Objective detection of coherent vortices from instantaneous flow data

Abstract

Vortices are swirling regions of fluid that structure motion in gases and liquids across a wide range of scales, from laboratory-scale experiments to vast atmospheric currents. They play a key role in mixing, transport, and energy transfer, yet their reliable identification in unsteady flows remained a major challenge. Most existing approaches rely on local, instantaneous properties of the velocity gradient, such as strain or rotation. Although effective in simple or steady flows, these criteria can fail in complex, time-dependent settings, falsely detecting vortices or overlooking coherent structures altogether. Lagrangian methods instead identify vortices as regions of material coherence by tracking fluid trajectories over time. While conceptually sound, these approaches are computationally intensive, require high-quality data, and are impractical for real-time applications. This motivates a central challenge: whether coherent vortices, inherently defined over finite times, can be detected objectively from instantaneous flow measurements. Here we introduce the first Eulerian criterion to overcome these challenges. By examining the temporal evolution of strain and removing from the velocity field the components attributable to rigid-body motion, we construct an objective velocity field that isolates genuine swirling dynamics. The resulting $Q_\text{s}$-criterion consistently identifies coherent vortices in both analytical examples and complex flow data, including cases where traditional methods fail. Our framework provides an observer-independent, computationally efficient tool for vortex detection from instantaneous data, enabling improved analysis and prediction of fluid flows across scales.