Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 57: Posters - Turbulence

DY 57.4: Poster

Thursday, March 23, 2017, 17:00–19:30, P1A

Quantum-like approach for a wave-particle system in fluid mechanics — •Remy Dubertrand, Maxime Hubert, Peter Schlagheck, Nicolas Vandewalle, Thierry Bastin, and John Martin — IPNAS CESAM Université de Liège, Liège, Belgium

A droplet bouncing on a vibrating bath can mimic, close to the Faraday instability threshold, a wave-particle system called a walker, see the pioneering experiment in [1]. It reported the observation of a diffraction pattern in a single slit geometry. This wave-like phenomenon can be linked to the coupling of the droplet with the associated bath surface wave. Yet a quantitative model in the presence of boundaries represents a highly difficult question while recent experiments have reported clear effects of the geometry [2, 3].

Here we present a simple model inspired from quantum mechanics for a walker in an arbitrary geometry [4]. We propose to describe its trajectory via a Green function approach. In the case of a single-slit geometry, our model is analytically and explicitly solvable, and reproduces some of the features observed experimentally.

[1] Y. Couder, and E. Fort, Phys. Rev. Lett. 97 154101 (2006)

[2] J. W. M. Bush, Ann. Rev. Fluid Mech. 47 269 (2015)

[3] B. Filoux, M. Hubert, N. Vandewalle, Phys. Rev. E 92 041004(R) (2015)

[4] R. Dubertrand et al., New J. Phys. 18 113037 (2016)