Axisymmetric gravity-capillary standing waves on the surface of a fluid

We report on the experimental study of axisymmetric gravity-capillary standing waves generated by a vertically vibrating ring partially immersed into a fluid. Different regimes of standing waves are highlighted at the basin center depending on the forcing parameters: linear, nonlinear, and ejection regimes. For weak forcing, the standing waves display a resonant response, close to a natural frequency of the circular basin, predicted by the linear theory. For stronger forcing, we observed that the experimental spatial profile of standing waves breaks the up-down symmetry, and is well described by a third-order nonlinear theory. When the forcing is further increased, the maximum height of the axisymmetric wave crest at the basin center is found to increase linearly with its wavelength, due to the saturation of its steepness, a result well captured by a proposed model.