Geoscience Reference
In-Depth Information
Table 3.4
Verification scores of multi-fraction bed-load formulas
(Ribberink
et al
., 2002)
Formula
Score for
Score for
Average
transport rate
mean diameter
score
Wu
et al
.
0.43
0.86
0.64
E&H
0.34
0.63
0.49
A&W
+
Day
0.37
0.59
0.48
Parker (surface)
0.23
0.73
0.48
A&W
+
P&S
0.34
0.49
0.42
Van Rijn
0.18
0.54
0.36
MP&M
+
Egiaz.
0.26
0.34
0.30
MP&M
+
A&M
0.29
0.29
0.29
correction factor of Day (1980). Surprisingly, also the Engelund-Hansen formula,
which was not developed for multi-fraction use for widely graded sediment mixtures,
is the second-best formula in the list. All the Meyer-Peter-Mueller formulas give the
worst scores, mainly due to many cases with zero predicted transport rate.
3.5 SUSPENDED-LOAD TRANSPORT
3.5.1 Vertical distribution of suspended-load
concentration
For equilibrium sediment transport under steady, uniform flow conditions,
the
suspended-load transport equation (2.72) is simplified to
−
∂(ω
s
c
)
=
∂
∂
s
∂
c
ε
(3.81)
∂
z
z
∂
z
By using the sediment condition (2.73) at the water surface, Eq. (3.81) is further
simplified to
s
∂
c
ω
s
c
+
ε
z
=
0
(3.82)
∂
s
is often assumed to be proportional to the eddy viscosity
of turbulent flow. By using Eq. (2.49), a parabolic distribution of
The diffusion coefficient
ε
ε
s
can be obtained:
U
∗
z
1
h
1
σ
s
κ
z
ε
=
−
(3.83)
s
σ
s
is the Schmidt number, related to sediment size, concentration, etc. Note that
z
is defined here as the vertical coordinate above the bed, for simplicity.
With
where
s
along the flow depth,
Eq. (3.82) can be solved to derive the following vertical distribution of suspended-load
ε
s
determined using Eq. (3.83) with constant
ω
s
and
σ
