Civil Engineering Reference
In-Depth Information
The local velocity
Uu
+
+
+
induced by the vortex in a shear
is compared to the case where
in
α =
0
α =
kk
= ±
0.2
z
y
Figure 5.3, when
z
+
. We can see that the profiles are
=
0
2
2
+
+
=≈
dU dy
=
0
yy
0
inflectional with
. The flow
induced, therefore, is unstable according to the Rayleigh
criterion [DRA 81]. However, the Fjortoft criterion
3
, which is
more restrictive and stipulates that
at
I
(
)
()
2
2
dU dy U U y
−
<
0
I
for instability in a flow, is not verified at
. On the other
hand, the effect of the structure on the local flow in the
spanwise direction
z
+
is profoundly destabilizing, according
to both the
Ra
yleigh and Fjortoft criteria. Figure 5.4 shows
the profiles
Uu
z
+
=
0
. All three
profiles are subjected to non-viscous instability, with the
inflection being more pronounced in the presence of a
negative shear
+
+= +
+
α
zu
+
+
for
at
y
+
=
0
α =±
0.2
k
(
) than when
.
α
<
0
k
>
0
z
Figure 5.4.
Local velocity induced by an Oseen vortex of intensity
,
Re
Γ
=
5
t
+
=
y
+
at
,
and
(dotted lines), compared with the case
0.1
=
0
α =±
0.2
where
(solid line). The streamwise vorticity associated with the
structure is positive
α =
0
3 Remember that the Rayleigh and Fjortoft criteria are established with
reference to a non-viscous flow.
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