Rotation and magnetism of Earth's inner core

Science

Volumn 274, Issue 5294, 1996, Pages 1887-1891

  Glatzmaier, Gary A ^a   Roberts, Paul H ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ASTRONOMY; MAGNETIC FIELD; MAGNETISM; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; ROTATION;

CORE (INNER); GEODYNAMO; GEOMAGNETIC FIELD; PLANETARY ROTATION;

EID: 0030303720     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.274.5294.1887     Document Type: Article

References (23)

1. In our original geodynamo simulation [G. A. Glatzmaier and P. H. Roberts, Phys. Earth Planet. Inter. 91, 63 (1995); Nature 377, 203 (1995)], the core was assumed to be nearly uniform in density and temperature; buoyancy was included in the Boussinesq approximation.
2. In our original geodynamo simulation [G. A. Glatzmaier and P. H. Roberts, Phys. Earth Planet. Inter. 91, 63 (1995); Nature 377, 203 (1995)], the core was assumed to be nearly uniform in density and temperature; buoyancy was included in the Boussinesq approximation.
3. Here we discuss the results of our most recent geodynamo simulation [G. A. Glatzmaier and P. H. Roberts, Physica D 97, 81 (1996)], which included thermal and compositional convection in the core within the anelastic approximation.
4. 5 S/m. The eddy viscosity in our simulations (1. 2) is, from computational necessity, about three orders of magnitude larger than what would be expected for small-scale turbulence in Earth's fluid core and many orders of magnitude larger than its molecular viscosity. However, the viscous forces in the bulk of our fluid core are still about five orders of magnitude smaller than the Coriolis and Lorentz forces.
5. Because the melting temperature of core material increases with pressure more rapidly than does the temperature along the adiabat, the core presents the unfamiliar situation of a system that is cooled from the top but freezes from the bottom [J. A. Jacobs, Nature 172, 297 (1953)].
6. For example, see S. I. Braginsky and P. H. Roberts, Geophys. Astrophys. Fluid Dyn. 79, 1 (1995).
7. The rate of heat flow out of Earth's core is poorly known. Global 3D mantle convection simulations [P. J. Tackley, D. J. Stevenson, G. A. Glatzmaier, G. Schubert, J. Geophys. Res. 99, 15877 (1994)] obtained 7.2 TW, the value we use. Stacey (17) estimates it to be 3.0 TW on the basis of the assumption that the age of the inner core is the same as the age of the Earth and that the rate of heat flow out of the core has remained constant during this time. However, we find in our (unpublished) simulations that a 3.0-TW boundary condition does not maintain a strong, Earth-like magnetic field. Because our 7.2-TW boundary condition (2) does maintain an Earth-like field, the age of Earth's inner core may be considerably less than the age of the Earth itself. Of course, many of the material properties that we assume are quite uncertain. For example, we assume that the mass of the light constituent released when a unit mass of alloy freezes at the inner core boundary is 0.065, and the corresponding entropy released is 190 J/(kg K); these have uncertainties of 10 and 50%, respectively (5). More significantly, the presence of radioactivity in the core would provide additional thermal buoyancy and therefore would require less compositional buoyancy to obtain similar convective vigor and magnetic field intensity with the same heat flow through the coremantle boundary but without such a rapid growth rate of the inner core.
8. IC.
9. B was small. Note also that our models (1, 2) have assumed phase equilibrium on the inner core boundary; that is, as thermodynamic conditions change, freezing and melting occurs instantaneously to maintain the boundary at the freezing point. No allowance has been made for a finite time of relaxation to such a state. If that relaxation time were long compared with the time scales of interest in our model, the inner core would behave as a solid. As B. A. Buffett [Geophys. Res. Lett. 23, 2279 (1996)] noted, the orientation of the inner core would then plausibly be gravitationally "locked" to that of the mantle by the inner core topography created by mantle inhomogeneities, which we have not included in our models. If Earth's inner core is rotating faster than the mantle, as recent observations suggest (9, 10), a short melting-freezing relaxation time, a "mushy zone" at the top of the inner core (D. E. Loper, private communication), or a low inner core viscosity (B. A. Buffett, private communication) may preclude this gravitational locking effect.
10. B was small. Note also that our models (1, 2) have assumed phase equilibrium on the inner core boundary; that is, as thermodynamic conditions change, freezing and melting occurs instantaneously to maintain the boundary at the freezing point. No allowance has been made for a finite time of relaxation to such a state. If that relaxation time were long compared with the time scales of interest in our model, the inner core would behave as a solid. As B. A. Buffett [Geophys. Res. Lett. 23, 2279 (1996)] noted, the orientation of the inner core would then plausibly be gravitationally "locked" to that of the mantle by the inner core topography created by mantle inhomogeneities, which we have not included in our models. If Earth's inner core is rotating faster than the mantle, as recent observations suggest (9, 10), a short melting-freezing relaxation time, a "mushy zone" at the top of the inner core (D. E. Loper, private communication), or a low inner core viscosity (B. A. Buffett, private communication) may preclude this gravitational locking effect.
11. X. Song and P. G. Richards, Nature 382, 221 (1996).
12. W. Su, A. M. Dziewonski, R. Jeanloz, Science 274, 1883 (1996).
13. R. Hollerbach and C. A. Jones, Nature 365, 541 (1993); Phys. Earth Planet. Inter. 87, 171 (1993).
14. R. Hollerbach and C. A. Jones, Nature 365, 541 (1993); Phys. Earth Planet. Inter. 87, 171 (1993).
15. 2/3 for both axisymmetric and nonaxisymmetric modes of convection, but that the nonaxisymmetric motions, later identified by F. H. Busse [J. Fluid Mech. 44, 441 (1970)] as rolls parallet to the rotation axis, have the smaller critical Ra. That such rolls are "preferred" can be qualitatively understood in terms of the Proudman-Taylor theorem: Slow, steady motions in an inviscid rotating fluid are 2D with respect to the rotation axis, so that a towed body in such conditions carries a column of fluid with it, a so-called Taylor column. The convective rolls are also often called, a little imprecisely, Taylor columns.
16. 2/3 for both axisymmetric and nonaxisymmetric modes of convection, but that the nonaxisymmetric motions, later identified by F. H. Busse [J. Fluid Mech. 44, 441 (1970)] as rolls parallet to the rotation axis, have the smaller critical Ra. That such rolls are "preferred" can be qualitatively understood in terms of the Proudman-Taylor theorem: Slow, steady motions in an inviscid rotating fluid are 2D with respect to the rotation axis, so that a towed body in such conditions carries a column of fluid with it, a so-called Taylor column. The convective rolls are also often called, a little imprecisely, Taylor columns.
17. Similar thermal wind and meridional circulation structures were obtained by P. Olson and G. A. Glatzmaier [Phys. Earth Planet. Inter. 92, 109 (1995)] using a fully 3D magnetoconvection model but with an imposed zonal magnetic field and a nonrotating, insulating inner core. Similar flow structures also have been obtained by C. Jones and R. Hollerbach (private communication) with their dynamo model using only one nonaxisymmetric mode.
18. Similar thermal wind and meridional circulation structures were obtained by P. Olson and G. A. Glatzmaier [Phys. Earth Planet. Inter. 92, 109 (1995)] using a fully 3D magnetoconvection model but with an imposed zonal magnetic field and a nonrotating, insulating inner core. Similar flow structures also have been obtained by C. Jones and R. Hollerbach (private communication) with their dynamo model using only one nonaxisymmetric mode.
19. Φ on the inner core boundary. Also, after writing this report we were given a preprint by J. Aurnou, D. Brito, and P, Olson (Geophys. Res. Lett., in press) that describes a simple, analytic model of inner core rotation that approximates the thermal wind and magnetic coupling present in our geodynamo simulations (1, 2).
20. em on the geodynamo mechanism and stabilize it against polarity reversals, a significant fact first suggested by Hollerbach and Jones (11) and confirmed by our simulations (1, 2). The absence of zonal field in an inner core coupled magnetically to a fluid core was noted by S. Braginsky [Geomagn. Aeron. 4, 572 (1964)].
21. ν vanishes there (7). This zero torque results in discontinuities in the horizontal velocity between the solid inner core surface and the fluid just above it, which make nonlinear contributions to the magnetic boundary conditions there.
22. F. D. Stacey, Physics of the Earth (Brookfield, Brisbane, Australia, ed. 3, 1992).
23. The computing resources were provided by the Pittsburgh Supercomputing Center under grant MCA94P016P and the Advanced Computing Laboratory at Los Alamos National Laboratory. Different aspects of this work were supported by Los Alamos Laboratory Directed Research and Development grant 96149, University of California Directed Research and Development grant 9636, Institute of Geophysics and Planetary Physics grant 713 and NASA grant NCCS5-147. P.H.R. was supported by NSF grant EAR94-06002. The work was conducted under the auspices of the U.S. Department of Energy, supported (in part) by the University of California, for the conduct of discretionary research by Los Alamos National Laboratory.