α2-Dynamos and taylor's constraint

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Abstract
An idealised α2ω-dynamo is considered in which the α-effect is prescribed. The additional ω-effect results from a geostrophic motion whose magnitude is determined indirectly by the Lorentz forces and Ekman suction at the boundary. As the strength of the α-effect is increased, a critical value α∗ c is reached at which dynamo activity sets in; α∗ c is determined by the solution of the kinematic α2-dynamo problem. In the neighbourhood of the critical value of α∗ the magnetic field is weak of order E 1/4(μηρω)½ due to the control of Ekman suction; E(≪1) is the Ekman number. At certain values of α∗, viscosity independent solutions are found satisfying Taylor's constraint. They are identified by the bifurcation of a nonlinear eigenvalue problem. Dimensional arguments indicate that following this second bifurcation the magnetic field is strong of order (μηρω)½. The nature of the transition between the kinematic linear theory and the Taylor state is investigated for various distributions of the α-effect. The character of the transition is found to be strongly model dependent.

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