Civil Engineering Reference
In-Depth Information
The strain parameter
()
represents the integral
α
t
shearing effect
t
t
∂
U
()
( )
()
∫
∫
[2.92]
α
t
=
β
t
′
dt
′
=
t
′
dt
′
∂
y
0
0
The coefficients of the distortion matrix
A
ij
depend
explicitly on
m
i
and are given in [MAX 82]. The Fourier
transform
of
the fluctuating pressure field is
2
k
1
a
2
/
k
2
,
ιρβ
where
1
. Time advancement is performed on the basis
of the spectrum
ι =−
G
of the initial turbulence and the
correlations of the velocity at two points are calculated by
way of
()
Φ
m
ij
G
G G
G G
G
(
)
(
)
(
)
(
)
()
(
)
∫
uxtu x rt s
,
++=
,
dmA m
3
,
α
t A m
,
α
t s
+
i
j
ip
jq
G
G G
{
}
(
)
( )
(
)
(
)
⎡
⎤
×Φ
m
exp
ι
m
•
r
+
m x
α
t
−
x
α
t
+
s
−
r
α
t
+
s
⎣
⎦
pq
12
2
2
The correlations are not homogeneous, even if the initial
turbulence
is
, unless the coordinates system moves along
with the mean flow.
The initial turbulence analyzed by [MAX 82] is
homogeneous and axisymmetrical. According to the
discussion given in section 2.10, the RDT should, in
these circumstances, qualitatively represent the physics
of the outer sublayer. The parameter of anisotropy
which defines the initial state of axisymmetrical turbulence
with
x
1
, the prevailing direction is
u
1
u
1
u
2
u
2
=
u
1
u
1
u
3
u
3
s
=
[MA
X 82
] analyzes the behavior of the Reynolds stress
ratios
u
i
u
j
/
K
for
s
which vary between 1 and 2 (
s
1
corresponds to the initial isotropic turbulence). The transport
equations, with the approximation of the RDT, are
=
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