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

Authors:
Mohammad M. Rahman;David R. Fearn
Affiliations:
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, P.C. 123 Al-Khod, Muscat, Oman;Department of Mathematics, University of Glasgow,Glasgow G12 8QW, United Kingdom
Venue:
Computers & Mathematics with Applications
Year:
2009

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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.