Geoscience Reference
In-Depth Information
ratio of the suspended load to the bed-material load,
C
k
/
C
tk
. To close Eq. (6.58),
r
sk
can be approximated by
r
sk
=
C
t
∗
k
. If the suspended load is dominant,
r
sk
is close
to 1 and may be lumped into the diffusivity
E
s
.
The bed change is determined by
C
/
∗
k
∂
k
=
α
z
b
∂
p
m
)
(
1
−
ω
sk
(
C
tk
−
C
t
∗
k
)
(6.59)
t
t
If the bed load is dominant,
r
sk
is close to 0 and the diffusion term in Eq. (6.58) can
be ignored, thus yielding
q
tk
β
tk
U
∂
∂
+
∂(α
tx
q
tk
)
∂
+
∂(α
ty
q
tk
)
∂
1
L
t
(
=
q
t
∗
k
−
q
tk
)
(6.60)
t
x
y
where
q
tk
and
q
t
∗
k
are the actual and equilibrium (capacity) transport rates of the
k
th
size class of bed-material load, respectively; and
ty
are the direction cosines
of bed-material load transport. Accordingly, the bed change is determined by
α
tx
and
α
∂
k
=
z
b
∂
1
L
t
(
p
m
)
(
1
−
q
tk
−
q
t
∗
k
)
(6.61)
t
The bed-material load transport capacity is determined using an equation similar to
Eq. (6.56), and the bed material sorting is simulated using the previous multiple-layer
model.
Because the bed-load and suspended-load model can cover the bed-material model
in the numerical solution sense, only issues regarding the former model are introduced
in the next subsections.
6.2.2 Boundary and initial conditions
Wall boundary conditions
At banks and islands, the bed-load transport rate and the suspended-load concentra-
tion gradient are set to zero:
∂
C
k
∂
q
bk
=
0,
=
0
(6.62)
n
where
n
is the coordinate in the direction normal to the boundary.
Inflow boundary conditions
In the depth-averaged 2-D sediment transport simulation, the sediment discharge must
be given at each point of the inflow boundary. In an unsteady case, a time series of
the inflow sediment discharge is needed. For non-uniform sediment transport, the
size distribution of the inflow sediment is also needed. Once the (fractional) bed-load
and suspended-load discharges
Q
bk
and
Q
sk
have been given, they may be distributed
