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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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References

Braginskií, S. I. 1964 Kinematic models of the earth's hydromagnetic dynamo. Geomag. Aeron., 4, 732. (English trans. p. 572.)Google Scholar
Bullard, E. C. & Gellman, H. 1954 Homogeneous dynamos and terrestrial magnetism. Phil. Trans. A 247, 213.Google Scholar
Cowling, T. G. 1933 The magnetic field of sunspots. Mon. Not. Roy. Astr. Soc., 94, 39.Google Scholar
Du Fort, E. C. & Frankel, S. P. 1953 Stability conditions in the numerical treatment of parabolic differential equations. Math. Tables & Aids to Comp., 7, 135.Google Scholar
Gibson, R. D. & Roberts, P. H. 1969 In The Application of Modern Physics to the Earth (ed. S.K. Runcorn), pp. 557–602. Wiley.
Gubbins, D. 1972 Kinematic dynamos and geomagnetism. Nature, 238, 119.Google Scholar
Lilley, B. E. M. 1970 On kinematic dynamos. Proc. Roy. Soc. A 316, 153.Google Scholar
Maunder, E. W. 1922 The sun and sunspots 1820–1920. Mon. Not. Roy. Astr. Soc., 82, 534Google Scholar
Moffatt, H. K. 1972 An approach to a dynamic theory of dynamo action in a rotating
Parker, E. N. 1971 The generation of magnetic fields in astrophysical bodies. IV. The
Roberts, P. H. 1972 Kinematic dynamo models. Phil. Trans. A 272, 663.Google Scholar
Roberts, P. H. & Stix, M. 1971 The turbulent dynamo. N.G.A.R. Tech. Note, TN/IA-60.Google Scholar
Roberts, P. H. & Stix, M. 1972 α-effect dynamos by the Bullard-Gellman formalism. Astron. Astrophys., 18, 453.Google Scholar
Steenbeck, M. & Krause, F. 1969 On the dynamo theory of stellar and planetary magnetic fields. I. A.c. dynamos of solar type. Astronom. Nachr., 291, 49. (Trans. in Roberts & Stix 1971.)Google Scholar
Steenbeck, M., Krause, F. & Radler, K.-H. 1966 A calculation of the mean electromotive force in an electrically conducting fluid in turbulent motion, under the influence of Coriolis forces. 2. Naturforsch. 21a, 369.Google Scholar
Stix, M. 1972 Nonlinear dynamo waves. Astron. Astrophys., 20, 9.Google Scholar