Geoscience Reference
In-Depth Information
where
c
1
¼
coefficient varying from 1 for noncohesive to 0.1 for cohesive sedi-
ments. Many researchers have categorically disapproved the concept of competent
velocity. The unanswered question is as to what is meant by the competent velocity
at particle level
u
cr
or the competent average-velocity
U
cr
. This confusion has
insisted the researchers to seek a more acceptable standard quantity like the
threshold boundary shear stress. Nevertheless, Yang's (
1973
) analysis for the
estimation of
U
cr
seems to be reasonable.
4 Lift Force Concept
Einstein (
1950
), Velikanov (
1955
), Yalin (
1963
), Gessler (
1966
), and Ling (
1995
)
thought that the sediment is entrained solely by the lift force. The lift force can
primarily be induced for the following reasons: (1) Sediment particles on the bed
surface experience maximum velocity gradient, and thus a lift acts on the particles
due to considerable pressure difference; (2) sediment particles may experience lift
due to the instantaneous vertical velocity fluctuations in the vicinity of the bed; and
(3) the spinning motion of sediment particles may result in lift due to Magnus effect
(Dey
1999
). Note that if the lift force equals the submerged weight of the particle,
then drag force is adequate to entrain the bed particles.
Jeffreys (
1929
) assumed a potential flow over a circular cylinder having its axis
perpendicular to the flow arguing that the lift is prevalent if (3
2
)
U
2
þ p
>
9
Dgr
1
,
where
r
1
¼
radius of the cylinder. To apply this result, modification factors should
be accounted for, as the two-dimensional model behaves in a different way than a
three-dimension spherical particle in a fluid flow. The drawback of the analysis was
that the drag force was ignored. Reitz (
1936
) discussed a similar idea to express the
sediment entrainment with a lift model, where circulation and viscosity were
important parameters of his analysis. Lane and Kalinske (
1939
) emphasized on
turbulence for the quantification of lift and assumed that (a) the particles experience
lift when their terminal fall velocity is smaller than the instantaneous vertical
velocity fluctuations in the vicinity of the bed, (b) the variation of velocity fluctua-
tions follows a normal-error law, and (c) a correlation exists between the velocity
fluctuations and shear velocities. Einstein and El-Samni (
1949
) measured the lift
force directly as a pressure difference and proposed the lift force per unit area
f
L
¼
(
u
0.35
d
)
2
, where
C
L
¼
lift coefficient assumed as 0.178; and
u
0.35
d
¼
flow velocity at an elevation 0.35
d
from the theoretical bed. They also studied the
turbulent fluctuations on the lift. The experiments revealed a constant average lift
force with superimposed random fluctuations that follow the normal-error law.
Their results were used by the Task Committee (
1966
) estimating
f
L
/
0.5
C
L
r
t
c
2.5;
where
threshold boundary shear stress. It suggests that the lift force is an
important mechanism of the threshold of sediment entrainment. However, Chepil
(
1961
) pointed out that once the particle moves, the lift and drag tend to diminish
and increase, respectively. Chepil (
1961
) measured that the lift to drag ratio is about
0.85 for 47
t
c
¼
10
3
, in a wind stream on hemispherical roughness
<
UD
/
u <
5
