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

» %
%QÄ
¾
Ó
turbulent velocity fluctuations · µÙá
Ä ¸ , ³*µ á
5.4 Properties of coherent velocity structures
layer appears as slightly-inclined low-speed regions with the geometrical dimensions given
above. Although the exact angle varies strongly in the instantaneous velocity fields, it can
be clearly seen that the angle between the wall and the shear-layer increases with increasing
wall distance, see also figure 5.16. This can be explained by the different shape of the low
momentum structures due to the strong flow gradients and the presence of the wall.
¾!¨
While the
Ä4Å
near-wall region below is dominated by low-speed streaks, which will
¾"¨
be considered
in the next chapter in detail, the ÄHÅ
log-law region above is dominated by large-scale
shear-layers without any obvious structural regularity in contrast to the streaks.
¾#¨
Another remarkable
result is the fact that the low Ä Å
momentum structures below are usually not
as long as the total length of the large-scale shear-layer. However, as the low-speed streaks are
only 30 wall-units in width and not often perfectly parallel to the main flow direction, as will
be seen later, only a cut through the streak can be áEÄ observed in the -plane while the length of
the cut depends on the orientation of the streak with respect to the measurement plane and its
geometrical properties. In figure 5.16 for example, a cross-section of a streak can
¾}þ©¨$
be
¾Sþ
observed
¢
from to 400, 500 to 800 and another starts á Å at . The lower vector field of
á Å
the same figure and the upper one of figure 5.15 indicate that on the top of these shear-layers
vortices can be frequently observed. The significance of these vortices for the turbulent mixing
will be investigated in the following.
5.4.2 Ejection
Ä ¸ and ´1µÙá
Ä ¸ . In this representation, the shear-
Since the pioneering near-wall flow visualisation experiments by Kline et al. (1967), Corino &
Brodkey (1969) and Kim et al. (1971), it is well established that the coherent structures, which
can be identified in the flow field, run through quite complex cycles. The most striking cycle
or process, which could be observed, was the movement of elongated low velocity regions,
designated as low-speed streaks, out in the buffer region. This motion away from the wall was
associated with an oscillation of the low-speed flow structure and a violent break-up into small
scale turbulence. A schematic representation of this process along with the typical velocity
profiles is shown in figure 1.2 on page 6. This near-wall process, which was observed to occur
suddenly and abruptly, was designated as ejection and it was speculated that a large part of
the turbulence production was associated with this observation. This becomes evident from
the production term shown in the following equation. Due to the fact that the mean velocity
gradient % »¿ %EÄ is quite large close to the wall, according to figure 5.2, and the product of
the two orthogonal velocity fluctuations · and ³ is negative, because the stream-wise velocity
fluctuation · is negative for low-speed streaks and their wall-normal velocity component positive
according to the observations, the total term becomes positive when multiplied with the
negative sign. This means that turbulence is produced according to equation (5.18).
turbulence production (5.21)
Î& · ³
Based on these considerations quantitative experiments were performed to determine the footprint
of this ejection process in detail. It was found that the typical velocity signal from
the process was quite regular provided the scales and intensity were normalised properly (an
example of the signal is shown on page 133). Figure 5.17 reveals two characteristic velocity
fields with significant peak intensities in the Reynolds shear stress component · ³ Z·(' ) . In
93