Interaction of two walkers: Wave-mediated energy and force

TL;DR

This study explores how two wave-interacting walkers exchange energy and influence each other's motion, revealing discrete binding states and energy relations through experiments and simple theoretical modeling.

Contribution

It provides the first detailed experimental and theoretical analysis of energy exchange and binding modes between two coupled wave-driven walkers.

Findings

Discrete binding distances for coupled walkers

Velocity depends on mutual binding

Energy relations between droplets and wave fields

Abstract

A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global surface wave field that retains information on its past trajectory. Here, we investigate the energy stored in this wave field for two coupled walkers and how it conveys an interaction between them. For this purpose, we characterize experimentally the "promenade modes" where two walkers are bound, and propagate together. Their possible binding distances take discrete values, and the velocity of the pair depends on their mutual binding. The mean parallel motion can be either rectilinear or oscillating. The experimental results are recovered analytically with a simple theoretical framework. A relation between the kinetic energy of the droplets and the total energy of the standing waves is established.