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arXiv · 1610.07760

Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation

Mark D. Groves·David J. B. Lloyd·Athanasios Stylianou
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Abstract

We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. It is shown that the ferrohydrostatic equations can be derived from a variational principle that allows one to formulate them as an (infinite-dimensional) spatial Hamiltonian system in which the unbounded free-surface direction plays the role of time. A centre-manifold reduction technique converts the problem for small solutions near onset to an equivalent Hamiltonian system with finitely many degrees of freedom. Normal-form theory yields the existence of homoclinic solutions to the reduced system, which correspond to spatially localised solutions of the ferrohydrostatic equations.

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Mark D. Groves, David J. B. Lloyd, Athanasios Stylianou. 2016-10-25. Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation. https://doi.org/10.1016/j.physd.2017.03.004

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