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

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6 Investigation of the xz-plane
function is not necessarily an even function with a Í5Î ¿ À maximum at in contrast to the
primary correlations, but there exists still an important symmetry property when the random
variables and are interchanged, namely Ã Ñ Ë ¹ Í5Î|¼ ¿ ÃË Ñ ¹ Í5Î|¼ . The left column
§
in figure 6.8 shows · Ñ the correlation function with the component fixed and § shifted in
ÃË
the two homogeneous directions. First of all it should be noted that the sign · Ñ of ÃË again
indicates that the transport of relatively low-momentum fluid outward into higher speed re-
) and the movement of high-momentum fluid toward the wall into
½þÀ
(§ßºöÀ gions and
lower speed regions ·
and · º¤À ) are the predominant processes in the near-wall region.
(§N½¤À
In addition, the strong elliptical shape implies that the turbulent mixing in the wall-normal
direction is related to the low-speed structures represented à êJî Ñí êJî Ñí by in figure 6.7. But obviously
only a small part of the low-momentum structures shows a correlated motion in both
−0.6
−0.6
R vu
−0.4
−0.2
æ
∆x + =+ 5
∆x + =−12
∆x + =−17
R vu
−0.4
−0.2
æ
∆z + =42
∆z + =50
∆z + =68
0.0
0.0
R uw
ã 0.2
−300 −200 −100 0 100
∆x +
−0.6
−0.4
−0.2
0.0
200
ã
æ
∆x + =−49
∆x + =−57
∆x + =−57
300
ã
R uw
â 0.2
−150 −100 −50 0 50 100
∆z +
−0.4
−0.2
0.0
0.2
æ
∆z + =27
∆z + =38
∆z + =50
150 â
R vw
ã 0.2
−300 −200 −100 0 100
∆x +
−0.6
−0.4
−0.2
200
ã
æ
∆x + =−10
∆x + =−28
∆x + =−35
300
ã
R vw
â 0.4
−150 −100 −50 0 50 100
∆z +
−0.4
−0.2
0.0
æ
∆z + =−16
∆z + =−24
∆z + =−31
150 â
0.0
0.2
ã
0.2
−300 −200 −100 0 100
∆x
200
ã
300
ã
â 0.4
−150 −100 −50 0 50 100
∆z
150 â
FIGURE 6.9: One-dimensional spatial cross-correlation function of Reynolds stress components measured
at different wall-normal location (Solid graph: Ó ® Ô Ü Ø
. Dotted graph: Ó ® Ô×Ú¥Ø
. Dashed graph:
Ó ®NÔõÖ¥Ø
) as a function of ®
and ®
. The symbols indicate the maximum of correlation and the
legend the distance from the minimum to the origin.
110