A route to magnetic field reversals: An example of an ABC-forced nonlinear dynamo

Geophysical and Astrophysical Fluid Dynamics

Volumn 97, Issue 2, 2003, Pages 149-174

  Podvigina, O M ^a,b,c  

^a INSTITUTE OF EARTHQUAKE PREDICTION THEORY AND MATHEMATICAL GEOPHYSICS   (Russian Federation)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

^c UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Bifurcations; Nonlinear magnetic dynamo; Reversals

Indexed keywords

BIFURCATION (MATHEMATICS); MAGNETIC FIELDS; PERTURBATION TECHNIQUES; REYNOLDS NUMBER;

CHAOTIC VARIATION; MAGNETIC FIELD REVERSALS;

ASTROPHYSICS;

BIFURCATION; GEODYNAMO; MAGNETIC FIELD; MAGNETIC REVERSAL; NUMERICAL MODEL;

EID: 1342329678     PISSN: 03091929     EISSN: None     Source Type: Journal    
DOI: 10.1080/0309192031000119740     Document Type: Article

References (31)

1. Armbruster, D., Chossat, P. and Oprea, I., "Structurally stable heteroclinic cycles and the dynamo dynamics", In: Dynamo and Dynamics, a Mathematical Challenge (Eds. Chossat, P., Armbruster, D. and Oprea, I.) pp. 313-322, Kluwer Academic Publishers, Dordrecht (2001).
2. Arnold, V.I., "On the evolution of magnetic field under the action of advection and diffusion", In: V.M. Tikhomirov (Ed.), Some Problems of Modern Analysis, pp. 8-21, Moscow Univ. Press (1984), Moscow (in Russian).
3. Arnold, V.I. and Korkina, E.I., "The growth of a magnetic field in a three-dimensional incompressible flow", Vestnik Moscow State Univ., Ser. Math. 3, 43-46 (1983) (in Russian).
4. Boyd, J.P., Chebyshev & Fourier Spectral Methods, Springer-Verlag, Berlin (1989).
5. Brummell, N.H., Cattaneo, F. and Tobias, S.M., "Linear and non-linear dynamo action", Phys. Lett. A 28, 437-442 (1998).
6. Brummell, N.H., Cattaneo, F. and Tobias, S.M., "Linear and non-linear dynamo properties of time-dependent ABC flows", Fluid Dyn. Res. 28, 237-265 (2001).
7. Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A., Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin (1988).
8. Childress, S. and Gilbert, A.D., Stretch, Twist, Fold: The Fast Dynamo, Springer-Verlag, Berlin (1995).
9. Crawford, J.D. and Knobloch, E., "Symmetry and symmetry-breaking bifurcations in fluid dynamics", Annu. Rev. Fluid Mech. A 23, 341-387 (1991).
10. Dombre, T., Frisch, U., Greene, J.M., Hénon, M., Mehr, A. and Soward, A., "Chaotic streamlines in the ABC flows", J. Fluid Mech. 167, 353-391 (1986).
11. Feudel, S., Seehafer, N., Galanti, B. and Schmidtmann, O., "Symmetry breaking bifurcation for the magnetohydrodynamic equation with helical forcing", Phys. Rev. E 54, 2589-2596 (1996).
12. Galanti, B., Sulem, P.L. and Pouquet, A., "Linear and non-linear dynamos associated with ABC flows", Geophys. Astrophys. Fluid Dynam. 66, 183-208 (1992).
13. Galloway, D.J. and Frisch, U., "Dynamo action in a family of flows with chaotic streamlines", Geophys. Astrophys. Fluid Dynam. 36, 53-83 (1986).
14. Galloway, D.J. and Frisch, U., "A note on the stability of a family of space-periodic Beltrami flows", J. Fluid Mech. 180, 557-564 (1987).
15. Glatzmaier, G.A. and Roberts P.H., "A three-dimensional self-consistent computer simulation of a geomagnetic field reversal", Nature 377, 203-209 (1995).
16. Glatzmaier, G.A. and Roberts, P.H., "An anelastic geodynamo simulation driven by compositional and thermal convection", Physica D 97, 81-94 (1996).
17. Hide, R., Skeldon, A.C. and Acheson, D.J., "A study of two novel self-exiting single-disc homopolar dynamos: theory", Proc. R. Soc. Lond. A 452, 1369-1395 (1996).
18. Jacobs, J.A., Reversals of the Earth's Magnetic Field, Cambridge University Press (1994).
19. Jones, C.A., "Convection driven geodynamo models", Phil. Trans. R. Soc. Lond. A 358, 873-897 (2000).
20. Matthews, P.C., "Dynamo action in simple convective flows", Proc. R. Soc. Lond A 455, 1829-1840 (1999).
21. Melbourne, I., Proctor, M.R.E. and Rucklidge, A.M., "A heteroclinic model of geodynamo reversals and excursions", In: Dynamo and Dynamics, a Mathematical Challenge (Eds. Chossat, P., Armbruster, D. and Oprea, I.) pp. 363-370, Kluwer Academic Publishers, Dordrecht (2001).
22. Merrill, R.T. and McFadden, P.L., "Secular variation and the origin of geomagnetic field reversals", J. Geophys. Res. 93, 11589-11597 (1988).
23. Merrill, R.T., McElhinny, M.W. and Stevenson, D.J., "Evidence for long-term asymmetries in the Earth's magnetic field and possible implications for dynamo theories", Phys. Earth Planet. Int. 20, 75-82 (1979).
24. Moroz, I.M., Hide, R. and Soward, A.M., "On self-exiting coupled Faraday disc homopolar dynamos driving series motors", Physica D 117, 128-144 (1998).
25. Podvigina, O.M., Spatially-periodic Evolutionary and Steady Solutions to the Three-dimensional Navier-Stokes Equation with the ABC-force, Institute of Mechanics, Lomonosov Moscow State University (1999).
26. Podvigina, O. and Pouquet, A., "On the non-linear stability of the 1:1:1 ABC flow", Physica D 75, 471-508 (1994).
27. Roberts, P.H. and Glatzmaier, G.A., "The geodynamo, past, present and future", Geophys. Astrophys. Fluid Dynam. 94, 47-84 (2001).
28. Roberts, P.H. and Stix, M., "α-Effect dynamos, by the Bullard-Gellman formalism", Astron. Astrophys. 18, 453-466,(1972).
29. Sarson, G.R., "Reversal models from dynamo calculations", Phil. Trans. Soc. Lond. A 358, 921-942 (2000).
30. Sarson, G.R. and Jones, C.A., "A convection driven geodynamo reversal model", Phys. Earth Planet. Int. 111, 3-20 (1999).
31. Zeldovich, Ya.B., Ruzmaikin, A.A. and Sokoloff, D.D., Magnetic Fields in Astrophysics, Gordon and Breach, Science Publishers (1983).