Streamline patterns and their bifurcations in two-dimensional
incompressible flow in the vicinity of a fixed wall has been
investigated from a topological point of view by Bakker
[Bifurcations in Flow Patterns. Kluwer Academic Publishers, 1991].
Bakkers work is revisited in a more general setting allowing
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 non-linear 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 are
obtained. Further the case of a non-simple degeneracy is
considered. Finally the effect of the Navier-Stokes equations on
the local topology is considered.

Publication status | Published - 1998 |
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