Collectivity and Turbulence: A Coherence–Based Extension of the Navier–Stokes Framework (Technical Note)

We introduce a scalar geometric diagnostic, termed collectivity, designed to quantify directional coherence of vorticity in turbulent flows independently of velocity or vorticity magnitude. Collectivity is constructed from local oscillations of the vorticity direction and provides a real-space measure of geometric organisation not captured by classical invariants. This technical note explores considerations of classical invariants, and combinations thereof, to enhance classification and study of turbulent structures.