Civil Engineering Reference
In-Depth Information
The imposition of a positive spanwise gradient
k
>
0
z
attenuates the severity of the inflectional profiles at
z
+
=
0
y
+
and has very little effect on the profiles at
=
0
. The
stabilizing effect of
, as
shown in Figure 5.5. Look again at Figure 5.1. For a flow
independent of
x
near to the streamwise structures, the
normal vorticity
reaches its peak of
α >
0
α =
0.4
is reduced to
ω
ω∂∂ ∂∂ ∂∂
=
uz wx uz
−
≡
y
y
a
nd
the spanwise vorticity is dominated by the mean shear
U
. As indicated in section 5.2, the intensity of the walls
of normal vorticity surrounding the QSVs varies exactly from
0.2
∂∂
y
to
. The mean shear, for its part, varies from
+
±
0.4
ω
±
=±
y
at the start of the buffer sublayer to
approximately
+
+
∂∂
Uy
=
1
at the start of the logarithmic
sublayer. If we assume a median value of
+
+
∂∂
Uy
=
0.08
∂∂
Uy
+
+
=
0.5
, we
find a range of parameter
in the buffer
sublayer. These values, oddly enough, correspond to the
range of
to
α =±
0.4
±
0.8
values which can “stabilize” or “destabilize” the
flow induced by the Oseen vortex. Indeed, we can see the
severity of the inflection in the profiles at
α
at
z
+
=
0
in
α =−
1
relation to
as shown in Figure 5.6. The results we have
presented correspond to a structure whose streamwise
vorticity is positive. We can clearly see that the inflectional
severity of
u
is increased or assuaged by the effect of
spanwise shear when, respectively,
α =
1
or
.
ω
k
<
0
ω
k
>
0
xz
xz
Another vortex structure
creates spanwise shear
ω >
0
x
immediately in its wake, by way of the kinematic
mechanism illustrated in Figure 5.1. Consequently, a
secondary vortex with vorticity
k
>
0
z
of opposite sign is more
likely to regenerate in the wake of the mother vortex,
because of its interactions with the pre-existing shear
ω <
0
x
k
>
0
z
(see Figure 5.7).
A variety of studies, including [BRO 93] and [BER 93b],
clearly indicate that the secondary QSVs form with
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