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

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5.3 Statistical properties of the flow
to a large extent. This illustrates clearly the difficulty associated with the interpretation of the
one-dimensional correlations. Nevertheless, this representation allows a convenient comparison
of the various correlations and their dependence on the location of the fixed point relative
to the wall. Especially the different size of the structures along the coordinates is clearly
visible (note different scale). Figure 5.11 reveals the two-dimensional correlation function of
the wall-normal velocity ¼ÐÑÑ fluctuations and the correlation function of the span-wise vorticity
¼ ø,úýø,ú component for different locations of the fixed point. It can be clearly seen that
¼âÑ²Ñ the correlations are relatively small with respect ¼ÐÏ'Ï to and also strongly deformed for
¾ÿþ¡ ¢ þ¥ ¢
wall locations Ä Å¤£
below . For , this deformation vanishes as can be seen
Ä Å
from the line representations in figure 5.9 and figure 5.10. Remarkable is the extension of
the overhang region which goes in stream-wise direction when the fixed point is below 40
wall-units and in up-stream direction for larger wall-distances. The vorticity structures shown
1
1
R uu
0.8
0.6
y + =100
y + =200
y + =300
y + =400
y + =100
y + =200
y + =300
y + =400
R uu
0.8
0.6
0.4
0.2
0.4
1
ã
0
100
ã
200
∆x
+ ¦
300
ã
400
ã
0
1
ã
0
100
ã
ã
200
y + +∆y + §
300
ã
400
ã
R vv
0.8
0.6
0.4
0.2
y + =100
y + =200
y + =300
y + =400
y + =100
y + =200
y + =300
y + =400
R vv
0.8
0.6
0.4
0.2
0
1
ã
0
100
ã
200
∆x
+ ¦
300
ã
400
ã
0
1
ã
0
100
ã
ã
200
y + +∆y + §
300
ã
400
ã
R ww
0.8
0.6
0.4
0.2
y + =100
y + =200
y + =300
y + =400
y + =100
y + =200
y + =300
y + =400
R ww
0.8
0.6
0.4
0.2
0
0
ã
0
100
ã
200
∆x
+ ¦
300
ã
400
ã
−0.2
ã
0
100
ã
ã
200
y + +∆y + §
300
ã
400
ã
FIGURE 5.12: Comparison ç Ï'Ï è ØUÚ Å/ÛeÜŒÅÛeÜÝÅ¦Þ Ø ÜŒÅêé of ç ÑÑ è ØÚ ÅÛeÜÝÅÛeÜÝÅ¦Þ Ø ÜÝÅêé ,
ߥß
àߥߥß
and
ÒHÒè ØUÚ Å ÛeÜ Å ÛeÜ Å Þ Ø Ü Å é measured at çNì
ç
symbols) ÜÝÅ Ë and 100, 200, 300, 400.
íî
(solid symbols) and çNì
Ë ÷
(opaque
87