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

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5.3 Statistical properties of the flow
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Reynolds number investigation is sometimes up to above the values of the low Reynolds
number measurements. Furthermore it should be noted that the largest difference appears
for the correlation. However, no unique statement can be given whether this is a real
¼ÐÒ4Ò
Reynolds number effect or a result of the tilted nature of the correlations, because in case of
non-isotropic turbulence it is not well defined how the correlations must be compared when
the Reynolds number varies (it is conceivable that only the main axis of the ellipse collapses).
Figure 5.13 and figure 5.14 finally display a line representation of the various double- and
triple-correlations, which are associated with the production of turbulence according to equation
(5.18) and (5.20), namely ¼ Ï®Ï Ï'Ï , ¼ ÑÑ ÑÑ , ¼ , ÎмÐÏ'Ñ , ÎмÐÑÏ , ¼ Ï'Ñ Ï'Ñ , ¼ Ï'쨄 Ï'Ï'Ñ ,
. It can be clearly seen that the width
½X¾ ¢
Ï'ÑÑ and ¼ ÑÒHÒ ÑÒ4Ò measured at ¼×
¼ Ï'ѲÑ
of the correlations at a particular value decreases in general with increasing complexity of
£ ¼ Ï'Ï Ï'Ï £ ¼ Ï'Ï'Ñ Ï'Ï'Ñ the correlations . This implies a decreasing importance of the
¼ÐÏ'Ï
higher order correlations and establishes the simplifications usually applied in the formulation
uv
−R
0.5
0.4
0.3
0.2
0.1
R (uuv)(uuv)
1
0.8
0.6
0.4
0.2
0
0.5
ã
0
100
ã
ã
200
y + +∆y + §
300
ã
400
ã
0
1
ã
0
100
ã
ã
200
y + +∆y + §
300
ã
400
ã
0.4
0.8
vu
−R
0.3
0.2
0.1
R (uvv)(uvv)
0.6
0.4
0.2
0
1
ã
0
100
ã
ã
200
y + +∆y +
300
ã
400
ã
0
1
ã
0
100
ã
ã
200
y + +∆y +
300
ã
400
ã
0.8
0.8
R (uv)(uv)
0.6
0.4
0.2
R (vww)(vww)
0.6
0.4
0.2
0
ã
0
100
ã
ã
200
y + +∆y +
300
ã
400
ã
0
ã
0
100
ã
ã
200
y + +∆y +
300
ã
400
ã
FIGURE Ï'Ñ 5.14: ç ÑÏ , ç Ï'Ñ Ï'Ñ and correlations (left) ç Ï'Ï'Ñ Ï'Ï'Ñ and ç Ï'ÑÑ Ï®ÑÑ , ç ÑÒ4Ò ÑÒ4Ò
and
ߥß
ç
(right) ÜÝÅ Ë measured at 20, 30, 50, 100, 200, 300, çNì 400 and .
89
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