Geoscience Reference
In-Depth Information
where
m
is the one for
sediment-laden flow. Van Rijn (1984b) determined the damping factor as
κ
is the von Karman constant for clear water flow, and
κ
c
c
0
0.8
2
c
c
0
0.4
φ
κ
=
1
+
−
(3.93)
where
c
is the local sediment concentration (by volume), and
c
0
is the maximum
sediment concentration (
=
0.65).
3.5.2 Near-bed concentration of suspended load
Empirical formulas were established by Engelund and Fredsøe (1976), Smith and
McLean (1977), van Rijn (1984b), Celik and Rodi (1988), Zyserman and Fredsøe
(1994), and Cao (1999) for the near-bed concentration of single-sized suspended load,
and by Einstein (1950), Garcia and Parker (1991), and Hu and Wang (1999) for
the near-bed fractional concentration of multi-sized (non-uniform) suspended load.
The Einstein, van Rijn, and Zyserman-Fredsøe formulas are introduced below as
examples.
Einstein formula
Einstein (1950) set the reference level of suspended-load concentration at two grain
diameters above the channel bed and related the near-bed concentration of suspended
load to the bed-load transport rate
q
b
∗
k
as follows:
1
11.6
q
b
∗
k
δ
c
b
∗
k
=
(3.94)
U
∗
where
c
b
∗
k
is the concentration of the
k
th size class of suspended load at the reference
level
(by weight per unit volume), and
U
∗
δ
is the skin friction velocity.
Van Rijn formula
Van Rijn (1984b) set the reference level
δ
at the equivalent roughness height
k
s
or half
the bed-form height and established
0.015
d
50
T
1.5
δ
c
b
∗
=
(3.95)
D
0.3
∗
where
c
b
∗
is the volumetric concentration of suspended load at the reference level, and
T
and
D
∗
are defined in Eqs. (3.57) and (3.70).
Zyserman-Fredsøe formula
Zyserman and Fredsøe (1994) set the reference level at two grain diameters above the
bed and determined the near-bed volumetric concentration of suspended load as
