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Parametric Forcing of Waves with Non-Monotonic Dispersion Relation: Domain Structures in Ferrofluids?

David Raitt·Hermann Riecke
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Abstract

Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a non-monotonic dispersion relation. The effect of a parametric driving on such waves is studied within suitable coupled Ginzburg-Landau equations. Due to the non-monotonicity the neutral curve for the excitation of standing waves can have up to three minima. The stability of the waves with respect to long-wave perturbations is determined $via$ a phase-diffusion equation. It shows that the band of stable wave numbers can split up into two or three sub-bands. The resulting competition between the wave numbers corresponding to the respective sub-bands leads quite naturally to patterns consisting of multiple domains of standing waves which differ in their wave number. The coarsening dynamics of such domain structures is addressed.

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David Raitt, Hermann Riecke. 1996-01-19. Parametric Forcing of Waves with Non-Monotonic Dispersion Relation: Domain Structures in Ferrofluids?. https://doi.org/10.1103/physreve.55.5448

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