Civil Engineering Reference
In-Depth Information
Figure 5.24 shows the growth rate as a function of the
intensity of the streaks, as found by Schoppa and Hussein
[SCH 00]. The variation of
γ
+
is expressed as a function of
both
ˆ
y
+
defined by equation [5.56] (top horizontal axis)
ω
max
y
+
=
and of the angle of tilt of the vorticity lines at
20
defined
(
)
⎡
⎤
by
=
⎢
⎣ ⎦
(bottom horizontal axis).
[SCH 00] opts
fo
r the second presentation. We have deduced
the shear
ˆ
y
θ
arctg
ω
∂
U
∂
y
20
max
+
y
=
20
+
+
using the semi-empirical profile
∂∂
Uy
(
)
, which adequately represents the
velocity distribution in the buffer sublayer [TAR 11a, TAR
11b], and leads us to
+
+
U
=
14.5
tgh
y
14.5
(
)
. Thus, we have
∂∂
+
=
=
Uy
0.22
20
y
γ
+
as a function of
determined the profile of
+
based on
the data from [SCH 00]. The streaks are linearly unstable
when the initial wall-normal vorticity is greater than the
critical threshold
ˆ
y
ω
max
), beyond which the
growth rate increases in approximately linear fashion.
ˆ
(
ω
+
≥
0.27
θ >°
50
y
max
20
Figure 5.24.
Growth rate as a function of the angle of the vorticity lines at
20
y
+
=
(bottom horizontal axis) and maximum initial wall-normal
vorticity (top horizontal axis). This figure is adapted from [SCH 00]
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