In this section we present two-dimensional time series extracted from the
first 50 timesteps of the volumetric data set. Movies of the processed
x-z data slices at y /
= 0.37, 0.74 and 1.12 (y+ = 111, 222, 333) have been generated. In addition to the movies, the individual images of the time series have been assembled into montages, so that the convection and evolution of the scalar structures may be tracked. The time series and montages may be accessed using the following links:
y /
= 0.37 (y+ = 111):
Movie 1 (MPEG 196 Kbytes)
Montage 1 (GIF 306 Kbytes)
y /
= 0.74 (y+ = 222):
Movie 2 (MPEG 272 Kbytes)
Montage 2 (GIF 289 Kbytes)
y /
= 1.12 (y+ = 333):
Movie 3 (MPEG 170 Kbytes)
Montage 3 (GIF 136 Kbytes)
These levels were chosen for presentation in order to deduce the relationship between ejections of fluid from the near-wall region and large-scale structure in the outer portion of the boundary layer. The data at y /
= 0.37 (y+ = 111) were examined in order to identify brightly-dyed fluid that was in the process of migrating from near the wall well into the middle regions of the boundary layer. In this respect, the data at this level were used as the spatial threshhold in a visually-based conditional sampling technique. Once it was determined that near-wall fluid had passed through the interrogation plane, the candidate ejections and nearby scalar structures were tracked from the near-wall region into the outer layers. Data at y /
= 1.12 (y+ = 333) are shown to reveal the large-scale orientation in the outer part of the boundary layer associated with the near-wall motions. The level y /
= 0.74 (y+ = 222) is shown to bridge these two levels, and to show the connectedness of the outer layer structure to the inner layer motions.
There are numerous large-scale structures evident in the time series, with
significant presence of dye-tagged structures in the outer region, at y /
= 1.12. There are a number of structures that might be inferred to be the cross-sections of vortex loops, and there is a clear diagonal orientation of the outer layer structure in timesteps 34-40. The outer layer structures are connected, though in a complex way, to the inner layer structures. In the middle levels of the boundary layer (y /
= 0.74), the scalar structures become more spatially extensive, with complex
inter-connections across the streamwise and spanwise extent of the images. Of particular interest are the final frames of the movie at this level (timesteps 42-50), which contain a scalar structure with the classic "mushroom" cross-section characteristic of a vortex loop.
Nearer to the wall (y /
= 0.37), brightly dyed structures in the form of streamwise streaks are
apparent. The streaks themselves are quite active, undergoing significant deformation in time. In many cases, the streaks exhibit sinuous motion; for example, there is a sinuous streak visible in the center of timestep 36, which is directly beneath a large-scale, streamwise oriented structure at y /
= 0.74. This structure, inclined slightly to the freestream, appears to be directly connected to the diagonal array of structures at y /
= 1.12 mentioned above. Although the middle and outer layer structures maintain their identity as they convect downstream, the bright streak is deformed stongly within a few timesteps. Some of the streaks appear to grow or shrink in size as they convect downstream, which is consistent with motion normal to the interrogation plane; bright fluid being ejected from the near-wall region would first appear to grow and then shrink as it passed through a given plane. As motion towards the wall would create the same effect, the data were resampled into x-y planes to definitively establish the direction of motion.
The image stacks were resampled in x-y planes at twenty z-locations to examine the behavior of the near-wall streaks. Three of these time series may be viewed as MPEG movies and as montages (z /
= 0.25, 0.92 and 1.59; z+ = 75, 275, 475) by using the following
links:
z /
= 0.25 (z+ = 75):
Movie 4 (MPEG 94 Kbytes)
Montage 4 (GIF 128 Kbytes)
z /
= 0.92 (z+ = 275):
Movie 5 (MPEG 77 Kbytes)
Montage 5 (GIF 136 Kbytes)
z /
= 1.59 (z+ = 475):
Movie 6 (MPEG 94 Kbytes)
Montage 6 (GIF 136 Kbytes)
In the resampled x-y slices, the skewed shape of the corrected image stack is manifested as curved boundaries on the left and right margins of the individual images. Bright fluid was seen to be ejected from the near-wall region in all the x-y time series, and in all cases the ejections appeared to be closely related to the passage of large-scale structure in the outer portion of the boundary layer.
As a case in point, consider timesteps 1-12 of the x-y time series at z /
= 1.59. In timestep 1, there is an area of bright fluid near the wall, beneath an inclined structure in the outer layer with the general appearance of a vortex loop (in cross section). As time progresses, the bright fluid lifts away from the wall in two main packets, in the manner to be expected by the induced velocity field of a horseshoe vortex. The ejection is followed by a series of downstream-leaning structures in the outer layer. Referring back to the x-z data at y /
= 1.12, the apparent vortex loop is visible in timestep 1 only as a small circular structure at mid-span, following a much more extensive structure. The small circular structure grows rapidly in time; examination of the x-y time series shows that the loop is moving away from the wall, and begins to lean further downstream and merge with the larger structure. Note that the downstream-leaning structures following the ejection do not share a common "signature" in the x-z plane at this level, although there are indications of mushroom-type cross-sections at y /
= 0.74. At y /
= 0.37, the bright streak is not yet visible in timestep 1, as it is too near the wall. In timestep 4, the bright fluid enters this level as two separate regions, and by timestep 10, has convected to the downstream end of the image, and is extensively distributed in both the streamwise and the spanwise directions. The highly complex nature of the scalar structures, especially the difficulty in identifying single structures with significant three-dimensionality through examination of two-dimensional visualizations led to the use of volumetric imaging.
The stereoscopic time series were calculated with viewpoints indicated in
Figure 10
. The first was from a viewpoint directly overhead, looking down on
the volumes in the negative y-direction. In this view, the flow is from bottom
to top, parallel to the viewing plane. The second time-series was from an
oblique viewpoint. For the stereoscopic renderings, a grid has been added to
the image stacks to represent the surface of the flat plate in order to orient
the viewer, to give a spatial reference for the location of structures, and to
impart a sense of scale (grid spacing 0.5
).
A third stereoscopic time series was generated with the component volumes
split along an x-y plane, and moved apart in the spanwise direction. A
resampled image was generated along the splitting plane and inserted between
the two halves (the x-y images correspond closely to the two-dimensional time series, z /
= 1.59 above). The volume is viewed from a viewpoint inclined to the y-axis,
with flow from left to right. The addition of the x-y slice helps to give a
clear indication of the motion of the near-wall streaks relative to the
large-scale structure in the outer layer. In this time series, the wall grid spacing is 1
.
In order to observe the stereoscopic effect, it is necessary to view the time series with red/blue or red/green anaglyph glasses (red lens over left eye). Various types of anaglyph glasses are available commercially from: Reel 3D Enterprises. Alternatively, the authors have a limited supply of cardboard-frame glasses which will be distributed upon request. The three stereoscopic time series can be accessed using the following links:
Overhead View: Movie 7a(Full Size) (MPEG 655 Kbytes) Movie 7b(Half Size) (MPEG 357 Kbytes)
Oblique View: Movie 8a(Full Size) (MPEG 876 Kbytes) Movie 8b(Half Size) (MPEG 417 Kbytes)
Split Volumes: Movie 9a(Full Size) (MPEG 1241 Kbytes) Movie 9b(Half Size) (MPEG 417 Kbytes)
The diagonal organization of the large-scale outer layer structure noted in the x-z data above is seen in the overhead view (timesteps 34-40). In addition, there is clearly diagonal organization in timesteps 6-14, which was only partly apparent in the x-z data alone. These diagonal arrays of structures were generally accompanied by coordinated ejections of near-wall fluid from locations distributed spanwise beneath the outer layer structure.
The mushroom cross-section noted in timesteps 42-50 of the x-z data at y /
= 0.74, appears to be part of a distorted, streamwise oriented vortex loop (in the center of timestep 45 in the overhead view). There is a bright streak faintly visible beneath the structure in the overhead view; from subsequent examination of the x-z and x-y time series, the streak was seen to be undergoing an ejection process similar to that in timesteps 1-12 above.
1. Introduction
2. Acquisition and Visualization of the Volumetric Data Set
3. Results: Two- and Three-Dimensional Visualizations
Next Section: 4. Discussion