Geoscience Reference
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but the continuity equation at the dry nodes in both methods can be written as
f
h
h U
+∇· (
) =
0
(6.51)
t
where f is the storativity in the “porous medium” method, or the slot width in the
“finite slot” method. The slot width is given as
e a ( z s z b )
ε
+ (
1
ε
)
z s
z b
0
0
f
=
(6.52)
1
z s
>
z b
where z b is the bed elevation;
ε
0 is the slot width, with a value between 0.02 and 0.05
when z s
z b ; and a is a coefficient, which is usually larger than 2.0.
6.2 DEPTH-AVERAGED 2-D SIMULATION OF SEDIMENT
TRANSPORT IN NEARLY STRAIGHT CHANNELS
6.2.1 Governing equations
As described in Section 5.1.2.1, sediment transport can be simulated by computing
bed load and suspended load separately, or bed-material (total) load jointly. The
depth-averaged 2-D sediment transport equations in both approaches are given
below.
Bed-load and suspended-load transport model
The governing equations of the bed-load and suspended-load transport model in
general situations were described in Section 2.7. For nearly straight channels,
the dispersion terms in the suspended-load transport equation (2.157) are usually
combined with the diffusion terms, thus yielding
E s , x h
E s , y h
+ ∂(
hU y C k )
∂(
hC k
)
+ ∂(
hU x C k
)
=
C k
+
C k
sk
t
x
y
x
x
y
y
+ αω
(
C
C k
)(
k
=
1, 2,
...
, N
)
sk
k
(6.53)
where E s , x and E s , y are the horizontal effective diffusion (mixing) coefficients of sed-
iment in the x - and y -directions, respectively. If the dispersion effect is negligible,
E s , x and E s , y are close to the turbulent diffusivity
ε
s and can thus be related to the
ν t . In general, the effective diffusivities depend on the flow, sediment,
and channel conditions, and may have different values in the longitudinal and trans-
verse directions. Their evaluation may refer to the methods for the horizontal effective
diffusivities of heat and salinity introduced in Section 12.1.3.
eddy viscosity
 
 
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