Geoscience Reference
In-Depth Information
An analysis on sheltering of particles revealed that remote sheltering induced by
the prominent upstream particles has an effect to increase the apparent threshold
boundary shear stress of exposed particles.
6 Probabilistic Concept
The sediment entrainment is probabilistic in nature. It depends primarily on the
turbulence characteristics in conjunction with the location of a specific particle
relative to the surrounding particles of various sizes and their orientations. Gessler
(
1970
) estimated the probability that particles of a specific size remain stationary. It
was revealed that the probability of a given particle to remain stationary depends
strongly on the Shields parameter and feebly on the shear Reynolds number. Grass
(
1970
) proposed to use a probabilistic description of the stresses acting on a single
particle to achieve motion. He identified two probability distributions: one for the
boundary shear stress
t
w
induced by the fluid and other for the boundary shear
stress
t
wc
required to put the particle in motion. When these two distributions start
overlapping (Fig.
5
), the particles that have the lowest threshold boundary shear
stress start to move. The representative magnitudes of the probability distributions
are their standard deviations being used to describe the distance of the two mean
boundary shear stresses as
t
wc
t
w
¼
n
ðs
c
s
t
Þ
. He experimentally obtained the
relationships as
s
t
¼
0
:
4
t
w
and
s
c
¼
0
:
3
t
wc
, which leads
to
t
w
¼ t
wc
ð
0.625, the result collapses with that of Shields.
Mingmin and Qiwei (
1982
), who developed a stochastic model, expressed
the statistical parameters using the velocity of bottom flow and particle size.
The probability of incipient motion, life distribution of stationary particles,
number of distributions of particles in incipient motion, and intensity of incipient
motion were derived. Wu and Chou (
2003
) studied the rolling and lifting prob-
abilities for sediment entrainment by introducing the probabilistic features of
the turbulent fluctuations and particle shape. These probabilities were linked to
the two separate criteria for incipient motion to study the threshold entrainment
probabilities.
The discovery of the turbulent bursting phenomena has encouraged the research-
ers in further studying the role of turbulence on sediment entrainment. In an attempt
1
0
:
3
n
Þ=
ð
1
þ
0
:
4
n
Þ
. For
n
¼
P
(τ)
n
(σ
c
+ σ
τ
)
Fig. 5 Probabilities of
boundary shear stress
t
w
due
to flow and threshold
boundary shear stress
t
wc
corresponding to the motion
of individual particles
τ
w
τ
wc
τ
