An objective definition of a vortex

TLDR

Current vortex definitions are frame‑dependent, misidentifying structures in rotating flows, making a frame‑independent definition essential for accurate analysis of rotating and interacting vortices. Here we define a vortex as a set of fluid trajectories along which the strain acceleration tensor is indefinite over directions of zero strain. This objective criterion identifies vortices as material tubes where material elements do not align with strain eigenvector directions. Using examples, we demonstrate that this criterion outperforms earlier frame‑dependent criteria and also yields an objective criterion for hyperbolic Lagrangian structures.

Abstract

The most widely used definitions of a vortex are not objective: they identify different structures as vortices in frames that rotate relative to each other. Yet a frame-independent vortex definition is essential for rotating flows and for flows with interacting vortices. Here we define a vortex as a set of fluid trajectories along which the strain acceleration tensor is indefinite over directions of zero strain. Physically, this objective criterion identifies vortices as material tubes in which material elements do not align with directions suggested by the strain eigenvectors. We show using examples how this vortex criterion outperforms earlier frame-dependent criteria. As a side result, we also obtain an objective criterion for hyperbolic Lagrangian structures.