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Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers

Published online by Cambridge University Press:  13 June 2018

Loïc Tadrist Open the ORCID record for Loïc Tadrist [Opens in a new window] ,
Jeong-Bo Shim ,
Tristan Gilet  and
Peter Schlagheck
Loïc Tadrist*
Affiliation:
Microfluidics Lab, Department of Mechanical and Aerospace Engineering, University of Liege, Allée de la découverte 9, 4000 Liège, Belgium
Jeong-Bo Shim
Affiliation:
IPNAS, CESAM research unit, University of Liege, Allee du 6 Août 15, 4000 Liège, Belgium
Tristan Gilet
Affiliation:
Microfluidics Lab, Department of Mechanical and Aerospace Engineering, University of Liege, Allée de la découverte 9, 4000 Liège, Belgium
Peter Schlagheck
Affiliation:
IPNAS, CESAM research unit, University of Liege, Allee du 6 Août 15, 4000 Liège, Belgium
*
†Email address for correspondence: Loic.tadrist@uliege.be
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Abstract

A walker is a fluid entity comprising a bouncing droplet coupled to the waves that it generates at the surface of a vibrated bath. Thanks to this coupling, walkers exhibit a series of wave–particle features formerly thought to be exclusive to the quantum realm. In this paper, we derive a model of the Faraday surface waves generated by an impact upon a vertically vibrated liquid surface. We then particularise this theoretical framework to the case of forcing slightly below the Faraday instability threshold. Among others, this theory yields a rationale for the cosine dependence of the wave amplitude to the phase shift between impact and forcing, as well as the characteristic time scale and length scale of viscous damping. The theory is validated with experiments of bead impact on a vibrated bath. We finally discuss implications of these results for the analogy between walkers and quantum particles.

JFM classification

Waves/Free-surface Flows: Faraday waves Instability: Parametric instability Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 848 , 10 August 2018 , pp. 906 - 945
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Copyright
© 2018 Cambridge University Press 

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