Discussion of “The Earth's core”

Abstract

Runcorn has given a very interesting outline of the dynamics of the Earth's core, much of which should meet with general agreement; parts of the argument are, however, open to serious objection. On page 53, he estimates the orders of magnitude of the terms in the equation of motion for a rotating sphere, and concludes that the buoyancy forces must be balanced by the pressure gradient and Coriolis forces. Since neither Coriolis forces nor the pressure can absorb energy, this is impossible, and, in fact, multiplying Runcorn's (3) by v and integrating through the core leads to a contradiction. If the motion is driven by the buoyancy forces, the energy must be absorbed either by viscous forces or by the magnetic field. From Runcorn's Table 1 this requires either that the eddies be about a kilometer across, or that the magnetic field, and therefore the electric currents, be a hundred times greater than he has assumed. Since small eddies are of little use for theories of geomagnetism, it seems wise to choose the latter alternative and to postulate a toroidal field much greater than the dipole field and than the three gauss assumed by Runcorn. The reasons for supposing such a field to exist have been extensively discussed by Elsasser and by the present writer, and it seems highly probable that any theory of the magneto‐hydrodynamics of the core must provide a magnetic field of such a size that the buoyancy forces the electromagnetic forces and Coriolis forces are all of the same order of magnitude.