Laboratoire Matière et Systèmes Complexes

Nouvelles vagues / New waves

Jean Rajchenbach

Laboratoire de Physique de la Matière Condensée CNRS,Université de Nice Sophia-Antipolis

Abstract : We describe some new types of large amplitude water waves that we have observed in the laboratory. These waves are parametrically sustained by vertical vibrations the container. First, we report the existence of two types of highly-localized, standing waves of large amplitude (1). They are respectively of odd and even symmetry. Both standing waves oscillate subharmonically with the forcing frequency. The even pattern presents a certain similarity in the shape with the 3D axisymmetric oscillon originally recognized at the surface of a vertically vibrated layer of brass beads by P. B. Umbanhowar and coll. (2). The stable, 2D odd standing wave has never been observed before. We show that hysteresis and dissipation are essential ingredients leading to the formation of such solitary waves. Then, we describe a standing gravity waves of large amplitude, having alternatively the shape of a star and of a polygon. The symmetry of the star (i.e. the number of branches) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration (3). We show that a nonlinear resonant coupling between three gravity waves can be envisaged to trigger the observed symmetry breaking, although more complex interactions certainly take place in the final periodic state.

(1) Phys. Rev. Lett. 107, 024502 (2011).

(2) Nature 382, 793 (1996).

(3) Phys. Rev. Lett. 110, 094502 (2013).