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

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6 Investigation of the xz-plane
in wall-normal direction, if the case is considered where both measurements were performed
simultaneously. The angle > indicates the inclination of the dominant flow structures between
­.®jÊ ¯ ¨ À and ¯ á
between ­®ôÊ ¨ À «¢À . The angles calculated from the primary
ª¥À
correlations are in good agreement with the observation of other authors. However, when the
wall-normal extent of flow structures which are associated with the production of turbulence
are considered, it turns out that the angles associated with ¨¬© events are in general quite large
with respect to the angles associated with low-speed streaks moving away from the wall. Another
interesting feature is the fact that the angles increases when the wall distance becomes
larger. This result can be explained by the strong velocity gradients in wall bounded flows.
−0.6
−0.6
R uu
(∆t + )
−0.4
−0.2
0.0
æ
∆x + =−21
∆x + =26
∆x + =73
t + )
R uu
(∆
−0.4
−0.2
0.0
I
∆x + =−67
∆x + =−3
∆x + =52
ã
0.2
−300 −200 −100 0 100
∆x
−0.6
200
ã
300
ã
0.2
−300 −200 −100
−0.6
ã
0
∆x
+
100
ã
200
ã
300
ã
R (v)(−u)
(∆t + )
−0.4
−0.2
0.0
æ
∆x + =19
∆x + =54
∆x + =116
t + )
R (v)(−u)
(∆
−0.4
−0.2
0.0
∆x + =−34
∆x + =25
∆x + =59
ã 0.2
−300 −200 −100 0 100
∆x +
−0.6
200
ã
300
ã
0.2
−300 −200 −100
−0.6
ã
0
∆x +
100
ã
200
ã
300
ã
R (v)(+u)
(∆t + )
−0.4
−0.2
0.0
æ
∆x + =−33
∆x + =20
∆x + =75
t + )
R (v)(+u)
(∆
−0.4
−0.2
0.0
I
∆x + =−91
∆x + =−10
∆x + =54
ã
0.2
−300 −200 −100 0 100
∆x
200
ã
300
ã
0.2
−300 −200 −100
ã
0
∆x
+
100
ã
200
ã
300
ã
Ð Ë Ñ
Ð ê Ë í êïî Ñí Ð ê Ë í ® ê Ñí
Ó ® óÜ Ø Ó ® Ú¥Ø
ù (J ® ú J J ® ® Q6 ù Ø
FIGURE 6.19: One-dimensional spatio-temporal cross-correlation function of stream-wise with wallnormal
velocity fluctuation (top), correlations of negative stream-wise with wall-normal fluctuation
(centre) and correlations of positive stream-wise with wall-normal fluctuation (bottom)
measured at (left column) and (right column) and different time delays between
a pair of measurements solid line, dotted line, dashed line). The
symbol indicates the maximum of correlation and the legend shows the exact position in wall-units.
120