The significance of coherent flow structures for the turbulent mixing ...

7.5 Properties of coherent velocity structures
accompanied by structural differences in the successively recorded particle image patterns due
to inhomogeneous displacement which leads to a broadened shape of the correlation peak.
In case of ªSÔÔ the correlation shown in figure 7.16 no peaks can be observed ×_ì » ¬\¯
with
for the near-wall correlations due to the small size. However, if the graphs ×_ì » ¬
¿ °
for to 30
are considered, the movement of ª^ÔËÔ the correlation through the second measurement plane
can be nicely seen. ªSÙ¥Ù The correlation, on the other hand, shown in figure 7.17, reveals peaks
for all wall locations and temporal separations but the height of the correlation is always lower
with respect to figure 7.15. This implies that the span-wise motion is less stable according
to the structures represented by ªS·· the correlation. Another interesting feature visible in
figure 7.17 is the strong increase of ¹¥» the location of the maximum as a function of the time
separation. This is fully consistent with figure 5.7 on page 82. Only the shift towards smaller
wall locations ×_ìË»A¬â¯ at is surprising. However, this is a necessary consequence of the
order of correlation. In the present case a line ¹¥» at was extracted from the results in the
down stream plane and shifted along the field measured upstream. This implies that the the
maximum appears at ¹ » smaller locations until the maximum of the correlation in figure 5.7
passes the down stream measurement plane. The same holds for the other correlations.
7.5 Properties of coherent velocity structures
7.5.1 Loop-shaped structures
In this section the significance of the stream-wise vortices for the turbulent mixing in wallbounded
flows will be examined and the existence of the loop-shaped structures, highlighted
on page 6 will be validated. Loop-shaped structures can be best detected in the ¹¥Ã -plane of
a turbulent boundary layer (wall-normal span-wise) because these structures are inclined in
stream-wise direction [13, 28, 49]. Their footprint is a counter-rotating vortex pair with a
strong velocity component being normal to the wall between the vortex pair as indicated in
figure 1.3. In planes which are parallel to the wall (stream-wise span-wise) these loops appear
as counter-rotating vortices with a typical out-of-plane motion between the vortex cores as
illustrated in section 6.4. Thus the basic turbulent mixing process associated with this hairpin
vortex is the transfer of low-speed fluid from the wall and high speed fluid towards the wall
such that /. äŸã becomes positive on average. Since the early flow visualisation experiments
performed in a laminar boundary layer, it is generally accepted that looped shaped structures
result from a progressive deformation of a span-wise vortex with an initial three dimensional
disturbance, as shown in the lower figure on page 6. The inclination of the vortices on the other
hand is explained by means of self-induction of the developing vortex loop, and the stretching
is assumed to be a result of the strong velocity gradients present in boundary layer flows [31].
However, it is still a point of discussion if these loop-shape structures are the predominant
coherent velocity regions in turbulent boundary layers which are mainly responsible for the
turbulent mixing. In the past, many attempts have been made in order to validate the existence
and significance of these structures. The continuing discussion implies that no convincing
experimental or theoretical evidence could be presented. As the signature of these coherent
structures is a counter-rotating vortex pair with a strong velocity component normal to the
wall between the vortex pair, as indicated in figure 1.3, they can be easily identified when the
measurement plane is perpendicular to the wall and mean flow direction. Figure 7.18 shows
two independent velocity fields where many well developed vortex pairs can be observed in
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