Geoscience Reference
In-Depth Information
3.8 TEMPORAL LAGS BETWEEN FLOW AND SEDIMENT
TRANSPORT
Sediment transport exhibits temporal lags with flow due to flow and sediment velocity
difference and bed form development. In particular, such lags become significant for
coarse sediment transport under strongly unsteady flow conditions (e.g., Bell, 1980;
Tsujimoto
et al
., 1988; Phillips and Sutherland, 1990; Song and Graf, 1997; de Sutter
et al
., 2001; Wu
et al
., 2006).
Lag between flow and suspended-load transport
There is a lag between the local flow and suspended-load velocities. This has been
observed experimentally by Muste and Patel (1997) and discussed in detail by Cheng
(2004). A two-phase flow model (Wu and Wang, 2000; Greimann and Holly, 2001)
can be used to describe this local velocity lag in general situations. However, according
to the experimental observations of Muste and Patel (1997), the local streamwise
velocity of suspended load with a diameter of 0.23 mm is less than the local flow
velocity by as much as 4%; this local velocity difference is negligible in comparison
with the depth-averaged flow and suspended-load velocity difference (Wu
et al
., 2006).
Thus, the local velocity lag may be ignored, and only the depth-averaged velocity lag
is discussed below.
The concentration-weighted velocity of suspended load can be defined as
u
s
cdz
h
δ
h
U
sed
=
cdz
(3.134)
δ
which is actually the overall velocity of suspended load from a depth-averaging point
of view. Therefore, the correction factor
s
defined in Eq. (2.87) also is the ratio of
the depth-averaged suspended-load and flow velocities:
β
β
=
U
sed
/
U
(3.135)
s
where
U
is the depth-averaged flow velocity.
Because higher sediment concentration corresponds to smaller flow velocity near
the channel bottom while lower sediment concentration corresponds to larger flow
velocity in the upper flow layer,
β
s
normally is less than 1 an
d
U
sed
≤
U
. By using
+
√
g
the logarithmic distribution of flow velocity,
u
,
and the Rouse distribution of suspended-load concentration introduced in Section
3.5.1 with the reference level set at 0.01
h
,Wu
et al
. (2006) obtained the relation
of
=
U
{
1
[
1
+
ln
(
z
/
h
)
]
/(
C
h
κ)
}
β
s
with the Rouse number
ω
/(κ
U
∗
)
and the Chezy coefficient
C
h
, as shown
s
in Fig. 3.26. It can be seen that
s
decreases as the Rouse number increases and
the Chezy coefficient decreases. For fine sediments,
β
β
s
is close to 1 and the lag
between the depth-averaged flow and sediment velocities can be ignored. However,
for coarse sediments, this lag can be up to 50% of the flow velocity and should be
considered.
