ON THE THEORY OF THE GEODYNAMO

I trace the development of geodynamo theory leading from Larmor's orig inal 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 (1 958, Ann. Phys., 4: 372-447) and Herzenberg (1958, Philos. Trans. R. S ec. London, Ser. A, 250: 543-585) that three-dimensional dynamo action is possible. I next rum to various mean-field and convective models i n which the fluid flow is no longer kinematically prescribed, but is i tself dynamically determined. In these dynamical models, I describe th e distinction between weak and strong field regimes that comes about o wing to the effect of the field on the pattern of convection in a rapi dly rotating system. I consider the dynamics of Taylor's constraint (T aylor, 1963, Proc. R. Sec. London, Ser. A, 274: 274-283), and demonstr ate how it makes the analysis of the geophysically appropriate strong field regime particularly difficult.