The structure of energy-containing turbulence in the outer region of a zero-pressuregradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 < Re θ < 6845 show that the boundary layer is densely populated by velocity fields associated with hairpin vortices. (The term 'hairpin' is here taken to represent cane, hairpin, horseshoe, or omega-shaped vortices and deformed versions thereof, recognizing these structures are variations of a common basic flow structure at different stages of evolution and with varying size, age, aspect ratio, and symmetry.) The signature pattern of the hairpin consists of a spanwise vortex core located above a region of strong second-quadrant fluctuations (u < 0 and v > 0) that occur on a locus inclined at 30-60 • to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12 • , and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent 'bursts', and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature 2 R.of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases. IntroductionThe structure of the turbulent wall layer continues to be one of the outstanding unsolved q...

The evolution of a single hairpin vortex-like structure in the mean turbulent field of a low-Reynolds-number channel flow is studied by direct numerical simulation. The structure of the initial three-dimensional vortex is extracted from the two-point spatial correlation of the velocity field by linear stochastic estimation given a second-quadrant ejection event vector. Initial vortices having vorticity that is weak relative to the mean vorticity evolve gradually into omega-shaped vortices that persist for long times and decay slowly. As reported in Zhou, Adrian & Balachandar (1996), initial vortices that exceed a threshold strength relative to the mean flow generate new hairpin vortices upstream of the primary vortex. The detailed mechanisms for this upstream process are determined, and they are generally similar to the mechanisms proposed by Smith et al. (1991), with some notable differences in the details. It has also been found that new hairpins generate downstream of the primary hairpin, thereby forming, together with the upstream hairpins, a coherent packet of hairpins that propagate coherently. This is consistent with the experimental observations of Meinhart & Adrian (1995). The possibility of autogeneration above a critical threshold implies that hairpin vortices in fully turbulent fields may occur singly, but they more often occur in packets. The hairpins also generate quasi-streamwise vortices to the side of the primary hairpin legs. This mechanism bears many similarities to the mechanisms found by Brooke & Hanratty (1993) and Bernard, Thomas & Handler (1993). It provides a means by which new quasi-streamwise vortices, and, subsequently, new hairpin vortices can populate the near-wall layer.

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Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.