The lifetimes of injected jet puffs are used to determine the critical point at which turbulent pipe flow is sustained.

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch.

Taming Turbulence: When fluid flows through a pipe, if the inertial forces are increased or the viscosity is decreased, the flow will become increasing noisy and will shift from being laminar to turbulent. Turbulence can be triggered by roughness in the pipe or other irregularities, which cause local eddies that grow into full-scale disruption of the otherwise smooth flow. Hof et al. (p. 1491 ; see the Perspective by McKeon ) show that a continuous turbulent eddy, downstream, eliminates the growth of upstream disturbances and can prevent the overall flow from becoming turbulent. Unlike many other control methods, the energy cost for implementing this strategy is less than the benefit gained by maintaining a laminar flow.

Symmetry reduction by the method of slices is applied to pipe flow in order to obtain a quotient of the streamwise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave solutions reduce to equilibria, and all relative periodic orbits reduce to periodic orbits. Projections of these solutions and their unstable manifolds from their infinite-dimensional symmetry-reduced state space onto suitably chosen two- or three-dimensional subspaces reveal their interrelations and the role they play in organizing turbulence in wall-bounded shear flows. Visualizations of the flow within the slice and its linearization at equilibria enable us to trace out the unstable manifolds, determine close recurrences, identify connections between different travelling wave solutions and find, for the first time for pipe flows, relative periodic orbits that are embedded within the chaotic saddle, which capture turbulent dynamics at transitional Reynolds numbers.