Geoscience Reference
In-Depth Information
where
R
=
6
ω
/(κ
U
∗
)
,
and
σ
is
the first positive root of
the following
s
1
equations:
(σ)
=−
R
(for erosion),
2
R
−
R
2
tg
2
ctg
(σ)
=
(for deposition)
(2.137)
σ
in cases of erosion and deposition, respec-
tively, as plotted in Fig. 2.8. The difference between these two curves is significant
for small Rouse numbers
Eq. (2.136) represents two curves for
α
, but gradually decreases as the Rouse number
increases. It should be noted that because the “concentration” boundary condition is
used, the curve for erosion case may have large errors for fine sediments (small Rouse
numbers), as discussed by Armanini and di Silvio (1986).
ω
/(κ
U
∗
)
s
Figure 2.8
Relation between adaptation coefficient and Rouse number.
/
=
0.017 is also plotted in
Fig. 2.8. It is shown that for small Rouse numbers Eq. (2.135) is close to Zhou and
Lin's curve for deposition case, and as the Rouse number increases, the difference
between Eqs. (2.135) and (2.136) increases. It is also shown that the values of
Armanini and di Silvio's function, Eq. (2.135) with
a
h
α
given
by these two methods are always larger than 1.
It should be noted that Eqs. (2.135) and (2.136) were derived for a pure vertical 2-D
case under many assumptions and simplifications. Their application in natural rivers
should be done with caution, because the adaptation coefficient
α
is affected by many
other factors, as discussed in Section 2.5.3.
2.5.3 Complexity of adaptation coefficient of
sediment
Effect of cross-sectional shape
The value of
in the 1-D model is related to the cross-sectional shape. This is
demonstrated by the following analysis suggested by Zhou and Lin (1998).
α