TY - JOUR
T1 - Faraday wave-droplet dynamics
T2 - Discrete-time analysis
AU - Durey, Matthew
AU - Milewski, Paul A.
N1 - Funding Information:
The authors thank J. Bush, C. Galeano-Rios, A. Oza and R. Rosales for useful contributions and discussions. M.D. gratefully acknowledges support through a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa) under the project EP/L015684/1. P.A.M. gratefully acknowledges support through the EPSRC project EP/N018176/1 and a Royal Society Wolfson award.
Publisher Copyright:
© 2017 Cambridge University Press.
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 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.
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 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.
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U2 - 10.1017/jfm.2017.235
DO - 10.1017/jfm.2017.235
M3 - Article
AN - SCOPUS:85019612671
SN - 0022-1120
VL - 821
SP - 296
EP - 329
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -