The significance of coherent flow structures for the turbulent mixing ...
The significance of coherent flow structures for the turbulent mixing ...
The significance of coherent flow structures for the turbulent mixing ...
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6.2 Statistical properties <strong>of</strong> <strong>the</strong> buffer layer<br />
joint−PDF (u + v + )<br />
u + =−6.4<br />
u + =−4.8<br />
u + =−3.2<br />
u + =−1.6<br />
u + =0.0<br />
u + =1.6<br />
u + =3.2<br />
u + =4.8<br />
u + =6.4<br />
joint−PDF (u + v + )<br />
† 1‡ 2ˆ<br />
0<br />
−2 −1 0<br />
v +<br />
† 1‡ 2ˆ<br />
0<br />
−2 −1 0<br />
v +<br />
joint−PDF (u + w + )<br />
u + =−6.4<br />
u + =−4.8<br />
u + =−3.2<br />
u + =−1.6<br />
u + =0.0<br />
u + =1.6<br />
u + =3.2<br />
u + =4.8<br />
u + =6.4<br />
joint−PDF (u + w + )<br />
0<br />
−5.0 ‰ −2.5<br />
Š<br />
0.0 2.5 5.0<br />
+<br />
w<br />
0<br />
−5.0 ‰ −2.5<br />
Š<br />
0.0 2.5 5.0<br />
+<br />
w<br />
joint−PDF (v + w + )<br />
w =−3.2<br />
Ž +<br />
w =−2.4<br />
Ž +<br />
w =−1.6<br />
Ž +<br />
w =−0.8<br />
Ž +<br />
w =0.0<br />
Ž +<br />
joint−PDF (v + w + )<br />
0‹ 1Œ<br />
0<br />
−2 −1 2<br />
v +<br />
0‹ 1Œ<br />
0<br />
−2 −1 2<br />
v +<br />
FIGURE 6.4: Joint-PDF functions <strong>of</strong> / v 0 v <strong>the</strong> / v v , v 0 v and (top to bottom) measured çNì‘_“’ at<br />
and two wall-normal locations: • vxw ÷–” (left) and • vxwzy ” (right).<br />
í¡”<br />
þ¡ ˜—$<br />
instantaneous values <strong>of</strong> <strong>the</strong> various velocity components u.v ;<br />
was<br />
¢<br />
calculated at and<br />
. <strong>The</strong> -distribution, shown in <strong>the</strong> lower left graphs <strong>of</strong> figure 6.5, is exactly symmetrical<br />
t‚8<br />
with respect to <strong>the</strong> centreline, and <strong>the</strong> range <strong>of</strong> angles increases when approaching <strong>the</strong> wall.<br />
This is clear as <strong>the</strong> magnitude <strong>of</strong> <strong>the</strong> span-wise velocity fluctuations increases slightly toward<br />
<strong>the</strong> wall according to 7.8<br />
figure 5.3. <strong>The</strong> -distribution on <strong>the</strong> o<strong>the</strong>r hand is asymmetric with<br />
103