Faraday pilot-wave dynamics in a circular corral

Durey, M. , Milewski, P. A. and Wang, Z. (2020) Faraday pilot-wave dynamics in a circular corral. Journal of Fluid Mechanics, 891, A3. (doi: 10.1017/jfm.2020.140)

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Abstract

A millimetric droplet of silicone oil may bounce and self-propel on the free surface of a vertically vibrating fluid bath due to the droplet’s interaction with its accompanying Faraday wave field. This hydrodynamic pilot-wave system exhibits many dynamics that were previously thought to be peculiar to the quantum realm. When the droplet is confined to a circular cavity, referred to as a ‘corral’, a range of dynamics may occur depending on the details of the geometry and the decay time of the subcritical Faraday waves. We herein present a theoretical investigation into the behaviour of subcritical Faraday waves in this geometry and explore the accompanying pilot-wave dynamics. By computing the Dirichlet-to-Neumann map for the velocity potential in the corral geometry, we can evolve the quasi-potential flow between successive droplet impacts, which, when coupled with a simplified model for the droplet’s vertical motion, allows us to derive and implement a highly efficient discrete-time iterative map for the pilot-wave system. We study the onset of the Faraday instability, the emergence and quantisation of circular orbits and simulate the exotic dynamics that arises in smaller corrals.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Durey, Dr Matthew
Authors: Durey, M., Milewski, P. A., and Wang, Z.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Fluid Mechanics
Publisher:Cambridge University Press
ISSN:0022-1120
ISSN (Online):1469-7645
Published Online:18 March 2020

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