State Space Properties of Transitional Pipe Flow

Transition to turbulence in pipe flow has puzzled scientists since thestudies of Hagen, Poiseuille and, most prominently, OsborneReynolds in the nineteenth century. Much of the difficulty in under-standing the transition is connected with the linear stability of thelaminar flow, which implies that a fully nonlinear analysis is required. In this work we apply methods from dynamical systems theory andnonlinear dynamics to explore the system's state space close to thetransition. We analyze lifetime distributions of turbulent signals indomains of different lengths and study their variation with Reynoldsnumber Re. Lifetimes are found to follow the exponential distributiontypical of a chaotic saddle, with a characteristic time that increasesrapidly with Re. The absence of a divergence in the lifetimes sug-gests that turbulence remains transient even at high flow velocities. The coherent states which appear transiently during the turbulentevolution are characterized. Correlation functions for their detectionare introduced and their statistical properties extracted. They can bedetected during more than 20% of the time. Finally, the stability border between laminar and turbulent dynamics isstudied. Using a specially tailored tracking algorithm the dynamicsbetween laminar and turbulent motion can be followed and an invari-ant dynamical object whose stable manifold separates the laminarfrom turbulent dynamics is identified. This object should provide use-ful for further studies on triggering turbulence or relaminarization.