Generic nonlinear processes in self-exciting dynamos and the long-term behaviour of the main geomagnetic field, including polarity superchrons

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 358, Issue 1768, 2000, Pages 943-955

  Hide, Raymond ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Geomagnetism; Magnetohydrodynamics; Nonlinear quenching; Polarity superchrons; Self exciting dynamos

Indexed keywords

EID: 0347373598     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2000.0568     Document Type: Article

References (54)

1. Braginsky, S. I. 1991 Towards a realistic theory of the geodynamo. Geophys. Astrophys. Fluid Dyn. 60, 89-134.
2. Childress, S. & Gilbert, A. D. 1995 Stretch, twist and fold: the fast dynamo. Springer.
3. Courtillot, V. & Besse, J. 1987 Magnetic field reversals, polar wander, and core-mantle coupling. Science 237, 1140-1147.
4. Dubois, J. 1995 La dynamique non-linéaire en physique du globe. Paris: Masson.
5. Elsasser, W. M. 1939 The origin of the Earth's magnetic field. Phys. Rev. 65, 489-498.
6. Elsasser, W. M. 1947 Induction effects in terrestrial magnetism. Part III. Electric modes. 72, 821-833.
7. Ershov, S. V., Malinetskii, G. G. & Ruzmaikin, A. A. 1989 A generalized two-disk dynamo model. Geophys. Astrophys. Fluid Dyn. 47, 251-277.
8. Frenkel, J. 1945 On the origin of terrestrial magnetism. C. R. Acad. Sci. URSS 49, 98-101.
9. Fuller, M., Laj, C. & Herrero-Bervera, E. 1996 The reversal of the Earth's magnetic field. Am. Scientist 84, 552-561.
10. Gallet, Y. & Hulot, G. 1997 Stationary and nonstationary behaviour within the geomagnetic polarity time scale. Geophys. Res. Lett. 24, 1875-1878.
11. Ghil, M. & Childress, S. 1987 Topics in geophysical fluid dynamics: atmospheric dynamics, dynamo theory and climate dynamics. Springer.
12. Glatzmaier, G. A. & Roberts, P. H. 1995 A three-dimensional convective dynamo solution with rotating and finitely-conducting inner core and mantle. Phys. Earth Planet. Interiors 91, 63-75.
13. Glatzmaier, G. A. & Roberts, P. H. 1997 Simulating the geodynamo. Contemp. Phys. 38, 269-288.
14. Greenspan, H. P. 1968 The theory of rotating fluids. Cambridge University Press.
15. Gubbins, D. 1998 Interpreting the palaeomagnetic field. In The core-mantle boundary region (ed. M. Gunis, M. E. Wysession, E. Knittel & B. A. Buffett), pp. 167-182. Washington, DC: American Geophysical Union.
16. Gubbins, D. 1999 The distinction between geomagnetic excursions and reversals. Geophys. J. Int. 137, F1-F3.
17. Hide, R. 1953 Some experiments on thermal convection in a rotating liquid. PhD dissertation, University of Cambridge.
18. Hide, R. 1965 On the dynamics of Jupiter's interior and the origin of his magnetic field. In Magnetism and the cosmos (ed. R. Hindmarsh, F. J. Lowes, P. H. Roberts & S. K. Runcorn), pp. 378-395. Edinburgh: Oliver & Boyd.
19. Hide, R. 1966 Free hydromagnetic oscillations of the Earth's core and the theory of the geomagnetic secular variation. Phil. Trans. R. Soc. Lond. A 259, 615-647.
20. Hide, R. 1967 Motions of the Earth's core and mantle and variations of the main geomagnetic field. Science 157, 55-56.
21. Hide, R. 1981 The magnetic flux linkage of a moving medium: a theorem and geophysical applications. J. Geophys. Res. 80, 11 681-11 687.
22. Hide, R. 1988 Towards the interpretation of Uranus's magnetic field. Geophys. Astrophys. Fluid. Dyn. 44, 207-209.
23. Hide, R. 1995 Structural instability of the Rikitake disk dynamo. Geophys. Res. Lett. 22, 1057-1059.
24. Hide, R. 1997 The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos. Phys. Earth Planet. Interiors 103, 281-291 (cited as H97).
25. Hide, R. 1998 Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo. Nonlinear Processes Geophys. 4, 201-205 (cited as H98).
26. Hide, R. & Moroz, I. M. 1999 Effects due to induced azimuthal eddy currents in the Faraday disk self-exciting homopolar dynamo with a nonlinear series motor. I. Two special cases. Physica D 134, 287-301 (cited as HM99).
27. Hide, R., Skeldon, A. C. & Acheson, D. J. 1996 A study of two novel self-exciting single-disk homopolar dynamos: theory. Proc. R. Soc. Lond. A 452, 369-1395.
28. Hirsching, W. & Busse, F. H. 1995 Stationary and chaotic dynamos in rotating spherical shells. Phys. Earth Planet. Interiors 90, 43-254.
29. Hollerbach, R. 1996 On the theory of the geodynamo. Phys. Earth Planet. Interiors 93, 163-185.
30. Hollerbach, R. & Jones, C. A. 1995 On the magnetically stabilising role of the Earth's inner core. Phys. Earth Planet. Interiors 87, 171-181.
31. Jacobs, J. A. 1994 Reversals of the Earth's magnetic field. Cambridge University Press.
32. Jones, C. A., Longbottom, A. W. & Hollerbach, R. 1995 A self-consistent convection-driven geodynamo model, using a mean field approximation. Phys. Earth Planet. Interiors 92, 119-141.
33. Jones, G. M. 1977 Thermal interaction of the core and mantle and long-term behaviour of the geomagnetic field. J. Geophys. Res. 82, 1703-1709.
34. Krause, F. (ed.) 1993 The cosmic dynamo. Dordrecht: Kluwer.
35. Lay, T., Williams, Q. & Garnero, E. J. 1998 The core-mantle boundary layer and deep Earth dynamics. Nature 392, 461-468.
36. LeMouël, J.-L., Allègre, C. J. & Narteau, C. 1997 Multiple scale dynamo. Proc. Natn. Acad. Sci. USA 94, 5510-5514.
37. Loper, D. E. 1997 Mantle plumes and their effects on the Earth's surface: a review and synthesis. Dynam. Atmos. Oceans 27, 35-54.
38. Love, J. J. 1998 Paleomagnetic volcanic data and geometric regularity of reversals and excursions. J. Geophys. Res. 103, 12 435-12 452.
39. Merrill, R. T. & McFadden, P. L. 1999 Geomagnetic polarity transitions. Rev. Geophys. 37, 201-226.
40. Moffatt, H. K. 1978 Magnetic field generation in electrically-conducting fluids. Cambridge University Press.
41. Olson, P., Christensen, U. & Glatzmaier, G. A. 1999 Numerical modelling of the geodynamo: mechanism of field generation. J. Geophys. Res. 104, 10 383-10 404.
42. Opdyke, N. D. & Channell, J. E. T. 1996 Magnetic stratigraphy. San Diego: Academic Press.
43. Parker, E. N. 1979 Cosmical magnetic fields. Oxford: Clarendon Press.
44. Plunian, F., Marty, P. & Alemany, A. 1998 Chaotic behaviour of the Rikitake dynamo with symmetrical mechanical friction and azimuthal currents. Proc. R. Soc. Lond. A 454, 1835-1842.
45. Proctor, M. R. E. & Gilbert, A. D. (eds) 1994 Lectures on solar and planetary dynamos. Cambridge University Press.
46. Sakuraba, A. & Kono, M. 1999 Effect of the inner core on numerical solution of the magnetohydrodynamic dynamo. Phys. Earth Planet. Interiors 111, 105-121.
47. Sarson, G. R. & Jones, C. A. 1999 A convection driven geodynamo reversal model. Phys. Earth Planet. Interiors 111, 3-20.
48. Smith, L. A. 1993 Does a meeting in Santa Fe imply chaos? In Time series prediction: forecasting the future and understanding the past (ed. A. S. Weigend & N. A. Gershenfeld), pp. 323-343. Santa Fe Institute Studies in the Sciences of Complexity, vol. XV. Addison-Wesley.
49. Soward, A. M. 1992 The Earth's dynamo. Geophys. Astrophys. Fluid Dyn. 62, 219-238.
50. Thomas, D. N., Rolph, T. N., Shaw, J., Gonzalez de Sherwood, S. & Zhuang, Z. 1998 Palaeomagnetic studies of the late lavas from the Guizhou Province, South China: implications for the post-Kiaman dipole behaviour. Geophys. J. Int. 134, 856-866.
51. Turcotte, D. L. 1992 Fractals and chaos in geology and geophysics. Cambridge University Press.
52. Zhang, K.-K. & Busse, F. H. 1989 Convection-driven magnetohydrodynamic dynamos in rotating spherical shells. Geophys. Astrophys. Fluid Dyn. 49, 97-116.
53. Zhang, K.-K. & Jones, C. A. 1997 The effect of hyperviscosity on geodynamo models. Geophys. Res. Lett. 24, 2869-2872.
54. Zhang, K.-K., Jones, C. A. & Sarson, G. R. 1998 The dynamical effects of hyperviscosity on geodynamo models. Studia Geophys. Geod. 42, 247-253.