Axisymmetric gravity-capillary standing waves on the surface
of a fluid
Jules Fillette1,2, Stéphan Fauve2
and Eric Falcon1
1Université Paris Cité, MSC Laboratory, UMR 7057 CNRS,
F-75 013 Paris, France
2Laboratoire de Physique de l'ENS, CNRS, PSL Research
University, F-75005 Paris, France
Reference: Physical
Review Fluids 7, 124801 (2022)
Abstract:
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.
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We conduct an experimental study of axisymmetric
gravity-capillary standing waves generated by a vertically
vibrating ring on a fluid surface. Different regimes of
standing waves are highlighted at the basin center: linear,
nonlinear, and ejection regimes. For moderate forcing, the
spatial profile of standing waves breaks the up-down symmetry
as predicted by a third-order nonlinear theory, whereas for
stronger forcing, the maximum height reached by the
axisymmetric gravity-wave crest, at the basin center, is found
to increase linearly with its wavelength, as a consequence of
the saturation of its steepness.