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

✍ Scribed by I.A. Lukovskii; A.N. Timokha

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 630 KB
• Volume: 65
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(01)00052-1

✦ Synopsis

Potential flows in a system consisting of compressible barotropic ideal fluids -a liquid and a gas with an interface and an acoustic high-frequency vibrator, placed in the gas, are considered. The system of two media completely occupies a bounded absolutely rigid vessel. The two-scale expansion method is applied to the problem in a differential and variational formulation in the Hamilton-Ostrogradskii form. This enables both averaged equations of motion and the principle of the minimum quasi-potential energy to be derived for averaged surface reliefs (capillary-acoustic forms of equilibrium). In the equations obtained and in the functional, terms appear corresponding to forces of vibration origin. The problem of the quasi-equilibrium of the bifurcation of quasi-equilibrium forms is discussed in the case when the plane interface is simultaneously a capillary and a capilla&acoustic equilibrium form. Spectral theorems are derived for the problem of normal oscillations about quasi-equilibrium, and spectral and variational criteria of stability are formulated.