Interfacial wave dynamics in a two-layer system of inviscid liquids subject to horizontal vibrations
We study the dynamics of waves at the interface in a two-layer system of inviscid immiscible liquids subject to high-frequency horizontal vibrations. The consideration is performed within the framework of the long-wavelength approximation, which is relevant as, for sufficiently thin layers, the linear instability of the flat-interface state is a long-wavelength one. Nonlinear governing equations of the interface dynamics for two- and three-dimensional flows are obtained for arbitrary ratio of the layer thicknesses. For the three-dimensional case, an analog of the Squire’s theorem can be formulated; the longitudinal perturbations are most dangerous. The wave dynamics equations are in-tegrable and can be compared with the Boussinesq equation for the gravity waves in shallow water. With the latter examination, one can compare the effect of the vibrational field to the action of gravity, and also consider the possibility of a sustainable existence of the state where the heavy liquid overlies the light one, that is, state which corresponds to an effective gravity inversion.