Walking droplets as a damped-driven system

TL;DR

This paper models the dynamics of a droplet on a vibrating fluid bath as a damped-driven system, revealing chaotic behavior and energy balance mechanisms that explain experimental instabilities.

Contribution

It introduces a nonlinear map framework for droplet-wave interactions, linking experimental phenomena to energy-based bifurcations in damped-driven systems.

Findings

Demonstrates period doubling route to chaos in droplet dynamics

Develops a gain-loss iterative map capturing system instabilities

Provides a geometric description of particle-wave interactions

Abstract

We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, including a period doubling route to chaos. By approximating the system as a compositional map between the gain and loss dynamics, the underlying nonlinear dynamics can be shown to be driven by energy balances in the systems. The gain-loss iterative mapping is similar to a normal form encoding for the pattern forming instabilities generated in such spatially-extended system. Similar to mode-locked lasers and rotating detonation engines, the underlying bifurcations persist for general forms of the loss and gain, both of which admit explicit representations in our approximation. Moreover, the resulting geometrical description of the particle-wave interaction completely characterizes the instabilities observed in experiments.