Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers

TL;DR

This paper develops a theoretical model for Faraday surface waves generated by impacts on a vibrated liquid surface, especially below the instability threshold, and validates it with experiments involving bead impacts.

Contribution

It introduces a new theoretical framework for subthreshold Faraday waves and explains wave amplitude dependence and damping, linking fluid dynamics to quantum-like behaviors in walkers.

Findings

Model accurately predicts wave amplitude dependence on impact phase

Characterizes viscous damping timescale and length scale

Experimental validation confirms theoretical predictions

Abstract

A walker is a fluid entity comprising a bouncing droplet coupled to the waves that it generates at the surface of a vibrated bath. Thanks to this coupling, walkers exhibit a series of wave-particle features formerly thought to be exclusive to the quantum realm. In this paper, we derive a model of the Faraday surface waves generated by an impact upon a vertically vibrated liquid surface. We then particularise this theoretical framework to the case of forcing slightly below the Faraday instability threshold. Among others, this theory yields a rationale for the dependence of the wave amplitude to the phase of impact, as well as the characteristic timescale and length scale of viscous damping. The theory is validated with experiments of bead impact on a vibrated bath. We finally discuss implications of these results for the analogy between walkers and quantum particles.