Geoscience Reference
In-Depth Information
As described in Section 2.1.2.2, the non-uniform sediment mixture is divided
into N size classes. Under the assumption of low sediment concentration,
Eq. (2.86) is applied to determine the transport of each size class of sus-
pended load:
hC k
β
+ ∂(
hU x C k )
+ ∂(
hU y C k
)
t
x
y
sk
h
D sxk
h
D syk
=
s
C k
+
s
C k
ε
+
ε
+
+ αω sk (
C
C k )
k
x
x
y
y
(
k
=
1, 2,
...
, N
)
(2.157)
where subscript k is the sediment size class index; C k and C
k are the actual and equi-
librium (capacity) depth-averaged concentrations of the k th size class of suspended
load, respectively; D sxk and D syk are the dispersion fluxes;
β sk is the correction factor
defined by Eq. (2.87) for size class k ; and
ω
sk is the settling velocity of the k th size
class of sediment.
Note that the size class index k in this topic is not subject to Einstein's summation
convention.
Extending Eq. (2.153) for the transport of each size class of bed load yields
q bk
u bk
+ ∂(α by q bk )
+ ∂(α bx q bk )
1
L (
=
q b k
q bk
)
(2.158)
t
x
y
where q bk and q b k are the actual and equilibrium (capacity) transport rates of the k th
size class of bed load, respectively, and u bk is the bed-load velocity.
Note that the values of
and L may vary with size classes. However, for simplicity,
they are not explicitly noted with the subscript k , because they are often treated as
calibrated parameters and each is given the same value for all size classes in most cases.
Extending Eq. (2.152) for the fractional bed change yields
α
k = αω
z b
1
L (
p m )
(
1
(
C k
C
) +
q bk
q b k
)
(2.159)
sk
k
t
where
k is the rate of change in bed elevation due to size class k .
The total rate of change in bed elevation,
(∂
z b
/∂
t
)
z b /∂
t , is determined by
N
z b
z b
=
(2.160)
t
t
k
k
=
1
Note that even though the sediment concentration is assumed to be low, the hiding
and exposure phenomena in non-uniform bed materials always exist. However, these
phenomena affect only the entrainment of sediment from the bed. Such effects are
accounted for through the fractional sediment transport capacities C
k and q b k . This
is discussed in Sections 3.4-3.6.
 
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