Abstract
The aim of this paper is to obtain streamline patterns of axisymmetric flow and their bifurcations for 2-D incompressible flows close to non-simple singular point. The streamlines of a Hamiltonian vector field system are simplified by using the homotopy invariance of the index theory. Using a homotopy invariance of the index, we develop a theory for the sufficient and necessary conditions for structural bifurcation of axisymmetric flow near non-simple degenerate critical points. The variation of parameters in the flow field can cause structural bifurcations. The bifurcation of the degenerate flow structure is obtained when it is perturbed slightly.
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