On multiplicity of vibrocapillary reliefs: symmetric and antisymmetric deformations (Q2754739)

Under high-frequency oscillations of a vessel, the averaged in time free surface of liquid differs from the capillary one and is determined by the solution of the vibrocapillary surface problem. The problem is reduced to minimization of some functional. A constraint of the minimization problem is represented by a boundary value problem for the potential of velocity. If frequencies of vibrations are much lower than principal eigenfrequencies of standing acoustic waves, however much larger than eigenfrequencies of surface waves, compressibility of liquid can be neglected. The solution of the boundary value problem for velocity potential by the mean-square method is reduced to an infinite algebraic system. By some simplifications, the functional to be minimized is reduced to a function of two variables. Each variable corresponds to symmetric and antisymmetric deformations of free boundary. Asymptotic analysis of solution and comparison with experimental data are performed.