Journal of Fluid Mechanics

Papers

Information stored in Faraday waves: the origin of a path memory

ANTONIN EDDIa1 c1, ERIC SULTANa2, JULIEN MOUKHTARa1, EMMANUEL FORTa3, MAURICE ROSSIa4 and YVES COUDERa1

a1 Laboratoire Matières et Systèmes Complexes, Université Paris Diderot and CNRS, UMR 7057, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France

a2 Laboratoire FAST, Université Pierre et Marie Curie, Université Paris-Sud and CNRS, UMR 7608, Bâtiment 502, Campus Universitaire, 91405 Orsay, France

a3 Institut Langevin, ESPCI ParisTech, Université Paris Diderot and CNRS, UMR 7587, 10 rue Vauquelin, 75231 Paris CEDEX 05, France

a4 Institut Jean Le Rond D'Alembert, Université Pierre et Marie Curie and CNRS, UMR 7190, 4 Place Jussieu, 75252 Paris CEDEX 05, France

Abstract

On a vertically vibrating fluid interface, a droplet can remain bouncing indefinitely. When approaching the Faraday instability onset, the droplet couples to the wave it generates and starts propagating horizontally. The resulting wave–particle association, called a walker, was shown previously to have remarkable dynamical properties, reminiscent of quantum behaviours. In the present article, the nature of a walker's wave field is investigated experimentally, numerically and theoretically. It is shown to result from the superposition of waves emitted by the droplet collisions with the interface. A single impact is studied experimentally and in a fluid mechanics theoretical approach. It is shown that each shock emits a radial travelling wave, leaving behind a localized mode of slowly decaying Faraday standing waves. As it moves, the walker keeps generating waves and the global structure of the wave field results from the linear superposition of the waves generated along the recent trajectory. For rectilinear trajectories, this results in a Fresnel interference pattern of the global wave field. Since the droplet moves due to its interaction with the distorted interface, this means that it is guided by a pilot wave that contains a path memory. Through this wave-mediated memory, the past as well as the environment determines the walker's present motion.

(Received September 09 2010)

(Revised December 17 2010)

(Accepted January 03 2011)

(Online publication March 25 2011)

Key words:

  • drops;
  • Faraday waves;
  • pattern formation

Correspondence:

c1 Email address for correspondence: antonin.eddi@univ-paris-diderot.fr

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