Civil Engineering Reference
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comparison is limited to moderate Reynolds n
umb
ers
2000
*
is
+
Re
=<
h
. We can see that the distribution of
u
P
u
P
τ
⎛
⎝
⎞
. The maximum
u
P
u
P
*
only slightly dependent on
Re
τ
is
⎜
⎟
i
max
⎠
located at
, and decreases slightly with
h
+
. This
decrease is limited to 20% in the range
180
y
+
=
15
h
+
.
≤≤
2000
⎝
⎠
⎛
⎞
The so-called composite distribution of
u
P
u
P
*
com
is the
⎜
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
sum of the components
u
P
u
P
*
e
and
u
P
u
P
*
i
. Thus, we need
to find what these two components have in common - i.e. the
value
C
2
=
⎜
⎟
⎜
⎟
⎛
⎝
⎞
⎠
*
⎜
⎟
e
at the wall. Therefore,
u
P
u
P
(
)
(
) (
)
*
*
*
*
[4.35]
uu
≡
uu
=
uu
+
uu
−
C
PP
PP
PP
PP
2
com
i
e
The value
u
P
u
P
*
thus obtained can be used to estimate the
distribution of the turbulent streamwise intensity on the
basis of equation [4.32]:
⎛
⎞
u
*
*
+
(
)
uu
=
u u
−
2
C
+
C
uv
U
τ
⎜
⎝⎠
P
P
AP
AA
c
Figure 4.29 shows the estimated profiles of the turbulent
streamwise intensity. The procedure is a simplified version
of more general disturbance analysis methods [VAN 75].
uu
+
The turbulent intensity increases with the Reynolds
number, under the influence of the passive structures. We
showed in Figure 1.14 that the maximum intensity in the
buffer sublayer varies as
)
(
+
[4.36]
uu
=
0.965ln
h
+
+
1.036
max
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