Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate changes results in a much simplified system of differential equations for the streamlines ͑a normal form͒ encapsulating all the features of the original system. From this, we obtain a complete description of bifurcations up to codimension three close to a simple linear degeneracy. As a special case we develop the theory for flows with reflectional symmetry. We show that all the patterns obtained can be realized in steady Navier-Stokes or Stokes flow, but an unresolved difficulty arises in the symmetric case for Navier-Stokes flow. The theory is applied to the patterns and bifurcations found numerically in two recent studies of Stokes flow in confined domains.

Bakker's work is revisited in a more general setting allowing a curvature of the fixed wall and a time dependence of the streamlines. The velocity field is expanded at a point on the wall, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate changes results in a much simplified system of differential equations for the streamlines (a normal form) encapsulating all the features of the original system. From this, a complete description of bifurcations up to codimension three close to a simple linear degeneracy is obtained. Further, the case of a non-simple degeneracy is considered. Finally the effect of the Navier-Stokes equations on the local topology is investigated.

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