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minimum. The outer structures
0
, on the
other hand, make little contribution to the Reynolds shear
stress, and the corresponding correlations
R
u
τ'
z
f
=
f
θ
U
=
0.008
0
0
∞
remain
consistently positive without the clear appearance of a local
minimum.
()
a) b)
(
)
Figure 4.18.
2D pre-multiplied spectral densities
k
x
k
z
E
uu
in inner
k
x
,
k
z
variables ranging from
u
to
590
in a fully developed
channel flow, found by the DNS performed by [BAU 14]. The dark-colored
areas correspond to (a) the low-pass filtered parts and b) high-pass filtered
parts. The active structures, whose size varies in the range
160
and
Re
y
+
τ
=
=
10
L
+
240
,
≤
≤
are detected on the left, and the large-scale structures with
L
+
2
h
+
3
on
≥
the right
We have recently conducted a similar study, using the
spatially filtered signals found by DNS at two moderate
Reynolds numbers
[BAU 14],
performed in boxes of sizes similar to those used in
[HOY 08]. Figure 4.18 shows the pre-multiplied spectral
densities
k
x
k
z
E
uu
k
x
,
k
z
and
Re
τ
=
395
Re
τ
=
590
(
)
of the streamwise fluctuating velocity
at
y
+
=
10
as a function of the wavelengths
L
+
k
x
+
and
=
2
π
k
z
+
, where
k
x
and
k
z
are the wavenumbers. We
applied a bandpass filter to
u
and
L
+
=
2
π
in the range
τ
′
240
and calculated the resulting correlation of the
signals shown in Figure 4.19(a). We can see that
R
u
L
+
160
≤
≤
changes
sign, with a behavior which is perfectly consistent with the
τ
′
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