A critical pattern of crossflow around a slender

Topological structure of a slender crossflow was discussed with topological analysis. It is pointed that the development of slender vortices leads to the change of topological structure about cross flow, and a critical flow pattern will appear. There is a high-order singular point in this critical flow pattern. And the index of the high-order singular is -3/2. The topological structure of this singular point is instable, so bifurcation will occur and the topological structure of flowfield will be changed by little disturbance.