Civil Engineering Reference
In-Depth Information
R
. The problem can be applied to
different cases. If, for example, the estimation relates to time
and space with
(
)
()
(
) ()
rR Euxrux
≡=
+
0
0
ij
i
j
(
)
(
)
(
)
ˆ
, the vector
u x rt t
++=
,
'
a rt u xt
, '
,
i
ij
j
()
is linked to the spatiotemporal correlations at two
R
0
r
,
t
'
points:
(
)
(
)
(
)
(
)
R
rt
,'
≡=
R
E u x
++
rt
,
t u
'
xt
,
0
0
ij
i
j
Other elements are reported in the review [ADR 94],
which also provides a detailed list of references on stochastic
estimation as applied to turbulence.
The stochastic estimation of the flow induced by a specific
coherent element is obtained, naturally, by restricting the
“measuring” space specifically to that element. Thus, for
instance, we might consider only the events in quadrant
II
(
)
at a fixed position
from the wall
uxyx
,,
<
0
,
x
2
=
y
11
3
(
)
uxyx
,,
>
0
in
the
linear
stochastic
estimation
21
3
. Figure 3.3 shows the contours of the
enstrophy linked to the linear stochastic estimation
conditioned by an event in quadrant detected at
The bases of a “hairpin” structure, similar to Figure 3.3, are
clearly visible near to the wall. These bases, whose spanwise
spacing is around 100 inner variables, engender streaks of
high and low velocity. The structure becomes arch-shaped
further from the wall. The stochastic estimation is an overall
mean. It cannot reflect the instantaneous local structures. It
is clearly established by way of DNS that the legs of hairpin-
type structures are skewed in the spanwise direction
[ROB 91b]. The “head” of a hairpin vortex detaches under
the influence of the velocity induced, and forms an arch
vortex far from the wall. The feet give rise to a
(
)
( )
( )
ˆ
i
ux r
+=
a ru x
ij
j
ω
ω
i
i
y
+
II
=
103.
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