Kinematics of Geomagnetic Secular Variation in a Perfectly Conducting Core

Details Kinematics of Geomagnetic Secular Variation in a Perfectly Conducting Core Kinematics of Geomagnetic Secular Variation in a Perfectly Conducting Core

Sep 1968

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1968rspta.263..239b&link_type=abstract

Philosophical Transactions for the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 263, Issue 1141

Physics

97

Scientific paper

The motions in the Earth's electrically conducting fluid core which are the probable cause of the geomagnetic secular variations have time scales of the order of a few centuries or less. Seismic bounds on the kinematic molecular viscosity of the core and order-of-magnitude arguments about the eddy viscosity make plausible the hypothesis that at such short periods the core motion consists of a boundary layer of Ekman-Hartmann type close to the core mantle boundary, and an interior free-stream motion where the viscosity and resistivity can be set equal to zero. This boundary-layer approximation requires that the unknown vertical length scale of the poloidal geomagnetic field deep in the core be at least as long as the 600 km horizontal length scales inferred at the surface of the core from observations above the mantle. For periods shorter than a century the Ekman and magnetic boundary layers are probably thinner than 120 km. If magnetic flux diffusion is neglected (i.e. if electrical conductivity is considered infinite) in the free stream in the core then the external geomagnetic field is completely determined by the fluid motion at the top of the free stream. Therefore the hypothesis of negligible flux diffusion in the free stream has implications for the geomagnetic secular variation, and these implications can be used as a test of whether there is any motion of a perfectly conducting core which will produce the observed secular variation. If the observed secular variation passes this test, we can write down explicitly all `eligible' velocity fields, i.e. all velocity fields at the top of the free stream in the core which are capable of producing exactly the observed secular variation. The different eligible velocity fields are obtained by different choices of an arbitrary stream function on the surface of the core. We describe a method of selecting from among all eligible velocity fields those which are of particular geophysical interest, such as the one which is most nearly a rigid rotation (westward drift) or the one which is most nearly a latitude dependent westward drift with m degrees of freedom.

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