Geoscience Reference
In-Depth Information
where
T
¼
time of sampling; and
l
i
,
H
(
t
) i
s the
detection function given by
l
i
,
H
(
t
)
¼
1,
0
:
5
0
:
5
,and
if (
u
0
,
w
0
)isinquadrant
i
and if |
u
0
w
0
|
w
0
w
0
Þ
H
ð
u
0
u
0
Þ
ð
l
i
,
H
(
t
)
¼
0, otherwise.
Here,
S
i
,
H
>
1and3
(
Q
1and
Q
3 events). Hence, at a point, the algebraic summation of the contributions-
from different bursting events to
0 when
i
¼
2and4(
Q
2and
Q
4 events), and
S
i
,
H
<
0 when
i
¼
0isunity,thatis,
P
i¼
4
u
0
w
0
for
H
¼
S
i;
0
¼
1.
i
¼
0
7.3 Earlier Developments
The role of turbulent bursting corresponding to the sediment entrainment seems to
have received increasing attention. Sutherland (
1967
) observed that the sediment
threshold is associated with a near-bed eddy impact onto the bed particles to pro-
duce a streamwise drag force that is large enough enabling to roll the particles. The
role of the turbulent structures on the sediment entrainment was investigated by
Heathershaw and Thorne (
1985
) in tidal channels. They argued that the entrainment
is not correlated with the instantaneous Reynolds shear stress but correlated with the
near-wall instantaneous streamwise velocity. Field observations by Drake et al.
(
1988
) on mobility of gravels in alluvial streams suggested that the majority of the
gravel entrainment is associated with the sweep events which give rise to the motion
of particles. These events occur during a small fraction of time at any particular
location of the bed. Thus, the entrainment process is rather episodic with short periods
of high entrainment together with long periods of relatively feeble or no entrainment.
Thorne et al. (
1989
) observed that sweeps and outward interactions play an important
role in sediment entrainment. It is the instantaneous increase in streamwise velocity
fluctuations that generate excess boundary shear stresses, governing entrainment
processes. Having studied the sediment entrainment by nonuniform flows over two-
dimensional dunes, Nelson et al. (
1995
) reported that the near-bed turbulence can
change considerably and hence the sediment entrainment; while the boundary shear
stress remains almost unchanged. They observed that when the magnitude of the
outward interactions increases relative to the other bursting events, the sediment flux
increases albeit the boundary shear stress decreases.
7.4 Recent Developments
Sarkar (
2010
) studied the turbulence characteristics on immobile and entrainment
threshold sediment beds having uniform sediment size of 4.1 mm. A summary of
the results obtained by him is furnished below:
In Fig.
6
, the distributions of nondimensional Reynolds shear stress
2
,
as a function of nondimensional height
z
/
h
, are shown. Here,
h
is
flow depth; and the
solid line in Fig.
6
represents gravity line that follows
u
0
w
0
=
u
2
h
for
free surface flows having a zero-pressure gradient. Near the bed, the experimental
distributions of Reynolds shear stress for immobile and entrainment threshold beds
u
0
w
0
=
u
¼
1
z
=
