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Solitary waves on a ferrofluid jet

Published online by Cambridge University Press:  09 June 2014

M. G. Blyth  and
E. I. Părău
M. G. Blyth*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
E. I. Părău
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully nonlinear travelling solitary waves, and the predictions of elevation waves and depression waves made by Rannacher and Engel (New J. Phys., vol. 8, 2006, pp. 108–123) using a weakly nonlinear theory are confirmed in the appropriate ranges of the magnetic Bond number. New nonlinear branches of solitary wave solutions are identified. As the Bond number is varied, the solitary wave profiles may approach a limiting configuration with a trapped toroidal-shaped bubble, or they may approach a static wave (i.e. one with zero phase speed). For a sufficiently large axial rod, the limiting profile may exhibit a cusp.

JFM classification

Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 750 , 10 July 2014 , pp. 401 - 420
Copyright
© 2014 Cambridge University Press 

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