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Numerical models of hydromagnetic dynamos

Published online by Cambridge University Press:  29 March 2006

S. A. Jepps
S. A. Jepps
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich, England Present address: Mathematical Services Department, British Aircraft Corporation, Warton Aerodrome, Preston PR4 1AX, England.
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Abstract

The magnetic induction equation is solved numerically in a sphere for a variety of prescribed fluid flows. The models considered are the so-called ‘αω dynamos’, in which both small-scale turbulence and large-scale shearing play a significant role. Solutions are obtained by marching the finite–difference equations forward in time from some initial field. For a critical value of the magnetic Reynolds number Rm solutions which neither grow nor decay are found.

Further calculations are performed with a ‘cut-off effect’ in which an attempt is made to simulate the effect of the Lorentz forces on the turbulence. For supercritical values of R, the magnetic field now stabilizes a t a finite value instead of increasing indefinitely. The form of the final field is compared with that produced at critical Rm in the absence of the cut-off effect.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 4 , 25 February 1975 , pp. 625 - 646
Copyright
© 1975 Cambridge University Press

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