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

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6.2 Statistical properties of the buffer layer
as long as expected by other authors as can be seen from the stream-wise extension of the
negative correlation region in figure 6.6. In case of the Ã Ñ‘Ñ correlation, shown in the upper
left plot of figure 6.7, only the function measured at ­®ÝÊ
direction and reveals a weak minimum at Í5Î ® ÊßÞ « , while the others slowly converge to zero
with increasing ÍeÏ ®
. This indicates a decreasing dynamic velocity range with increasing wall
distance, as expected from the à §(á profiles in figure 5.3, and implies that the coherent velocity
regions rapidly loose their identity with increasing wall distance ­ . To deduce the statistical
properties of the dominant low- and high-momentum flow structures which are convecting
downstream, the measured data was subdivided according to the sign of the stream-wise velocity
fluctuation before calculating the correlation functions. This conditional correlation
approach allows to identify the structures associated with ejection and sweeps for instance.
ª¡À changes its sign in span-wise
R uu
R uu
(u0)
1
0.8
0.6
0.4
0.2
0
â −0.2
−150 −100 −50 0 50 100
∆z +
1
0.8
0.6
0.4
0.2
0
â −0.2
−150 −100 −50 0 50 100
∆z +
1
0.8
0.6
0.4
0.2
0
æ
∆z + =63
æ
∆z + =46/112
∆z + =46
∆z + =70
æ
∆z + =70
â −0.2
−150 −100 −50 0 50 100
∆z
150 â
150 â
150 â
R vv
R vv
(u0)
1
0.8
0.6
0.4
0.2
0
â −0.2
−150 −100 −50 0 50 100
∆z +
1
0.8
0.6
0.4
0.2
0
â −0.2
−150 −100 −50 0 50 100
∆z +
1
0.8
0.6
0.4
0.2
0
æ
∆z + =31
∆z + =44
∆z + =53
æ
∆z + =35
∆z + =38
∆z + =42
æ
∆z + =27
∆z + =44
∆z + =53
â −0.2
−150 −100 −50 0 50 100
∆z
150 â
150 â
150 â
FIGURE 6.7: One-dimensional spatial correlation function of fluctuating stream-wise and wall-normal
velocity components measured at Ó ® Ô
graph) as a function of the span-wise coordinate. The symbols indicate the location of the minimum
and the legend the displacement of the minimum from the origin.
Ü Ø
(solid graph), Ó ® Ô×Ú¥Ø
(dotted graph) and Ó ® ÔéÖ¥Ø
(dashed
107