Geology Reference
In-Depth Information
measurements when both bedload and suspended
load exist, the Bagnold definition is difficult, if not
impossible, to apply. Experimentally, the bedload is
sometimes defined as the part of the total load that
travels below a certain level (Nielsen
1992
). Several
modes of bedload motion have been described, includ-
ing rolling, sliding, and saltating.
Numerous empirical formulas predicting bedload
transport by currents have been developed Van Rijn
(
1984a
). One of the earliest and still a commonly used
bedload transport formulas was developed by Meyer-
Peter and Mueller (
1948
) as
the velocity cubed, much greater rate of transport
occurs during period of greater velocity (Fig.
2.5
).
Therefore, this time-velocity asymmetry will result in
a net transport in the direction of the faster (often flood)
flow. Time-velocity asymmetry may have significant
influence on sedimentation and morphology in a
certain tidal environment or a certain part of a tidal
environment.
2.2.2.3
Suspended-Load Transport
Bagnold (
1966
) suggested that when turbulent eddies
have dominant vertical velocity components exceed-
ing the particle fall velocity (
w
s
), the particle may
remain in suspension. Experiments indicate that the
vertical turbulent intensity (
w'
) has a maximum value
of the same order as the bed-shear velocity (
u
*
).
Therefore, assuming the vertical turbulent velocity
roughly equals bed-shear velocity and modifying the
Shields parameter, the initiation of sediment suspen-
sion (not to be confused with the initiation of motion
discussed above) can be described as
1.5
0.5
0.5
1.5
Q
8(
mq
0.047)
(
s
1)
g
d
(2.14)
b
m
where
Q
b
= volumetric bed-load transport rate,
q
= the
Shields parameter (Eq.
2.7
), and
m
= an efficiency
factor to incorporate the influence of bedforms on
bedload transport. Meyer-Peter and Mueller (
1948
)
used mean grain size (
d
m
) in both
Q
b
and
q
instead of
the
d
50
used by many other formulas. Since the Shields
parameter
q
is proportional to velocity squared,
the 1.5 power of
q
implies that bedload transport
rate is proportional to velocity cubed. This strong
non-linear relationship yields much greater transport
rates at larger velocities, e.g., during peak ebbing or
flooding.
Another commonly used bedload transport formula
and approach were developed by Bagnold (
1966
), via
balancing the work needed to be done by the grain-
shear stress in moving the bedload particles and the
fluid energy per unit area. The Bagnold (
1966
) formula
can account for the gravity forcing associated with a
sloping bed. Similar to the Meyer-Peter and Mueller
(
1948
) formula, the Bagnold (
1966
) formula also
suggests that bedload transport rate is proportional to
velocity cubed.
Due to nonlinear distortion by bottom friction, the
tidal wave may become asymmetrical, with half of the
tidal cycle shorter but with faster flow, while the other
half lasts longer with slower flow. Generally, the non-
linear friction (e.g., Eq.
2.3
) in shallow water may
result in greater resistance during low tide than during
high tide. Therefore, the time delay between low water
in the inlet and low water in the inner tidal basin is
longer than the time delay at high water. Due to mass
conservation, this leads to a shorter duration of the
flood and higher flood velocity, as compared to the
ebbing tide. Because transport rate is proportional to
u
2
w
2
(2.15)
*_
( )
crs
q
s
crs
s
Ds
( )
D
where the subscription “
crs
” denotes critical value for
sediment suspension. Generally, suspended particles
are assumed to move at the same velocity (
u
) as the
fluid and the suspended sediment transport (
q
s
) is com-
puted as
h
¯
q
u z c z dz
()()
(2.16)
s
a
where
c
= suspended sediment concentration, and
a
= the top level of the bedload layer. The sediment
concentration at the
a
level,
c
a
, is often referred to as
the reference concentration, which is a key parameter
in the determination of suspended sediment concen-
tration profile
c
(
z
). Equation
2.16
can also be used in
designing field or laboratory measurements of sus-
pended sediment transport rate. In other words, both
c
(
z
) and
u
(
z
) should be measured simultaneously to
obtain the transport rate. As discussed above, the
current velocity profile typically follows a logarithmic
curve (Eq.
2.1
). Numerous studies have been con-
ducted on sediment suspension resulting in various
models quantifying suspended sediment concentra-
tion profiles. Given that many tidal environments tend
to have a large amount of fine-grain sediments,
