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Dynamically consistent magnetic fields produced by differential rotation

Published online by Cambridge University Press:  21 April 2006

D. R. Fearn  and
M. R. E. Proctor
D. R. Fearn
Affiliation:
Department of Mathematics, University Gardens, Glasgow, G12 8QW, UK
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

We investigate the dynamical consequences of an axisymmetric velocity field with a poloidal magnetic field driven by a prescribed e.m.f. E. The problem is motivated by previous investigations of dynamically driven dynamos in the magnetostrophic range. A geostrophic zonal flow field is added to a previously described velocity, and determined by the requirement that Taylor's constraint (Taylor 1963) (guaranteeing dynamical self-consistency of the fields) be satisfied. Several solutions are exhibited, and it is suggested that self-consistent solutions can always be found to this ‘forced’ problem, whereas the usual α-effect dynamo formalism in which E is a linear function of the magnetic field leads to a difficult transcendentally nonlinear characteristic value problem that may not always possess solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 521 - 534
Copyright
© 1987 Cambridge University Press

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References

Braginskii, S. I. 1964a Kinematic models of the Earth's hydromagnetic dynamo. Geomag. Aeron. 4, 572–683.Google Scholar
Braginskii, S. I. 1964b Magnetohydrodynamics of the Earth's core. Geomag. Aeron. 4, 698–711.Google Scholar
Braginskii, S. I. 1975 Nearly axially symmetric model of the hydromagnetic dynamo of the Earth I. Geomag. Aeron. 15, 122–128.Google Scholar
Braginskii, S. I. 1978 Nearly axially symmetric model of the hydromagnetic dynamo of the Earth II. Geomag. Aeron. 18, 225–231.Google Scholar
Childress, S. 1969 A class of solutions of the magnetohydrodynamic dynamo problem. In Applications of Modern Physics to the Earth and Planetary Interiors (ed. S. K. Runcorn), p. 629. Wiley-Interscience.
Fearn, D. R. & Proctor, M. R. E. 1983a Hydromagnetic waves in a differentially rotating sphere. J. Fluid Mech. 128, 1–20.Google Scholar
Fearn, D. R. & Proctor, M. R. E. 1983b The stabilizing role of differential rotation on hydromagnetic waves, J. Fluid Mech. 128, 21–36.Google Scholar
Fearn, D. R. & Proctor, M. R. E. 1984 Self-consistent dynamo models driven by hydromagnetic instabilities, Phys. Earth Planet Int. 36, 78–84.Google Scholar
Fearn, D. R. & Proctor, M. R. E. 1987 Self-consistent hydromagnetic dynamos. Geophys. Astrophys. Fluid Dyn. (to appear).Google Scholar
Greenspan, H. P. 1974 On α-dynamos. Stud. Appl. Maths 43, 35–39.Google Scholar
Ierley, G. 1985 Macrodynamics of α2-dynamos. Geophys. Astrophys. Fluid Dyn. 34, 143–173.Google Scholar
Malkus, W. V. R. & Proctor, M. R. E. 1975 The macrodynamics of α-effect dynamos in rotating fluid systems. J. Fluid Mech. 67, 417–444.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
Proctor, M. R. E. 1975 Nonlinear mean field dynamo models and related topics. PhD thesis, University of Cambridge.
Proctor, M. R. E. 1977 Numerical solutions of the nonlinear α-effect dynamo equations, J. Fluid Mech. 80, 769–784.Google Scholar
Soward, A. M. 1986 Nonlinear marginal convection in a rotating magnetic system. Geophys. Astrophys. Fluid Dyn. 35, 329–371.Google Scholar
Soward, A. M. & Jones, C. A. 1983 α2-dynamos and Taylor's constraint, Geophys. Astrophys. Fluid Dyn. 27, 87–122.Google Scholar
Taylor, J. B. 1963 The magnetohydrodynamics of a rotating fluid and the earth's dynamo problem. Proc. R. Soc. Lond. A 274, 274–283.Google Scholar