Geoscience Reference
In-Depth Information
2.7.2 Bed material sorting
The size gradation (composition) of bed material may vary along the vertical direction
due to historical sedimentation. To consider this variation, the bed material above
the nonerodible layer is often divided into multiple layers, as shown in Fig. 2.9. The
top layer is the mixing layer. All sediment particles in the mixing layer are subject to
exchange with those moving with flow, i.e., entraining from the mixing layer to the
water column or depositing from the water column to the mixing layer. The second
layer is a subsurface layer. More underlying subsurface layers can be added, if needed.
However, the sediment particles in the subsurface layers do not directly exchange with
the moving particles.
Figure 2.9
Multiple-layer model of bed material sorting.
The mixing layer concept was adopted by Hirano (1971), Bayazit (1975), Karim
and Kennedy (1982), Rahuel
et al
. (1989), Armanini and di Silvio (1988), Wu (1991),
and van Niekerk
et al.
(1992). The temporal variation of the bed-material gradation
in the mixing layer can be determined by (Wu, 1991; also see Wu, 2004)
∂
k
+
p
bk
∂δ
∂(δ
m
p
bk
)
z
b
∂
t
−
∂
z
b
∂
m
=
(2.161)
∂
t
t
∂
t
δ
m
is the mixing layer thickness;
p
bk
is the fraction of the
k
th size class of bed
material contained in the mixing layer; and
p
bk
is
p
bk
when
where
0 and
the fraction of the
k
th size class of bed material contained in the second layer when
∂
∂
z
b
/∂
t
−
∂δ
/∂
t
≥
m
z
b
/∂
−
∂δ
m
/∂
<
0.
The first term on the right-hand side of Eq. (2.161) represents the exchange between
moving sediment and bed material, while the last term accounts for the exchange
between the mixing and second layers, due to rise or descent of the lower bound of
the mixing layer.
The bed-material gradation in the second layer is calculated by
t
t
p
bk
∂δ
∂(δ
s
p
sbk
)
∂
−
∂
z
b
∂
m
=−
(2.162)
t
∂
t
t
