Geoscience Reference
In-Depth Information
D
b
(
s
c
b
) is usually determined by relating
c
b
to the depth-averaged suspended-
load concentration
C
through
c
b
=
ω
=
α
c
C
, in which
α
c
is the adaptation or recovery
coefficient.
The entrainment flux
E
b
(
) can be determined by directly using an empirical
formula for the near-bed suspended-load transport capacity
c
b
∗
=
ω
s
c
b
∗
. The net exchange flux
thus reads
D
b
−
E
b
=
α
ω
s
C
−
ω
s
c
b
∗
(2.128)
c
Examples of this model can be found in Spasojevic and Holly (1990) and Minh
Duc (1998).
The coefficient
α
c
in non-equilibrium sediment transport states is little known and
very difficult to determine theoretically. It is often approximately evaluated using
the Rouse, Lane-Kalinske, or another distribution of suspended-load concentration
introduced in Section 3.5.1, established under equilibrium conditions. For example,
the use of the Rouse distribution yields (Minh Duc, 1998)
h
h
ω
s
/κ
U
∗
dz
=
h
−
δ
−
z
δ
α
(2.129)
c
−
δ
z
h
δ
Lin (1984) proposed the following relation for
α
c
:
0.55 ln
ω
s
α
=
3.25
+
(2.130)
c
κ
U
∗
which was used by Spasojevic and Holly (1990).
2.5.2 Exchange model using average capacity formula
The entrainment flux
E
b
can also be determined by relating
c
b
∗
to the equilibrium
(capacity) depth-averaged suspended-load concentration
C
∗
through
c
b
∗
=
α
c
∗
C
∗
,
in which
is the adaptation coefficient under the equilibrium condition and
C
∗
is determined using an empirical formula. Therefore, the net exchange flux is
determined by
α
c
∗
D
b
−
E
b
=
α
ω
s
C
−
α
∗
ω
s
C
∗
(2.131)
c
c
In the equilibrium sediment transport state,
α
=
α
, but in a non-equilibrium state,
c
c
∗
α
. Because equilibrium is acquired through exchange between bed material and
moving sediment near the bed, the sediment in the lower layer near the bed usually
reaches equilibriummore promptly than the sediment in the upper layer near the water
surface. In other words, the relative difference between the actual and equilibrium
sediment concentrations in the lower layer is usually smaller than that in the upper
=
α
c
c
∗
