An idealised #x3B1;2#x3C9;-dynamo is considered in which the #x3B1;-effect is prescribed. The additional #x3C9;-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 #x3B1;-effect is increased, a critical value #x3B1;*cis reached at which dynamo activity sets in; #x3B1;*cis determined by the solution of the kinematic #x3B1;2-dynamo problem. In the neighbourhood of the critical value of #x3B1;* the magnetic field is weak of orderE1/4(#x3BC;#x3B7;#x3C1;#x3C9;)#xBD;due to the control of Ekman suction;E(#x226A;1) is the Ekman number. At certain values of #x3B1;*, 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 (#x3BC;#x3B7;#x3C1;#x3C9;)#xBD;. The nature of the transition between the kinematic linear theory and the Taylor state is investigated for various distributions of the #x3B1;-effect. The character of the transition is found to be strongly model dependent.
展开▼