Unified Hydrodynamic Analogue of Aharonov-Bohm and Lense-Thirring Effects

TL;DR

This paper demonstrates that surface waves in a draining vortex mimic Aharonov-Bohm and Lense-Thirring effects, linking topological phases and inertial phenomena to measurable fluid flows in a laboratory setting.

Contribution

It introduces a unified hydrodynamic model capturing both Aharonov-Bohm and Lense-Thirring effects within a single experimental system.

Findings

Wavefront dislocations characteristic of Aharonov-Bohm scattering observed.

Nodal patterns rotate at an angular velocity fixed by circulation, analogous to frame dragging.

Experimental results confirm theoretical predictions in a controlled vortex setup.

Abstract

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.