Scaling Behaviour of the Maximal Growth Rate in the Rosensweig Instability

Details Scaling Behaviour of the Maximal Growth Rate in the Rosensweig Instability Scaling Behaviour of the Maximal Growth Rate in the Rosensweig Instability

2001-07-16

arxiv.org/abs/nlin/0107033v1

Europhys. Lett. 55 (2001) 327

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1209/epl/i2001-00419-1

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.

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