Faraday wave-droplet dynamics: discrete-time analysis

Matthew Durey, Paul Milewski

Research output: Contribution to journal › Article

  • 6 Citations

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.
LanguageEnglish
Pages296-328
JournalJournal of Fluid Mechanics
Volume821
Early online date22 May 2017
DOIs
StatusPublished - 25 Jun 2017

Fingerprint

baths
walking
fluids
circular orbits
interactions
statistical analysis
Fluids
hydrodynamics
trajectories
harmonics
Statistical methods
Orbits
Hydrodynamics
Trajectories

Cite this

Faraday wave-droplet dynamics : discrete-time analysis. / Durey, Matthew; Milewski, Paul.

In: Journal of Fluid Mechanics, Vol. 821, 25.06.2017, p. 296-328.

Research output: Contribution to journal › Article

Durey, M & Milewski, P 2017, 'Faraday wave-droplet dynamics: discrete-time analysis' Journal of Fluid Mechanics, vol. 821, pp. 296-328. DOI: 10.1017/jfm.2017.235
Durey M, Milewski P. Faraday wave-droplet dynamics: discrete-time analysis. Journal of Fluid Mechanics. 2017 Jun 25;821:296-328. Available from, DOI: 10.1017/jfm.2017.235
Durey, Matthew ; Milewski, Paul. / Faraday wave-droplet dynamics : discrete-time analysis. In: Journal of Fluid Mechanics. 2017 ; Vol. 821. pp. 296-328
@article{d222074bac68422ca00a24354ce3cbd6,
title = "Faraday wave-droplet dynamics: discrete-time analysis",
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.",
author = "Matthew Durey and Paul Milewski",
year = "2017",
month = "6",
day = "25",
doi = "10.1017/jfm.2017.235",
language = "English",
volume = "821",
pages = "296--328",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Faraday wave-droplet dynamics

T2 - Journal of Fluid Mechanics

AU - Durey,Matthew

AU - Milewski,Paul

PY - 2017/6/25

Y1 - 2017/6/25

N2 - 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.

AB - 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.

UR - https://doi.org/10.1017/jfm.2017.235

U2 - 10.1017/jfm.2017.235

DO - 10.1017/jfm.2017.235

M3 - Article

VL - 821

SP - 296

EP - 328

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -

Access to Document