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

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5 Investigation of the xy-plane
visible is the elliptical shape of all correlated area, with the principal axis slightly inclined
with respect to á the -axis, and the variation of the correlation size from the exact location of
the fixed point. The elliptical shape of the structures and their inclination can be explained
by the strong gradients in wall-normal direction, which tend to elongate the flow pattern (a
circular cloud embedded in a shear flow for instance would appear elliptical and tilted after a
short time). Reynolds number effects can be investigated by comparing the right column of
figure 5.5 with the left column of figure 5.6 as the wall locations of the fixed point is identical
in viscous (ÄHÅ units 100, 200, 300, 400). Qualitatively, the agreement is quite good
when the scale in the legend is considered. Figure 5.7 and figure 5.8 show the functional dependence
of ¼âÒ4Ò the correlation on the Reynolds number and on the location of the fixed
point. The two-dimensional structure of this correlation function reveals surprising features
which were not known previously. Especially the different dependence of the correlation in
up-stream and down-stream direction on the fixed-point should be noted as well as the incli-
R uu
1
0.8
0.6
0.4
y + =10
y + =30
y + =50
y + =100
y + =200
y + =300
y + =400
R uu
1
0.8
0.6
0.4
0.2
0.2
1
ã
0
100
ã
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 + =10
y + =30
y + =50
y + =100
y + =200
y + =300
y + =400
R vv
0.8
0.6
0.4
0.2
0
1
ã
0
100
ã
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 + =10
y + =30
y + =50
y + =100
y + =200
y + =300
y + =400
R ww
0.8
0.6
0.4
0.2
0
0
ã
0
100
ã
ã
200
∆x +
300
ã
400
ã
−0.2
ã
0
100
ã
ã
200
y + +∆y +
300
ã
400
ã
FIGURE ç Ï'Ïlè ØUÚ Å/ÛeÜŒÅÛeÜÝÅ¿Þ Ø ÜŒÅêé 5.9: ç ÑÑzè ØUÚ Å/ÛeÜŒÅ/ÛeÜÝÅëÞ Ø ÜÝÅ%é , ç ÒHÒ/è ØÚ Å/ÛeÜŒÅ/ÛeÜÝÅëÞ Ø ÜŒÅ%é
ߥß
and
.
measured at çNì
84
ËBíî