Recent progress in understanding the transition to turbulence in a pipe

The problem of understanding the nature of fluid flow through a circular straight pipe remains one of the oldest problems in fluid mechanics. So far no explanation has been substantiated to rationalize the transition process by which the steady unidirectional laminar flow state gives way to a temporally and spatially disordered three-dimensional (turbulent) solution as the flow rate increases. Recently, new travelling wave solutions have been discovered which are saddle points in phase space. These plausibly represent the lowest level in a hierarchy of spatio-temporal periodic flow solutions which may be used to construct a cycle expansion theory of turbulent pipe flows. We summarize this success against the backdrop of past work and discuss its implications for future research.