Averaging method and long-wave asymptotics in vibrational convection in layers with an interface

A scheme for applying an averaging method to the problem of convection in a two-layer system with an interface under the influence of high-frequency vibration is proposed. The derivation of the averaging equations is given, and the stability of the equilibrium of the averaged problem is considered. Long-wavelength asymptotics of steady and oscillatory instability are constructed. The results of numerical calculations for acetonitrile?Cn-hexane and silicone oil?Cfluorinert systems are given. The directions in which the investigation of thermovibrational convection in problems with free surfaces and interfaces can be continued, are indicated.