Space Science Reviews

, Volume 155, Issue 1–4, pp 177–218 | Cite as

Short Timescale Core Dynamics: Theory and Observations

  • C. C. FinlayEmail author
  • M. Dumberry
  • A. Chulliat
  • M. A. Pais


Fluid motions in the Earth’s core produce changes in the geomagnetic field (secular variation) and are also an important ingredient in the planet’s rotational dynamics. In this article we review current understanding of core dynamics focusing on short timescales of years to centuries. We describe both theoretical models and what may be inferred from geomagnetic and geodetic observations. The kinematic concepts of frozen flux and magnetic diffusion are discussed along with relevant dynamical regimes of magnetostrophic balance, tangential geostrophy, and quasi-geostrophy. An introduction is given to free modes and waves that are expected to be present in Earth’s core including axisymmetric torsional oscillations and non-axisymmetric Magnetic-Coriolis waves. We focus on important recent developments and promising directions for future investigations.


Geomagnetism Secular variation Core dynamics Core-mantle coupling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. R. Abarca del Rio, D. Gambis, D.A. Salatein, Interannual signals in length of day and atmospheric angular momentum. Ann. Geophys. 18, 347–364 (2000) ADSGoogle Scholar
  2. D.J. Acheson, On hydromagnetic stability of a rotating fluid annulus. J. Fluid Mech. 52(3), 529–541 (1972) zbMATHMathSciNetADSCrossRefGoogle Scholar
  3. D.J. Acheson, R. Hide, Hydromagnetics of rotating fluids. Rep. Prog. Phys. 36, 159–221 (1973) ADSCrossRefGoogle Scholar
  4. H. Alfvén, On the existence of electromagnetic-hydromagnetic waves. Nature 150, 405–406 (1942) ADSCrossRefGoogle Scholar
  5. D.W. Allan, E.C. Bullard, The secular variation of the Earth’s magnetic field. Proc. Camb. Philos. Soc. 62(3), 783–809 (1966) CrossRefGoogle Scholar
  6. H. Amit, U.R. Christensen, Accounting for magnetic diffusion in core flow inversions from geomagnetic secular variation. Geophys. J. Int. 175, 913–924 (2008) ADSCrossRefGoogle Scholar
  7. H. Amit, P. Olson, Helical core flows from geomagnetic secular variations. Phys. Earth Planet. Inter. 147, 1–25 (2004) ADSCrossRefGoogle Scholar
  8. H. Amit, P. Olson, Time-average and time-dependent parts of core flows. Phys. Earth Planet. Inter. 155, 120–139 (2006) ADSCrossRefGoogle Scholar
  9. H. Amit, P. Olson, U. Christensen, Tests of core flow imaging methods with numerical dynamos. Geophys. J. Int. 168, 27–39 (2007) ADSCrossRefGoogle Scholar
  10. H. Amit, J. Aubert, G. Hulot, P. Olson, A simple model for mantle-driven flow at the top of the Earth’s core. Earth Planets Space 60, 845–854 (2008) ADSGoogle Scholar
  11. S. Asari, H. Shimizu, H. Utada, Robust and less robust features in the tangential geostrophy core flows. Geophys. J. Int. 178, 678–692 (2009) ADSCrossRefGoogle Scholar
  12. J. Aubert, Steady zonal flows in spherical shell fluid dynamos. J. Fluid Mech. 542, 53–67 (2005) zbMATHADSCrossRefGoogle Scholar
  13. J. Aubert, N. Gillet, P. Cardin, Quasigeostrophic models of convection in rotating spherical shells. Geochem. Geophys. Geosyst. 4, 1052 (2003). doi: 10.1029/2002GC000456 ADSCrossRefGoogle Scholar
  14. J. Aubert, H. Amit, G. Hulot, Detecting thermal boundary control in surface flows from numerical dynamos. Phys. Earth Planet. Inter. 160, 143–156 (2007) ADSCrossRefGoogle Scholar
  15. J. Aubert, J. Aurnou, J. Wicht, The magnetic structure of convection-driven numerical dynamos. Geophys. J. Int. 172, 945–966 (2008) ADSCrossRefGoogle Scholar
  16. J. Aubert, J. Tarduno, C. Johnson, Observations and models of the long-term evolution of Earth’s Magnetic Field. Space Sci. Rev. (2010). doi: 10.1007/s11214-010-9684-5 Google Scholar
  17. G. Backus, Kinematics of geomagnetic secular variation in a perfectly conducting core. Philos. Trans. R. Soc. Lond. A 263, 239–266 (1968) ADSCrossRefGoogle Scholar
  18. G. Backus, Bayesian inference in geomagnetism. Geophys. J. Int. 92, 125–142 (1988) zbMATHADSCrossRefGoogle Scholar
  19. G.E. Backus, J.L. Le Mouël, The region on the core-mantle boundary where a geostrophic velocity field can be determined from frozen-flux magnetic data. Geophys. J. R. Astron. Soc. 85, 617–628 (1986) Google Scholar
  20. E.R. Benton, K.A. Whaler, Rapid diffusion of the poloidal geomagnetic field through the weakly conducting mantle: a perturbation solution. Geophys. J. Int. 75, 77–100 (1983) zbMATHADSCrossRefGoogle Scholar
  21. J. Bloxham, The expulsion of magnetic flux from the Earth’s outer core. Geophys. J. R. Astron. Soc. 87, 669–678 (1986) Google Scholar
  22. J. Bloxham, D. Gubbins, Geomagnetic field analysis—IV. Testing the frozen-flux hypothesis. Geophys. J. R. Astron. Soc. 84, 139–152 (1986) ADSGoogle Scholar
  23. J. Bloxham, A. Jackson, Lateral temperature variations at the core-mantle boundary deduced from the magnetic field. Geophys. Res. Lett. 17, 1997–2000 (1990) ADSCrossRefGoogle Scholar
  24. J. Bloxham, A. Jackson, Fluid flow near the surface of Earth’s outer core. Rev. Geophys. 29, 97–120 (1991) ADSCrossRefGoogle Scholar
  25. J. Bloxham, A. Jackson, Time dependent mapping of the geomagnetic field at the core-mantle boundary. J. Geophys. Res. 97, 19537–19564 (1992) ADSCrossRefGoogle Scholar
  26. J. Bloxham, D. Gubbins, A. Jackson, Geomagnetic secular variation. Philos. Trans. R. Soc. Lond. A 329(1606), 415–502 (1989) ADSCrossRefGoogle Scholar
  27. J. Bloxham, S. Zatman, M. Dumberry, The origin of geomagnetic jerks. Nature 420, 65–68 (2002) ADSCrossRefGoogle Scholar
  28. S.I. Braginsky, Magnetohydrodynamics of the Earth’s core. Geomagn. Aeron. 4, 698–712 (1964) Google Scholar
  29. S.I. Braginsky, Magnetic waves in the Earth’s core. Geomagn. Aeron. 7, 851–859 (1967) Google Scholar
  30. S.I. Braginsky, Torsional magnetohydrodynamic vibrations in the Earth’s core and variations in day length. Geomagn. Aeron. 10, 1–10 (1970) ADSGoogle Scholar
  31. S.I. Braginsky, Analytic description of the geomagnetic field of past epochs and determination of the spectrum of magnetic waves in the core of the Earth I. Geomagn. Aeron. 12, 947–957 (1972) ADSGoogle Scholar
  32. S.I. Braginsky, Short-period geomagnetic secular variation. Geophys. Astrophys. Fluid Dyn. 30, 1–78 (1984) zbMATHADSCrossRefGoogle Scholar
  33. S.I. Braginsky, P.H. Roberts, Equations governing convection in Earth’s core and the geodynamo. Geophys. Astrophys. Fluid Dyn. 79, 1–97 (1995) ADSCrossRefGoogle Scholar
  34. B.A. Buffett, Free oscillations in the length of day: inferences on physical properties near the core-mantle boundary, in The Core-mantle Boundary Region, ed. by M. Gurnis, M.E. Wysession, E. Knittle, B.A. Buffett. Geodynamics Series, vol. 28 (AGU Geophysical Monograph, Washington, 1998), pp. 153–165 Google Scholar
  35. B.A. Buffett, J. Mound, A. Jackson, Inversion of torsional oscillations for the structure and dynamics of Earth’s core. Geophys. J. Int. 177, 878–890 (2009) ADSCrossRefGoogle Scholar
  36. F.H. Busse, The dynamical coupling between inner core and mantle of the Earth and the 24-year libration of the pole, in Earthquake Displacement Fields and the Rotation of the Earth, ed. by D. Mansinha, D.E. Smylie, A.E. Beck. Astrophysics and Space Science Library, vol. 20 (Reidel, Dordrecht, 1970), pp. 88–98 Google Scholar
  37. F.H. Busse, C. Carrigan, Laboratory simulation of thermal convection in rotating planets and stars. Science 191, 81–83 (1976) ADSCrossRefGoogle Scholar
  38. F.H. Busse, R. Simitev, Convection in rotating spherical fluid shells and its dynamo states, in Fluid Dynamics and Dynamos in Astrophysics and Geophysics, ed. by A.M. Soward, C.A. Jones, D.W. Hugues, N.O. Weiss. The Fluid Mechanics of Astrophysics and Geophysics (Taylor & Francis, London, 2005), pp. 359–392 Google Scholar
  39. E. Canet, Modèle dynamique et assimilation de données de la variation séculaire du champ magnétique terrestre. Ph.D. thesis, Université Joseph Fourier de Grenoble (2009) Google Scholar
  40. E. Canet, A. Fournier, D. Jault, Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation. J. Geophys. Res. 114 (2009). doi: 10.1029/2008JB006189
  41. P. Cardin, P. Olson, An experimental approach to thermochemical convection in the Earth’s core. Geophys. Res. Lett. 19, 1995–1998 (1992) ADSCrossRefGoogle Scholar
  42. P. Cardin, P. Olson, Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core. Phys. Earth Planet. Inter. 82, 235–259 (1994) ADSCrossRefGoogle Scholar
  43. C. Carrigan, F.H. Busse, An experimental and theoretical investigation of the onset of convection in rotating spherical shells. J. Fluid Mech. 126, 287–305 (1983) zbMATHADSCrossRefGoogle Scholar
  44. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon, Oxford, 1961), pp. 196–219 zbMATHGoogle Scholar
  45. U.R. Christensen, J. Aubert, Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields. Geophys. J. Int. 166, 97–114 (2006) ADSCrossRefGoogle Scholar
  46. U.R. Christensen, P. Olson, Secular variation in numerical geodynamo models with lateral variations of boundary heat flow. Geophys. J. Int. 138, 39–54 (2003) Google Scholar
  47. U.R. Christensen, J. Wicht, Numerical dynamo simulations, in Treatise on Geophysics, vol. 8, ed. by P. Olson (Elsevier, Amsterdam, 2007), pp. 245–282 Google Scholar
  48. A. Chulliat, Geomagnetic secular variation generated by a tangentially geostrophic flow under the frozen-flux assumption—II. Sufficient conditions. Geophys. J. Int. 157, 537–552 (2004) ADSCrossRefGoogle Scholar
  49. A. Chulliat, G. Hulot, Local computation of the geostrophic pressure at the top of the core. Phys. Earth Planet. Inter. 117, 309–328 (2000) ADSCrossRefGoogle Scholar
  50. A. Chulliat, G. Hulot, Geomagnetic secular variation generated by a tangentially geostrophic flow under the frozen-flux assumption—I. Necessary conditions. Geophys. J. Int. 147, 237–246 (2001) ADSCrossRefGoogle Scholar
  51. A. Chulliat, N. Olsen, Observation of magnetic diffusion in the Earth’s outer core from Magsat, Oersted and CHAMP data. J. Geophys. Res. 115, B05105 (2010). doi: 10.1029/2009JB006994 CrossRefGoogle Scholar
  52. A. Chulliat, G. Hulot, L. Newitt, Magnetic flux expulsion from the core as a possible cause of the unusually large acceleration of the north magnetic pole during the 1990s. J. Geophys. Res. 115, B07101 (2010). doi: 10.1029/2009JB007143 CrossRefGoogle Scholar
  53. C.G. Constable, R.L. Parker, P. Stark, Geomagnetic field models incorporating frozen-flux constraints. Geophys. J. Int. 113, 419–433 (1993) ADSCrossRefGoogle Scholar
  54. P. Davidson, An Introduction to Magnetohydrodynamics (Cambridge University Press, Cambridge, 2001) zbMATHCrossRefGoogle Scholar
  55. E. Dormy, A.M. Soward, C.A. Jones, D. Jault, Cardin, The onset of thermal convection in rotating spherical shells. J. Fluid Mech. 501, 43–70 (2004) zbMATHMathSciNetADSCrossRefGoogle Scholar
  56. E. Dormy, P.H. Roberts, A.M. Soward, Core, boundary layers, in Encyclopedia of Geomagnetism and Paleomagnetism (Springer, Berlin, 2007) Google Scholar
  57. S.J. Drew, Magnetic field expulsion into a conducting mantle. Geophys. J. Int. 115, 303–312 (1993) ADSCrossRefGoogle Scholar
  58. M. Dumberry, Gravity variations induced by core flows. Geophys. J. Int. 180, 635–650 (2010) ADSCrossRefGoogle Scholar
  59. M. Dumberry, J. Bloxham, Torque balance, Taylor’s constraint and torsional oscillations in a numerical model of the geodynamo. Phys. Earth Planet. Inter. 140, 29–51 (2003) ADSCrossRefGoogle Scholar
  60. M. Dumberry, J.E. Mound, Constraints on core-mantle electromagnetic coupling from torsional oscillation normal modes. J. Geophys. Res. 113, B03102 (2008). doi: 10.1029/2007JB005135 CrossRefGoogle Scholar
  61. A.M. Dziewonski, D.L. Anderson, Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981) ADSCrossRefGoogle Scholar
  62. C. Eymin, G. Hulot, On core surface flows inferred from satellite magnetic data. Phys. Earth Planet. Inter. 152, 200–220 (2005) ADSCrossRefGoogle Scholar
  63. D.R. Fearn, Differential rotation and thermal convection in a rapidly rotating hydromagnetic system. Geophys. Astrophys. Fluid Dyn. 49, 173–193 (1989) zbMATHMathSciNetADSCrossRefGoogle Scholar
  64. D.R. Fearn, Magnetic instabilities in rapidly rotating systems, in Theory of Solar and Planetary Dynamos, ed. by M.R.E. Proctor, P.C. Matthews, A.M. Rucklidge (1993), pp. 59–68 Google Scholar
  65. D.R. Fearn, Nonlinear planetary dynamos, in Lectures on Solar and Planetary Dynamos, ed. by M.R.E. Proctor, A.D. Gilbert (Cambridge University Press, Cambridge, 1994) Google Scholar
  66. D.R. Fearn, Hydromagnetic flow in planetary cores. Rep. Prog. Phys. 61, 175–235 (1998) ADSCrossRefGoogle Scholar
  67. C.C. Finlay, Waves in the presence of magnetic fields, rotation and convection. Les Houches Summer School Proc. 88, 403–450 (2008) CrossRefGoogle Scholar
  68. C.C. Finlay, A. Jackson, Equatorially dominated magnetic field change at the surface of Earth’s core. Science 300, 2084–2086 (2003) ADSCrossRefGoogle Scholar
  69. A. Fournier, G. Hulot, D. Jault, W. Kuang, A. Tangborn, N. Gillet, E. Canet, J. Aubert, F. Lhuillier, An introduction to data assimilation and predictability in geomagnetism. Space Sci. Rev. (2010, accepted). doi: 10.1007/s11214-010-9669-4
  70. E. Friis-Christensen, H. Lühr, G. Hulot, Swarm: A constellation to study the Earth’s magnetic field. Earth Planets Space 58, 351–358 (2006) ADSGoogle Scholar
  71. H. Gellibrand, A Discourse Mathematical on the Variation of the Magnetic Needle. Together with Its Admirable Diminution Lately Discovered (William Jones, London, 1635) Google Scholar
  72. A.D. Gilbert, Dynamo Theory, ed. by S. Friedlander, D. Serre. Handbook of Mathematical Fluid Dynamics, vol. 2 (Elsevier, New York, 2003), pp. 355–441 Google Scholar
  73. A.E. Gill, Atmosphere-Ocean Dynamics (Academic Press, San Diego, 1982) Google Scholar
  74. N. Gillet, C.A. Jones, The quasi-geostrophic model for rapidly rotating spherical convection outside the tangent cylinder. J. Fluid Mech. 554, 343–369 (2006) zbMATHMathSciNetADSCrossRefGoogle Scholar
  75. N. Gillet, V. Lesur, N. Olsen, Geomagnetic core field secular variation models. Space Sci. Rev. (2009a). doi: 10.1007/s11214-009-9586-6 Google Scholar
  76. N. Gillet, A. Pais, D. Jault, Ensemble inversion of time-dependent core flow models. Geochem. Geophys. Geosyst. 10, Q06004 (2009b). doi: 10.1029/2008GC002290 CrossRefGoogle Scholar
  77. N. Gillet, D. Jault, E. Canet, A. Fournier, Fast torsional waves and strong magnetic field within the Earth’s core. Nature 465, 764–777 (2010) CrossRefGoogle Scholar
  78. G.A. Glatzmaier, P.H. Roberts, A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Phys. Earth Planet. Inter. 91, 63–75 (1995) CrossRefGoogle Scholar
  79. H.P. Greenspan, The Theory of Rotating Fluids (Cambridge University Press, Cambridge, 1968) zbMATHGoogle Scholar
  80. D. Gubbins, Finding core motions from magnetic observations. Philos. Trans. R. Soc. Lond. A 306, 247–254 (1982) ADSCrossRefGoogle Scholar
  81. D. Gubbins, Mechanism for geomagnetic polarity reversals. Nature 326, 167–169 (1987) ADSCrossRefGoogle Scholar
  82. D. Gubbins, Dynamics of the secular variation. Phys. Earth Planet. Int. 68, 170–182 (1991) ADSCrossRefGoogle Scholar
  83. D. Gubbins, A formalism for the inversion of geomagnetic data for core motions with diffusion. Phys. Earth Planet. Inter. 98, 193–206 (1996) ADSCrossRefGoogle Scholar
  84. D. Gubbins, Geomagnetic constraints on stratification at the top of the Earth’s core. Earth Planets Space 59, 661–664 (2007) ADSGoogle Scholar
  85. D. Gubbins, P. Kelly, A difficulty with using the frozen flux hypothesis to find steady core motions. Geophys. Res. Lett. 23, 1825–1828 (1996) ADSCrossRefGoogle Scholar
  86. D. Gubbins, P.H. Roberts, Magnetohydrodynamics of the Earth’s core. Geomagnetism 2, 1–183 (1987) Google Scholar
  87. E. Halley, A theory of the variation of the magnetical compass. Philos. Trans. R. Soc. Lond. A 13, 208–221 (1683) CrossRefGoogle Scholar
  88. E. Halley, An account of the cause of the change of the variation of the magnetic needle; with an hypothesis of the structure of the internal part of the Earth. Philos. Trans. R. Soc. Lond. A 17, 563–578 (1692) Google Scholar
  89. R. Hide, Free hydromagnetic oscillations of the Earth’s core and the theory of geomagnetic secular variation. Philos. Trans. R. Soc. Lond. A 259, 615–647 (1966) ADSCrossRefGoogle Scholar
  90. R. Hide, A note on short-term core-mantle coupling, geomagnetic secular variation impulses, and potential magnetic field invariants as Lagrangian tracers of core motions. Phys. Earth Planet. Int. 39, 297–300 (1985) ADSCrossRefGoogle Scholar
  91. R. Hide, K. Stewartson, Hydromagnetic oscillations of the Earth’s core. Rev. Geophys. Space Phys. 10, 579–598 (1972) ADSCrossRefGoogle Scholar
  92. R. Hide, D.H. Boggs, J.O. Dickey, Angular momentum fluctuations within the Earth’s liquid core and torsional oscillations of the core-mantle system. Geophys. J. Int. 143, 777–786 (2000) ADSCrossRefGoogle Scholar
  93. R.G. Hills, Convection in the Earth’s mantle due to viscous shear at the core-mantle interface and due to large-scale buoyancy. Ph.D. thesis, New Mexico State University (1979) Google Scholar
  94. R. Hollerbach, On the theory of the geodynamo. Phys. Earth Planet. Inter. 98, 163–185 (1996) ADSCrossRefGoogle Scholar
  95. R. Holme, Large-scale flow in the core, in Treatise on Geophysics, vol. 8, ed. by P. Olson (Elsevier, Amsterdam, 2007) Google Scholar
  96. R. Holme, N. Olsen, Core surface flow modelling from high-resolution secular variation. Geophys. J. Int. 166, 518–528 (2006) ADSCrossRefGoogle Scholar
  97. S.S. Hough, On the application of harmonic analysis to the dynamic theory of the Tides, part I. On Laplace’s “oscillations of the first species” and on the dynamics of ocean currents. Philos. Trans. R. Soc. Lond. A 189, 201–257 (1897) ADSCrossRefGoogle Scholar
  98. G. Hulot, A. Chulliat, On the possibility of quantifying diffusion and horizontal Lorentz forces at the Earth’s core surface. Phys. Earth Planet. Inter. 135, 47–54 (2003) ADSCrossRefGoogle Scholar
  99. G. Hulot, C. Eymin, B. Langlais, M. Mandea, N. Olsen, Small-scale structure of the geodynamo inferred from Oersted and Magsat satellite data. Nature 416, 620–623 (2002) ADSCrossRefGoogle Scholar
  100. A. Jackson, Kelvin’s theorem applied to the Earth’s core. Proc. R. Soc. London, Ser. A 452, 2195–2201 (1996) zbMATHADSCrossRefGoogle Scholar
  101. A. Jackson, Time-dependency of tangentially geostrophic core surface motions. Phys. Earth Planet. Inter. 103, 293–311 (1997) ADSCrossRefGoogle Scholar
  102. A. Jackson, Intense equatorial flux spots on the surface of Earth’s core. Nature 424, 760–763 (2003) ADSCrossRefGoogle Scholar
  103. A. Jackson, C.C. Finlay, Geomagnetic secular variation and its applications to the core, in Treatise on Geophysics, vol. 5, ed. by G. Schubert (Elsevier, Amsterdam, 2007), pp. 147–193 CrossRefGoogle Scholar
  104. A. Jackson, J. Bloxham, D. Gubbins, Time-dependent flow at the core surface and conservation of angular momentum in the coupled core-mantle system, in Dynamics of the Earth’s Deep Interior and Earth Rotation, vol. 72, ed. by J.L. Le Mouël, D.E. Smylie, T. Herring (AGU Geophysical Monograph, Washington, 1993), pp. 97–107 Google Scholar
  105. A. Jackson, A.R.T. Jonkers, M.R. Walker, Four centuries of geomagnetic secular variation from historical records. Philos. Trans. R. Soc. Lond. A 358, 957–990 (2000) ADSCrossRefGoogle Scholar
  106. A. Jackson, C.G. Constable, M.R. Walker, R.L. Parker, Models of Earth’s main magnetic field incorporating flux and radial vorticity constraints. Geophys. J. Int. 171, 133–144 (2007) ADSCrossRefGoogle Scholar
  107. D. Jault, Electromagnetic and topographic coupling, and lod variations, in Earth’s Core and Lower Mantle, ed. by C.A. Jones, A. Soward, K. Zhang. The Fluid Mechanics of Astrophysics And Geophysics (Taylor & Francis, London, 2003), pp. 56–76 Google Scholar
  108. D. Jault, Axial invariance of rapidly varying diffusionless motions in the Earth’s core interior. Phys. Earth Planet. Inter. 166, 67–76 (2008) ADSGoogle Scholar
  109. D. Jault, J.L. Le Mouël, Physical properties at the top of the core and core surface motions. Phys. Earth Planet. Inter. 68, 76–84 (1991) ADSCrossRefGoogle Scholar
  110. D. Jault, G. Légaut, Alfvén waves within the Earth’s core, in Fluid Dynamics and Dynamos in Astrophysics and Geophysics, ed. by A.M. Soward, C.A. Jones, D.W. Hugues, N.O. Weiss. The Fluid Mechanics of Astrophysics and Geophysics (Taylor & Francis, London, 2005), pp. 277–293 Google Scholar
  111. D. Jault, C. Gire, J.L. Le Mouël, Westward drift, core motions and exchanges of angular momentum between core and mantle. Nature 333, 353–356 (1988) ADSCrossRefGoogle Scholar
  112. D. Jault, G. Hulot, J.L. Le Mouël, Mechanical core-mantle coupling and dynamo modelling. Phys. Earth Planet. Inter. 98, 187–191 (1996) ADSCrossRefGoogle Scholar
  113. C.A. Jones, Dynamos in planets, in Stellar Astrophysical Fluid Dynamics, ed. by M. Thompson, J. Christensen-Dalsgaard (Cambridge University Press, Cambridge, 2003), pp. 159–178 CrossRefGoogle Scholar
  114. C.A. Jones, Thermal and compositional convection in the outer core, in Treatise in Geophysics, Core Dynamics, vol. 8, ed. by P. Olson (Amsterdam, 2007), pp. 131–185 Google Scholar
  115. C.A. Jones, A.N. Soward, A.I. Mussa, The onset of convection in a rapidly rotating sphere. J. Fluid Mech. 405, 157–179 (2000) zbMATHMathSciNetADSCrossRefGoogle Scholar
  116. C.A. Jones, A.I. Mussa, S.J. Worland, Magnetoconvection in a rapidly rotating sphere: the weak-field case. Proc. R. Soc. Lond. A 459, 773–797 (2003) zbMATHMathSciNetADSCrossRefGoogle Scholar
  117. A. Kageyama, T. Miyagoshi, T. Satu, Formation of current coils in geodynamo simulations. Nature 454, 1106–1109 (2008) ADSCrossRefGoogle Scholar
  118. R.R. Kerswell, Tidal excitation of hydromagnetic waves and their damping in the Earth. J. Fluid Mech. 274, 219–241 (1994) zbMATHMathSciNetADSCrossRefGoogle Scholar
  119. M.D. Kohler, D.J. Stevenson, Modeling core fluid motions and the drift of magnetic field patterns at the CMB by use of topography obtained by seismic inversion. Geophys. Res. Lett. 17, 1473–1476 (1990) ADSCrossRefGoogle Scholar
  120. J.L. Le Mouël, Outer core geostrophic flow and secular variation of Earth’s geomagnetic field. Nature 311, 734–735 (1984) ADSCrossRefGoogle Scholar
  121. J.L. Le Mouël, C. Gire, T. Madden, Motions at core surface in the geostrophic approximation. Phys. Earth Planet. Inter. 39, 270–287 (1985) ADSCrossRefGoogle Scholar
  122. B. Lehnert, Magnetohydrodynamic waves under the action of the Coriolis force. Astrophys. J. 119, 647–654 (1954) MathSciNetADSCrossRefGoogle Scholar
  123. V. Lesur, I. Wardinski, M. Rother, M. Mandea, GRIMM: the GFZ reference internal magnetic model based on vector satellite and observatory data. Geophys. J. Int. 173, 382–394 (2008) ADSCrossRefGoogle Scholar
  124. V. Lesur, I. Wardinski, S. Asari, B. Minchev, M. Mandea, Modelling the Earth’s core magnetic field under flow constraints. Earth Planets Space 62, 503–516 (2010) ADSCrossRefGoogle Scholar
  125. P.W. Livermore, G. Ierley, A. Jackson, The structure of Taylor’s constraint in three dimensions. Proc. R. Soc. Lond. A 464, 3149–3174 (2008) zbMATHMathSciNetADSCrossRefGoogle Scholar
  126. P.W. Livermore, G. Ierley, A. Jackson, The construction of exact Taylor states. I: The full sphere. Geophys. J. Int. 179, 923–928 (2009) ADSCrossRefGoogle Scholar
  127. J.J. Love, A critique of frozen-flux inverse modelling of a nearly steady geodynamo. Geophys. J. Int. 138, 353–365 (1999) ADSCrossRefGoogle Scholar
  128. W.V.R. Malkus, Hydromagnetic planetary waves. J. Fluid Mech. 28(4), 793–802 (1967) zbMATHMathSciNetADSCrossRefGoogle Scholar
  129. M. Mandea, R. Holme, A. Pais, A. Jackson, E. Qamili, Geomagnetic jerks: rapid core field variations and core dynamics (2010). doi: 10.1007/s11214-010-9663-x
  130. J. Matzka, A. Chulliat, M. Mandea, C. Finlay, E. Qamili, Direct observations from main field studies: from ground to space (2010). doi: 10.1007/s11214-010-9693-4
  131. S. Maus, On the applicability of the frozen flux approximation in core flow modelling as a function of temporal frequency and spatial degree. Geophys. J. Int. 175, 853–856 (2008) ADSCrossRefGoogle Scholar
  132. T. Miyagoshi, A. Kageyama, T. Sato, Zonal flow formation in the Earth’s core. Nature 463, 793–796 (2010) ADSCrossRefGoogle Scholar
  133. H.K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, 1978) Google Scholar
  134. V. Morin, E. Dormy, Time dependent β-convection in rapidly rotating spherical shell. Phys. Fluids 16, 1603–1609 (2004) MathSciNetADSCrossRefGoogle Scholar
  135. J.E. Mound, B.A. Buffett, Interannual oscillations in the length of day: implications for the structure of mantle and core. J. Geophys. Res. 108(B7), 2334 (2003). doi: 10.1029/2002JB002054 ADSCrossRefGoogle Scholar
  136. J.E. Mound, B.A. Buffett, Mechanisms of core-mantle angular momentum exchange and the observed spectral properties of torsional oscillations. J. Geophys. Res. 110, 08103 (2005). doi: 10.1029/2004JB003555 CrossRefGoogle Scholar
  137. J.E. Mound, B.A. Buffett, Detection of a gravitational oscillation in length-of-day. Earth Planet. Sci. Lett. 243, 383–389 (2006) ADSCrossRefGoogle Scholar
  138. H.C. Nataf, N. Gagnière, On the peculiar nature of turbulence in planetary dynamos. C. R. Phys. 9, 702–710 (2008) ADSGoogle Scholar
  139. M. Nornberg, H. Ji, E. Schartman, A. Roach, J. Goodman, Observation of magnetocoriolis waves in a liquid metal Taylor-Couette Experiment. Phys. Rev. Lett. 104, 074501 (2010) ADSCrossRefGoogle Scholar
  140. M.S. O’Brien, C.G. Constable, R.L. Parker, Frozen-flux modelling for epochs 1915 and 1980. Geophys. J. Int. 128, 434–450 (1997) ADSCrossRefGoogle Scholar
  141. N. Olsen, M. Mandea, Rapidly changing flows in the Earth’s core. Nature Geosci. 1, 390–394 (2008) ADSCrossRefGoogle Scholar
  142. N. Olsen, H. Lühr, T. Sabaka, M. Mandea, M. Rother, L. Tøffner-Clausen, S. Choi, CHAOS—A model of Earth’s magnetic field derived from CHAMP ørsted and SAC-C magnetic satellite data. Geophys. J. Int. 166, 67–75 (2006) ADSCrossRefGoogle Scholar
  143. N. Olsen, M. Mandea, T.J. Sabaka, L. Tøffner-Clausen, CHAOS-2—A geomagnetic field model derived from one decade of continuous satellite data. Geophys. J. Int. 142 (2009) Google Scholar
  144. P. Olson, J. Aurnou, A polar vortex in the Earth’s core. Nature 402, 170–173 (1999) ADSCrossRefGoogle Scholar
  145. P. Olson, U.R. Christensen, The time-averaged magnetic field in numerical dynamos with non-uniform boundary heat flow. Geophys. J. Int. 151, 809–823 (2002) ADSCrossRefGoogle Scholar
  146. P. Olson, U.R. Christensen, G.A. Glatzmaier, Numerical modeling of the geodynamo: mechanisms of field generation and equilibration. J. Geophys. Res. 104, 10383–10404 (1999) ADSCrossRefGoogle Scholar
  147. A. Pais, G. Hulot, Length of day decade variations, torsional oscillations and inner core superrotation: evidence from recovered core surface zonal flows. Phys. Earth Planet. Inter. 118, 291–316 (2000) ADSCrossRefGoogle Scholar
  148. M.A. Pais, D. Jault, Quasi-geostrophic flows responsible for the secular variation of the Earth’s magnetic field. Geophys. J. Int. 173, 421–443 (2008) ADSCrossRefGoogle Scholar
  149. M.A. Pais, O. Oliveira, F. Nogueira, Nonuniqueness of inverted core-mantle boundary flows and deviations from tangential geostrophy. J. Geophys. Res. 109, B08105 (2004). doi: 10.1029/2004JB003012 CrossRefGoogle Scholar
  150. J. Pedlosky, Geophysical Fluid Dynamics (Springer, New-York, 1987) zbMATHGoogle Scholar
  151. M.R.E. Proctor, Convection and magnetoconvection in a rapidly rotating sphere, in Lectures on Solar and Planetary Dynamos, ed. by M.R.E. Proctor, A.D. Gilbert (1994), pp. 97–115 Google Scholar
  152. J. Proudman, On the motions of solids in a liquid possessing vorticity. Proc. R. Soc. Lond. A 92, 408–424 (1916) ADSCrossRefGoogle Scholar
  153. S. Rau, U.R. Christensen, A. Jackson, J. Wicht, Core flow inversion tested with numerical dynamo models. Geophys. J. Int. 141, 485–497 (2000) ADSCrossRefGoogle Scholar
  154. P.H. Roberts, On the thermal instability of a self-gravitating fluid sphere containing heat sources. Philos. Trans. R. Soc. Lond. A 263, 93–117 (1968) zbMATHADSCrossRefGoogle Scholar
  155. P.H. Roberts, G.A. Glatzmaier, A test of the frozen-flux approximation using a new geodynamo model. Philos. Trans. R. Soc. Lond. A 358, 1109–1121 (2000) zbMATHADSCrossRefGoogle Scholar
  156. P.H. Roberts, S. Scott, On analysis of the secular variation. J. Geomagn. Geoelectr. 17, 137–151 (1965) Google Scholar
  157. P.H. Roberts, K. Stewartson, On finite amplitude convection in a rotating magnetic system. Philos. Trans. R. Soc. Lond. 277, 287–315 (1974) ADSCrossRefGoogle Scholar
  158. T.J. Sabaka, N. Olsen, M.E. Purucker, Extending comprehensive models of the Earth’s magnetic field with Ørsted and CHAMP data. Geophys. J. Int. 159, 521–547 (2004) ADSCrossRefGoogle Scholar
  159. A. Sakuraba, P. Roberts, Generation of a strong magnetic field using uniform heat flux at the surface of the core. Nature Geosci. 2, 802–805 (2009) ADSCrossRefGoogle Scholar
  160. N. Schaeffer, P. Cardin, Quasi-geostrophic model of the instabilities of the Stewartson layer in flat and depth varying containers. Phys. Fluids 17, 104111 (2005) MathSciNetADSCrossRefGoogle Scholar
  161. N. Schaeffer, P. Cardin, Quasi-geostrophic kinematic dynamos at low magnetic Prandtl number. Earth Planet. Sci. Lett. 245, 595–604 (2006) ADSCrossRefGoogle Scholar
  162. D. Schmitt, Magneto-inertial waves in a rotating sphere. Geophys. Astrophys. Fluid Dyn. 104, 135–151 (2010) CrossRefGoogle Scholar
  163. D. Schmitt, T. Alboussière, D. Brito, P. Cardin, N. Gagnière, D. Jault, H.C. Nataf, Rotating spherical Couette flow in a dipolar magnetic field: experimental study of magneto-inertial waves. J. Fluid Mech. 604, 175–197 (2008) zbMATHADSCrossRefGoogle Scholar
  164. B. Sreenivasan, C.A. Jones, Structure and dynamics of the polar vortex in the Earth’s core. Geophys. Res. Lett. 32, L20301 (2005). doi: 10.1029/2005GL023841 ADSCrossRefGoogle Scholar
  165. B. Sreenivasan, C.A. Jones, Azimuthal winds, convection and dynamo action in the polar regions of planetary cores. Geophys. Astrophys. Fluid Dyn. 100, 319–339 (2006) MathSciNetADSCrossRefGoogle Scholar
  166. F.D. Stacey, Core properties, physical, in Encyclopedia of Geomagnetism and Paleomagnetism, ed. by D. Gubbins, E. Herrero-Bervera (Springer, Dordrecht, 2007), pp. 91–94 CrossRefGoogle Scholar
  167. F. Takahashi, M. Matsushima, Dynamo action in a rotating spherical shell at high Rayleigh numbers. Phys. Fluids 17, 076601 (2005) MathSciNetADSCrossRefGoogle Scholar
  168. F. Takahashi, M. Matsushima, Y. Honkura, Simulations of a quasi-Taylor state geomagnetic field including polarity reversals on the Earth simulator. Science 309, 459–461 (2005) ADSCrossRefGoogle Scholar
  169. F. Takahashi, M. Matsushima, Y. Honkura, Scale variability in convection-driven mhd dynamos at low Ekman number. Phys. Earth Planet. Inter. 167, 168–178 (2008a) ADSCrossRefGoogle Scholar
  170. F. Takahashi, H. Tsunakawa, M. Matsushima, N. Mochizuki, Y. Honkura, Effects of thermally heterogeneous structure in the lowermost mantle on geomagnetic field strength. Earth Planet. Sci. Lett. 272, 738–746 (2008b) ADSCrossRefGoogle Scholar
  171. B.D. Tapley, M. Bettadpur, M. Watkins, C. Reigber, The gravity recovery and climate experiment: Mission overview and early results. Geophys. Res. Lett. 31, L09607 (2004). doi: 10.1029/2004GL019920 CrossRefGoogle Scholar
  172. G.I. Taylor, Motions of solids in fluid when the flow is not irrotational. Proc. R. Soc. Lond. A 93, 99–113 (1917) ADSCrossRefGoogle Scholar
  173. G.I. Taylor, Experiments with rotating fluids. Proc. R. Soc. Lond. A 100, 114–124 (1921) ADSCrossRefGoogle Scholar
  174. G.I. Taylor, Experiments on the motion of solid bodies in rotating fluids. Proc. R. Soc. Lond. A 104, 213–218 (1923) ADSCrossRefGoogle Scholar
  175. J.B. Taylor, The magneto-hydrodynamics of a rotating fluid and the Earth’s dynamo problem. Proc. R. Soc. Lond. A 274, 274–283 (1963) zbMATHADSCrossRefGoogle Scholar
  176. A. Tilgner, F.H. Busse, Finite amplitude convection in rotating spherical fluid shells. J. Fluid Mech. 332, 359–376 (1997) zbMATHADSGoogle Scholar
  177. I. Wardinski, R. Holme, A time-dependent model of the Earth’s magnetic field and its secular variation for the period 1980–2000. J. Geophys. Res. 111, B12101 (2006). doi: 10.1029/2006JB004401 ADSCrossRefGoogle Scholar
  178. I. Wardinski, R. Holme, S. Asari, M. Mandea, The 2003 geomagnetic jerk and its relation to the core surface flows. Earth Planet. Sci. Lett. 267, 468–481 (2008) ADSCrossRefGoogle Scholar
  179. K.A. Whaler, Does the whole of the Earth’s core convect. Nature 287, 528–530 (1980) ADSCrossRefGoogle Scholar
  180. J. Wicht, U.R. Christensen, Torsional oscillations in dynamo simulations. Geophys. J. Int. 181, 1367–1380 (2010) ADSGoogle Scholar
  181. A. Willis, B. Sreenivasan, D. Gubbins, Thermal core-mantle interaction: Exploring regimes for ‘locked’ dynamo action. Phys. Earth Planet. Inter. 165(1–2), 83–92 (2007). doi: 10.1016/j.pepi.2007.08.002 ADSCrossRefGoogle Scholar
  182. S. Zatman, J. Bloxham, Torsional oscillations and the magnetic field within the Earth’s core. Nature 388, 760–763 (1997) ADSCrossRefGoogle Scholar
  183. K. Zhang, G. Schubert, Magnetohydrodynamics in rapidly rotating spherical systems. Ann. Rev. Fluid Mech. 32, 409–443 (2000) MathSciNetADSCrossRefGoogle Scholar
  184. K. Zhang, P. Earnshaw, X. Liao, F. Busse, On inertial waves in a rotating fluid sphere. J. Fluid Mech. 437, 103–119 (2001) zbMATHMathSciNetADSCrossRefGoogle Scholar
  185. K. Zhang, X. Liao, G. Schubert, Nonaxisymmetric instabilities of a toroidal magnetic field in a rotating sphere. J. Fluid Mech. 585, 1124–1137 (2004) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • C. C. Finlay
    • 1
    Email author
  • M. Dumberry
    • 2
  • A. Chulliat
    • 3
  • M. A. Pais
    • 4
  1. 1.Institut für GeophysikETH ZürichZürichSwitzerland
  2. 2.Department of PhysicsUniversity of AlbertaEdmontonCanada
  3. 3.Equipe de GéomagnétismeInstitut de Physique du Globe de ParisParis Cedex 05France
  4. 4.Physics DepartmentUniversity of CoimbraCoimbraPortugal

Personalised recommendations