TAYLOR CONSTRAINT IN A SPHERICAL ALPHA-OMEGA-DYNAMO

The alpha2-dynamo of Hollerbach and Ierley (1991) is converted into an alphaomega-dynamo, and the analysis of Barenghi and Jones (1991) is extended. Only one choice of alpha and omega is considered in detail, for both negative and positive dynamo numbers. The solutions in the viscously limited regime are qualitatively distinct, with negative D solutions oscillating about a zero mean, and positive D solutions oscillating about a non-zero mean. The existence of nonlinear eigenvalues D(x) is demonstrated, beyond which the solutions are no longer viscously limited. The subsequent evolution would appear to be independent of the viscosity in some average sense, but there is no evidence of a true Taylor state.