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 language | English |
---|---|
Pages (from-to) | 296-328 |
Number of pages | 33 |
Journal | Journal of Fluid Mechanics |
Volume | 821 |
Early online date | 22 May 2017 |
DOIs | |
Publication status | Published - 25 Jun 2017 |