Geoscience Reference
In-Depth Information
5.4 1-D COUPLED CALCULATION OF FLOW
AND SEDIMENT TRANSPORT
Fluvial processes in a river consist of simultaneous motions of water and sediment. Any
change in flow conditions may be associated with a variation in sediment transport and
channel topography, and vice versa. Thus, the decoupled flow and sediment transport
models introduced in Sections 5.1-5.3 have limitations and are only applicable in
the case of weak or mild sediment transport. In the case of strong sediment trans-
port, a coupled model should be used, to take into account the interactions between
flow and sediment transport. How to couple the flow and sediment calculations is
introduced below.
5.4.1 1-D coupled flow and sediment transport
equations
In general, 1-D unsteady sediment-laden flows are described by Eqs. (2.126) and
(2.127), which are rewritten below to consider side flows:
∂(ρ
A
)
+
∂(ρ
Q
)
+
ρ
b
∂
A
b
∂
=
ρ
0
q
l
(5.177)
∂
t
∂
x
t
Q
2
A
∂(ρ
Q
)
+
∂
∂
ρβ
gA
∂
z
s
1
2
gAh
p
∂ρ
+
ρ
x
+
x
+
ρ
gAS
f
=
ρ
0
q
l
v
x
(5.178)
∂
∂
∂
t
x
where
is the density of the water and sediment mixture in the water column, deter-
mined by
ρ
ρ
=
ρ
f
(
1
−
C
t
)
+
ρ
s
C
t
, with
C
t
being the volumetric concentration of
sediment; and
ρ
0
is the density of the water and sediment mixture from tributaries
and banks.
The effect of alluvial bed roughness is accounted for through the dependence of the
Manning roughness coefficient on flow and sediment conditions:
n
=
f
(
U
,
B
,
h
,
τ
b
,
d
50
,
...)
(5.179)
which can be one of the formulas introduced in Section 3.3.3.
Sediment transport, bed change, and bed material sorting equations are the same
as those introduced in Section 5.1.2.1. For simplicity, the bed-material load transport
model is presented here. The governing equations include the total-load transport
equation (5.34), bed change equations (5.31) and (5.36), mixing-layer bed mate-
rial sorting equation (5.32), and sediment transport capacity (5.35). Note that
Eq. (5.33) should also be included, but it is not listed here because the bed material
sorting in subsurface layers can be computed separately. In addition, the sedi-
ment settling velocity is related to sediment concentration, but it can be set as an
intermediate variable.
The system described above has 4
N
+
4 equations that are used to determine 4
N
+
4
unknowns:
A
,
Q
,
n
,
∂
A
b
/∂
t
,
(∂
A
b
/∂
t
)
k
,
Q
tk
,
Q
t
∗
k
, and
p
bk
(
k
=
1, 2,
...
,
N
).
