### 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 |
---|---|

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 |

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### 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

### Cite this

**Evolution of non-linear α ^{2}-dynamos and Taylor's constraint.** / Fearn, D. R.; Rahman, M. M.

Research output: Contribution to journal › Article

^{2}-dynamos and Taylor's constraint',

*Geophysical and Astrophysical Fluid Dynamics*, vol. 98, no. 5, pp. 385-406. https://doi.org/10.1080/03091920410001724124

}

TY - JOUR

T1 - Evolution of non-linear α2-dynamos and Taylor's constraint

AU - Fearn, D. R.

AU - Rahman, M. M.

PY - 2004/10

Y1 - 2004/10

N2 - 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 α2-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 = α0 cos θ sin π(r - ri) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of α0. 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.

AB - 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 α2-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 = α0 cos θ sin π(r - ri) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of α0. 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.

KW - α-dynamo

KW - Earth's core

KW - Geodynamo

KW - Taylor's constraint

UR - http://www.scopus.com/inward/record.url?scp=1842462279&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842462279&partnerID=8YFLogxK

U2 - 10.1080/03091920410001724124

DO - 10.1080/03091920410001724124

M3 - Article

VL - 98

SP - 385

EP - 406

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 5

ER -