Faraday wave–droplet dynamics: discrete-time analysis

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)

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
• 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