Pilot-wave dynamics of two identical, in-phase bouncing droplets

Area of Science:

• Fluid Dynamics
• Wave Phenomena
• Nonlinear Dynamics

Background:

• Bouncing droplets on vibrating baths act as macroscopic pilot-wave systems.
• Interactions are mediated by surface waves generated by the droplets.
• The Oza-Rosales-Bush model describes walking droplet dynamics.

Purpose of the Study:

• Investigate the dynamics of two interacting, in-phase bouncing droplets.
• Analyze the influence of inertia-to-drag and wave-forcing-to-drag ratios.
• Explore the rich behaviors and bifurcations in this pilot-wave system.

Main Methods:

• Theoretical analysis using the Oza-Rosales-Bush pilot-wave model.
• Numerical simulations, including linear stability and fully nonlinear approaches.
• System parameter variation to map different dynamic regimes.

Main Results:

• Droplets typically form tightly bound pairs, but can unbind under specific parameter conditions.
• Bound pairs exhibit diverse trajectories: straight, sub-diffusive random walks, and closed loops.
• Relative droplet motion includes fixed positions, oscillations, and regular or chaotic interchanges.

Conclusions:

• The two-droplet system displays a rich variety of behaviors governed by inertia and wave forcing.
• Bifurcations between different dynamic regimes were identified.
• This study advances the understanding of coupled pilot-wave dynamics.