Geoscience Reference
In-Depth Information
sweeps and s
for ejections. The domains of occurrence of each event, once
detected, are:
(
)
s
ðIÞ
h
u
0
<
s
þ
u
0
;
v
0
2
R
:
u
0
>
v
0
>
1. Outward interactions,
Q
out
¼
0
^
u
0
^
(
(
)
)
s
ðIIÞ
h
u
0
j >
s
u
0
;
v
0
2
R
:
u
0
<
v
0
>
2. Ejections,
Q
ej
¼
0
^
u
0
j
_j
j
(
)
s
ðIIIÞ
h
j
u
0
;
v
0
2
R
:
u
0
<
v
0
j >
u
0
j <
s
3. Inward interactions,
Q
in
¼
^j
u
0
j
^j
0
(
(
)
)
s
ðIVÞ
h
u
0
;
v
0
2
R
:
u
0
>
v
0
j >
u
0
>
s
þ
4. Seeps,
Q
sw
¼
0
^j
u
0
_
After a survey of the data, it was adopted s
ðIÞ
h
s
ðIIÞ
h
s
ðIIIÞ
h
s
ðIVÞ
h
¼
¼
¼
¼
s
h
with
s
h
¼
Hu
rms
v
rms
, where
u
rms
and
v
rms
are the turbulent intensities associated to the
longitudinal and normal velocities, respectively, and
H
is the hole size. Figure
20
shows the variation of the fraction of transported moment with the hole size for two
experiments. The increase of the hole size filters out small events and contributes
to counter the fragmentation of coherent events. A too large value of
H
would,
however, eliminate, small legitimate events (note that, at
H
2.5, events in the first
and third quadrants almost disappear and the respective statistics are unreliable).
The compromise eventually employed,
H
¼
1.7, was determined heuristically
and was found to be close to the half-value threshold level (Nezu and Nakagawa
1993
, p. 182). The values of s
+
and s
depend on the value of s
h
. It was adopted
s
+
¼
2.5
u
rms
and s
¼
2.5
u
rms
.
The domains of persistence of each of the events can be seen in Fig.
21
for two
sets of data taken at
y
/
k
s
¼
¼
0.8, where
y
is the normal (upwards) coordinate.
1
0.8
0.6
QII
QI
0.4
0.2
0
-0.2
-0.4
QIII
QIV
-0.6
-0.8
-1
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
Hole size (-)
Fig. 20 Fraction of transported momentum in one of the realizations of tests E1 and E1D. Mobile
bed,
y
/
h
¼
0.52
; mobile bed,
y
/
h
¼
0.07
; fixed bed,
y
/
h
¼
0.51
; fixed
bed,
y
/
h
¼
0.07
