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Star-shaped waves published in Physical Review Letters


The movement of the waves on the water surface is governed by a set of nonlinear equations. This medium is also dispersive, i.e., the wave speed depends on the length. The combination of dispersive and nonlinear effects can lead to remarkable phenomena, such as solitary waves, tsunamis and rogue waves [1,2]. Another remarkable consequence of the properties of the medium is that they can generate waves with specific geometries [3]. For example, wave-shaped "horseshoe" [4] resulting from the nonlinear interaction between five waves [5]. Although we would expect the existence of a large variety of waves on the surface of the water, as a result of these nonlinearities, the identification of a new type of waves is a fairly rare event [6].

In this article, researchers from LPMC, in collaboration with a researcher from LJAD, have reported star- and polygon-shped waves. The symmetry of the star (i.e., the number of branches) is independent of the container form, and varies with the parameters of the vibration. This kind of wave appears, under certain conditions, when the surface of a liquid is subjected to vertical vibrations. The results show that resonant coupling of three waves can be the cause of the instability leading to the occurrence of such geometries.

[1] D. J. Korteweg, G. de Vries Philosophical Magazine 39, 422 (1895)

[2] A. Chabchoub, A.P. Hoffmann, & H. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011)

[3] M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)

[4] M.Y. Su, J. Fluid Mech. 124, 73 (1982)

[5] D. Fructus, C. Kharif, M. Francius, O. Kristiansen, D. Clamond & J. Grue, J. Fluid Mech. 537, 155 (2005)

[6] J. Rajchenbach, A. Leroux & D. Clamond, Phys. Rev. Lett. 107, 024502 (2011)

- Link to the article in Physical Review Letters.

- Link to the article in HAL.

- This article was selected to be presented in "Physics", the website which highlights a selection of papers from the Physical Review journals.


Fluides & Matériaux Complexes, Fluides Complexes