Numerical Models of the Geodynamo: From Fundamental Cartesian Models to 3D Simulations of Field Reversals

Advances in Geophysical and Environmental Mechanics and Mathematics

Volumn , Issue , 2009, Pages 107-158

  Wicht, Johannes ^a   Stellmach, Stephan ^a   Harder, Helmut ^a  

^a MAX PLANCK INSTITUT FÜR SONNENSYSTEMFORSCHUNG   (Germany)

Author keywords

Dynamo Model; Ekman Number; Polarity Interval; Rayleigh Number; Spherical Shell

Indexed keywords

EID: 85091237042     PISSN: 18668348     EISSN: 18668356     Source Type: Book Series    
DOI: 10.1007/978-3-540-76939-2_4     Document Type: Chapter

References (86)

1. Acton, G., Clement, B., Lund, S., Okada, M., and Williams, T. (1998). Initial paleomagnetic results from ODP leg 172: High resolution geomagnetic field behavior for the last 1.2 Ma. EOS, 79:178–179.
2. Aubert, J., Aurnou, J., and Wicht, J. (2008). The magnetic structure of convection-driven numerical dynamos. Geophys. J. Int., 172:945–956.
3. Blankenbach, B., Busse, F., Christensen, U., Cserepes, L., Gunkel, D., Hansen, U., Harder, H., Jarvis, G., Koch, M., Marquard, G., Moore, D., Olson, P., Schmeling, H., and Schnaubelt, T. (1989). A benchmark comparison for mantle convection codes. Geophys. J. Int., 98:23–38.
4. Bullard, E. C. and Gellman, H. (1954). Homogeneous dynamos and terrestrial magnetism. Philos. Trans. R. Soc. Lond., A. 247:213–278.
5. Busse, F. and Heikes, K. (1980). Convection in a rotating layer: A simple case of turbulence. Science, 208:173–175.
6. Busse, F. H. and Clever, R. M. (1979). Nonstationary convection in a rotating system, pp. 376–385. Recent developments in theoretical and experimental fluid mechanics: Compressible and in-compressible flows. (A79-29651 11-34) Berlin, Springer-Verlag, 1979, pp. 376-385.
7. Cande, S. and Kent, D. (1995). Revised calibration of the geomagnetic polarity timescales for the Late Cretaceous and Cenozoic. Geophys. Res. Lett., 100:6093–6095.
8. Cataneo, F. and Hughes, D. W. (2006). Dynamo action in a rotating convective layer. J. Fluid. Mech., pp. 401–418.
9. Chan, K., Li, L., and Liao, X. (2006). Modelling the core convection using finite element and finite difference methods. Phys. Earth Planet. Int., 157:124–138.
10. Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
11. Childress, S. and Soward, A. (1972). Convection driven hydromagnetic dynamo. Phys. Rev. Lett., 29:837–839.
12. Christensen, U. and Aubert, J. (2006). Scaling properties of convection-driven dynamos in rotating spherical shells and applications to planetary magnetic fields. Geophys. J. Int., 116:97–114.
13. Christensen, U. and Tilgner, A. (2004). Power requirement of the geodynamo from Ohmic losses in numerical and laboratory dynamos. Nature, 429:169–171.
14. Christensen, U. and Wicht, J. (2007). Core Dynamics, chapter Numerical Dynamo Simulations. Treatise on Geophysics. Elsevier.
15. Christensen, U. R. (2006). A deep rooted dynamo for Mercury. Nature, 444:1056–1058.
16. Christensen, U. R., Aubert, J., Busse, F. H., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G. A., Honkura, Y., Jones, C. A., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wicht, J., and Zhang, K. (2001). A numerical dynamo benchmark. Phys. Earth Planet. Int., 128:25–34.
17. Clement, B. (2004). Dependency of the duration of geomagnetic polarity reversals on site latitude. Nature, 428:637–640.
18. Clune, T., Eliott, J., Miesch, M., Toomre, J., and Glatzmaier, G. (1999). Computational aspects of a code to study rotating turbulent convection in spherical shells. Parallel Comp., 25:361–380.
19. Clune, T. and Knobloch, E. (1993). Pattern selection in rotating convection with experimental boundary conditions. Phys. Rev. E, 47:2536–2549.
20. Constable, C. (2000). On the rate of occurence of geomagnetic reversals. Phys. Earth Planet. Int., 118:181–193.
21. Demircan, A., Scheel, S., and Seehafer, N. (2000). Heteroclinic behavior in rotating Rayleigh-Bénard convection. Eur. Phys. J. B, 13.
22. Dormy, E., Cardin, P., and Jault, D. (1998). MHD flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field. Earth Planet. Sci. Lett., 158:15–24.
23. Eltayeb, I. (1972). Hydromagnetic convection in a rapidly rotating fluid layer. Proc. R. Soc. Lond. A., 326:229–254.
24. Eltayeb, I. (1975). Overstable hydromagnetic convection in a rotating fluid layer. J. Fluid Mech., 71:161–179.
25. Fautrelle, Y. and Childress, S. (1982). Convective dynamos with intermediate and strong fields. Geophys. Astrophys. Fluid Dyn., 22:235–279.
26. Fournier, A., Bunge, H.-P., Hollerbach, R., and Vilotte, J.-P. (2005). A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers. J. Comp. Phys., 204:462–489.
27. Glassmeier, K.-H., Auster, H.-U., and Motschmann, U. (2007). A feedback dynamo generating Mercury’s magnetic field. Geophys. Res. Lett., 34:22201–22205, doi:10.1029/2007GL031662.
28. Glatzmaier, G. (1984). Numerical simulation of stellar convective dynamos. 1. The model and methods. J. Comput. Phys., 55:461–484.
29. Glatzmaier, G., Coe, R., Hongre, L., and Roberts, P. (1999). The role of the Earth’s mantle in controlling the frequency of geomagnetic reversals. Nature, 401:885–890.
30. Glatzmaier, G. and Roberts, P. (1995). A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Phys. Earth Planet. Int., 91:63–75.
31. Glatzmaier, G. and Roberts, P. (1996). An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection. Physica D, 97:81–94.
32. Gubbins, D., Alfè, D., Masters, G., Price, G., and Gillan, M. (2004). Gross thermodynamics of 2-component core convection. Geophys. J. Int., 157:1407–1414.
33. Gubbins, D., N., B. C., Gibbons, S., and J., L. J. (2000a). Kinematic dynamo action in a sphere i. effects of differential rotation and meridional circulation on solutions with axial dipole symmetry. Proc. Roy. Soc. Lond., 456:1333–1353.
34. Gubbins, D., N., B. C., Gibbons, S., and J., L. J. (2000b). Kinematic dynamo action in a sphere ii. symmetry selection. Proc. Roy. Soc. Lond., 456:1669–1683.
35. Gubbins, D. and Sarson, G. (1994). Geomagnetic field morphologies from a kinematic dynamo model. Nature, 368:51–55.
36. Harder, H. and Hansen, U. (2005). A finite-volume solution method for thermal convection and dynamo problems in spherical shells. Geophys. J. Int., 161:522–532.
37. Harland, W., Armstrong, R., Cox, A., Craig, L., Smith, A., and Smith, D. (1990). A Geological Time Scale. Cambridge University Press, Cambridge.
38. Hejda, P. and Reshetnyak, M. (2003). Control volume method for the thermal dynamo problem in the sphere with the free rotating inner core. Stud. Geophys. Geod., 47:147–159.
39. Hejda, P. and Reshetnyak, M. (2004). Control volume method for the thermal convection problem in a rotating spherical shell: test on the benchmark solution. Stud. Geophys. Geod., 48:741–746.
40. Hulot, G. and Gallet, Y. (2003). Do superchrons occur without any paleomagnetic warning? Earth Planet. Sci. Lett., 210:191–201.
41. Jackson, A., Jonkers, A., and Walker, M. (2000). Four centuries of geomagnetic secular variation from historical records. Philos. Trans. R. Soc. Lond., A, 358:957–990.
42. Jones, C. (2000). Convection-driven geodynamo models. Philos. Trans. R. Soc. Lond., A, 358:873–897.
43. Jones, C. and Roberts, P. (2000a). Convection driven dynamos in a rotating plane layer. J. Fluid Mech., 404:311–343.
44. Jones, C. and Roberts, P. (2000b). The onset of magnetoconvection at large Prandtl number in a rotating layer II. Small magnetic diffusion. Geophys. Astrophys. Fluid Dyn., 93:173–226.
45. Jonkers, A. (2003). Long-range dependence in the cenozoic reversal record. Phys. Earth Planet. Int., 135:253–266.
46. Julien, K., Legg, S., McWilliams, J., and Werne, J. (1996). Rapidly rotating turbulent Rayleigh-Bénard convection. J. Fluid Mech., 322:243–272.
47. Kageyama, A. and Watanabe, K. and Sato, T. (1993). Simulation study of a magnetohydrodynamic dynamo: Convection in a rotating shell. Phys. Fluids, B24:2793–2806.
48. Kageyama, A. and Sato, T. (1997c). Generation mechanism of a dipole field by a magnetohydrodynamic dynamo. Phys. Rev. E, 55:4617–4626.
49. Kageyama, A. and Yoshida, M. (2005). Geodynamo and mantle convection simulations on the Earth simulator using the Yin-Yang grid. J. Phys.: Conf. Ser., 16:325–338.
50. Kono, M. and Roberts, P. (2001). Definition of the Rayleigh number for geodynamo simulation. Phys. Earth Planet. Int., 128:13–24.
51. Krause, F. and Rädler, K. (1980). Mean-Field Magnetohydrodynamics and Dynamo Theory. Akademie-Verlag, Berlin.
52. Kuang, W. and Bloxham, J. (1999). Numerical modeling of magnetohydrodynamic convection in a rapidly rotating spherical shell: Weak and strong field dynamo action. J. Comp. Phys., 153:51–81.
53. Kutzner, C. and Christensen, U. (2000). Effects of driving mechanisms in geodynamo models. Geophys. Res. Lett., 27:29–32.
54. Kutzner, C. and Christensen, U. (2002). From stable dipolar to reversing numerical dynamos. Phys. Earth Planet. Int., 131:29–45.
55. Kutzner, C. and Christensen, U. (2004). Simulated geomagnetic reversals and preferred virtual geomagnetic pole paths. Geophys. J. Int., 157:1105–1118.
56. Leonhardt, R., Matzka, J., Hufenbecher, F., and Soffel, H. (2002). A reversal of the Earth’s magnetic field recorded in mid-Miocene lava flows of Gran Canaria: Paleodirections. J. Geophys. Res., 107:DOI 10.1029/2001JB000322.
57. Lister, J. and Buffett, B. (1995). The strength and efficiency of thermal and compositional convection n the geodynamo. Phys. Earth Planet. Int., 91:17–30.
58. Love, J. (1998). Paleomagnetic volcanic data and geomagnetic regularity of reversals and excursions. J. Geophys. Res., 103(B6):12435–12452.
59. Lund, S., Haskell, B., and Johnson, T. (1989). Paleomagnetic secular variation records for the last 100,000 years from deep sea sediments of the northwest Atlantic Ocean. EOS, 70:1073.
60. Lund, S., Williams, T., Acton, G., Clement, D., and Okada, M. (2001). Brunes chron magnetic field excursions recovered from leg 172 sediments. In Keigwin, L., Acton, D., and Arnold, E., editors, Proceedings of the Ocean Drilling Program, Scientific Results, Volume 172.
61. Mauersberger, P. (1956) Das Mittel der Energiedichte des geomagnetischen Hauptfeldes and der Erdoberfläche und seine säkulare Änderung. Gerlands Beitr. Geophys., 65:207–215.
62. Matsui, H. and Okuda, H. (2005). Mhd dynamo simulation using the GeoFEM platform-verification by the dynamo benchmark test. Int. J. Comput. Fluid Dyn., 19:15–22.
63. Maus, S., Rother, M., Stolle, C., Mai, W., Choi, S., Lühr, H., Cooke, D., and Roth, C. (2006). Third generation of the Potsdam Magnetic Model of the Earth (POMME). Geochem. Geophys. Geosyst., 7:7008.
64. Olson, P. and Amit, H. (2006). Changes in Earth’s dipole. Naturwissenschaften., 93:519–542.
65. Olson, P. and Christensen, U. (2006). Dipole moment scaling for convection-driven planetary dynamos. Earth Planet. Sci. Lett., 250:561–571.
66. Olson, P., Christensen, U., and Glatzmaier, G. (1999). Numerical modeling of the geodynamo: Mechanism of field generation and equilibration. J. Geophys. Res., 104:10,383–10,404.
67. Roberts, P. and Jones, C. (2000). The onset of magnetoconvection at large Prandtl number in a rotating layer I. Finite magnetic diffusion. Geophs. Astrophys. Fluid Dyn., 92:289–325.
68. Rotvig, J. and Jones, C. (2002). Rotating convection-driven dynamos at low ekman number. Phys. Rev. E., 66:DOI:056308.
69. Sarson, G. and Jones, C. (1999). A convection driven geodynamo reversal model. Phys. Earth Planet. Int., 111:3–20.
70. Singer, B., Hoffman, K., Coe, R., Brown, L., Jicha, B., Pringle, M., and Chauvin, A. (2005). Structural and temporal requirements for geomagnetic field reversals deduced from lava flows. Nature, 434:633–636.
71. Soward, A. (1974). A convection driven dynamo I: The weak field case. Phil. Trans. R. Soc. Lond. A, 275:611–651.
72. St. Pierre, M. (1993). The strong-field branch of the Childress-Soward dynamo. In Proctor, M. R. E. et al., editors, Solar and Planetary Dynamos, pp. 329–337.
73. Stanley, S. and Bloxham, J. (2004). Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields. Nature, 428:151–153.
74. Stanley, S., Bloxham, J., Hutchison, W., and Zuber, M. (2005). Thin shell dynamo models consistent with Mercury’s weak observed magnetic field. Earth Planet. Sci. Lett., 234:341–353.
75. Stellmach, S. and Hansen, U. (2004). Cartesian convection-driven dynamos at low Ekman number. Phys. Rev. E, 70:056312.
76. Takahashi, F. and Matsushima, M. (2006). Dipolar and non-dipolar dynamos in a thin shell geometry with implications for the magnetic field of Mercury. Geophys. Res. Lett., 33:L10202.
77. Vorobieff, P. and Ecke, E. (2002). Turbulent rotating convection: an experimental study. J. Fluid Mech., 458:191–218.
78. Wicht, J. (2002). Inner-core conductivity in numerical dynamo simulations. Phys. Earth Planet. Int., 132:281–302.
79. Wicht, J. (2005). Palaeomagnetic interpretation of dynamo simulations. GeoPhys. J. Int., 162:371–380.
80. Wicht, J. and Aubert, J. (2005). Dynamos in action. GWDG-Bericht, 68:49–66.
81. Wicht, J., Mandea, M., Takahashi, F., Christensen, U., Matsushima, M., and Langlais, B. (2007). The origin of Mercury’s internal magnetic field. Space Sci. Rev., 132:261–290.
82. Wicht, J. and Olson, P. (2004). A detailed study of the polarity reversal mechanism in a numerical dynamo model. Geochem., Geophys,. Geosyst., 5:doi:10.1029/2003GC000602.
83. Willis, A. and Gubbins, D. (2004). Kinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry. Geophys. Astrophys. Fluid. Dyn., 98(6):537–554.
84. Zhang, K.-K. and Busse, F. (1988). Finite amplitude convection and magnetic field generation in in a rotating spherical shell. Geophys. Astrophys. Fluid. Dyn., 44:33–53.
85. Zhang, K.-K. and Busse, F. (1989). Convection driven magnetohydrodynamic dynamos in rotating spherical shells. Geophys. Astrophys. Fluid. Dyn., 49:97–116.
86. Zhang, K.-K. and Busse, F. (1990). Generation of magnetic fields by convection in a rotating spherical fluid shell of infinite Prandtl number. Phys. Earth Planet. Int., 59:208–222.