Durey, M. and Milewski, P. A. (2018) Faraday wave–droplet dynamics: discrete-time analysis. Journal of Fluid Mechanics, 821, pp. 296-329. (doi: 10.1017/jfm.2017.235)
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Abstract
A droplet may ‘walk’ across the surface of a vertically vibrating bath of the same fluid, due to the propulsive interaction with its wave field. This hydrodynamic pilot-wave system exhibits many dynamics previously believed to exist only in the quantum realm. Starting from first principles, we derive a discrete-time fluid model, whereby the bath–droplet interactions are modelled as instantaneous. By analysing the stability of the fixed points of the system, we explain the dynamics of a walking droplet and capture the quantisations for multiple-droplet interactions. Circular orbits in a harmonic potential are studied, and a double quantisation of chaotic trajectories is obtained through systematic statistical analysis.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Durey, Dr Matthew |
Authors: | Durey, M., and Milewski, P. A. |
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: | 22 May 2017 |
Copyright Holders: | Copyright © 2017 Cambridge University Press |
First Published: | First published in Journal of Fluid Mechanics 821: 296-329 |
Publisher Policy: | Reproduced under a Creative Commons License |
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