Transition to Turbulence in Pipe Flow

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