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The Relief of the Rosensweig Instability -- a Quantitative Comparison between Experiment and Numerical Simulation

The normal field instability in magnetic liquids is investigated experimentally by means of a radioscopic measurement technique which is capable to determine the surface relief quantitatively. The dependance of the relief on the magnetic field is compared to results obtained by numerical simulations via the finite element method. Quantitative agreement has been found for the critical field of the instability, the scaling of the pattern amplitude and the detailed shape of the magnetic spikes. Over 90% of the shape turns out to be contained in the fundamental fourier mode within a 40% range of the control parameter of this subcritical bifurcation. The measured control parameter dependance of the wavenumber differs qualitatively from the analytical prediction.