Motion of the Earth's Fluid Core: A Geophysical Problem

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Abstract
The earth's core may be assumed to have a very low viscosity, such as is characteristic of molten metals. The angular acceleration of the earth is sufficiently large, and the radius of the core is sufficiently great, to raise the question whether the rotation of the central part of the core lags appreciably behind the rotation of the solid mantle. The angular acceleration of the mantle, which is known astronomically, consists of a gradual deceleration and a more pronounced change of direction of the angular velocity, the 27,000-year precession. These two aspects are discussed separately. Three types of force might accelerate the core, viscous force in laminar flow, resistance caused by turbulent flow, and the force of induction associated with the earth's magnetic field. The viscous force is so weak that the interior would be practically unaccelerated if the flow were laminar, and the magnetic induction is expected to be weak enough to permit a large lag between the rotation of the mantle and interior of the core. But the core is so large that the flow should be turbulent. Reasonable assumptions on the nature of the flow in this case, based on empirical data on turbulence near a flat boundary, are used to estimate the lag. It is concluded that the axis of rotation of the interior of the core may be expected to lag behind the axis of the mantle in the precession by an angle of the order of magnitude of a few degrees. Apartfrom the superposed eddies, points rather near the surface of the core would then move relative to the mantle around horizontal closed paths, approximately a hundred kilometers across, with a period of a day. This would cause a diurnal variation of the earth's magnetism much larger than observed if it were not for the shielding of metallic layers above the core.

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