Abstract
Similar to the classic three-dimensional Rosensweig instability, a ferrofluid confined in a vertical Hele-Shaw cell subjected to an in-plane normal magnetic field develops a periodic array of peaked interfacial structures. We perform a weakly nonlinear analysis that is able to reproduce the morphology of such pattern formation phenomenon at lowest nonlinear order. A mode-coupling theory is applied to compare the early nonlinear evolution of the interface with static shapes obtained when relevant forces equilibrate. Our nonlinear results indicate that the time-evolving shapes tend to approach stable stationary solutions.
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