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

D. R. Fearn, M. M. Rahman

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 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
Volume98
Issue number5
DOIs
Publication statusPublished - Oct 2004

Fingerprint

DC generators
rotating generators
Momentum
Lorentz force
Electromagnetic induction
momentum
Hydrodynamics
Boundary conditions
Magnetic fields
rotating fluid
rotating fluids
geodynamo
Fluids
reversing
inner core
magnetic induction
spherical shells
inertia
induction
Earth mantle

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 α2-dynamos and Taylor's constraint. / Fearn, D. R.; Rahman, M. M.

In: Geophysical and Astrophysical Fluid Dynamics, Vol. 98, No. 5, 10.2004, p. 385-406.

Research output: Contribution to journalArticle

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