### Abstract

A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear α^{2}-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudospectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5 × 10^{-3} to 5.0 × 10^{-5}, for α = α_{0} cos θ sin π(r - r_{i}) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of α_{0}. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos.

Original language | English |
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Pages (from-to) | 385-406 |

Number of pages | 22 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 98 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 2004 |

### Keywords

- α-dynamo
- Earth's core
- Geodynamo
- Taylor's constraint

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Mechanics of Materials
- Computational Mechanics
- Astronomy and Astrophysics
- Space and Planetary Science