Frequencies of oscillations of free boundaries in a perfect fluid - Correa Abendaño, María Lorena (2020)
We compute the natural frequencies for the oscillations of the free boundary of capillary standing waves in contact with a solid container. First, we study the case of the half-plane. We deduce an integrodifferential evolutionary equation for the linearized free boundary and impose pinned-end and free-end boundary conditions. For both cases, the natural oscillations frequencies for the free surfaces are provided and compared with the frequencies in the absence of solid walls. Then, by conformal mappings, the same analysis can be done to arbitrary 2D containers, with all the information on their geometry contained into a matrix that appears as a factor in a linear system for the computation of eigenfrequencies. In particular, we make the analysis to a vertical-infinite strip and a rounded container.