A novel algorithm for visualizing and quantifying vortices in complex 3D flows based on marching and converging vortex atoms

Numerous investigations aiming to reveal the underlying physics behind complex flows highlighted the important roles of vortices. This article proposes an integrative algorithm for visualizing and quantifying the vortices in three-dimensional flows. The algorithm not only extracts the vortex centerlines but also returns the vortex radii and circulations varying along the centerlines. The novel aspect of this algorithm is to represent the vortex field as a collection of discrete vortex atoms. By iteratively updating the positions of these vortex atoms, the algorithm manipulates them into marching toward the underlying vortex centerlines. The radii and circulations varying along the centerlines are estimated based on the vortex atoms converged on the vortex centerlines. The accuracy and robustness of the algorithm are first accessed by numerical tests based on a synthetic vortex ring. Subsequently, the algorithm is employed to investigate the complex vortices in a turbulent boundary layer, validating the scaling law of the vortices reported in the literature. At last, the algorithm is applied to the three-dimensional experimental data of the wake flow behind a wall-mounted hemisphere. It concludes that the algorithm can be used as an effective tool for analyzing vortices in complex flows.