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

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6.3 Spatio-temporal buffer layer statistics
First of all it can be seen that the shift of the maximum (indicated by the symbols and the
legend) strongly depends on the sign of the stream-wise velocity fluctuation considered for
the calculation of the conditional correlation and from the wall-distance for all correlations.
This becomes clear as structures whose velocity is larger than the mean velocity are travelling
faster. Secondly, it turns out that the height of the conditional correlations is always lower
than the correlations based on all fluctuations. Finally, it should be noted by comparing the
values in the legend that the movement of high-speed structures towards and away from the
wall differs to a large extent. Since the distance between each of a pair of measurement planes
was 10 wall-units, it is possible to obtain information about the extension of the structures
1.0
1.0
R vv
(∆t + )
0.8
0.6
0.4
æ
∆x + =−41
∆x + =13
∆x + =67
t + )
R vv
(∆
0.8
0.6
0.4
I
∆x + =−52
∆x + =10
∆x + =73
0.2
0.2
ã
0.0
−300 −200 −100 0 100
∆x
1.0
200
ã
300
ã
0.0
−300 −200 −100
1.0
ã
0
∆x
+
100
ã
200
ã
300
ã
R vv
(∆t + ,u0)
0.8
0.6
0.4
0.2
∆x + =−56
∆x + =12
∆x + =80
ã 0.0
−300 −200 −100 0 100
∆x +
200
ã
300
ã
0.0
−300 −200 −100
ã
0
∆x +
100
ã
200
ã
300
ã
FIGURE 6.18: One-dimensional spatio-temporal correlation function of wall-normal velocity fluctuation
Ð ËÛË (top), and correlations of wall-normal fluctuation extracted in regions with N Ø
(centre) and
O! Ø
(bottom) measured at Ó ® Ü Ø
(left column) and Ó ® Ú¥Ø
(right column) and different time delays
between a pair of measurements (KJ ® ú ù
solid line, KJ ® Ø
dotted line, J ® P6 ù
dashed
line). The symbol indicates the maximum of correlation and the legend shows the exact position in
wall-units.
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