Using time-dependent compressible laminar Navier-Stokes equations with a finite volume method incorporating a third-order-accurate discretization scheme, the flow structures around a slender at certain incidences are numerical simulated and typical crossflow patterns are presented. At incidence 10°, these vortical configurations are different at dissimilar axial locations though they are symmetric. At 35°, the symmetric vortical structures still maintain over the slender, yet their interaction at afterbody is intense than that at the forebody since the two vortices have fully developed downstream. The unstable topological structure of trajectory of saddle-to-saddle points and multiple limit cycle are further discussed in topological stability theory. These structures easily produce bifurcation with perturbation. The results support the view of hydrodynamic instability of vortices flow field. Using time-dependent compressible laminar Navier-Stokes equations with a finite volume method incorporating a third-order-accurate discretization scheme, the flow structures around a slender at certain incidences are numerical simulated and typical cross-flow patterns are presented. At incidence 10 °, these at 35 °, the symmetric vortical structures still maintain over the slender, yet their interaction at after the body is intense than that at the forebody since the two vortices have fully developed downstream. topological structure of trajectory of saddle-to-saddle points and multiple limit cycle are further discussed in topological stability theory. These structures easily produce bifurcation with perturbation. The results support the view of hydrodynamic instability of vortices flow field.