Local vortex line topology and geometry in turbulence

TL;DR

This paper extends the local streamline topology classification to vortex lines in turbulence, revealing universal statistical properties and consistent reconnection structures across different flow configurations.

Contribution

It introduces a novel application of topology classification to vortex lines, demonstrating universal invariant PDFs and reconnection geometries in turbulent flows.

Findings

The joint PDF of vorticity gradient invariants asymptotes to a universal bell shape.

Vortex reconnection bridges exhibit identical topology with elliptic and hyperbolic structures.

Universal features are observed across different turbulent and vortex breakdown scenarios.

Abstract

The local streamline topology classification method of Chong et al. (1990) is adapted and extended to describe the geometry of infinitesimal vortex lines. Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that joint probability density function (PDF) of the second ($q_\omega$) and third ($r_\omega$) normalized invariants of the vorticity gradient tensor asymptotes to a self-similar bell form beyond $Re_\lambda > 200$. The same PDF shape is also seen at the late stages of breakdown of Taylor-Green vortex suggesting the universality of the bell-shaped pdf form in turbulent flows. Additionally, vortex reconnection from different initial configurations is examined. The local topology and geometry of the reconnection bridge is shown to be identical in all cases with elliptic vortex lines on one side and hyperbolic filaments on the other. Overall, topological characterization of vorticity field provides a useful analytical basis for examining vorticity dynamics in turbulence and other fluid flows.