Asymptotic and variational methods in non-linear problems of the interaction of surface waves with acoustic fields

Potential flows in a system consisting of compressible barotropic ideal flu ids - a liquid and a gas with an interface and an acoustic high-frequency v ibrator, placed in the gas, are considered, The system of two media complet ely occupies a bounded absolutely rigid vessel. The two-scale expansion met hod is applied to the problem in a differential and variational formulation in the Hamilton-Ostrogradskii form. This enables both averaged equations o f motion and the principle of the minimum quasi-potential energy to be deri ved for averaged surface reliefs (capillary-acoustic forms of equilibrium). In the equations obtained and in the functional, terms appear correspondin g to forces of vibration origin. The problem of the quasi-equilibrium of th e bifurcation of quasi-equilibrium forms is discussed in the case when the plane interface is simultaneously a capillary and a capillary-acoustic equi librium form. Spectral theorems are derived for the problem of normal oscil lations about quasi-equilibrium, and spectral and variational criteria of s tability are formulated. (C) 2001 Elsevier Science Ltd. All rights reserved .