A search for axisymmetric dynamos

Some general theorems on the necessary level of symmetry in the velocity field of a kinematic dynamo have been proposed: the analytic difficulties of direct proofs of these appear insurmountable at present. Explicit axisymmetric counter-examples are here sought in an attempt to disprove one such general hypothesis numerically. The usual Bullard-Gellman technique, and a new time-dependent extension of it, are used. Despite extensive computation on a number of different models, no axisymmetric dynamo is found: possible reasons for this are discussed.