Exploring the Phase Space of Transitional Pipe Flow

Well-controlled experiments in pipe flow began at least as early as those by Reynolds himself (1883).  Forming a model for transition to turbulence, however, has taken a long time to develop.  The first nonlinear solutions to the equations governing fluid flow in a pipe were discovered only 10 years ago (Faisst and Eckhardt 2003), but since this time our understanding of the underlying nonlinear dynamics has developed thick and fast.  I begin by reviewing some of the progress that followed the discovery of travelling wave solutions.  For the future, it will be necessary to isolate periodic orbits, which will require some development in computational methodology.