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

6 Investigation of the xz-plane
appear as elongated and twisted low-speed regions, sometimes 1000 wall-units in length and
on average 30 wall-units in width, with a span-wise periodicity of about 100 wall-units. The
dependence on the Reynolds number according to [25] and the exact wall distance is still a
point of discussion. It has been assumed that hairpin-vortices induce these low-speed region
between the inclined legs while they are travelling downstream but a convincing experimental
proof is still missing [46]. Some authors [7, 54] proposed that the low-speed streaks are
generated between pairs of relatively weak, but highly elongated stream-wise vortices, similar
to the legs of the hairpin model, but the existence of these vortices is still an open and
controversial question [94, 44]. Other authors assume that the streaks might originate from a
weak vertical oscillation of the fluid layers which produces strong oscillations in stream-wise
direction [66]. However, a general agreement based on the experimental and numerical results
could not be achieved [14]. From flow visualisation experiments it is evident that the lowspeed
streaks play a dominant role in a sequence of events referred to as bursting phenomena.
Kline observed in the near-wall region of a turbulent boundary layer that extended low-speed
flow structures, which move away from the wall, start to oscillate and burst finally after a certain
life time into small scale turbulence [58]. The bursting of these low-speed structures may
be related to an inflectional instability which is going to develop in the low-speed regions.
This Kelvin-Helmholtz instability may cause an ejection of local vortices above the streaks
which is associated with the production of turbulence. However, another explanation is that
the ejection of low-speed fluid from the wall is associated with flow structures which transfer
momentum towards the wall (sweeps or inrush bursts), located directly upstream of the region
where the ejection takes place [84]. The connection between the bursting phenomenon near
the wall and the large scale motion in the outer part is one of the key questions. In the vertical
plane, the footprint of the sweep-streak interaction would appear as a near-wall shear-layer as
discussed above, but of smaller extent in both wall-normal and stream-wise directions. From
what has been said, it is obvious that the reality and relevance of the proposed models require
detailed experimental information of the spatio-temporal flow structure in the near wall region.
Figure 6.21 shows two characteristic velocity fields measured in the Î9Ï -plane at ­® ¿ ª¥À .
The flow direction is from left to right and the local mean velocity ¦
is subtracted from the
instantaneous velocity ¦ field to display the turbulent velocity § ¿ ¦ ¦ fluctuations and
. Predominant structures are the elongated flow regions that convect downstream with approximately
half the local mean velocity, indicated by the vectors going from right to left. The
¾
shape, extent and span-wise separation of these slightly tilted flow regions is in quantitative
agreement with the literature [86], but it should be noted that the instantaneous values of the
geometrical properties can deviate strongly from the averaged ones, presented in figure 6.6.
The width of the structures visible in figure 6.21 for example varies between 20 and 100 wall
units, but also broader streaks can be found. Another important property of the streaks is their
extent in wall-normal direction as the statistical variation of their height is responsible for
the increasing separation on average between the streaks with increasing wall distance. This
can be concluded from the velocity fields in figure 6.22 which were measured simultaneously
with the vector fields presented in figure 6.21 but at ® ¿[¨ À . First of all, it is obvious that the
­
strong variation of the streak-width vanishes. Whereas the small ones in both figures conserve
their geometrical properties to a large extent, the width of the streak located at Ï ®¤Ê
the top image becomes smaller with increasing wall distance. This is in agreement with the
results presented in 6.7. The lower image on the other hand nicely shows that the length of
these flow regions seems to decrease as well with increasing wall distance. However, as the
ª Ç À in
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