Vortex organization in the outer region of the turbulent boundary layer

Abstract

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...

Three-dimensional structure of a low-Reynolds-number turbulent boundary layer

“…Considering the stereoscopic views of figure 6, it is apparent that, although complicated, the data set is populated by a relatively small number of large-scale vortical structures. This is consistent with the observation of Adrian et al (2000) that, at low Reynolds numbers, packets (bulges) contain 2-3 hairpins. The resliced images, because they do not incorporate the spanwise dimension, sometimes cut a single contorted structure into several 'pieces' which may not appear to be connected.…”

“…Strong confirmation of the statistical significance of coherent hairpin packets has been provided by Marusic (2001) and Christensen & Adrian (2001). Of particular relevance to the present project is the observation by Adrian et al (2000) that at low-Reynolds-number, such packets contain 2-3 vortices, and that the number of vortices and the range of scales present increases with increasing Reynolds numbers. Praturi & Brodkey (1978) recognized the need to study the three-dimensional structure of the turbulent boundary layer in order to understand its mechanisms.…”

“…An elegant conceptual model of nested packets of hairpins (or fragments thereof) growing from the wall was developed. This model is illustrated in figure 25 of Adrian et al (2000). The resulting hierarchy of motions, with changes of scale as a result of vortex pairing, is in the same spirit as the mechanism of wall turbulence proposed by Perry & Chong (1982).…”

Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

“…It is also seen that the vortex heads convect with slightly different velocities, what will result in the interaction or merging of the vortices at a later stage. Furthermore, the vortices are of approximately the same size and do not appear to be aligned along a 12 • -20 • slope with the wall as in Head & Bandyopadhyay (1981) or in the logarithmic layer vortex packets observed in Adrian et al (2000). Near the top of the volume at y/δ = 0.45 the velocity direction and magnitude is very irregular, which may indicate the presence of (vortical) flow structures just above this packet.…”

“…Therefore a detail taken from the volume of figure 2 is enlarged and shown in figure 4(a). Over the low-speed zone the heads from a series of streamwise aligned hairpin (or arch) vortices are visible, which can be considered a hairpin packet (Adrian et al 2000). Note that the arch located at x/δ = 1.7 is partially contained in the lowspeed zone and may therefore appear fragmented due to the blue isosurface blocking the view.…”