Decay of metastable patterns for the Rosensweig instability: revisiting the dispersion relation

The decay of metastable patterns in the form of magnetic liquid ridges is studied in the frame of a linear stability analysis where the ridges are the most unstable linear pattern of the Rosensweig instability. The analysis of the corresponding dispersion relation reveals that different sets of solutions exist. Two of them are associated with an oscillatory and a pure exponential decay, respectively.