Streamline Patterns and their Bifurcations using Methods from Dynamical Systems

Patterns in viscous flow are studied with the aid of tools from low-dimensional nonlinear dynamics. We consider in particular change of patterns as parameters are varied, and show how normal form theory can be used to simplify the differential equations that describe the streamlines. The approach is used to obtain a basic qualitative description of separation and attachment close to a wall and to axisymmetric flow, and we illustrate how the ideas can be applied to a specific flow exhibiting secondary flow in the form of vortex breakdown.

We describe how the possibility of chaotic streamlines in 3-dimensional flow complicates the classification of patterns in this case.