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Electrical currents produced by motions in the Earths fluid outer core are thought to be responsible for the planets magnetic field. Numerical modelling of this process first became possible a decade or so ago1,2, and progress continues at a fast pace3. Owing to computational constraints, all of the early models assumed unrealistically high viscosity and thermal diffusivity for the outer core, but were nevertheless remarkably successful in reproducing an Earth-like magnetic field4. Surprisingly, however, as computations improved and incorporated more realistic parameter values, the resulting magnetic fields became less Earth-like5. On page 802 of this issue, Ataru Sakuraba and Paul Roberts6 show that a simple change in boundary conditions causes a surprising transformation in the structure of the solution, a finding that could alter the course of future modelling.
The low viscosity of the Earths liquid core poses a challenge for numerical models. Low viscosities permit small-scale motions, which prohibit realistic simulations; all calculations therefore adopt high viscosities to suppress the small-scale motion. It seems that the large-scale flow is mainly responsible for producing the Earth-like features in the magnetic field4, but the strength and structure of this flow is strongly influenced by small-scale motion. In fact, geodynamo models show a decrease in the strength of the large-scale flow as the value of viscosity is reduced. As Sakuraba and Roberts note, explicitly simulating small-scale motion weakens the dipole component of the field; extrapolating these trends to realistic values of viscosity would not produce a strong Earth-like dipole field.
Most geodynamo modellers have assumed that the temperature at the top of the core is constant. Indeed, lateral variations in temperature at the top of the core are probably only a few milli-Kelvin7, which is small compared with the temperature increase of ~1,200 K with depth in the liquid core. However, much of the temperature change with depth is due to the effect of pressure,
which does not contribute to convection in the core. Instead, the temperature fluctuations that drive flow are no larger than a few milli-Kelvin, which means that the temperature variations at the boundaries exert an important influence on core dynamics. Such effects are not present in numerical models when constant temperature conditions are imposed.
To overcome this problem, Sakuraba and Roberts6 explored the effect of a different boundary condition a uniform heat flux at the surface of the core. By prescribing a constant heat flux at the boundaries, the researchers permit temperature to vary along the cores surface. The researchers found that the use of uniform-heat-flux conditions in the model yields a strong,
dipolar magnetic field. They were also able to reproduce large-scale patches of magnetic flux that were similar to structures inferred at the Earths coremantle boundary from surface observations (Fig. 1). In contrast, models that assumed a constant surface temperature led to a weak magnetic field that was less Earth-like.
Differences in the two solutions are attributed to the presence of a large-scale circulation in the case of uniform-heat-flux conditions. This circulation organizes the magnetic field and enhances the dipole. Such a flow probably originates owing to the strong effects of rotation on convection in the core8. More heat is carried by convection in the equatorial region than in the polar region, leading to a build
a matter of boundariesThe use of more realistic parameters in numerical geodynamo simulations tends to generate less Earth-like magnetic fields. This paradox could be resolved by considering uniform heat flux instead of uniform temperature at the cores surface.
Radial field (mT)
Figure 1 | The radial component of the Earths magnetic field at the coremantle boundary11 reveals a strong dipole component. The field enters the core in blue regions and exits the core in red regions. Superimposed on this broad dipole pattern are patches of magnetic field at high latitudes and near the Equator. The use of heat-flux boundary conditions by Sakuraba and Roberts6 promotes the formation of these large-scale features. However the number and persistence of these features in the historical record is not understood.
ngeo_N&V's November 2009 .indd 741 21/10/09 11:30:59
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up of heat at the Equator. Temperature variations along the boundary drive a large-scale flow that redistributes the excess heat. The large-scale circulation becomes more prominent at low viscosities6, which may explain why the effect had not been noticed in previous calculations that used higher viscosities.
It should be noted that heat flux from the core is not expected to be constant all along the coremantle boundary, as assumed by the researchers. Fluctuations in mantle temperature are several hundred Kelvin or more, and must cause lateral variations in heat flux from the core. The structure of flow in the core caused by such variations is likely to be more complex than that simulated by Sakura and Roberts6. A far more realistic condition would be a variable heat flux at the top of the core, but at present we lack the information needed to specify this condition.
Previous efforts9 to model the effects of a variable heat flux have relied on variations
in seismic properties of the mantle to constrain the location of temperature anomalies. The resulting flows do resemble those inferred from observed changes in the magnetic field7, but there are important differences between the large-scale magnetic field simulated by such models and the Earths magnetic field. In particular, it has been difficult to explain the persistence of high-latitude patches of the Earths radial magnetic field. Heat-flux variations at the base of the mantle must have a role, but our understanding of the process is incomplete.
Sakuraba and Roberts6 are not the first to draw attention to the importance of heat-flux conditions in convection problems10. But it had not been appreciated how dramatic the influence of such conditions can be in numerical geodynamo models. Incorporating all the complexities in models is challenging, but the improvements in specific comparisons with the observed magnetic
field as reported in this study are a step in the right direction.
Bruce Buffett is in the Department of Earth and Planetary Science, University of California, Berkeley, 383 McCone Hall, Berkeley, California 947204767, USA. email: firstname.lastname@example.org
References1. Glatzmaier, G. A. & Roberts, P. H. Nature 377, 203209 (1995).2. Kageyama, A. et al. Phys. Plasmas 2, 14211431 (1995).3. Takahashi, F., Matsushima, M. & Honkura, Y. Science
309, 459461 (2005).4. Christensen, U. R., Olson, P. & Glatzmaier, G. A. Geophys. Res. Lett.
25, 15651568 (1998).5. Takahashi, F., Matsushima, M. & Honkura, Y. Phys. Earth Planet.
Inter. 167, 168178 (2008).6. Sakuraba, A. & Roberts, P. H. Nature Geosci. 2, 802805 (2009).7. Bloxham, J. & Jackson, A. Geophys. Res. Lett.
17, 19972000 (1990).8. Zhang, K. J. Fluid Dyn. 236, 535556 (1992).9. Olson, P. & Christensen, U. R. Geophys. J. Int. 151, 809823 (2002).10. Hewitt, J. M., McKenzie, D. P. & Weiss, N. O. Earth Planet. Sci. Lett.
51, 370380 (1980).11. Jackson, A., Constable, C. & Gillet, N. Geophys. J. Int.
171, 9951004 (2007).
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