Packets of hairpin-shaped vortices and streamwise counter-rotating vortex pairs (CVPs) appear to be key structures during the late stages of the transition process as well as in low-Reynolds-number turbulence in wall-bounded flows. In this work we propose a robust model consisting of minimal flow elements that can produce packets of hairpins. Its three components are: simple shear, a CVP having finite streamwise vorticity magnitude and a two-dimensional (2D) wavy (in the streamwise direction) spanwise vortex sheet. This combination is inherently unstable: the CVP modifies the base flow due to the induced velocity forming an inflection point in the base-flow velocity profile. Consequently, the 2D wavy vortex sheet is amplified, causing undulation of the CVP. The undulation is further enhanced as the wave continues to be amplified and eventually the CVP breaks down into several segments. The induced velocity generates highly localized patches of spanwise vorticity above the regions connecting two consecutive streamwise elements of the CVP. These patches widen with time and join with the streamwise vortical elements situated beneath them forming a packet of hairpins. The results of the unbounded (having no walls) model are compared with pipe and channel flow experiments and with a direct numerical simulation of a transition process in Couette flow. The good agreement in all cases demonstrates the universality and robustness of the model.

The vast majority of experiments on transition in pipe flow have been concerned with high-amplitude disturbance (of »10% of the centerline velocity) at Reynolds numbers around 2000 and above. In this experimental study, we concentrate on the transition process in water pipe flow where the level of the disturbance is at least an order of magnitude smaller. We follow the sequence of transitional events while varying gradually the disturbance level from a laminar state to an almost fully turbulent one, using flow visualization, pressure-drop and hot-wire measurements. This is accomplished by injection of a very small diameter jet perpendicular to the main stream at a controllable flow rate, in a downstream distance where the flow is approximately fully developed. The injection flow rate normalized by the main stream rate is of O 0.001 ( ). With increasing injection flow rates the friction coefficient (λ) increases along with changes in the nature of the flow structures. The transition begins with the generation of a streamwise counter-rotating vortex pair, followed by the formation of a packet of hairpins and their breakdown. As the injection level is increased, the separation distance between two consecutive bursts (wavelength) decreases and the breakdown to turbulence begins further upstream and consequently the value of the friction coefficient λ increases. Above and below a certain threshold of the disturbance level, turbulence is either triggered or the flow is relaminarized, respectively. Finally, it is established that the evolution of the packet of hairpins is a key element during this transition scenario, and is well explained by the three-element model recently proposed by Cohen et al (2014).