Effect of Vertical Vibrations on a Two-Layer System with a Deformable Interface

摘要

The effect of single- and two-frequency vibrations on the behavior of a system consisting oftwo homogeneous viscous fluids bounded by rigid walls is analyzed. It is assumed that the system as awhole is under vertical vibrations obeying a certain law. An eigenvalue problem is obtained in order toanalyze the stability of the relative equilibrium. The case of finite frequencies and arbitrary modulationamplitudes is treated along with the case of high frequencies and small modulation amplitudes. In theformer case, the parametric resonance domains are examined depending on the parameters of the sys-tem. In the latter case, the high-frequency vibration is shown to create effective surface tension, thus flat-tening the interface, and can suppress instability when the heavy fluid is over the light one.