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 modeled as instantaneous. By analysing the stability of the system's fixed points, we explain the dynamics of a walking droplet, and capture the quantizations for multiple-droplet interactions. Circular orbits in a harmonic potential are studied, and a double-quantization of chaotic trajectories is obtained through systematic statistical analysis.
Original languageEnglish
Pages (from-to)296-328
Number of pages33
JournalJournal of Fluid Mechanics
Volume821
Early online date22 May 2017
DOIs
Publication statusPublished - 25 Jun 2017

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