On kinematic dynamos

Abstract

The method developed by Bullard & Gellman, to test flows of electrically conducting fluid in a sphere for dynamo action, is applied further to the two-component T$_{1}$S$_{2}^{2\text{c}}$ flow pattern they proposed. In agreement with Gibson & Roberts, it is found that the results of the test are negative, which substantiates the indication from Braginskii's work that the T$_{1}$S$_{2}^{2\text{c}}$ flow pattern has too great a symmetry for it to act as a dynamo. However, the addition of a third component, S$_{2}^{2\text{s}}$, to the flow pattern reduces the symmetry and produces results which indicate strongly that the three-component T$_{1}$S$_{2}^{2\text{c}}$S$_{2}^{2\text{s}}$ flow does act as a dynamo. Harmonics of magnetic field up to degree six have been taken into account, and this level of truncation appears to be justified. The streamlines of the T$_{1}$S$_{2}^{2\text{c}}$S$_{2}^{2\text{s}}$ flow form a distinctive whirling pattern in three dimensions, and this may be a physical characteristic necessary for dynamo action. The main magnetic fields of the T$_{1}$S$_{2}^{2\text{c}}$S$_{2}^{2\text{s}}$ dynamo are all toroidal, and the possibility is established that the geomagnetic dynamo is similar, with the dominant components of field being completely contained within the core. Variation of the subsidiary poloidal components of the field may then produce secular variation and even dipole reversals, without major change in the series of interactions between the toroidal components that form the basic dynamo.