Effect of internal motions on the decay of a magnetic field in a fluid conductor

Abstract

The decay of a magnetic field in a fluid conductor with internal motions is considered in case the magnetic and velocity fields have symmetry about an axis The underlying characteristic value problems are solved for certain simple velocity fields The method of solution is based on a new classification of the basic axisymmetric modes of the magnetic field in terms of Gegenbauer polynomials. The principal conclusion of the paper is that velocity fields of reasonable patterns and magnitudes can alter the time of decay that will obtain in the absence of motions by quite large factors. The bearing of this result on the problem of the origin of the earth's magnetic field is briefly discussed Certain other related questions are also considered.