Regensburg 2004 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 11: Ferrofluids

DY 11.4: Vortrag

Montag, 8. März 2004, 11:15–11:30, H3

Wave number selection and secondary instabilities of ridge patterns on magnetic fluids — •Rene Friedrichs — ABB AG, Corporate Research Center Germany, Wallstadter Str. 59, D-68526 Ladenburg

When the free surface of a magnetizable fluid is subjected to a homogeneous vertical magnetic field the flat surface becomes unstable above a certain threshold for the field strength. If, additionally, an appropriate magnetic field oriented tangential to the fluid interface is applied this so called “Rosensweig instability“ gives rise to parallel fluid ridges [1].

We perform a nonlinear analysis of the static ridge pattern by means of an energy variational method [2]. The dependence of the wave number on the external magnetic field and the detailed shape of the corresponding ripples are theoretically determined. Using a high order expansion of the energy we investigate the influence both of the wave number and the permeability of the fluid on the bifurcations of the periodic patterns. Secondary instabilities of the quasi-one-dimensional surface and the nonlinear wave number selection are studied by combining a Floquet Ansatz with the variational approach.

[1] Y. D. Barkov and V. G. Bashtovoi, Magnetohydrodynamics 13, 497 (1977)

[2] R. Friedrichs, Phys. Rev. E 66, 066215 (2002)