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

Rahman, M.M. and Fearn, D.R. (2009) A spectral solution of nonlinear mean field dynamo equations: with inertia. Computers and Mathematics with Applications, 58(3), pp. 422-435. (doi: 10.1016/j.camwa.2009.04.016)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fearn, Professor David
• Authors: Rahman, M.M., and Fearn, D.R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Computers and Mathematics with Applications
• ISSN: 0898-1221
• Published Online: 09 June 2009