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A dynamic runaway effect associated with flux expulsion in magnetohydrodynamic channel flow

Published online by Cambridge University Press:  20 April 2006

H. Kamkar  and
H. K. Moffatt
H. Kamkar
Affiliation:
School of Mathematics, University of Bristol Present address: Berkeley Nuclear Laboratories, Berkeley, Gloucester, England.
H. K. Moffatt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
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Abstract

Pressure-driven flow along a channel in the presence of an applied magnetic field which is periodic in the streamwise direction is considered. The configuration is such that the transverse component of field By, is non-zero on the centreline y = 0, but its streamwise average 〈By〉 is zero. In this situation, flux expulsion due to reconnection of field lines occurs when the pressure gradient is sufficiently large. This leads to a decrease in the Lorentz forces, hence to an acceleration of the flow, and hence to stronger flux expulsion. When viscous effects are weak (i.e. at high Hartmann number) this creates a runaway effect, which appears at a critical value of the pressure gradient. This critical value is determined in the inviscid limit, and numerical and analytical methods are used to explore the associated ‘cusp-catastrophe’ behaviour when effects of weak viscosity are taken into account.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 107 - 122
Copyright
© 1982 Cambridge University Press

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References

Alemany, A. & Moreau, R. 1977 Écoulement d'un fluide conducteur de l’électricité en présence d'un champ magnétique tournant. J. Méc. 16, 625–646.Google Scholar
Galloway, D. J., Proctor, M. R. E. & Weiss, N. O. 1978 Magnetic flux ropes and convection. J. Fluid Mech. 87, 243–261.Google Scholar
Gimblett, C. G. & Peckover, R. S. 1979 On the mutual interaction between rotation and magnetic fields for axisymmetric bodies. Proc. R. Soc. Lond. A 368, 75–97.Google Scholar
Hunt, J. C. R. & Shercliff, J. A. 1971 Magnetohydrodynamics at high Hartmann number. Ann. Rev. Fluid Mech. 3, 37.Google Scholar
Kamkar, H. 1981 Kinematic and dynamic aspects of flux expulsion in magnetohydrodynamics. Ph.D. thesis, Bristol University.
Lock, R. C. 1955 The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field. Proc. R. Soc. Lond. A 233, 105–125.Google Scholar
Moffatt, H. K. 1980 Rotation of a liquid metal under the action of a rotating magnetic field. In MHD-Flows and Turbulence (ed. H. Branover & A. Yakhot), pp. 45–62. Israel Universities Press.
Parker, E. N. 1963 Kinematical hydromagnetic theory and its applications to the low solar photosphere. Astrophys. J. 138, 552–575.Google Scholar
Parker, R. L. 1966 Reconnexion of lines of force in rotating spheres and cylinders. Proc. R. Soc. Lond. A 291, 60–72.Google Scholar
Proctor, M. R. E. & Galloway, D. J. 1979 The dynamic effect of flux ropes on Rayleigh–Bénard convection. J. Fluid Mech. 90, 273–287.Google Scholar
Weiss, N. O. 1966 The expulsion of magnetic flux by eddies. Proc. R. Soc. Lond. A 293, 310–328.Google Scholar
Zel'Dovich, Ya. B.1957 The magnetic field in the two-dimensional motion of a conducting turbulent fluid. Sov. Phys. J.E.T.P. 4, 460–462.Google Scholar