Civil Engineering Reference
In-Depth Information
“leading edge”) and disappears at (end of the ejection,
known as the “trailing edge”), it is held that the ejection
occurs at time
t
2
i
(
)
.
t
1
i
+
t
2
i
2
The signatures of the streamwise and normal fluctuating
velocity, and of the local Reynolds stress related to the
events detected, can be determined by way of overall means
of these quantities conditioned by the arrival of the
structures [ANT 88]. Thus, for a value
, the conditional
q
average is defined by:
N
1
e
(
)
()
∑
[3.4]
qt
=
qt t
+
c
j
N
j
=
1
e
where
is the time reference of the detected event and
t
j
N
e
is the total number of events.
Fi
gu
re 3.7 show
s
t
he
conditional averages ,
and , based on all of the ejections
detected by the quadrants technique. These results are
obtained at . At , which corresponds to the middle
of an ej
ec
tion; as we would expect, we find a n
eg
ative peak of
u
( ), a positive
pe
a
k
of
v
( ) and a
negative peak of ( ). In addition, these
conditional averages are perfec
tly
symmetrical in relation to
. We also note that is slightly more stretched
over time around . We can estimate the
du
r
ati
on of an
ejection by plotting a line representing ,
as shown in Figure 3.7. This estimation gives us a duration
of . This value is comparable with the results found by
Alfredsson and Johansson [ALF 84], in spite of the
differences between the threshold
u
c
uu
(
uv
uu
vv
v
c
vv
c
y
+
=
15
t
=
0
u
c
uu
=−
1.4
v
c
vv
=
1.5
()
c
uv
uu
vv
=−
2.0
uv
t
+
=
0
u
c
uu
t
+
=
0
(
uv
uu
vv
=
H
=−
1
c
D
e
+
=
5
and the position of
=
2
H
detection (
y
+
) in their study.
=
50
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