The structure of energy-containing turbulence in the outer region of a zero-pressure-
 gradient 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 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 of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.

Vortex organization in the outer region of the turbulent boundary layer

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.

Hairpin vortex organization in wall turbulencea)

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume The technique makes use of several simultaneous views of the illuminated particles and their 3D reconstruction as a light intensity distribution by means of optical tomography The technique is therefore referred to as tomographic particle image velocimetry (tomographic-PIV) The reconstruction is performed with the MART algorithm, yielding a 3D array of light intensity discretized over voxels The reconstructed tomogram pair is then analyzed by means of 3D cross-correlation with an iterative multigrid volume deformation technique, returning the three-component velocity vector distribution over the measurement volume The principles and details of the tomographic algorithm are discussed and a parametric study is carried out by means of a computer-simulated tomographic-PIV procedure The study focuses on the accuracy of the light intensity field reconstruction process The simulation also identifies the most important parameters governing the experimental method and the tomographic algorithm parameters, showing their effect on the reconstruction accuracy A computer simulated experiment of a 3D particle motion field describing a vortex ring demonstrates the capability and potential of the proposed system with four cameras The capability of the technique in real experimental conditions is assessed with the measurement of the turbulent flow in the near wake of a circular cylinder at Reynolds 2,700

Tomographic particle image velocimetry

Numerical experiments on modified turbulent channels at moderate Reynolds numbers are used to differentiate between several possible regeneration cycles for the turbulent fluctuations in wall-bounded flows. It is shown that a cycle exists which is local to the near-wall region and does not depend on the outer flow. It involves the formation of velocity streaks from the advection of the mean profile by streamwise vortices, and the generation of the vortices from the instability of the streaks. Interrupting any of those processes leads to laminarization. The presence of the wall seems to be only necessary to maintain the mean shear. The generation of secondary vorticity at the wall is shown to be of little importance in turbulence generation under natural circumstances. Inhibiting its production increases turbulence intensity and drag.

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The autonomous cycle of near-wall turbulence

We analyse the currently popular vortex identification criteria that are based on point-wise analysis of the velocity gradient tensor. A new measure of spiralling compactness of material orbits in vortices is introduced and using this measure a new local vortex identification criterion and requirements for a vortex core are proposed. The inter-relationships between the different criteria are explored analytically and in a few flow examples, using both zero and non-zero thresholds for the identification parameter. These inter-relationships provide a new interpretation of the various criteria in terms of the local flow kinematics. A canonical turbulent flow example is studied, and it is observed that all the criteria, given the proposed usage of threshold, result in remarkably similar looking vortical structures. A unified interpretation based on local flow kinematics is offered for when similarity or differences can be expected in the vortical structures educed using the different criteria.

On the relationships between local vortex identification schemes

A model of the dynamic physical processes that occur in the near-wall region of a turbulent flow at high Reynolds numbers is described The hairpin vortex is postulated to be the basic flow structure of the turbulent boundary layer It is argued that the central features of the near-wall flow can be explained in terms of how asymmetric hairpin vortices interact with the background shear flow, with each other, and with the surface layer near the wall The physical process that leads to the regeneration of new hairpin vortices near the surface is described, as well as the processes of evolution of such vortices to larger-scale motions farther from the surface The model is supported by recent important developments in the theory of unsteady surface-layer separation and a number of `kernel' experiments which serve to elucidate the basic fluid mechanics phenomena believed to be relevant to the turbulent boundary layer Explanations for the kinematical behaviour observed in direct numerical simulations of low Reynolds number boundary-layer and channel flows are given An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper mathematical description of high Reynolds number flow

On the dynamics of near-wall turbulence

Ultimately, control of turbulent shear flows must center around the selected modification of the flow structure of the turbulence, or the conditions which gives rise to the flow structure. Consequently, in order to develop rational methods of control, it is necessary to understand the basic dynamical elements of the turbulent boundary layer. In this paper, a model of the turbulent boundary layer, based upon a series of complimentary computational and experimental studies, is described in which the hairpin vortex is suggested to be a basic flow structure of boundary-layer turbulence. The paper discusses the development of single hairpin vortices, how such vortices interact with a shear flow and with one another, and how they interact with the flow near a wall to produce new vortices through a viscous interaction. It is demonstrated how key features of turbulent flow structure (e.g. low-speed streaks, bursting, pockets, etc.) can be explained in terms of the motion and effects of convecting hairpin vortices. The implications of this model in reducing drag are also discussed.

A. H. Haidari

Papers

On the dynamics of near-wall turbulence

Hairpin Vortices in Turbulent Boundary Layers: The Implications for Reducing Surface Drag

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