Numerical study of soliton-like surface configurations on a magnetic fluid layer in the Rosensweig instability

In the Rosensweig instability, a perpendicular, uniform magnetic field applied to a pool of magnetic fluid generates an ordered periodic pattern on the liquid–air interface when the field exceeds a critical threshold. Decreasing the field strength, a lower critical threshold is observed at which the developed pattern disappears. In this respect, the deformation of the free surface shows a hysteretic behaviour with changing field strength. Recently, in experiments, a novel soliton-like surface configuration has been generated within the hysteretic regime of the Rosensweig instability. The main objective of this paper is a numerical study of this new configuration by means of two models, an axisymmetric two-dimensional one and a fully three-dimensional one.