A spectral solution of nonlinear mean field dynamo equations

With inertia

Mohammad M. Rahman, David R. Fearn

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume58
Issue number3
DOIs
Publication statusPublished - Aug 2009

Fingerprint

Mean Field Equation
Inertia
Momentum
Nonlinear Equations
Lorentz force
Electromagnetic induction
Proof by induction
Hydrodynamics
Boundary conditions
Rotating Fluid
Spherical Shell
Fluids
Time Stepping
Slip
Mean Field
Numerical Solution
Term

Keywords

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

ASJC Scopus subject areas

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

Cite this

A spectral solution of nonlinear mean field dynamo equations : With inertia. / Rahman, Mohammad M.; Fearn, David R.

In: Computers and Mathematics with Applications, Vol. 58, No. 3, 08.2009, p. 422-435.

Research output: Contribution to journalArticle

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