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are given as a critical value of the overall dimensionless
boundary shear stress,
(2) comprise bedload as defined previously. Suspended
motion begins when bursts of fluid turbulence are able to
lift saltating grains upward from their regular ballistic
trajectories, a crude statistical criterion being when the
mean upward turbulent velocity fluctuation exceeds the
particle fall velocity, that is,
w
. The threshold value is thus an
important practical parameter in environmental engineer-
ing. A particular fluid shear velocity,
u
*
, above the thresh-
old for motion may also be expressed as a ratio with
respect to the critical threshold velocity,
u
*c
. This is the
transport stage
, defined as the ratio
u
*
/
u
*c
. Once that
threshold is reached, grains may travel (Fig. 4.38) by
(1) rolling or intermittent sliding (2) repeated jumps or
saltations
(3) carried aloft in
suspension
. Modes (1) and
/
V
p
1.
4.8.2 Fluids as transporting machines: Bagnold's
approach
It is axiomatic that sediment transport by moving fluid
must be due to momentum transfer between fluid and
sediment and that the resulting forces are set up by the
t
zz
Suspended
load
z
t
zx
Bedload
x
Bed
Fig. 4.34
Stresses responsible for sediment transport.
Wind flow
Note decay of pressure lift force to
zero at >3 sphere diameters away
from surface as the Bernoulli
effect is neutralized by
symmetrical flow above and
below the sphere
z
Lift
Drag
x
Surface
Fig. 4.36
(left) W.S. Chepil made the quantitative measurements of
lift and drag used as a basis for Fig. 4.35. Here he is pictured
adjusting the test section of his wind tunnel in the 1950s. Much
research into wind blown transport in the United States was
stimulated by the Midwest “dust bowl” experiences of the 1930s.
Fig. 4.35
Relative magnitude of shear force (drag) and pressure lift
force acting on spheres by constant air flow at various heights above
a solid surface.
10
-0
10
-1
Envelope of data
10
-2
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
Grain Reynolds number,
u
*
d
/
n
Fig. 4.37
Variation of dimensionless shear stress threshold,
, for sediment motion in water flows as a function of grain Reynolds number.
is
known as the Shields function, after the engineer who first proposed it in the 1930s.
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