Civil Engineering Reference
In-Depth Information
and
2
u
3
u
3
Du
3
u
3
Dt
∂
2
ρ
p
∂
u
3
x
3
+ ν
∂
ν
∂
u
3
∂
u
3
=
0
−
u
2
u
3
u
3
+
x
2
−
2
∂
x
2
∂
∂
x
2
∂
∂
x
l
∂
x
l
[2.8]
P
33
Τ
33
π
33
D
33
ε
33
We can see that there are no production term
s in
the
equa
tions governing the transport of the stresses
u
2
u
2
and
u
3
u
3
. These stresses can only be fed and sustained by way of
the pressure/velocity gradient correlations
π
22
and
π
33
,
which, in reality, must be positive. However, if
⎛
⎞
⎠
2
ρ
∂
u
2
x
2
+
∂
u
3
π
22
+ π
33
=
p
>
0
⎜
⎟
∂
∂
x
3
⎝
then
⎛
⎝
⎞
⎠
2
ρ
p
∂
u
1
∂
2
ρ
∂
u
2
x
2
+
∂
u
3
π
=
x
1
=−
p
<
0
⎜
⎟
11
∂
∂
x
3
because of the co
ntin
uity
0
.
The
com
ponent with
greatest intensity
u
1
u
1
feeds into
u
2
u
2
and
u
3
u
3
b
y
∂
u
i
∂
x
i
=
π
11
.
The
inter-component transfer rates
u
1
u
1
→
u
2
u
2
an
d
u
1
u
1
→
u
3
u
3
are higher when the differences
u
1
u
1
−
u
2
u
2
and
u
1
u
1
−
u
3
u
3
are
greater.
Th
e correlations
π
ii
thus tend to equalize the
stresses
u
i
u
i
, and it is reasonable to assume that
2
∂
u
(
)
⎡
⎤
⎦
π
=
p
1
∝ −
2
uu
−
u u
+
uu
⎣
11
1
1
2
2
3
3
ρ∂
x
1
(
)
The term
is negative if
. In this
uu
>
u u
+
uu
3 3
/2
π
11
11
2 2
case,
and
. If the turbulence is locally
π
22
>
0
π
33
>
0
anisotropic, and if
is the most energetic component, then
u
1
Search WWH ::
Custom Search