Nonlinear water waves.

New standing solitary waves in water.

By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are respectively of odd and even symmetry. Both standing waves oscillate subharmonically with the forcing frequency. The two-dimensional even pattern present a certain similarity in the shape with the 3D axisymmetric oscillon originally recognized at the surface of a vertically vibrated layer of brass beads. The stable, 2D odd standing wave has never been observed before in any media.

Localized pattern of even symmetry.

Localized pattern of odd symmetry.

Observation of star-shaped water waves.

In this experiment, a container partly filled with a Newtonian fluid is vibrated vertically . A new type of standing gravity waves of large amplitude, having alternatively the shape of a star and of a polygon, is reported. The symmetry of the star (i.e. the number of tips) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration. We show that a nonlinear resonant coupling between three gravity waves is relevant to trigger the instability leading to these wave patterns, although more complex interactions take certainly place in the final permanent state.

Using a circular tank it appears two contrapropagative axisymmetric gravity waves just above the Faraday instability threshold.

Increasing then the vibration amplitude, it is observed the appearanceof five tips, that testifies to the breaking of the axial symmetry.

Still increasing the vibration amplitude, it appears a new type of standing gravity waves having alternatively the shape of a star and of a polygon.

Varying the vibration parameters can lead to the formation of patterns displaying other symmetry (here, 6-fold symmetry).

J. Rajchenbach, D. Clamond, and A. Leroux, Observation of Star-Shaped Surface Gravity Waves. Phys. Rev. Lett. (2013) (preprint)

J. Rajchenbach and D. Clamond, Faraday waves: their dispersion relation, nature of bifurcation and wavenumber selection revisited, J. Fluid Mech. 777, R1-2 (2015) (preprint)