Geoscience Reference
In-Depth Information
Rouse number is smaller, the effect of turbulent diffusion is stronger and the distribu-
tion of sediment concentration is more uniform. It can be seen fromFig. 3.19 that when
the Rouse number is larger than about 5.0, the relative concentration of suspended
load is very small, and thus
5.0 can be used as the critical condition
for suspension. When the Rouse number is less than about 0.06, the suspended-
load concentration almost uniformly distributes along the flow depth, and thus
ω
ω
/(κ
U
∗
)
≈
s
0.06may be used as a condition to divide wash load and bed-material load.
Brush
et al
. (1962), Matyukhin and Prokofyev (1966), and Majumdar and Carstens
(1967) experimentally showed that for fine particles
/(κ
U
∗
)
≈
s
=
σ
1, and for coarse par-
s
ticles
σ
>
1. However, Einstein and Chien (1954) obtained the relation between
s
ω
shown in Fig. 3.20 by comparing the measured suspended-
load distribution with Eq. (3.84), and suggested that
/(κ
U
∗
)
and
σ
ω
/(κ
U
∗
)
s
s
s
s
should be smaller than 1. This
contradiction might be due to differences in flow and sediment conditions in which
the data were measured.
σ
Figure 3.20
Relation between
ω
s
/(κ
U
∗
)
and
σ
s
ω
s
/(κ
U
∗
)
(Einstein and Chien, 1954).
Van Rijn (1984b) proposed a formula to determine the Schmidt number
σ
s
:
2
ω
2
1
σ
s
=
<
ω
s
U
∗
s
U
∗
<
1
+
for 0.1
1
(3.91)
The von Karman constant has a value of about 0.4 for clear water flow and is a
function of the depth-averaged concentration, settling velocity, and bed shear velocity
for sediment-laden flow (Einstein and Chien, 1955). Yalin and Finlayson (1972)
introduced a damping factor for the von Karman constant:
κ
=
φ
κ
κ
(3.92)
m
