STRUCTURAL BIFURCATION OF DIVERGENCE-FREE VECTOR FIELDS NEAR NON-SIMPLE DEGENERATE POINTS WITH SYMMETRY
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, vol.9, no.2, pp.718-738, 2019 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 9 Issue: 2
- Publication Date: 2019
- Doi Number: 10.11948/2156-907x.20180151
- Journal Name: JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.718-738
- Erciyes University Affiliated: Yes
Abstract
In this study, topological features of an incompressible two-dimensional flow far from any boundaries is considered. A rigorous theory has been developed for degenerate streamline patterns and their bifurcation. The homotopy invariance of the index is used to simplify the differential equations of fluid flows which are parameter families of divergence-free vector fields. When the degenerate flow pattern is perturbed slightly, a structural bifurcation for flows with symmetry is obtained. We give possible flow structures near a bifurcation point. A flow pattern is found where a degenerate cusp point appears on the x-axis. Moreover, we also show that bifurcation of the flow structure near a non-simple degenerate critical point with double symmetry is generic away from boundaries. Finally, we give an application of the degenerate flow patterns emerging when index 0 and -2 in a double lid driven cavity and in two dimensional peristaltic flow.