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

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6 Investigation of the xz-plane
0.04
0.04
0.03
y + =10
y + =20
y + =30
0.03
y =10
ž +
y =20
ž +
y =30
ž +
α]
PDF [tan
α]
0.02
PDF [tan
0.02
0.01
0.01
0.00
−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3
tanα=v/U
0.01
y + =10
y + =20
y + =30
0.00
−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3
tanα=v/U when UU mean
• v w ÷–”¢Ÿ y ” ¥” 0¢¡k¢ £¡k¢ 0¢¡k¢
¢¤1 ¢ 0¡k¢ ¢¥4 ¢
FIGURE 6.5: Probability density distribution of the flow angle between the instantaneous values of the
various velocity components at and . (upper left), (lower left), with
(upper right), with (lower right).
a large range of scales for positive angles and a maximum located at R negative in agreement
with [61]. The right column of figure 6.5 shows the distribution of the characteristic angles for
the velocity structures whose instantaneous stream-wise ¦ velocity is below (upper graphs)
or above the mean motion (lower graphs). As a stream-wise velocity which is larger than the
mean velocity indicates a positive § fluctuation , the positive domain of the lower right plot indicates
high-speed flow structures which move away from the wall, whereas the negative part
indicates large momentum fluid moving towards the wall. The asymmetry of the measurements
clearly indicates that the probability of finding a large momentum fluid moving towards
the wall (so called sweeps according to section 5.4.3, ¨„© or events based on the definitions on
page 71) is quite high relative to high-speed fluid moving away from the wall. This implies
the dominance ¨„© of events ëª over when large magnitude events are considered, and the
upper right plots state ¨ that events or ejection dominate ¨¬« over movements. Furthermore,
it should be noted that the largest angles are always associated ¨ with ¨„© and events.
Table 6.3 reveals the statistical properties of the absolute flow angles between the instantaneous
velocity components with respect to the stream-wise direction for three different wall
locations. The angles are quite small in relation to values from other experiments and numerical
flow simulations [86] as here the instantaneous stream-wise flow velocity ¦ was used to
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