Civil Engineering Reference
In-Depth Information
The streamwise velocity is governed by the spanwise
vorticity at the wall in the sublayer
y
+
because
<
3
+
⎛
⎞
∂
u
()
()
++
'
++
ω
t
=−
= −
τ
t
⎜
⎝ ⎠
z
0
0
∂
y
0
and
(
)
+++
uyt
,
()
'
0
++
τ
t
≈
y
+
to the first order in the lower viscous sublayer.
10
A relation
similar to equation [6.4], i.e.
(
)
( )
(
)
⎡
⎤
'
++
'*
++
′
+
+
τ
tRe t u tRe
;
=
τ
1
+
β
;
⎣
⎦
0
p
τ
0
OM
τ
[6.5]
(
)
+
α
'
ut e
+
+
;
OM
τ
should, therefore, be able to predict the fluctuations in wall
shear stress. It is easy to show that the parameter
in
α
'
()
equation [6.5] and
+
in relation [6.4] are linked by
α
y
()
α
y
y
+
α
'
=
im
y
+
→
0
+
Mathis
et al.
[MAT 13] “calibrate” relation [6.5] using both
experimental measured data and DNS. The parameters
α
'
and
are determined by a procedure similar to that used
β
'
()
()
for
+
, which is described below. The results
of the “calibration” on the basis of the experimental data
+
and
α
y
β
y
10 See Chapter 1.
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