Civil Engineering Reference
In-Depth Information
The result is not much different from the conventional
decomposition into passive and active components
analyzed in Chapter 4, although the models are completely
different. Remember that, indeed,
uu u
=+
A
P
()
()
()
2
(
)
(
)
uy euy u yuy e
τ
+
2
+
,
=
+
2
+
−
2
+
+
+
+
2
+
,
A
A
P
τ
if we assume, as does Panton
[PAN 07], that t
he
o
ver
all
mean of the active and passive components and
is
not necessarily null. Indeed, we can see that the turbulent
intensity of the streamwise velocity is a superposition of two
functions, which are, respectively, dependent on and
independent of the Reynolds number.
uu
=−
A
P
The fundamental question remaining to be answered is
the extent to which the modulation caused by the large-scale
structures affects the Reynolds shear stress
uv
+
−
. In light of
equation [6.4], we can write
+
++
*
++
+
+
*
++ +
[6.8]
−≡− =−
uv
u v
u v
−
α
u
v
−
β
u v u
p
OM
OM
where a triple correlation term resulting from the
modulation is clearly visible on the right-hand side. At
present, there are no experimental measured data and/or
DNS available evaluating the contribution of each term on
the right-hand side of equation [6.8], to our knowledge. It
does not seem completely illogical to attribute the role of
Townsend's active and passive structures, respectively, to
u
*
and
. If this hypothesis is correct, the contribution of
u
OM
to
uv
+
would be negligible because of the
dissimilarity of scales between the fluctuations in wall-
normal velocity which are essentially governed by local
structures and the large-scale velocity
O
u
coming from the
center of the logarithmic zone. The dissimilarity should
logically be more persistent between the fluctuations
O
u
++
−
uv
Search WWH ::
Custom Search