Taylor's constraint in a spherical αω-dynamo

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Abstract
The α2-dynamo of Hollerbach and Ierley (1991) is converted into an αω-dynamo, and the analysis of Barenghi and Jones (1991) is extended. Only one choice of α and ω 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.

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