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Electrically driven vortices in a strong magnetic field

Published online by Cambridge University Press:  21 April 2006

Joël Sommeria
Joël Sommeria
Affiliation:
Madylam, Institute de Mécanique de Grenoble, BP 95, 38402 Saint-Martin D'Hères Cedex, France
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Abstract

A steady isolated vortex is produced in a horizontal layer of mercury (of thickness a), subjected to a uniform vertical magnetic field. The vortex is forced by an electric current going from an electrode in the lower plane to the circular outer frame. The flow is investigated by streak photographs of small particles following the free upper surface, and by electric potential measurements. The agreement with the asymptotic theory for high values of the Hartmann number M is excellent for moderate electric currents. In particular all the current stays in the thin Hartmann layer of thickness a/M, except in the vortex core of horizontal extension a/M½. For higher currents, the size of the core becomes larger and depends only on the local interaction parameters. When the current is switched off, we measure the decay due to the Hartmann friction. A similar study is carried out for a vortex created by an initial electric pulse, and for a pair of vortices of opposite sign. For all these examples, the dynamics can be described by the two-dimensional Navier-Stokes equations with Hartmann friction, except in the vortex cores. Finally a vortex is produced near a lateral wall and a detachment of the boundary layer parallel to the magnetic field occurs, by which a second vortex of opposite sign is generated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 189 , April 1988 , pp. 553 - 569
Copyright
© 1988 Cambridge University Press

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References

Alemany, A., Moreau, R., Sulem, P. L. & Frisch, U. 1979 Influence of an external magnetic field on homogeneous turbulence. J. Méc. (Paris) 18, 277.Google Scholar
Baylis, J. A. 1971 Experiments on laminar flow in curved channels of square section. J. Fluid Mech. 48, 417–422.Google Scholar
Branover, H. 1978 Magnetohydrodynamic Flows in Ducts. Halsted.
Branover, H. & Gershon, P. 1979 Experimental investigation of the origin of residual disturbances in turbulent MHD flows after laminarization. J. Fluid Mech. 94, 629–647.Google Scholar
Gel'fgat, Yu. M., Kit, L. G., Peterson, D. A. & Tsinober, A. B. 1971 Realization of the laminar regime in magnetohydrodynamic flow in an annular channel at high Reynolds number. Magnitnaya Gidrodinamiks, 3, 35–42.Google Scholar
Hua, H. M. & Lykoudis, P. S. 1974 Turbulent measurements in a magneto-fluid mechanics channel. Nucl. Sci. Eng., 54, 445.Google Scholar
Hunt, J. C. R. & Leibovich, S. 1967 Magnetohydrodynamic flow in channels of variable cross-section with strong transverse magnetic fields. J. Fluid Mech. 28, 241–260.Google Scholar
Hunt, J. C. R. & Malcolm, D. G. 1968 Some electrically driven flows in magnetohydrodynamics: Part 2. J. Fluid Mech. 33, 775–801.Google Scholar
Hunt, J. C. R. & Shercliff, J. A. 1971 Magnetohydrodynamics at high Hartmann number. Ann. Rev. Fluid Mech. 3, 37–62.Google Scholar
Hunt, J. C. R. & Stewartson, K. 1969 Some electrically driven flows in magnetohydrodynamics. Part 3. J. Fluid Mech. 38, 225–242.Google Scholar
Hunt, J. C. R. & Williams, W. E. 1968 Some electrically driven flows in magnetohydrodynamics. Part 1. J. Fluid Mech. 31, 705–722.Google Scholar
Kalis, Kh. E. & Kolesnikov, Yu. B. 1980 Numerical study of a single vortex of a viscous incompressible electrically conducting in an homogeneous axial magnetic field. Magnitnaya Gidrodinamika 2, 57–61.Google Scholar
Kapila, A. K. & Ludford, G. S. S. 1977 MHD with inertia: flow over blunt obstacles in channels. Intl J. Engng Sci. 15, 465–480.Google Scholar
Kolesnikov, Yu. B. & Tsinober, A. B. 1974 Experimental investigation of two-dimensional turbulence behind a grid. Isv. Akad. Nauk. SSSR Mech. Zhid. i Gaza 4, 146.Google Scholar
Lehnert, B. 1952 Experiments on non-laminar flow of mercury in presence of a magnetic field. Tellus, 4, 63–67.Google Scholar
Lielausis, O. 1975 Liquid metal magnetohydrodynamics. Atomic Energy Rev. 13, 527.Google Scholar
Lock, R. G. 1955 The stability of the flow in an electrically conducting fluid between parallel planes under a transverse magnetic field. Proc. R. Soc. A 233, 105–125.Google Scholar
Malcolm, D. G. 1970 An investigation of the stability of a magnetohydrodynamic shear layer. J. Fluid Mech. 41, 531–544.Google Scholar
Shercliff, J. A. 1965 A Textbook of Magnetohydrodynamics. Pergamon.
Shercliff, J. A. 1975 Some duct flow problems at high Hartmann number. Z. angew. Math. Phys. 26, 537–547.Google Scholar
Sommeria, J. 1985 Two-dimensional behaviour of electrically driven flows at high Hartmann numbers. 4th Beer Sheva Seminar on MHD flows and turbulence. AIAA Prog. ser. 100.Google Scholar
Sommeria, J. 1986 Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139–168.Google Scholar
Sommeria, J. & Morreau, R. 1982 Why, how, and when, MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507–518.Google Scholar
Tabeling, P. & Chabrerie, J. P. 1981 Magnetohydrodynamic secondary flows at high Hartmann numbers. J. Fluid Mech. 103, 225–239.Google Scholar
Tabeling, P. & Trakas, C. 1984 Structures spiralées dans une instabilité de Taylor en présence de champ magnétique. J. Phys. Paris (Lett.) 45, L159–L167.Google Scholar
Verron, J. & Sommeria, J. 1987 Numerical simulation of a two-dimensional turbulence experiment in magnetohydrodynamics. Phys. Fluids 30, 732–739.Google Scholar