Evolution of velocity gradient tensor invariants in wing-tip vortices

This study presents a comprehensive investigation into the near-field dynamics of the wing-tip tri-vortex system on a supercritical wing, employing high-resolution, compressible Wall-Resolved Large-Eddy Simulations (WR-LES) validated by Stereo-Particle Image Velocimetry (PIV). The research focuses on the formation and evolution of the primary (PV), secondary (SV), and tertiary (TV) vortices at Reynolds number ( R e c = 620 , 000 ) and angles of attack of α = 5 ° and α = 10 ° . By performing a Lagrangian analysis of the velocity gradient tensor (VGT) invariants along each vortex core trajectory, the fundamental strain-vorticity relationship governing their distinct behaviors are quantified. The results demonstrate that the PV exhibits wake-like characteristics, dominated by vortex stretching and significant dissipation due to consistent biaxial strain. In contrast, the SV retains a stable, jet-like profile, characterized by a highly rotation-dominated core with low strain. The TV is identified as a youthful PV that acquires wake-like statistics downstream. A comparison between LES and PIV reveals that the absence of streamwise gradients in the experimental data obscures the canonical “teardrop” shape in the Q – R plane, underscoring the necessity of a full VGT for accurate turbulence characterization. This work motivates the link between the unique near-field dynamics of each vortex and their connection to wall-pressure fluctuations and far-field acoustics, identifying the strain-dominated PV as the dominant source of surface pressure unsteadiness and providing insights for future targeted flow control and noise reduction strategies at the wingtip.