Figure 1 and Figure 2 are visualizations of coherent structure in turbulent boundary layers by Falco (1977) and by Cantwell et al. (1978). In Figure 1 , the boundary layer is visualized in the x-y plane by illuminating oil vapor with a light sheet. The region marked with the vapor is highly complex, and consists of numerous small scale structures superimposed on large-scale turbulent "bulges" (LSM). The LSM are inclined in the downstream direction and extend from the wall into the outer layer, often well past the mean edge of the boundary layer. The LSM are delineated by a contorted interface between the marked and unmarked fluid, with regions of unmarked, non-rotational fluid extending in deep valleys between the LSM, almost to the floor of the boundary layer. Of particular interest are the "backs" of the LSM; the upstream interface between the turbulent fluid within the LSM and the non-rotational fluid behind it. The backs of the LSM are highly active three-dimensional shear layers with superimposed small-scale structures.
The characteristic "streaky structure" in the near-wall region of the boundary
layer is clearly shown in
Figure 2
, where the flow has been visualized with
aluminum particles suspended in water. The x-z plane near the wall is seen to
be densely populated by long, streamwise-oriented streaks which "meander" in
the spanwise direction. The streaks have a mean spanwise spacing of
~ 80-100 over a wide range of Reynolds number. The simultaneous side view (x-y
plane) in the figure shows that the near-wall streaks exist beneath the
large-scale structure in the outer layer, and the wide range of structure size
in the boundary layer is clearly revealed. The near-wall streaks are a
ubiquitous feature of turbulent boundary layers (Kim et al.,
1971).
Early investigation of the near-wall streaks identified them as streamwise
regions of low-speed fluid (relative to the mean), and revealed their
participation in the "bursting cycle". A turbulent burst begins when a
low-speed streak is perturbed and begins to oscillate. The sinuous
oscillations increase in magnitude and the streak gradually lifts up, away from
the wall. A portion (or portions) of the streak is then rapidly "ejected" from
the near-wall region into the outer portion of the flow. The ejection is a
strong contributor to the Reynolds stress; the low speed fluid (-u') moving
away from the wall (+v') creates a positive product, -
.
From continuity considerations, the ejection of near-wall fluid is followed by
an inrush of high-speed fluid from farther out in the boundary layer. This
"sweep" motion constitutes another positive contribution to the Reynolds stress
(+u', -v') (Corino and Brodkey (1969)). Taken together, the ejection/sweep
sequence is termed a turbulent burst (this definition will be used here
although other definitions of bursting have been employed elsewhere).
Estimates of the contribution of the bursting process to the production of
turbulent stress vary, but it is generally considered to be responsible for
60-80% of the total (see e.g. Grass (1971), Kim et al. (1971)).
The source of the initial perturbation which triggers the oscillation of the near-wall streaks is an open question. Brown and Thomas (1977) showed that the passage of large-scale structures in the outer layer can create conditions in which streamlines in the near-wall region become curved, so that a Taylor-Görtler-type instability is possible. Similar explanations of the instability based on the influence of outer-layer structures through an imposed pressure field have been proposed by, for example, Kovasznay et al. (1970), Rao et al. (1971), and Blackwelder (1978). In contrast, Offen and Kline (1974) and Offen and Kline (1975) suggest that the instability is imposed by localized sweep motions from the logarithmic region near the wall, which are caused by earlier bursting events upstream.
There have been many attempts to link the near-wall bursting cycle to
structures in the outer portion of the boundary layer. Consequently, the
large-scale structure in that region has been the subject of numerous
investigations. The downstream-leaning "horseshoe vortex" was first proposed
by Theodorsen (1955) as the basic structure of all turbulent shear flows. Head
and Bandyopadhyay (1979), (1981) found indications of the existence of such
vortices through the use of spanwise laser sheets inclined ±45
to the streamwise direction, i.e. aligned parallel and normal to the plane of
the proposed vortex structure. From their visualizations, Head and
Bandyopadhyay made the important observation that the spanwise separation of the "legs" of the horseshoe vortices remains approximately constant and equal to the mean spanwise spacing of the low-speed streaks (
~ 100) over a range of Reynolds number. As the thickness of the boundary layer (in viscous units) increases with Reynolds number, the aspect ratio of the horseshoe vortices increases. Additional visual evidence for the prevalence of horseshoe vortices (in the form of ejected dye loops) is given in the visualizations of Antonia et. al. (1989). Assemblies of horseshoes have been related to the turbulent bulges; Head and Bandyopadhyay proposed that the LSM are in fact a dense collection of horseshoe vortices, with a range of heights such that they line up to create the observed size and shape of the LSM. MacAuley and Gartshore (1991) put forth a somewhat more refined model, which accounts for many aspects of the observed variation of the LSM with Reynolds number. Kline and Robinson (1990) combined the results from visual and statistical studies over a wide range of Reynolds number to create a general taxonomy of the types of coherent structures found in turbulent boundary layers. Their survey represents an extensive investigation of the literature on turbulent boundary layers, and includes the structures already mentioned (i.e. ejections, sweeps, low-speed streaks, horseshoe vortices, LSM) as well as features of the velocity field (strong internal shear layers in the near-wall region, and 
-scale discontinuities in streamwise velocity).
As with a majority of models of boundary layer structure, little attempt is
made to represent the global spanwise arrangement of either the small or
large-scale coherent structures. Acarlar and Smith (1984) noted the formation
of horseshoe vortices in the near-wall bursting cycle. Coles and Barker (1975), Perry et al. (1981), and Savas and Coles (1985) examined the structure of turbulent spots as a
possible "building block" of turbulent boundary layer structure. The sequence
of events leading to the formation of a turbulent spot in terms of vortex
filaments is illustrated in
Figure 3
. Of particular interest is the final form
of the spot, Figure 3c, in which the tips of the deformed vortex filaments are
arranged in a diagonal checker-board array, within the heart-shaped outline of
the turbulent spot. Perry et al. found that the spacing of wall streaks
beneath the spot was approximately
~ 80-105, in support of the connection between spot structure and turbulent
boundary layers.
The possibility of detecting such a spatial arrangement of structures in the boundary layer influenced the design of the experiment carried out here; the flow volume examined was chosen to give a large field of view in the spanwise and streamwise directions in order to detect complete, inclined horseshoe vortices, and the desire to establish (if possible) their general physical characteristics and their spatial relationship with each other and the near-wall streaks found in the boundary layer.
The highly complex nature of the three-dimensional, time-evolving velocity and vorticity fields suggested the use of volumetric imaging of a passive scalar to reveal the spatial and temporal characteristics of the large-scale structure. As noted by Brown and Thomas (1977) (among others), the essentially three-dimensional character of boundary layer motions makes unambiguous detection of a complex process such as the bursting cycle from a fixed measurement station difficult. Part of the problem is no doubt due to the fact that more than one fluid packet may be ejected from a given low speed streak, so the identification of a single bursting event becomes ambiguous (Luchik and Tiederman (1987)). Additionally, the different detection methods employed add to the confusion (e.g. visual identification, quadrant analysis, conditional sampling, see Bogard and Tiederman (1986)). In this respect, visual studies have an advantage since an overall view of the flowfield may be used to judge what part of a turbulent motion is being investigated in a given realization. Extending this concept, it is logical to assume that a complete three-dimensional visualization of the flowfield is more appopriate for revealing the complex spatial interrelationships in the boundary layer. A full volumetric view may be subsampled into standard two-dimensional renderings, but knowledge of the entire volume may be necessary in order for the 2-D sampling to effectively reveal the important dynamics.
To this end, a time series of 1600 consecutive volumes of boundary layer data were collected. The volumes were collected in the form of image stacks; each volume was composed of 20 x-z images of scalar intensity, uniformly separated in the y-direction. Initially, stereoscopic renderings of a 50-volume subset of the complete time series were generated, in order to gain an overall picture of the structures present, and to guide subsequent analysis. The stereoscopic views were in the form of "anaglyph stereograms"; two separate two-dimensional projections of a volume were generated from viewpoints corresponding to human binocular vision. The separate views were colored, combined, and viewed on the computer screen with colored glasses. The glasses act as filters, causing the correct view to be presented to each eye of the viewer. The optical synthesis of the two views results in the stereoscopic effect.
Preliminary evidence of ejection events beneath large-scale structures in the stereoscopic views led to resampling the data set in various two-dimensional planes. x-y time series were extracted from the volumetric data at twenty spanwise locations, and indicated that ejection events were indeed occurring. The use of the two visualization methods to examine the structure and dynamics of the boundary layer was an iterative process. For example, if a stereoscopic visualization suggested the occurrence of an ejection-type event, the given volume was resliced in various planes to investigate the time-dependent behavior of the near-wall fluid and its spatial relationship to neighboring outer-layer structure. There was frequent reference back to the original x-z data slices to confirm any inferences drawn.
1. Introduction
Next Section: 2.Acquisition and Visualization of the Volumetric Data Set
3. Results: Two- and Three-Dimensional Visualizations
4. Discussion