Oscillation or rotation: A comparison of two simple reversal models

Geophysical and Astrophysical Fluid Dynamics

Volumn 101, Issue 3-4, 2007, Pages 227-248

  Stefani, F ^a   Xu, M ^b   Sorriso Valvo, L ^a   Gerbeth, G ^a   Gunther U ^a  

^a INSTITUTE OF ION BEAM PHYSICS AND MATERIALS RESEARCH   (Germany)

^b INFM   (Italy)

Author keywords

Effect; Dynamo; Earth's magnetic field reversals; Inner core; Poisson statistics

Indexed keywords

DYNAMICS; MAGNETISM; POISSON DISTRIBUTION; TIME SERIES ANALYSIS;

PALEOMAGNETISM; POISSON STATISTICS; RELAXATION OSCILLATION; SUPERCHRON;

MAGNETIC FIELDS;

DYNAMICS; MAGNETIC FIELDS; MAGNETISM; POISSON DISTRIBUTION; TIME SERIES ANALYSIS;

GEODYNAMO; INNER CORE; MAGNETIC FIELD; OSCILLATION; PALEOMAGNETISM; POISSON RATIO; TIME SERIES;

EID: 34548809083     PISSN: 03091929     EISSN: 10290419     Source Type: Journal    
DOI: 10.1080/03091920701523311     Document Type: Article

References (61)

1. Aubert, J. and Wicht, J. (2004) Axial versus equatorial dipolar dynamo models with implications for planetary magnetic fields. Earth. Plan. Sci. Lett., 221, pp. 409-419.
2. Cande, SC and Kent, DV (1995) Revised calibration of the geomagnetic polarity timescale for the late Cretacious and Cenozoic. J. Geophys. Res.-Solid Earth, 100, pp. 6093-6095.
3. Carbone, V., Sorriso-Valvo, L., Vecchio, A., Lepreti, F., Veltri, P., Harabaglia, P. and Guerra, I. (2006) Clustering of polarity reversals of the geomagnetic field. Phys. Rev. Lett., 96, p. Art.
4. Childress, S. and Gilbert, AD (1995) Stretch, Twist, Fold: The Fast Dynamo., Springer, Berlin
5. Clement, BM (2004) Dependence of the duration of geomagnetic polarity reversals on site latitude. Nature, 428, pp. 637-640.
6. Constable, C. (2000) On rates of occurrence of geomagnetic reversals. Phys. Earth Planet. Int., 118, pp. 181-193.
7. Cox, A. (1968) Length of geomagnetic polarity intervals. J. Geophys. Res., 73, pp. 3247-3259.
8. Christensen, UR and Aubert, J. (2006) Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields. Geophys. J. Int., 166, pp. 97-114.
9. De Michelis, P. and Consolini, G. (2003) Some new approaches to the study of the Earth's magnetic field reversals. Ann. Geophys., 46, pp. 661-670.
10. Gailitis, A., Lielausis, O., Platacis, E., Gerbeth, G. and Stefani, F. (2002) Laboratory experiments on hydromagnetic dynamos. Rev. Mod. Phys., 74, p. 2002.
11. Glatzmaier, GA and Roberts, PH (1995) A 3-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature, 377, pp. 203-209.
12. 2-dynamos and the reversal phenomenon of the global geodynamo. Astron. Nachr., 326, pp. 693-700.
13. Giesecke, A., Ziegler, U. and Rüdiger, G. (2005) Geodynamo α-effect derived from box simulations of rotating magnetoconvection. Phys. Earth Planet. Int., 152, pp. 90-102.
14. Gould, SJ and Eldredge, N. (1993) Punctuated equilibrium comes of age. Nature, 366, pp. 223-227.
15. Grote, E. and Busse, FH (2000) Hemispherical dynamos generated by convection in rotating spherical shells. Phys. Rev. E, 62, pp. 4457-4460.
16. Gubbins, D. (1999) The distinction between geomagnetic excursions and reversals. Geophys. J. Int., 137, pp. F1-F3.
17. Gubbins, D. and Gibbons, S. (2002) Three-dimensional dynamo waves in a sphere. Geophys. Astrophys. Fluid Dyn., 96, pp. 481-498.
18. Gubbins, D. and Love, JJ (1998) Preferred VGP paths during geomagnetic polarity reversals: Symmetry considerations. Geophys. Res. Lett., 25, pp. 1079-1082.
19. Gubbins, D., Barber, CN, Gibbons, S. and Love, JJ (2000) Kinematic dynamo action in a sphere. II Symmetry selection. Proc. R. Soc. Lond. A, 456, pp. 1669-1683.
20. 2 dynamos and resonant unfolding of diabolic points. J. Phys. A, 39, pp. 10057-10076.
21. Heller, R., Merrill, RT and McFadden, PL (2003) The two states of paleomagnetic field intensities for the past 320 million years. Phys. Earth Planet. Int., 135, pp. 211-223.
22. Hollerbach, R. and Jones, CA (1993) Influence of the inner core on geomagnetic fluctuations and reversals. Nature, 365, pp. 541-543.
23. Hollerbach, R. and Jones, CA (1995) On the magnetically stabilizing role of the Earth's inner core. Phys. Earth Planet. Int., 87, pp. 171-181.
24. Hoyng, P. and Duistermaat, JJ (2004) Geomagnetic reversals and the stochastic exit problem. Europhys. Lett., 68, pp. 177-183.
25. Hoyng, P., Ossendrijver, MAJH and Schmidt, D. (2001) The geodynamo as a bistable oscillator. Geophys. Astrophys. Fluid Dyn, 94, pp. 263-314.
26. Krause, F. and Rädler, K-H (1980) Mean-field Magnetohydrodynamics and Dynamo Theory., Akademie-Verlag, Berlin
27. Labrosse, S., Poirier, J-P and LeMouel, JL (2001) The age of the inner core. Earth Planet. Sci. Lett., 190, pp. 111-123.
28. McFadden, PL (1984) Statistical tools for the analysis of geomagnetic reversal sequences. J. Geophys. Res., 89, pp. 3363-3372.
29. Meinel, R. and Brandenburg, A. (1990) Behaviour of highly supercritical α-effect dynamos. Astron Astrophys., 238, pp. 369-376.
30. Melbourne, I., Proctor, MRE and Rucklidge, AM (2001) A heteroclinic model of geodynamo reversals and excursions. Dynamo and Dynamics, a Mathematical Challenge, pp. 363-370. Dordrecht, Kluwer
31. Merrill, RT, McElhinny, MW and McFadden, PL (1996) The Magnetic field of the Earth, Academic Press, San Diego
32. Mininni, PD, Gomez, DO and Mindlin, GB (2000) Stochastic relaxation oscillator model for the solar cycle. Phys. Rev. Lett., 85, pp. 5476-5479.
33. Narteau, C. (2005) Private communication
34. Olson, P., Christensen, U. and Glatzmaier, GA (1999) Numerical modelling of the geodynamo: Mechanisms of field generation and equilibration. J. Geophys. Res., 104, pp. 10383-10404.
35. Pavlov, V. and Gallet, Y. (2005) A third superchron during early Paleozoic. Episodes, 28, pp. 78-84.
36. Perrin, M. and Shcherbakov, VP (1997) Paleointensity of the Earth's magnetic field for the paste 400 Ma: Evidence for a dipole structure during the mesozoic low. J. Geomagn. Geoelectr., 49, pp. 601-614.
37. Phillips, CG (1993) Ph.D. Thesis, University of Sidney
38. Pontieri, A., Lepreti, F., Sorriso-Valvo, L., Vecchio, A. and Carbone, V. (2003) A simple model for the solar cycle. Solar Phys., 213, pp. 195-201.
39. Sarson, GR and Jones, CA (1999) A convection driven geodynamo reversal model. Phys. Earth Planet. Int., 111, pp. 3-20.
40. Schmidt, D. and Ossendrijver, MAJH (2001) and Hoyng P., Magnetic field reversals and secular variation in a bistable geodynamo model. Phys. Earth Planet. Int., 125, pp. 119-124.
41. Schrinner, M., Rädler, K-H, Schmitt, D., Rheinhardt, M. and Christensen, UR (2005) Mean-field view on rotating magnetoconvection and a geodynamo model. Astron. Nachr, 326, pp. 245-249.
42. Schrinner, M., Rädler, K-H, Schmitt, D., Rheinhardt, M. and Christensen, UR (2007) Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo. Geophys. Astrophys. Fluid Dyn, 101, pp. 81-116.
43. Shcherbakov, VP, Solodovnikov, GM and Sycheva, NK (2002) Variations in the geomagnetic dipole during the past 400 million years (volcanic rocks). Izvestiya, Phys. Solid Earth, 38, pp. 113-119.
44. Sorriso-Valvo, L., Stefani, F., Carbone, V., Nigro, G., Lepreti, F., Vecchio, A. and Veltri, P. (2006) A statistical analysis of polarity reversals of the geomagnetic field. Phys. Earth Planet. Int
45. Stefani, F., Gerbeth, G. and Rädler, K-H (2000) Steady dynamos in finite domains: An integral equation approach. Astron. Nachr., 321, pp. 65-73.
46. Stefani, F. and Gerbeth, G. (2003) Oscillatory mean-field dynamos with a spherically symmetric, isotropic helical turbulence parameter α. Phys. Rev. E, 67, p. Art.
47. Stefani, F. and Gerbeth, G. (2005) Asymmetry polarity reversals, bimodal field distribution, and coherence resonance in a spherically symmetric mean-field dynamo model. Phys. Rev. Lett., 94, p. Art.
48. Stefani, F., Gerbeth, G. and Günther, U. (2006) Why dynamos are prone to reversals. Earth Planet. Sci. Lett., 143, pp. 828-840.
49. Stefani, F., Gerbeth, G. and Günther, U. (2006) A paradigmatic model of Earth's magnetic field reversals. Magnetohydrodynamics, 42, pp. 123-130.
50. Stefani, F., Gerbeth, G., Ravelet, F., Chiffaudel, A., Daviaud, F. and Leorat, J. (2006) Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: Application to the VKS experiment. Eur. J. Mech. B/Fluids, 25, pp. 894-908.
51. Takahashi, F., Matsushima, M. and Honkura, Y. (2005) Simulations of a quasi-Taylor state geomagnetic field including polarity reversals on the Earth simulator. Science, 309, pp. 459-461.
52. Tarduno, JA, Cottrell, RD and Smirnov, AV (2001) High geomagnetic intensity during the mid-Cretaceous from Thellier analysis of simple plagioclase crystals. Science, 291, p. 1779.
53. Valet, J-P and Meynadier, L. (1993) Geomagnetic field intensities and reversals during the last 4 million years. Nature, 366, pp. 234-238.
54. Valet, J-P, Meynadier, L. and Guyodo, Y. (2005) Geomagnetic dipole strength and reversal rate over the past two million years. Nature, 435, pp. 802-805.
55. van der Pol, B. (1926) On relaxation oscillations. Phil. Mag., 2, pp. 978-992.
56. Weisshaar, E. (1982) A numerical study of α2-dynamos with anisotropic α-effect. Geophys. Astrophys. Fluid Dyn, 21, pp. 285-301.
57. Wicht, J. (2002) Inner-core conductivity in numerical dynamo simulations. Phys. Earth Planet. Int., 132, pp. 281-302.
58. Wicht, J. and Olson, P. (2004) A detailed study of the polarity reversal mechanism in a numerical dynamo model. Geochem. Geophys. Geosys., 5, p. Art.
59. Stefani, F. and Gerbeth, G. (2004) The integral equation method for a steady kinematic dynamo problem. J. Comp. Phys., 196, pp. 102-125.
60. Stefani, F. and Gerbeth, G. (2004) Integral equation approach to time-dependent kinematic dynamos in finite domains. Phys. Rev. E, 70, p. Art.
61. Yoshimura, H. and Wang, Z. (1984) Linear astrophysical dynamos in rotating spheres: Mode transition between steady and oscillatory dynamos as a function of dynamo strength and anisotropic turbulent diffusivity. Astrophys. J., 283, pp. 870-878.