Abstract
AbstractWe study viscous gravity‐driven films flowing over periodically undulated substrates. Linear analysis describes resonance in steady flow along small bottom corrugations for films of arbitrary thickness. Depending on the dimensionless film thickness we find different regimes for the resonance, which is associated with the interaction of the undulated film with capillary‐gravity waves traveling against the flow. Nonlinear terms produce higher harmonics resonance which in particular may lead to bistable resonance similar to that of the driven Duffing oscillator. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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