Transition to Turbulence in Pipe Flow

Since the seminal studies by Osborne Reynolds in the nineteenth century, pipe flow has served as a primary prototype for investigating the transition to turbulence in wall-bounded flows. Despite the apparent simplicity of this flow, various facets of this problem have occupied researchers for more than a century. Here we review insights from three distinct perspectives: (a) stability and susceptibility of laminar flow, (b) phase transition and spatiotemporal dynamics, and (c) dynamical systems analysis of the Navier-Stokes equations. We show how these perspectives have led to a profound understanding of the onset of turbulence in pipe flow. Outstanding open points, applications to flows of complex fluids, and similarities with other wall-bounded flows are discussed.

Automated summary

Since Reynolds' seminal studies in the nineteenth century, pipe flow has been a primary prototype for studying the transition to turbulence in wall-bounded flows. Despite its apparent simplicity, researchers have been studying various aspects of this problem for over a century. This review provides insights from three different perspectives: stability and susceptibility of laminar flow, phase transition and spatiotemporal dynamics, and dynamical systems analysis of the Navier-Stokes equations. The review highlights how these perspectives have contributed to a profound understanding of the onset of turbulence in pipe flow, as well as discussing open points, applications to complex fluid flows, and similarities with other wall-bounded flows.