By Alton Parrish (Reporter)
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French scientists report a new type of standing gravity waves of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vibrating vertically a tank. 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. We show that this wave geometry results from nonlinear resonant couplings between three waves, although this possibility was denied for pure gravity waves up to now.

Waves at the surface of water are described by a set of nonlinear equations. These nonlinearities can induce the emergence of new patterns. In this experiment, a container partly filled with a Newtonian fluid is vibrated vertically. (Newtonian fluids include most common liquids and gases; examples are water and air.) The vibrations give rise to the formation of standing waves at the free surface of the fluid, a phenomenon known as the ‘Faraday instability.’

This image shows a surface wave alternating in shape between a pentagon and a star. The number of axes of symmetry (in this case, five) can be varied according to the frequency and amplitude of the vibrations. Surprisingly, this number does not depend on the container’s size or shape. The geometry of the standing wave can be interpreted as resulting from nonlinear resonant couplings between three waves. This project has been partially supported by CNRS, Société ACRI and Région PACA.

Snapshot of a wave with five-fold symmetry in a vibrating Newtonian liquid.

Image Credit: Jean Rajchenbach, Alphonse Leroux, and Didier Clamond (CNRS and Université de Nice, France)

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