Bifurcation phenomena in the flow through a sudden expansion in a pipe.

Flows through a pipe with a sudden expansion are of both fundamental and practical interest. They arise in many engineering applications ranging from heat exchangers to combustion chambers and in physiological problems such as the flow past stenoses. They also provide examples of open fluid flows with the complexities of separation and reattachment and have been used to test computational fluid dynamics algorithms. In some situations the flow geometry canusefully be considered as two-dimensional where we showed that mid-plane symmetry of the flow is broken at pitchfork bifurcation as the Reynolds number, Re, is increased. Thus the symmetric flow loses stability to a pair of asymmetric states at a critical Re. The bifurcation structure was revealed in a combinednumerical and experimental investigation which also highlighted the importance of imperfections in the experiment and this has stimulated a great deal of other research on the topic and our paper has more than eighty citations to date.The equivalent problem of laminar flows in the axisymmetric geometry on the other hand remains largely uninvestigated and is untested as a bifurcation problem. The primary objective of the planned investigation will be to establish the precise nature of the instability and obtain quantitative agreement with the results of a parallel numerical bifurcation study.We will also seek possible connections with modern research on finite amplitude states in pipe flow, if time permits.