Civil Engineering Reference
In-Depth Information
(
)
(
)
ττ
′′
ω ω
+
+
00
z
0
z
0
ττ
′′
==
σ
+
=
=
ω ω
=
σ
+
00
τ
′
z
0
z
0
ω
τ
Ω
x
z
0
0
z
0
[1.67]
(
)
ωω
+
x
00
x
ττ
′′
==
σ
+
=
σ
+
zz
τ
′
ω
Ω
z
x
0
z
0
in inner scales. The value
corresponds to the quadratic
mean of
q
.
11
Considering the asymptotic behaviors of the
mean velocity and the fluctuations of velocity near to the
wall:
σ
q
⎛
⎞
∂
∂
U
()
()
Uy
=
yOy
+
2
⎜
⎝ ⎠
⎛
⎞
y
0
∂
∂
u
()
2
u
=
y O y
+
⎜
⎝ ⎠
⎛
⎞
y
0
∂
∂
w
()
2
w
=
y O y
+
⎜
⎝ ⎠
y
0
()
where
O
indicates terms of order greater than
y
it is
easy to show that:
uu
U
w
w
U
σ
+
′
=
lim
τ
y
→
0
x
[1.68]
+
′
σ
=
lim
τ
y
→
0
z
The statistics on the fluctuating wall shear stress can,
therefore, be determined on the basis of the velocity field
near to the wall. However, this requires us to determine
(either experimentally or by precise direct numerical
11 For the sake of conciseness, the quantities
2
q
σ
and the variance
σ
q
will be used indiscriminately to denote the turbulent intensity of
q
.
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