On the theory of the geodynamo

Physics of the Earth and Planetary Interiors

Volumn 98, Issue 3-4 SPEC. ISS., 1996, Pages 163-185

  Hollerbach, Rainer ^a,b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMO THEORY; GEODYNAMO; GEOMAGNETIC FIELD;

EID: 0030391651     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0031-9201(96)03185-8     Document Type: Article

References (91)

1. Anufriev, A.P., 1994. The influence of solid core on Earth's hydrodynamics. Geophys. Astrophys. Fluid Dyn., 77: 15-25.
2. Anufriev, A.P., Cupal, I. and Hejda, P., 1995. The weak Taylor state in an αω-dynamo. Geophys. Astrophys. Fluid Dyn., 79: 125-145.
3. Backus, G.E., 1958. A class of self-sustaining dissipative spherical dynamos. Ann. Phys., 4: 372-447.
4. Barenghi, C.F. and Jones, C.A., 1991. Nonlinear planetary dynamos in a rotating spherical shell. Geophys. Astrophys. Fluid Dyn., 60: 211-243.
5. Batchelor, G.K., 1967. An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge.
6. Bloxham, J., Gubbins, D. and Jackson, A., 1989. Geomagnetic secular variation. Philos. Trans. R. Soc. London, Ser. A, 329: 415-502.
7. Braginsky, S.I., 1964. Kinematic models of the Earth's hydromagnetic dynamo. Geomagn. Aeron. USSR, 4: 572-583.
8. Braginsky, S.I., 1965. Self-excitation of a magnetic field during the motion of a highly conducting fluid. Sov. Phys. JETP, 20: 726-735.
9. Braginsky, S.I., 1975. Nearly axially symmetric model of the hydromagnetic dynamo of the Earth. Geomagn. Aeron., USSR, 15: 122-128.
10. Braginsky, S.I., 1991. Towards a realistic theory of the geodynamo. Geophys. Astrophys. Fluid Dyn., 60: 89-134.
11. Braginsky, S.I., 1994. The nonlinear dynamo and model-Z. In: M.R.E. Proctor and A.D. Gilbert (Editors), Lectures on Solar and Planetary Dynamos. Cambridge University Press, Cambridge, pp. 267-304.
12. Braginsky, S.I. and Roberts, P.H., 1987. A model-Z geodynamo. Geophys. Astrophys. Fluid Dyn., 38: 327-349.
13. Braginsky, S.I. and Roberts, P.H., 1995. Equations governing convection in Earth's core and the geodynamo. Geophys. Astrophys. Fluid Dyn., 79: 1-97.
14. Bullard, E.C. and Gellman, H., 1954. Homogeneous dynamos and terrestrial magnetism. Philos. Trans. R. Soc. London, Ser. A, 247: 213-278.
15. Busse, F.H., 1970. Thermal instabilities in rapidly rotating systems. J. Fluid Mech., 44: 441-460.
16. Busse, F.H., 1975a. A necessary condition for the geodynamo. J. Geophys. Res., 80: 278-280.
17. Busse, F.H., 1975b. A model of the geodynamo. Geophys. J. R. Astron. Soc., 42: 437-459.
18. Busse, F.H., 1983. Recent developments in the dynamo theory of planetary magnetism. Annu. Rev. Earth Planet. Sci., 11: 241-268.
19. Cardin, P. and Olson, P., 1992. An experimental approach to thermochemical convection in the Earth's core. Geophys. Res. Lett., 19: 1995-1998.
20. Childress, S., 1969a. Théorie magnetohydrodynamique de l'effet dynamo. Rep. Dept. Mech. Fac. Sci., University of Paris.
21. Childress, S., 1969b. A class of solutions of the magnetohydrodynamic dynamo problem. In: S.K. Runcorn (Editor), The Application of Modern Physics to the Earth and Planetary Interiors. Wiley, London, pp. 629-648.
22. Childress, S. and Soward, A.M., 1972. Convection-driven hydromagnetic dynamos. Phys. Rev. Lett., 29: 837-839.
23. Cowling, T.G., 1934. The magnetic field of sunspots. Mon. Not. R. Astron. Soc., 94: 39-48.
24. Cuong, P.G. and Busse, F.H., 1981. Generation of magnetic fields by convection in a rotating sphere. Phys. Earth Planet. Inter., 24: 272-283.
25. Dudley, M.L. and James, R.W., 1989. Time-dependent kinematic dynamos with stationary flows. Proc. R. Soc. London, Ser. A, 425: 407-429.
26. Elsasser, W.M., 1946. Induction effects in terrestrial magnetism. Phys. Rev., 69: 106-116.
27. Eltayeb, I.A., 1972. Hydromagnetic convection in a rapidly rotating fluid layer. Proc. R. Soc. London, Ser. A, 326: 229-254.
28. Fautrelle, Y. and Childress, S., 1982. Convective dynamos with intermediate and strong fields. Geophys. Astrophys. Fluid Dyn., 22: 235-279.
29. Fearn, D.R., 1979. Thermal and magnetic instabilities in a rapidly rotating sphere. Geophys. Astrophys. Fluid Dyn., 14: 103-126.
30. Fearn, D.R., 1994. Nonlinear planetary dynamos. In: M.R.E. Proctor and A.D. Gilbert (Editors), Lectures on Solar and Planetary Dynamos. Cambridge University Press, Cambridge, pp. 219-244.
31. Fearn, D.R., 1996. The geodynamo. In: D. Crossley (Editor), Earth's Deep Interior, Gordon and Breach, London, pp. 79-114.
32. Fearn, D.R. and Proctor, M.R.E., 1987. Dynamically consistent magnetic fields produced by differential rotation. J. Fluid Mech., 178: 521-534.
33. Fearn, D.R. and Proctor, M.R.E., 1992. Magnetostrophic balance in non-axisymmetric, non-standard dynamo models. Geophys. Astrophys. Fluid Dyn., 67: 117-128.
34. Fearn, D.R., Roberts, P.H. and Soward, A.M., 1988. Convection, stability, and the dynamo. In: G.P. Galdi and B. Straughan (Editors), Energy, Stability, and Convection. Longman, Harlow, UK, pp. 60-324.
35. Glatzmaier, G.A. and Roberts, P.H., 1995a. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Phys. Earth Planet. Inter., 91: 63-75.
36. Glatzmaier, G.A. and Roberts, P.H., 1995b. A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature, 377: 203-209.
37. Gubbins, D., 1973. Numerical solutions of the kinematic dynamo problem. Philos. Trans. R. Soc. London, Ser. A, 274: 493-521.
38. Gubbins, D., 1981. Rotation of the inner core. J. Geophys. Res., B, 86: 11695-11699.
39. Gubbins, D. and Zhang, K., 1993, Symmetry properties of the dynamo equations for palaeomagnetism and geomagnetism. Phys. Earth Planet. Inter., 75: 225-241.
40. Herzenberg, A., 1958. Geomagnetic dynamos. Philos. Trans. R. Soc. London, Ser. A, 250: 543-585.
41. Hide, R. and Palmer, T.N., 1982. Generalization of Cowling's theorem. Geophys. Astrophys. Fluid Dyn., 19: 301-309.
42. 2-dynamos. Geophys. Astrophys. Fluid Dyn., 60: 245-260.
43. Hollerbach, R., 1994a. Magnetohydrodynamic Ekman and Stewartson layers in a rotating spherical shell. Proc. R. Soc. London, Ser. A, 444: 333-346.
44. Hollerbach, R., 1994b. Imposing a magnetic field across a nonaxisymmetric shear layer in a rotating spherical shell. Phys. Fluids, 6: 2540-2544.
45. Hollerbach, R., 1996a. The dynamical balance in semi-Taylor states. Geophys. Astrophys. Fluid Dyn., in press.
46. Hollerbach, R., 1996b. Magnetohydrodynamic shear layers in a rapidly rotating plane layer. Geophys. Astrophys. Fluid Dyn., 82: 237-253.
47. 2-dynamo in the limit of asymptotically small viscosity. Geophys. Astrophys. Fluid Dyn., 56: 133-158.
48. Hollerbach, R. and Jones, C.A., 1993a. A geodynamo model incorporating a finitely conducting inner core. Phys. Earth Planet. Inter., 75: 317-327.
49. Hollerbach, R. and Jones, C.A., 1993b. Influence of the Earth's inner core on geomagnetic fluctuations and reversals. Nature, 365: 541-543.
50. Hollerbach, R. and Jones, C.A., 1995. On the magnetically stabilising role of the Earth's inner core. Phys. Earth Planet. Inter., 87: 171-181.
51. Hollerbach, R. and Proctor, M.R.E., 1993. Non-axisymmetric shear layers in a rotating spherical shell. In: M.R.E. Proctor, P.C. Matthews and A.M. Rucklidge (Editors), Solar and Planetary Dynamos. Cambridge University Press, Cambridge, pp. 145-152.
52. Hollerbach, R., Barenghi, C.F. and Jones, C.A., 1992. Taylor's constraint in a spherical αω-dynamo. Geophys. Astrophys. Fluid Dyn., 67: 3-25.
53. 2-dynamos. Geophys. Astrophys. Fluid Dyn., 34: 143-173.
54. Ivers, D.J. and James, R.W., 1984. Axisymmetric antidynamo theorems in compressible non-uniform conducting fluids. Philos. Trans. R. Soc. London, Ser. A, 312: 179-218.
55. James, R.W., Roberts, P.M. and Winch, D.E., 1980. The Cowling anti-dynamo theorem. Geophys. Astrophys. Fluid Dyn., 15: 149-160.
56. Jault, D., 1995. Model Z by computation and Taylor's condition. Geophys. Astrophys. Fluid Dyn., 79: 99-124.
57. Jones, C.A., 1991. Dynamo models and Taylor's constraint. In: E.R. Priest and A.W. Hood (Editors), Advances in Solar System Magnetohydrodynamics. Cambridge University Press, Cambridge, pp. 25-50.
58. Jones, C.A. and Wallace, S.G., 1992. Periodic, chaotic, and steady solutions in αω-dynamos. Geophys. Astrophys. Fluid Dyn., 67: 37-64.
59. Jones, C.A., Longbottom, A.W. and Hollerbach, R., 1995. A self-consistent convection driven geodynamo model, using a mean field approximation. Phys. Earth Planet. Inter., 92: 119-141.
60. Krause, F. and Rädler, K.H., 1980. Mean-field Magnetohydrodynamics and Dynamo Theory. Pergamon, Oxford.
61. Larmor, J., 1919. How could a rotating body such as the Sun become a magnet? Rep. Br. Assoc. Adv. Sci. A, 159-160.
62. Lilley, F.E.M., 1970. On kinematic dynamos. Proc. R. Soc. London, Ser. A, 316: 153-167.
63. Malkus, W.V.R., 1959. Magnetoconvection in a viscous fluid of infinite electrical conductivity. Astrophys. J., 130: 259-275.
64. Malkus, W.V.R. and Proctor, M.R.E., 1975. The macrodynamics of α-effect dynamos in rotating fluids. J. Fluid Mech., 67: 417-443.
65. Moffatt, H.K., 1978. Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press, Cambridge.
66. Parker, E.N., 1955. Hydromagnetic dynamo models. Astrophys. J., 122: 293-314.
67. Parker, E.N., 1979. Cosmical Magnetic Fields: their Origin and their Activity. Clarendon Press, Oxford.
68. Proctor, M.R.E., 1977a. The role of mean circulation in parity selection by planetary magnetic fields. Geophys. Astrophys. Fluid Dyn., 8: 311-324.
69. Proctor, M.R.E., 1977b. On Backus' necessary condition for dynamo action in a conducting sphere. Geophys. Astrophys. Fluid Dyn., 9: 89-93.
70. Proctor, M.R.E., 1977c. Numerical solutions of the nonlinear α-effect dynamo equations. J. Fluid Mech., 80: 769-784.
71. Proctor, M.R.E., 1994. Convection and magnetoconvection in a rapidly rotating sphere. In: M.R.E. Proctor and A.D. Gilbert (Editors), Lectures on Solar and Planetary Dynamos. Cambridge University Press, Cambridge, pp. 97-115.
72. Roberts, P.H., 1967. An Introduction to Magnetohydrodynamics. Elsevier, New York.
73. Roberts, P.H., 1968. On the thermal instability of a rotating fluid sphere containing heat sources. Philos. Trans. R. Soc. London, Ser. A, 263: 93-117.
74. Roberts, P.H., 1972. Kinematic dynamo models. Philos. Trans. R. Soc. London, Ser. A, 272: 663-703.
75. Roberts, P.H., 1978. Magnetoconvection in a rapidly rotating fluid. In: P.H. Roberts and A.M. Soward (Editors), Rotating Fluids in Geophysics. Academic Press, London, pp. 421-435.
76. Roberts, P.H., 1988. Future of geodynamo theory. Geophys. Astrophys. Fluid Dyn., 44: 3-31.
77. Roberts, P.H. and Soward, A.M., 1992. Dynamo theory. Annu. Rev. Fluid Mech., 24: 459-512.
78. Soward, A.M., 1974. A convection driven dynamo: the weak field case. Philos. Trans. R. Soc. London, Ser. A, 275: 611-651.
79. Soward, A.M., 1977. On the finite amplitude thermal instability of a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dyn., 9: 19-74.
80. Soward, A.M., 1979. Convection driven dynamos. Phys. Earth Planet. Inter., 20: 134-151.
81. Soward, A.M., 1991. The Earth's dynamo. Geophys. Astrophys. Fluid Dyn., 62: 191-209.
82. 2-dynamos and Taylor's constraint. Geophys. Astrophys. Fluid Dyn., 27: 87-122.
83. Steenbeck, M., Krause, F. and Rädler, K.H., 1966. A calculation of the mean emf in an electrically conducting fluid in turbulent motion, under the influence of Coriolis forces. Z. Naturforsch., 21: 369-376.
84. Stewartson, K., 1966. On almost rigid rotations. J. Fluid Mech., 26: 131-144.
85. St. Pierre, M.G., 1993. The strong field branch of the Childress-Soward dynamo. In: M.R.E. Proctor, P.C. Matthews and A.M. Rucklidge (Editors), Solar and Planetary Dynamos. Cambridge University Press, Cambridge, pp. 295-302.
86. Taylor, J.B., 1963. The magnetohydrodynamics of a rotating fluid and the Earth's dynamo problem. Proc. R. Soc. London, Ser. A, 274: 274-283.
87. Zhang, K., 1992. Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech., 236: 535-556.
88. Zhang, K. and Busse, F.H., 1988. Finite amplitude convection and magnetic field generation in a rotating spherical shell. Geophys. Astrophys. Fluid Dyn., 44: 33-53.
89. Zhang, K. and Busse, F.H., 1989. Convection driven magnetohydrodynamic dynamos in rotating spherical shells. Geophys. Astrophys. Fluid Dyn., 49: 97-116.
90. Zhang, K. and Busse, F.H., 1990. Generation of magnetic fields by convection in a rotating spherical fluid shell of infinite Prandtl number. Phys. Earth Planet. Inter., 59: 208-222.
91. Zhang, K. and Jones, C.A., 1996. On small Roberts number magnetoconvection in rapidly rotating systems. Proc. R. Soc. London, Ser. A, 452: 981-995.