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The formation of iterated structures, such as satellite and sub-satellitedrops, filaments and bubbles, is a common feature in interfacial hydrodynamics.Here we undertake a computational and theoretical study of their origin in thecase of thin films of viscous fluids that are destabilized by long-rangemolecular or other forces. We demonstrate that iterated structures appear as aconsequence of discrete self-similarity, where certain patterns repeatthemselves, subject to rescaling, periodically in a logarithmic time scale. Theresult is an infinite sequence of ridges and filaments with similarityproperties. The character of these discretely self-similar solutions as theresult of a Hopf bifurcation from ordinarily self-similar solutions is alsodescribed.

Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures