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Kim [KIM 85]. We can see two layers of vorticity with
opposite signs located at . They are separated by
in the spanwise direction. We would immediately
tend to identify these layers with counter-rotating vortices.
However, “vorticity” is not equivalent to the “vortex”, and we
need to be vigilant in such interpretations. We will clarify
this important point later on in this chapter.
y
+
=
25
z
+
=
120
Figure 3.15.
Conditional average of the streamwise vorticity associated
with events in VISA. The detection point is at
y
+
=
21
. The detection
L
+
parameters for VISA are
and
H
VS
=
1.2
. The conditional averages
=
500
ω
x
+
of
vary between . The dotted-line contours correspond to
. This figure is adapted from [KIM 85]
±
0.024
ω
x
+
<
0
3.4. Stochastic estimation
Let us begin by summarizing the principle of least-squares
estimation [PAP 84] to introduce the readers to the notions of
stochastic estimation of coherent turbulent structures.
Consider random variables . Generally speaking,
these random variables may be complex, and we use the
notation
n
x
1
,
x
2
....
x
n
x
*
s
for their complex conjugates. We wish to estimate
a signal
in a linear fashion by finding the sum
n
{
}
∑
ˆ
ˆ
[3.10]
s
=
a
x
=
E
s x
,
x
,...
x
ii
12
n
i
=
1
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