6.3 Spatio-temporal buffer layer statistics
6.4.1 Low-speed streaks
Low-speed streaks are the most striking structures in the near wall region between®øÊ Ç and
.®òÊ
©À
Ç À which can be clearly observed inÎ9Ï -planes close to the wall [58, 38, 44]. They
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 experimen-tal 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, sim-ilar 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 low-speed 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 cer-tain 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 ® ¿ ªÀ . 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
¾ . Predominant structures are the elongated flow regions that convect downstream with ap-proximately half the local mean velocity, indicated by the vectors going from right to left. The 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 ª Ç À in 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
6.4 Properties of coherent velocity structures
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FIGURE6.21: Velocity fluctuations measured atÓ ® óÜ Ø .
streaks which appear separated in stream-wise direction at.® ¿\ À belong to the same streak visible at.® ¿ ªÀ , the decreasing length of these structures can be considered as an artefact related to the statistical variation of their height. When the dynamic of the streaks is investi-gated, it turns out that these structures tend to move away from the wall, which can be deduced from the out-of-plane motion (blue contours denote a motion away from the wall · ½ À and red towards the wall · º À ). It is clear that this process is associated with the production of turbulence according to the Reynolds equation as] turb ¿ ^R § · becomes positive on average.
However it is important to note the extent of this vertical motion is usually significantly shorter than the total length of the low-speed streaks at the same -value. This is in agreement with the
6 Investigation of the xz-plane
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Q2
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FIGURE6.22: Velocity fluctuations measured atÓ ® ÚØ (red: C_ Ø ; blue: CG! Ø ).
Ã Ñ Ë correlation in figure 6.8 and 6.9 and implies that no pairs of stream-wise counter-rotating vortices flank the low-speed regions over their total length, as proposed by some authors [54].
Otherwise, one would expect to detect a sign change in the out-of-plane motion on both sides of the streaks or at least a large· variation over the length of the streaks.