Sediment Movement in Alluvial Rivers - River Dynamics and Integrated River Management - page 324

Because only one kind of light grains has been tested a final conclusion can only be worked out after
more experiments with various light bed materials are done.
There is still a lot of work to do to understand riverbed inertia and its application in fluvial processes.
For a simple application I b is introduced into the Exner equation and the partial differential equation is
changed into a normal differential equation. The variation of bed elevation is related to the spacious
variation of the sediment transport rate by the well-known Exner sediment-continuity equation

w g w Z

b

J

s (1

p ) 0 (5.75)

w x w t

If g b is smaller than the capacity g b * the channel bed is scoured. Substituting Eq. (5.74) into (5.75) yields

d g gg

b

J (1 p )

b* b

(5.76)

s

d x I

b

The equation can be solved as follows

gg ª x º

b* b

exp J (1 p ) (5.77)

« » s

g g I

¬ ¼ b* b0 b

in which g b0 is the transport rate at x 0. The equation shows that if the bed inertia is large, the exponent
is small and the flood has to travel a long distance for the transport rate to reach equilibrium. For instance,
the bed load of mountain rivers has a large riverbed inertia, hence, the transport rate is often much less
than the capacity. For a straight, plain riverbed composed of relatively uniform sand, the inertia is small and
the transport rate responds to the flow variation quickly, therefore, the bed deforms following the rising
and receding of floods.
The exponent in Eq. (5.77) is a dimensionless number,

J (1 pL )

A

s s

(5.78)

r

I

b

in which L s is a specific length and can be represented by the distance that the flood travels in a channel
with uniform flow and boundary conditions. The dimensionless number represents the ability of the channel
to respond to the variation of the flow. The larger is the dimensionless number, the quicker the channel
deforms following the flow variation.

5.4.3 Water-Sediment Chart
The Water-Sediment Chart is a diagrammatic expression of the distribution and variation of water and
sediment load of a river in a period of time. The significance of the chart is discussed with the Yangtze
River as an example. Figure 5.58 shows the water-sediment charts for the four main hydrological stations,
i.e. Pingshan, Yichang, Hankou, and Datong Stations, along the main course of the Yangtze River. The
long-term average ratio of sediment to water is 0.479 kg/m 3 at Datong, which is the station between the
river and the estuary. Then, the chart is drawn with the horizontal axis as the time of measurement, the
left vertical axis as the annual water and the right vertical axis as the annual sediment load. Make the
scale of the sediment load equal to the annual water volume with the sediment/water ratio, or 0.479 kg of
sediment equal to 1 m 3 of water. If the sediment curve is higher than water curve, the area between the
two curves is black and represents an over load of sediment for the flow to carry into the ocean. If the
water curve is higher than the sediment curve, the area between the two curves is gray and represents
more water than is needed to carry sediment into the ocean.
At Pingshan Station flow is low and sediment load is high, which means that the drainage area upstream
from Pingshan station is a sediment yield area. From Pingshan to Yichang both flow and sediment load
increase but sediment load increases much more than flow, thence, the black area becomes larger.