Geoscience Reference
In-Depth Information
Fig. 21 Quadrant plot of the instantaneous velocity data with thresholds.
Left
: data set E1 (mobile
bed).
Right
: data set E1D (immobile bed). Gray lines (
) stand for the |
u
0
v
0
| and |
u
0
| thresholds
Fig. 22 Detail of a |
u
0
v
0
| series with definition of the parameters that characterize sweep and
ejection events
The data plotted in Fig.
21
were treated to eliminate spurious points - values that
differ more than 600% from the average of neighboring points. In data sets of
12,000 entries, bad data were no more than 22 points.
Four parameters will be used to characterize the sweep and the ejection events of
the bursting cycle: the duration,
T
k
, the transported momentum,
M
k
, the maximum
shear stress,
A
k
(absolute value), and the period,
P
k
, computed as seen in Fig.
22
.
For each data series, a record of the detected events is created and analyzed. All
events with a duration smaller than 2d
t
, where d
t
1/
f
LDA
is the sampling interval,
were eliminated. The
N
j
valid events in a given data series
j
are used to compute the
average value
X
ðjÞ
.
Three data series were collected in each test of series E and ED. The ensemble
averages of the parameters that characterize the events are
¼
3
P
j¼
1
X
ð jÞ
,
h X
i¼
1
¼
Ð
T
u
0
v
0
h X
h T
h M
d
t
,
where
i
stands for
i
T
, the duration of the event,
i
M
j
j
h A
i
A
, the maximum instantaneous shear stress or
the transported momentum
h P
P
, the period between events. To simplify the notation, the brackets and the
overbar will be dropped.
i¼
