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Kelvin's Theorem Applied to the Earth's Core

Andrew Jackson
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 452, No. 1953 (Oct. 8, 1996), pp. 2195-2201
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52965
Page Count: 7
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Kelvin's Theorem Applied to the Earth's Core
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Abstract

We examine the consequences of adopting simplifying assumptions of a highly electrically conducting core and an insulating mantle for the magnetic field at the top of the core. These approximations form a zeroth-order model for the Earth, but may be quite accurate. We find that in addition to the well-known invariants which apply to patches of radial magnetic flux on the core surface which are bounded by contours on which the radial field vanishes, additional constraints apply to the same patches. These constraints are precisely those related to Kelvin's theorem, which is well-known in rotating systems when magnetic fields are absent. In principle, the constraints can be tested by repeated observations of the field through time.

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