Geoscience Reference
In-Depth Information
Figure 6.15
Measured and calculated velocities at cross-sections in Steffler's bend
(Wu and Wang, 2004a).
6.3.3 Dispersion of suspended load
The distribution of suspended-load concentration along the flow depth can be writ-
ten as
c
=
Cf
(
z
)
(6.88)
where
c
is the local suspended-load concentration,
C
is the depth-averaged suspended-
load concentration, and
f
=
h
δ
u
s
cdz
with the Lane-Kalinske distribution for the suspended-load concentration
c
and the
power law for the flow velocity
u
s
, one can derive
f
(
z
)
is a distribution function. By using
U
s
hC
−
1
exp
h
with
15
ω
s
U
m
m
z
(
z
)
=
−
+
1
∗
=
1
δ/
/
m
e
−
15
ω
s
ζ/
U
∗
d
1
is the thickness of the bed-load layer.
Integrating the
x
-direction suspended-load convection flux along the flow depth
yields
ζ
ζ
. Here,
δ
h
h
U
s
C
h
δ
12
U
n
C
h
δ
z
h
1
/
m
m
+
1
u
x
cdz
=
α
f
(
z
)
dz
+
α
f
(
z
)
dz
11
m
δ
12
b
s
IC
h
δ
2
z
1
f
+
α
h
−
(
z
)
dz
(6.89)
Using relations
m
+
m
h
h
1
/
m
f
h
and
h
δ
(
z
)
dz
=
f
(
z
)
dz
≈
h
in Eq. (6. 89) leads to
δ
