Faraday instability on viscous ferrofluids in a horizontal magnetic field: oblique rolls of arbitrary orientation.
A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability threshold on the magnetic field is found at high frequencies of the vibrations. The reasons for the decrease of the critical acceleration amplitude caused by a horizontal magnetic field are discussed. It is revealed that the magnetic field can be used to select the first unstable pattern of Faraday waves. In particular, a rhombic pattern as a superposition of two different oblique rolls can occur. A scaling law is presented which maps all data into one graph for the tested range of viscosities, frequencies, magnetic fields, and layer thicknesses.
Institut für Theoretische Physik, Universität Magdeburg, Universitätsplatz 2, D-39106, Magdeburg, Germany.
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Mekhonoshin
Adrian
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Lange