Geoscience Reference
In-Depth Information
m ¼ m
t
ð
t
T
t
L
Þþ
t
L
(7)
2
2
2
t
s
¼ s
ð
t
T
t
L
Þ
(8)
which reflect that the area is related to the height and width of a profile, the centroid
time is related to the timing and width of a profile, and the variance is related only
to the width of a profile. Finally, the reach-average velocity and dispersion coeffi-
cient were evaluated using the following equations:
L
m
4
m
3
U
¼
(9)
ð
Þ
4
3
s
s
5
L
2
D
¼
0
:
(10)
3
ð
m
4
m
3
Þ
where
L
is the reach length and the subscripts refer to the sampling sites that define
the reach boundaries. By using values of
2
at the reach boundaries at the same
non-dimensional time, (
9
) and (
10
) were used to explore how the reach-average
velocity and dispersion coefficient changed as the non-dimensional time at which
they were evaluated increased. Figure
5
shows some results from experiments 3-5.
Three things should be noted. Firstly, because the non-dimensional times at which
data is available cannot be controlled a priori the closest data to integer values of
non-dimensional times were used. Secondly, because non-dimensional times
also vary between sampling sites, an average of the non-dimensional times at the
two sites was used to plot the data. Thirdly, the average non-dimensional centroid
time and variance (derived from experiments 3-5) were used in (
6
)-(
8
). Figure
5
m
and
s
U(3)
D(3)
U(4)
D(4)
U(5)
D(5)
1.5
1.2
0.9
0.6
0.3
0
0
1
2
3
4
5
6
7
8
Non-dimensional time
Fig. 5 Cumulative development of velocity,
U
(m/s), and dispersion coefficient,
D
(m
2
/s), for
experiments 3-5
