Europhys. Lett.
Volume 63, Number 6, September 2003
Page(s) 826 - 832
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00605-7
Europhys. Lett., 63 (6) , pp. 826-832 (2003)

Non-linear analysis of the Rosensweig instability

R. Friedrichs1, 2 and A. Engel1

1  ITP, Otto-von-Guericke-Universität - Postfach 4120, 39016 Magdeburg, Germany
2  ABB AG, Corporate Research Center - Wallstadter Str. 59 68526 Ladenburg, Germany

(Received 6 February 2003; accepted in final form 10 July 2003)

We derive a closed equation for the shape of the free surface of a magnetic fluid subject to an external magnetic field. The equation is non-local due to the long-range character of the magnetic interaction. We develop a systematic multiple-scale perturbation expansion with a non-local linear operator involving the Hilbert transform of the surface profile. The resulting amplitude equation describing the slow modulation of the basic pattern is shown to remain local.

47.20.Ma - Interfacial instability.
47.20.Lz - Secondary instability.
75.50.Mm - Magnetic liquids.

© EDP Sciences 2003