Civil Engineering Reference
In-Depth Information
Remember that
ww
by way of
π
11
, as shown in Figure 2.1. The contribution of
π
33
feeds into the stress
u
3
u
3
=
π
33,
S
is
greatest at
y
+
<
10
, but the rapid term becomes predominant
beyond the lower buffer sublayer (Figure 2.22).
0.06
π
33
0.04
π
3
3
,
R
0.02
π
33,
S
0
π
33,
St
-0.02
y
+
0
50
100
150
Figure 2.22.
Decomposition of
π
33
into slow, rapid and Stokes
terms in a turbulent channel flow with a small Reynolds
number
Re = 180 , according to [MAN 88]
τ
We now propose to briefly discuss certain aspects relating
to the modeling of the terms of the pressure/velocity
gradient. For greater detail, readers can consult [LAU 75], in
parallel to [MAN 88]. Let us first consider the asymptotic
behavior of
ij
near to the wall. The local pressure adjacent
to the wall is expressed by the Taylor series
π
⎛
⎝
⎞
∂
p
(
)
=
(
)
...
[2.69]
px
,
y
,
z
;
t
p
0
+
y
+
...
=
p
0
+
a
p
x
,
z
;
t
y
+
⎜
⎟
0
∂
y
⎠
where the subscript 0 refers to the wall and
( )
0
is the
local pressure gradient in direction
y
, which is a function of
x
,
z
;
t
∂
p
∂
y
(
)
. The behavior of the velocity field, asymptotic to the
first order, is
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