Geoscience Reference
In-Depth Information
z
H
0.90
0.80
1
Including riverbanks' influence
1
2
0.70
2
Not including riverbanks' influence
0.60
0.50
0.40
0.30
0.20
υ
x
υ
0
0.10
0.00
0.00
0.50
1.00
1.50
Fig. 4 Influence of river banks upon the diagram of modified tachoida (Data taken from Stone and
Hotchkiss
2007
)
We can also use the relationship between Manning roughness coefficient and the
parameter
U
derived in the earlier paper (Meyer
2009a
). So we have:
h
i
p
ln
2
n
2
þ
3
2
ln
U
2
¼
ln
n
2
þ
2
ln
n
2
(35)
h
i
p
ln
2
n
1
þ
3
2
ln
U
1
¼
ln
n
1
þ
2
ln
n
1
The resultant approximation is shown in Fig.
4
. It can be seen that there exists
strong influence of river banks on the tachoida shape at the river meridian. And the
problem cannot be treated generally as two dimensional; a three-dimensional
approach must be applied. The results shown in Fig.
4
indicate that the river
banks influence makes the flow more concentrated and so at the meridian we
have higher water velocities, especially at the upper layer.
The author tried to use data presented in literature, that is, Helmi
o(
2001
), to con-
firm the river banks influence. These data seem to confirm the model presented here.
€
4 Conclusions
1. The chapter presents the method for estimation of the river banks influence on
the shape of tachoida at the river meridian.
2. It is a commonly accepted opinion that if the ratio of river's breadth to depth is
big enough (
B/H
>
30), then a 2D model (i.e., in the
z
,
x
coordinates) can be
