Pilot-wave hydrodynamics of a particle in a density-stratified fluid

TL;DR

This paper introduces a hydrodynamic pilot-wave system using particles in density-stratified fluids, demonstrating wave-particle interactions, symmetry breaking, and complex dynamics validated through theory and simulations.

Contribution

It presents a minimal hydrodynamic theory and numerical validation for wave-particle interactions in stratified fluids, establishing a new macroscopic pilot-wave system.

Findings

Wave-particle interactions induce symmetry breaking and self-propulsion.

Numerical simulations confirm the growth of instability depends on oscillation amplitude.

Reflections create a Casimir-like potential that influences long-term dynamics.

Abstract

Inspired by bouncing drop experiments that revealed how macroscopic systems can exhibit wave-particle properties previously thought to be exclusive to quantum systems, we introduce here a new wave-particle system based on internal gravity waves propagating in density-stratified fluids. Recent experiments on particles (called ludions) oscillating in such a fluid medium suggest that wave-particle interactions can induce symmetry breaking, leading to spontaneous self-propulsion of the particle in the horizontal plane. Here, we propose a minimal hydrodynamic theory showing that this instability can be explained by a Doppler force emerging from interactions between the ludion and its own wave field. We validate our theoretical predictions using direct numerical simulations, which confirm that the growth of the instability is determined by the particle oscillation amplitude. In wall-bounded domains, reflections of the internal waves create a Casimir-like potential that rapidly develops and constrains the particle motion. Despite the presence of the Doppler force, this potential governs the ludion long-term dynamics, leading to capture in fixed points or chaotic attractors near the potential wells. We show that the essential features of this behavior are well captured by a minimal dynamical model. Our findings establish the ludion as a novel hydrodynamic pilot-wave system, offering a new platform for exploring macroscopic wave-particle behaviors, particularly in three-dimensional configurations.