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

D. R. Fearn*, M. M. Rahman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)385-406
Number of pages22
JournalGeophysical and Astrophysical Fluid Dynamics
Issue number5
Publication statusPublished - Oct 2004


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

ASJC Scopus subject areas

  • Computational Mechanics
  • Astronomy and Astrophysics
  • Geophysics
  • Mechanics of Materials
  • Geochemistry and Petrology


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