Integrated River Management - River Dynamics and Integrated River Management - page 743

dunes (Chien et al., 1998):

2

2

U §·

h D

¨ ©¹

(11.14)

L

2 g h

in which ' is the height of the sand dune, and D is a coefficient. Chang (1970) found from his experiments
that the coefficient Į equals 1.9 and the exponent of (/) ' is not 2 but 1.8. If there are n sand dunes per

length, i.e. , in which / is the wave length of sand dunes, the total water head loss per length is

the energy slope due to sand dunes:

n 1/ /

2

h

2

U §·

J

L

D

/ ©¹

(11.15)

¨¸

S

/ 2 g h

Fig. 11.27 Reactionary force on the bed particles resulting from bed load motion

For sand dunes in large rivers the ratio / ' is much smaller than 1. The water head loss, or the
resistance, caused by the form drag of sand dunes is much larger than the resistance caused by the
sediment on the bed. For instance, Simons and Richardson (1960) concluded from their experiments that
the friction factor of ripples and dunes is 2-3 times the grain friction factor for sand of diameter of 0.28
mm, and the friction factor of ripples and dunes is 2-4 times the grain friction factor for sand of diameter
of 0.45 mm.
In mountain streams with step-pool systems the resuistance reslting from the step-pools may be regarded
as similar to that for sand dunes and Eq. (11.14) is applicable. The resistance resulting from step-pool
systems, however, is much greater than that for sand dunes because the ratio of / ' is larger than 1.
Most of the flow energy is consumed in the step-pool system. A step-pool system consumes the flow
energy and also protects the bed sediment from erosion, which is similar to the protective action of bed
load motion.
The potential energy exerted on the bed the water body is consumed to overcome the resistance created
by bed structures and grain friction, and the remainder is consumed by bed load motion, thus
( p s U J qJ J J ) (11.16)

S b g

in which J g is the energy slope due to skin friction of the sediment grains on the bed. In mountain streams,
J g is very small and often negligible. If a step-pool system develops well, such as the Jiuzhai Creek, the
energy slope resulting from bed structures is so large as to be equal to the bed slope, s , and there is no
bed load motion. If the bed structure is destroyed by a great flood or buried by sediment, J b must be large
enough to match the stream power. Therefore, intensive bed load motion occurs.

11.2.2.2 Relation of Bed Structures and Bed Load Motion in Rivers
Field measurements were performed in 15 tributaries of the Xiaojiang River during the flood season of