1-97.
  20. Zhang K., Busse F.H. On the onset of convection in rotating spherical shells // Geophys. Astrophys. Fluid. Dyn. 1987. 39. 119-147.
  21. Ruzmaikin A.A., Starchenko S.V. On the origin of Uranus and Neptune magnetic fields // Icarus. 1991. 93. 82-87.
  22. Cupal I., Hejda P., Reshetnyak M. Dynamo model with thermal convection and free-rotating inner core // Planetary and Space Science. 2002. 50. 1117-1122.
  23. Stanley S., Bloxham J. Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields // Letters to Nature. 2004. 428. 151-153.
  24. Sarson G.R., Jones C.A. A convection driven geodynamo reversal model // Phys. Earth Planet. Inter. 1999. 111. 3-20.