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The Geodynamo

Paleomagnetic records indicate that the geomagnetic field has existed for at least three billion years. However, based on the size and electrical conductivity of the Earth's core, the field, if it were not continually being generated, would decay away in only about 20,000 years since the temperature of the core is too high to sustain permanent magnetism. In addition, paleomagnetic records show that the dipole polarity of the geomagnetic field has reversed many times in the past, the mean time between reversals being roughly 200,000 years with individual reversal events taking only a couple thousand years.

These observations argue for a mechanism within the Earth's interior that continually generates the geomagnetic field. It has long been speculated that this mechanism is a convective dynamo operating in the Earth's fluid outer core, which surrounds its solid inner core, both being mainly composed of iron. The solid inner core is roughly the size of the moon but at the temperature of the surface of the sun. The convection in the fluid outer core is thought to be driven by both thermal and compositional buoyancy sources at the inner core boundary that are produced as the Earth slowly cools and iron in the iron-rich fluid alloy solidifies onto the inner core giving off latent heat and the light constituent of the alloy. These buoyancy forces cause fluid to rise and the Coriolis forces, due to the Earth's rotation, cause the fluid flows to be helical. Presumably this fluid motion twists and shears magnetic field, generating new magnetic field to replace that which diffuses away.

However, until now, no detailed dynamically self-consistent model existed that demonstrated this could actually work or explained why the geomagnetic field has the intensity it does, has a strongly dipole-dominated structure with a dipole axis nearly aligned with the Earth's rotation axis, has non-dipolar field structure that varies on the time scale of ten to one hundred years and why the field occasionally undergoes dipole reversals. In order to test the convective dynamo hypothesis and attempt to answer these longstanding questions, the first self-consistent numerical model, the Glatzmaier-Roberts model, was developed that simulates convection and magnetic field generation in a fluid outer core surrounding a solid inner core (Figure 1) with the dimensions, rotation rate, heat flow and (as much as possible) the material properties of the Earth's core [1-5]. The magnetohydrodynamic equations that describe this problem are solved using a spectral method (spherical harmonic and Chebyshev polynomial expansions) that treats all linear terms implicitly and nonlinear terms explicitly [4]. These equations are solved over and over, advancing the time dependent solution 15 days at a time.

Fig.1 A snapshot of the region (yellow) where the fluid flow is the greatest. The core-mantle boundary is the blue mesh; the inner core boundary is the red mesh. Large zonal flows (eastward near the inner core and westward near the mantle) exist on an imaginary "tangent cylinder" due to the effects of large rotation, small fluid viscosity, and the presence of the solid inner core within spherical shell of the outer fluid core. (click on image to download, 0.15 Mb)

The resulting three-dimensional numerical simulation of the geodynamo, run on parallel supercomputers at the Pittsburgh Supercomputing Center and the Los Alamos National Laboratory, now spans more than 300,000 years. The simulated magnetic field has an intensity and a dipole dominated structure that is very similar to the Earth's (Figure 2) and a westward drift of the non-dipolar structures of the field at the surface that is essentially the same as the 0.2 degrees/year measured on the Earth. Our solution illustrates how the influence of the Earth's rotation on convection in the fluid outer core is responsible for this magnetic field structure and time dependence [1].

Fig.2 A snapshot of the 3D magnetic field structure simulated with the Glatzmaier-Roberts geodynamo model. Magnetic field lines are blue where the field is directed inward and yellow where directed outward. The rotation axis of the model Earth is vertical and through the center. A transition occurs at the core-mantle boundary from the intense, complicated field structure in the fluid core, where the field is generated, to the smooth, potential field structure outside the core. The field lines are drawn out to two Earth radii. Magnetic field is rapped around the "tangent cylinder" due to the shear of the zonal fluid flow (Fig. 1). (click on image to download, 0.15 Mb)

In addition, about 36,000 years into the simulation the magnetic field underwent a reversal of its dipole moment (Figure 3), over a period of a little more than a thousand years. The intensity of the magnetic dipole moment decreased by about a factor of ten during the reversal and recovered immediately after, similar to what is seen in the Earth's paleomagnetic reversal record. Our solution shows how convection in the fluid outer core is continually trying to reverse the field but that the solid inner core inhibits magnetic reversals because the field in the inner core can only change on the much longer time scale of diffusion [2]. Only once in many attempts is a reversal successful, which is probably the reason why the times between reversals of the Earth's field are long and randomly distributed.

Fig.3 Like in Fig. 2, but 500 years before the middle of a magnetic dipole reversal, at the middle of the reversal, and 500 years after the middle of the reversal. (click on images to download, 0.15 Mb each)

After the first magnetic reversal, we continued our simulation on two different branches: one by continuing to prescribe a uniform heat flux out of the core at the core-mantle boundary and the other by prescribing a heterogeneous heat flux there that is similar to the Earth's present pattern. The former has not reversed again; the latter underwent two more reversals, roughly 100,000 years apart. This demonstrates the influence the thermal structure in the lower mantle has on the style of convection and magnetic field generation in the fluid core below. View a movie of one of our simulated magnetic reversals.

One part of this numerical solution is the rotation rate of the solid inner core relative to the surface, which evolves according to the torque applied on the inner core by the generated magnetic field. Our solution shows how the field couples the inner core to the eastward flowing fluid above it (Figure 4a), keeping it in co-rotation [5]. This mechanism is analogous to a synchronous electric motor for which the field, carried eastward by the fluid, acts like the rotating field in the stator and the inner core acts like the rotor.

Fig.4 (a) A snapshot of the simulated magnetic field structure within the core, with lines blue where outside the solid inner core and yellow where inside. Again, the rotation axis is vertical. (click on image to download, 0.24 Mb) (b) A schematic image illustrating the super-rotation of the inner core relative to the Earth's surface.

The inner core in our simulation initially rotated between 2 and 3 degrees longitude per year faster than the solid mantle and surface [1, 5]. This prediction in 1995 [1] for the Earth motivated two seismologists from Columbia University in early 1996 to search for evidence of this super-rotation in 30 years of seismic data. They found evidence that supports our prediction and published it in July 1996 [6], (Figure 4b). More recent simulations of ours that now include a simple parameterization for the gravitational coupling that may exist between the mantle and the inner core have a much smaller inner core rotation amplitude; however, this rotation is still predominantly eastward relative to the model Earth's surface.

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[1] G.A. Glatzmaier and 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).

[2] G.A. Glatzmaier and P.H. Roberts, "A three-dimensional self-consistent computer simulation of a geomagnetic field reversal," Nature, 377, 203-209 (1995).

[3] G.A. Glatzmaier and P.H. Roberts, "On the magnetic sounding of planetary interiors," Phys. Earth Planet. Inter., 98, 207-220 (1996).

[4] G.A. Glatzmaier and P.H. Roberts, "An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection," Physica D, 97, 81-94 (1996).

[5] G.A. Glatzmaier and P.H. Roberts, "Rotation and magnetism of Earth's inner core," Science, 274, 1887-1891 (1996).

[6] X. Song and P. Richards, "Seismological evidence for differential rotation of the Earth's inner core," Nature, 382, 221-224 (1996).