Topological Analysis Of A Junction Vortex Flow

When a two-dimensional boundary layer on a plane surface encounters an obstacle, a three-dimensional separation is induced, and a complex necklace vortex system is created. In this paper, numerical solutions for the laminar vortex flow generated at a cylinder-wall intersection are analysed with respect to their topological structures. The nature and connections of singular points for the velocity and shear stress fields are identified. The topological consistency of the resulting vortex pattern is thoroughly discussed, as well as its robustness to changes in the physical and numerical parameters. Similar numerical and experimental results in the literature are considered for a comparison. Our analysis shows that both an insufficient spatial resolution and numerical or experimental errors may easily lead to misinterpretation of the vortex patterns or even to the impossibility of a unique identification of the topological structures. Our results, together with literature data, show that the three stable topological structures indicated in Baker [1] are inadequate to describe the juncture vortex systems in different flow conditions, both from a qualitative and a quantitative point of view. We therefore propose alternative topological classification criteria, which are suitable for a wider variety of structures.