Civil Engineering Reference
In-Depth Information
quasi-streamwise vortex because of the spanwise
asymmetry.
5
These details cannot be revealed by the
stochastic estimation unless we impose a large spanwise
component on the ejection ,
. The streamwise vorticity layer engendered by
can thus add to the vorticity of one of the legs
and eliminate the vorticity of the other, thus giving rise to
structures asymmetrical in the direction [ADR 94].
This example shows that the stochastic estimations are
closely linked to the conditions imposed, as might be
expected.
(
)
(
)
< 0
w
=
u
3
x
1
,
y
,
x
3
u
1
x
1
,
y
,
x
3
(
)
> 0
u
2
x
1
,
y
,
x
3
(
)
∂
u
3
x
1
,
y
,
x
3
/
∂
y
z
=
x
3
using
(
)
It is sometimes necessary to estimate
ux r
+
ux
and
ux
.
()
()
“measurements” at two different positions
1
2
In such cases, the linear estimation is written as
(
)
(
)
ˆ
(
)
(
) (
)
() ( )
() ( )
ˆ
i
ux r
+=
Eux ruxux
+
=
a ru x
+
bru x
i
1
2
ij
j
1
ij
j
2
ij
br
are, again, determined
by the least squares method. This type of analysis is useful,
e.g. for determining the signature of the events detected by
VITA. We have already pointed out the incoherence of the
conditional averages deduced from this scheme
(Figure 3.13). The signature of suggests that there is a
transition between an event in quadrant-
II
and an event in
quadrant-
IV
or
III
, at (Figure 3.12 and Figure 3.14).
[ADR 87] found the linear stochastic estimation of the wall-
normal velocity component, conditioned by an event in
quadrant-
II
at a position
x
and quadrant-
IV
at
x
. A shear
layer in which the normal velocity alternately changes sign
emerges with this procedure, as Figure 3.17 shows.
ij
ar
and
()
()
and the coefficients
()
c
uv
(
u
)
c
t
+
=
0
5 See Chapter 4 and the discussion on the topology of coherent wall
structures.
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