Geoscience Reference
In-Depth Information
Eq. (2.90) yields the following bed-load transport equation:
q
b
u
b
+
∂(α
by
q
b
)
∂
∂
∂
+
∂(α
bx
q
b
)
∂
1
L
(
=
q
b
∗
−
q
b
)
(2.153)
t
x
y
which is similar to Eq. (2.151) except that
L
t
is replaced by
L
.
By using Eq. (2.153) for bed-load transport, Eq. (2.86) for suspended-load transport,
and Eq. (2.152) or the overall sediment continuity equation (2.91) for bed change, the
depth-averaged 2-D sediment transport model is closed. Similar closures can be derived
for the 1-D, width-averaged 2-D, and 3-D models, which are explained in detail in
Chapters 5-7.
2.6.3 Adaptation length of sediment
The adaptation length is a characteristic distance for sediment to adjust from
non-equilibrium to equilibrium transport. It is a very important parameter in the
non-equilibrium sediment transport model. For suspended load, the adaptation length
L
s
is calculated by
Uh
αω
s
L
s
=
(2.154)
where
is the adaptation coefficient described in Section 2.5.
For bed load, the adaptation length
L
b
has been given significantly different values
in the literature. Bell and Sutherland (1983) found that
L
b
was a function of time
t
in
an experimental case of bed degradation downstream of a dam due to clear water
inflowing. In numerical modeling studies, Nakagawa and Tsujimoto (1980), Phillips
and Sutherland (1989), Thuc (1991), and Wu
et al.
(2000a) set
L
b
as the average
saltation step length of sand on the bed for laboratory cases, whereas Rahuel
et al.
(1989) and Fang (2003) gave much larger values, such as one or two times the grid
spacing for field cases.
One reason for the aforementioned differences in values of
L
b
is that the bed-load
movement is closely associated with bed forms, which are usually on a small scale
in laboratory experiments and on a larger scale in natural rivers. Naturally,
L
b
may
take the value related to the length scale of the dominant bed form (Wu
et al.
, 2004a;
Wu, 2004). For example, in Bell and Sutherland's (1983) experiments of channel
degradation due to clear water, the transport of sediment (mainly bed load) was sig-
nificantly influenced by the scour hole near the flume inlet, and thus the adaptation
length was related to the dimension of the scour hole as a function of time
t
. In the case
where the bed is mainly covered by sand ripples, which usually occurs in laboratory
experiments,
L
b
may take the average saltation step length of sand or the length of
sand ripples, as adopted by Nakagawa and Tsujimoto (1980), Phillips and Sutherland
(1989), Thuc (1991), and Wu
et al
. (2000a). If sand dunes are the dominant bed form,
L
b
may take the length of sand dunes, which is about 5-10 times the flow depth. If
alternate bars are the dominant bed form,
L
b
may take the length of alternate bars,
which is about 6.3 times the channel width (Yalin, 1972).
α
