Bifurcations in Viscous Flow Fields on the Genesis and Development of Topologically Complicated Separated Flow Structures

摘要

The qualitative theory of dynamical systems together with topological considerations is applied to steady viscous flows. Local solutions of the Navier-Stokes equations are constructed in the phase space and a classification of possible flow topologies (including separations, vortices, bubbles, etc.) near fixed and moving walls is presented. The local solutions are associated with singular points (of various kind) in the trajectory pattern of the phase space. For example, the first order saddle points are recognized as the classical Oswatitsch-Legendre solution for flow separation or flow attachment in two dimensions. The report gives a detailed study of the unfoldings and bifurcation behavior of higher-order singular points. In this way local solutions of the Navier-Stokes equations are obtained describing flow patterns having topologies of increased complexity. The study supports the general conclusion that higher-order singularities, regardless of their rare appearance in practice, are the cornerstones in a method that provide these local solutions of the Navier-Stokes equations.