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Note on a Hamiltonian formalism for the flow of a magnetic fluid with a free surface

Published online by Cambridge University Press:  21 April 2006

O. Sero-Guillaume  and
D. Bernardin
O. Sero-Guillaume
Affiliation:
Laboratoire D'Energetique et de Mecanique Theorique et Appliquee, 24–30, rue Lionnois, 54013 Nancy Cedex, France
D. Bernardin
Affiliation:
Laboratoire D'Energetique et de Mecanique Theorique et Appliquee, 24–30, rue Lionnois, 54013 Nancy Cedex, France
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Abstract

The potential flow of an inviscid ferromagnetic fluid is formulated as a Hamiltonian system: the conjugate coordinates are the normal displacement of the free surface and the velocity potential on the free surface. If we take the equation of the magnetic field as a constraint, we can see that the flow of a magnetic liquid is a control-theory problem; the potential of the magnetic self-field is the control variable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 381 - 386
Copyright
© 1987 Cambridge University Press

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References

Benjamin, T. B. & Olver, P. J. 1982 Hamiltonian structure, symmetries and conservation laws for water waves. J. Fluid Mech. 125, 137–185.Google Scholar
Brancher, J. P. 1980 Sur l'hydrodynamique des ferrofluides. Thèse, University of Nancy.
Cowley, M. D. & Rosensweig, R. E. 1967 The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 30, 671–688.Google Scholar
Joffre, G. H. 1984 Profils de ménisques électrisés avec ou sans émission de charge. Thèse, University of Paris VI.
Luke, J. C. 1977 A variational principle for a fluid with a free surface. J. Fluid Mech. 27, 395–397.Google Scholar
Mestel, A. J. 1983 Magnetic levitation of liquid metals. Ph.D. thesis, University of Cambridge.
Milder, D. M. 1977 A note regarding ‘On Hamilton's principle for surface waves’. J. Fluid Mech. 83, 159–161.Google Scholar
Miles, J. W. 1977 On Hamilton's principle for surface waves. J. Fluid Mech. 83. 153–158.Google Scholar
Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.
Sero-Guillaume, O. 1983 Sur l’équilibre des ferrofluides et des métaux liquides. Thèse. University of Nancy, France.
Sneyd, A. D. & Moffatt, H. K. 1982 Fluid dynamical aspects of the levitation melting process. J. Fluid Mech. 117, 46–70.Google Scholar