Characterisation of the density, shape, and orientation of three-dimensional vortices in turbulent channel flow

Vortex research is critical for environmental and engineering applications. Quantitative evaluation on vortex properties were centred on two-dimensional (2D) contours (based on 2D or three-dimensional (3D) flow fields) in previous studies. In this study we proposed a 3D isosurface-based method with higher ability and accuracy for vortex extraction to characterise 3D vortices. The key lies in the usage of a fast triangle-triangle intersection method together with a triangular cutting plane. Vortices were extracted as polygons from intersection lines between the 3D isosurface and the triangular cutting plane. Vortex population density, morphological descriptors (circularity, radius, convex solidity, and axis ratio), and orientation for different thresholds and wall distances were analysed. As the threshold increases, the number of extracted vortices decreases logarithmically, and vortices become smaller, more circular and convex. Similar to the threshold case, a logarithmic relationship between vortex density and wall distance exists. And as the wall distance increases, vortices also become more circular and convex, and inclination angle increases and stabilises in the wake layer. Compared with findings based on 2D contours in previous studies, the isosurface-based method in this study represented 3D vortices in a clearer perspective. Due to the usage of threshold varied with the wall distance, vortex radius increased with the increasing wall distance in previous studies. However, results based on 3D isosurface show that in the fully developed channel flow vortex size is strongly correlated with the velocity gradient, and vortex size only increases in the near-wall region, beyond which it remains nearly constant. The proposed method may help to delve into turbulent structures along with their interactions and evolutionary mechanisms.