On the theory of the geodynamo

I trace the development of geodynamo theory leading from Larmor's original hypothesis (Larmor, 1919, Rep. Br. Assoc. Adv. Sci., A, 159-160) to the present. I consider a number of kinematic results, from Cowling's proof(Cowling, 1934, Mon. Not. R. Astron. Sec., 94: 39-48) that two-dimensional dynamo action is not possible, to the proofs by Backus (1958, Ann. Phys., 4: 372-447) and Herzenberg (1958, Philos. Trans. R. Sec. London, Ser. A, 250: 543-585) that three-dimensional dynamo action is possible. I next rum to various mean-field and convective models in which the fluid flow is no longer kinematically prescribed, but is itself dynamically determined. In these dynamical models, I describe the distinction between weak and strong field regimes that comes about owing to the effect of the field on the pattern of convection in a rapidly rotating system. I consider the dynamics of Taylor's constraint (Taylor, 1963, Proc. R. Sec. London, Ser. A, 274: 274-283), and demonstrate how it makes the analysis of the geophysically appropriate strong field regime particularly difficult.