Sound–vortex conversion on droplets: Velocity field decoupling methodology for acoustic quantum vortex cascades

Characterizing velocity fields is fundamental to understanding vortices. While classical models (e.g., Burgers and Rankine) effectively describe single-vortex profiles, composite fields in vortex cascades—where large vortices hierarchically fragment into smaller structures—remain poorly understood. Analyzing such cascades requires decomposing observed velocity Vobs(r) = vcir(r) + V0, separating intrinsic rotational velocity vcir(r) from background velocity V0. Current flow field measurements rely on reference frames, but determining a frame's velocity inherently depends on additional frames, creating a chain of interdependent measurements. Uncertainties in each frame propagate, accumulating significant errors in flow field analyses. This study develops a reference-frame-independent vortex velocity-field decoupling methodology based on angular momentum conservation. It eliminates background velocity from cascades and reference frame effects to derive the vortex's absolute rotational velocity. We establish the method's theoretical basis, validate it experimentally, and use high-resolution microscopy and particle image velocimetry to investigate sound-driven quantum-like vortex cascades in water, achieving rigorous separation of vcir(r) and V0. Excellent experimental-theoretical agreement provides a framework for reference-frame-independent velocity field measurement. This work establishes angular momentum conservation as a universal principle governing vortex velocity fields, with implications for classical and quantum fluids. It facilitates exploring acoustic quantum vortices and developing room-temperature quantum fluid analogs and related technologies.