Two complementary eigen-based geometric properties of a vortex

Abstract

In our previous paper [V. Kolář and J. Šístek, “Orbitally compact and loose vortex regions,” Phys. Fluids 35, 121708 (2023)], the eigenvalue-based measure of orbital compactness of particle motion inside a vortex for compressible flows has been proposed. Here, a complementary eigenvector-based geometric property of cylindricity (three-dimensional /3D/ aspect) is introduced. This property is closely related to the local flow axisymmetry in the swirl plane (two-dimensional /2D/ aspect) which explains the positive response of the vortex-identification Δ-criterion, and closely related criteria swirling strength and Rortex (Liutex), for almost no vorticity and a large (without any limitation) rate-of-strain magnitude. A relatively high correlation between orbital compactness, cylindricity, and widely used vortex-identification criteria has been found for several flow examples.