Faraday wave-droplet dynamics: Discrete-time analysis

Matthew Durey, Paul A. Milewski

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)296-329
Number of pages34
JournalJournal of Fluid Mechanics
StatePublished - Jun 25 2017

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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