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|
Non-linear analysis of the Rosensweig instability
ITP, Otto-von-Guericke-Universität - Postfach 4120, 39016 Magdeburg, Germany
2 ABB AG, Corporate Research Center - Wallstadter Str. 59 68526 Ladenburg, Germany
Accepted: 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.
PACS: 47.20.Ma – Interfacial instability / 47.20.Lz – Secondary instability / 75.50.Mm – Magnetic liquids
© EDP Sciences, 2003
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