Dynamically consistent magnetic fields produced by differential rotation

Abstract

We investigate the dynamical consequences of an axisymmetric velocity field with a poloidal magnetic field driven by a prescribed e.m.f. E. The problem is motivated by previous investigations of dynamically driven dynamos in the magnetostrophic range. A geostrophic zonal flow field is added to a previously described velocity, and determined by the requirement that Taylor's constraint (Taylor 1963) (guaranteeing dynamical self-consistency of the fields) be satisfied. Several solutions are exhibited, and it is suggested that self-consistent solutions can always be found to this ‘forced’ problem, whereas the usual α-effect dynamo formalism in which E is a linear function of the magnetic field leads to a difficult transcendentally nonlinear characteristic value problem that may not always possess solutions.