Physical Processes in Earth and Environmental Sciences Phần 5 pptx

122 Chapter 4

are given as a critical value of the overall dimensionless

boundary shear stress,

. 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

(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

/Vp

 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

tzz

tzx

Suspended

load

Bedload

Bed

z

x

Fig. 4.34 Stresses responsible for sediment transport.

Wind flow

Lift

Drag Surface

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

x

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.

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.

10–1

10–0

10–2

10–2 10–1 100 101 102 103 104

Grain Reynolds number, u*

d/n

Dimensionless bed shear stress,

u = t/(

s–r)gd

Envelope of data

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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Flow, deformation, and transport 123

differential motion of the fluid over an initially stationary

boundary. Working from dynamic principles Bagnold

assumed that

1 In order to move a layer of stationary particles, the layer

must be sheared over the layer below. This process involves

lifting the immersed mass of the topmost layer over the

underlying grains as a dilatation (see Section 4.11.1), hence

work must be done to achieve the result.

2 The energy for the transport work must come from the

kinetic energy of the shearing fluid.

3 Close to the bed, fluid momentum transferred to any

moving particles will be transferred in turn to other sta￾tionary or moving particles during impact with the loose

boundary; a dispersion of colliding grains will result.

The efficacy of particle collisions will depend upon the

immersed mass of the particles and the viscosity of

the moving fluid (imagine you play pool underwater).

4 If particles are to be transported in the body of the fluid

as suspended load, then some fluid mechanism must act to

effect their transfer from the bed layers. This mechanism

must be sought in the processes of turbulent shear,

chiefly in the bursting motions considered previously

(Section 4.5).

The fact that fluids may do useful work is obvious from

their role in powering waterwheels, windmills, and tur￾bines. In each case flow kinetic energy becomes machine

mechanical energy. Energy losses occur, with each machine

operating at a certain efficiency, that is, work rate avail￾able power  efficiency. Applying these basic principles to

nature, a flow will try to transport the sediment grains

supplied to it by hillslope processes, tributaries, and bank

erosion. The quantity of sediment carried will depend

upon the power available and the efficiency of the energy

transfer between fluid and grain.

4.8.3 Some contrasts between sediment transport in

air and water flows

Although both air and water flows have high Reynolds

numbers, important differences in the nature of the two

transporting systems arise because of contrasts in fluid

material properties. Note in particular that

1 The low density of air means that air flows set up lower

shearing stresses than water flows. This means that the com￾petence of air to transport particles is much reduced.

2 The low buoyancy of mineral particles in air means

that conditions at the sediment bed during sediment

transport are dominated by collision effects as particles

exchange momentum with the bed. This causes a fraction

of the bed particles to move forward by successive grain

impacts, termed creep.

3 The bedload layer of saltating and rebounding grains

is much thicker in air than water and its effect adds signif￾icant roughness to the atmospheric boundary layer.

4 Suspension transport of sand-sized particles by the

eddies of fluid turbulence (Cookie 13) is much more

Lift

Drag

Gravity

Resultant

Pivot

angle Impact Lift off

Saltation trajectory Flow

Suspension

trajectory

Turbulent

burst

Grain lifted aloft by

turbulent

burst

z

x

Fig. 4.38 Grain motion and pathways.

Table 4.3 Some physical contrasts between air and water flows.

Material or flow property Air Water

Density, (kg m3) at STP 1.3 1,000

Sediment/fluid density ratio 2,039 2.65

Immersed weight of sediment per unit volume (N m3) 2.6 104 1.7 104

Dynamic viscosity,  (Ns m2) 1.78 105 1.00 103

Stokes fall velocity, Vp (m s1

) for a 1 mm particle ~8 ~0.15

Bed shear stress, zx (N m2) for a 0.26 m s1 ~0.09 ~68

shear velocity

Critical shear velocity, u*c, needed to 0.35 0.02

move 0.5 mm diameter sand

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124 Chapter 4

difficult in air than in water, because of reduced fluid shear

stress and the small buoyancy force. On the other hand the

widespread availability of mineral silt and mud (“dust”)

and the great thickness of the atmospheric boundary layer

means that dust suspensions can traverse vast distances.

5 Energetic grain-to-bed collisions mean that wind￾blown transport is very effective in abrading and rounding

both sediment grains and the impact surfaces of bedrock

and stationary pebbles.

4.8.4 Flow, transport, and bedforms in

turbulent water flows

As subaqueous sediment transport occurs over an initially

flat boundary, a variety of bedforms develop, each adjusted

to particular conditions of particle size, flow depth and

applied fluid stress. These bedforms also change the local

flow field; we can conceptualize the interactions between

flow, transport, and bedform by the use of a feedback

scheme (Fig. 4.39).

Current ripples (Fig. 4.40c) are stable bedforms above

the threshold for sediment movement on fine sand beds at

relatively low flow strengths. They show a pattern of flow

separation at ripple crests with flow reattachment down￾stream from the ripple trough. Particles are moved in bed￾load up to the ripple crest until they fall or diffuse from the

separating flow at the crest to accumulate on the steep rip￾ple lee. Ripple advance occurs by periodic lee slope

avalanching as granular flow (see Section 4.11). Ripples

form when fluid bursts and sweeps to interact with the

boundary to cause small defects. These are subsequently

Turbulent

flow

Transport Bedform

Turbulent

flow structures

Modifications

(+ve and –ve) to

turbulence intensity

Local transport rate

Bedform initiation and development

1 ry causes

2 ry feedback

Flow separation,

shear layer eddies,

outer flow modification

Fig. 4.39 The flow–transport–bedform “trinity” of primary causes and secondary feedback.

(b)

(c)

(a)

Fig. 4.40 Hierarchy of bedforms revealed on an estuarine tidal bar becoming exposed as the tidal level falls. (a) Air view of whole bar from

Zeppelin. Light colored area with line (150 m) indicates crestal dunes illustrated in (b). (b) Dunes have wavelengths of 5–7 m and heights of

0.3–0.5 m. (c) Detail of current ripples superimposed on dunes, wavelengths c.12–15 cm.

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