Civil Engineering Reference
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because
0
for reasons of homogeneity. Equation
[2.38] can therefore be expressed as
∂
pv
∂
x
=
⎛
⎝
⎞
∂
uv
∂
U
i
∂
uv
∂
vv
dU
dy
∂
∂
1
ρ
u
∂
p
∂
v
∂
p
=−
x
i
−
−
uvv
−
+
⎜
⎟
t
y
y
∂
x
⎠
A
12
P
12
T
12
N
12
2
u
1
u
2
∂
+ ν
∂
ν
∂
u
1
∂
u
2
[2.39]
−
2
y
2
∂
x
l
∂
x
l
D
12
ε
12
The terms for advection
A
12
disappear in a turbulent flow
which is homogeneous in directions
x
and
z
. We note the
presence of the transport mechanisms previously discussed,
i.e. production
12
and turbulent transport
1
T
, and the term representing the
velocity/pressure gradient correlation,
1
P
, molecular diffusion
D
, dissipation
ε
12
N
. Readers will
notice that the transport term
1
T
(or turbulent diffusion) is
modified in the new decomposition introduced here.
12
Figure 2.4 illustrates the distribution of the different
terms appearing in equation [2.39]. All the quantities are
rendered dimensionless in relation to the inner variables
ν
and
u
. Production is approximately at equilibrium with the
pressure term
N
12
in the majority of the outer layer at
y
+
≥
τ
50
. Molecular diffusion reaches equilibrium with
dissipation in the viscous sublayer. Turbulent transport
plays a significant role essentially in the buffer su
bla
yer
5
y
+
30
. The transport mechanism for the stress
uv
, in
which the velocity/pressure gradient correlations play an
important role, differs fundamentally from the kinetic
energy transport mechanism.
≤
≤
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