Dynamo-alpha in the Earth's fluid core
The magnetic field of the Earth is generated by the flow of electrically conducting matter inside the planet. There is a shell of metal-rich fluid below the solid mantle. The innermost core of the Earth is solid (blue in the graph).
The flow patterns in the outer core are formed by the rotation of the Earth and convection due to heat sources in the core. Such flows are of small scale compared with the size of the Earth, but they can lead to the generation of a large-scale magnetic field. The generation of a large-scale magnetic field by small-scale helical fluid motions was described as the alpha-effect by Steenbeck, Krause and Rädler in 1966.
Does alpha exist in the Earth's core?
Graph: R. Arlt
Direct numerical simulations have shown that magnetic dynamos can be excited in convective and rotating flows in spherical shells, but they fail to access the parameters provided by the real Earth. The idea of parameterizing the small-scale flows by the alpha-effect thus needs parallel investigation. Today's simulations of magneto-convection are able to detect the effect and compare its efficiency in the Earth and in the Sun. The red box in the above figure is such a small computational domain which is studied with high resolution. The magnetohydrodynamic equations are integrated with the NIRVANA computer code by Udo Ziegler (AIP).
Simulation: A. Giesecke [MPEG 1.5 MB]
The picture shows the velocity pattern in the simulation box - red is rising matter and green is sinking matter. The small red box from above now corresponds to the x-z surface here. The y-direction is pointing in longitude on the Earth. The tilted elongated patterns on the x-z surface are aligned with the rotation axis of the Earth. The box consists of 100 x 100 x 80 grid cells in x, y, z, respectively.
The fluid core of the Earth has a nearly uniform density, while the solar convection zone is highly stratified. Two simulations of magneto-convection show the difference between the two. The graphs show the average alpha in dependence on the z coordinate which corresponds to the radial coordinate in the Earth. The left graph is from a simulation with a small density gradient in the box. This is the Earth-like case. The dynamo-alpha exists, but shows the peculiarity of negative sign in the deep layers and positive sign in the upper layers. The grey lines are alpha at various times and reveal enormous fluctuations. The distribution together with the strong temporal variations may lead to complex solutions for the variation of the magnetic field with time - perhaps similar to the field reversals in the real Earth. The right graph is the solar-like case with a density contrast of 10 between bottom and top. The average alpha is dominated by a positive sign (in the northern hemisphere).
Credits: A. Giesecke, R. Arlt, G. Rüdiger (MHD group)