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

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.

References in corpus (5)

• Chaos driven by interfering memory
• Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits
• Interaction of two walkers: Wave-mediated energy and force
• Build-up of macroscopic eigenstates in a memory-based constrained system
• Scattering theory of walking droplets in the presence of obstacles

Cited by in corpus (10)

• Interaction of Wave-Driven Particles with Slit Structures
• Collective vibrations of confined levitating droplets
• Collective vibrations of a hydrodynamic active lattice
• Emergence of superwalking droplets
• Bouncing oil droplets, de Broglie's quantum thermostat and convergence to equilibrium
• Anderson localization of walking droplets
• Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave-particle entity in a periodic potential
• Controlled Locomotion of a Minimal Soft Structure by Stick-Slip Nonlinearity
• Statistical self-organization of a gas of interacting walking drops in a confining potential
• Effective gravity and effective quantum equations in a system inspired by walking droplets experiments