Abstract
The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed.
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