Scaling Behaviour of the Maximal Growth Rate in the Rosensweig Instability

Abstract

The dependence of the maximal growth rate of the modes of the Rosensweig instability on the properties of the magnetic fluid and the external magnetic induction is studied. An expansion and a fit procedure are applied in the appropriate ranges of the supercritical induction $\hat{B}$. With increasing $\hat{B}$ the scaling of the maximal growth rate changes from linear to a combination of linear and square-root-like scaling. The scaling of the corresponding wave number alternates from quadratic to primarily linear. For very small $\hat{B}$ the dependence of the maximal growth rate on the viscosity is given. Suggestions are made for experiments to test the predicted scaling behaviours.

8 pages, 4 figures; to appear in Europhys. Lett

Cited by in corpus (5)

• The Surface Topography of a Magnetic Fluid -- a Quantitative Comparison between Experiment and Numerical Simulation
• Growth of surface undulations at the Rosensweig instability
• From Phase Space Representation to Amplitude Equations in a Pattern Forming Experiment
• Retarding the growth of the {Rosensweig} instability unveils a new scaling regime
• The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids