A spectral solution of nonlinear mean field dynamo equations: With inertia

Mohammad M. Rahman*, David R. Fearn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper presents a numerical solution method for the nonlinear mean field dynamo equations in a rotating fluid spherical shell. A finite amplitude 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. This equilibration process is a key aspect of the full hydrodynamic dynamo as well as mean field dynamo. Including full inertial term we present pseudo-spectral time-stepping procedure to solve the coupled nonlinear momentum equation and induction equation with no-slip velocity boundary conditions in the core for a finitely conducting inner core and an insulating mantle. The method is found suitable for solving many geophysical problems.

Original languageEnglish
Pages (from-to)422-435
Number of pages14
JournalComputers and Mathematics with Applications
Issue number3
Publication statusPublished - Aug 2009


  • Earth's core
  • Inertial effect
  • Mean field dynamo
  • Spectral method
  • Spherical shell

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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