Basic Concepts and Management Issues of Rivers - River Dynamics and Integrated River Management - page 14

flow. Hence, the existence of suspended load reduces the turbulence intensity.
As shown in Fig. 1.12, the concentration distribution of suspended load is heterogeneous, with a
negative concentration gradient. The coarser the sediment, the more heterogeneous is the distribution. In
steady turbulent flow, the amount of sediment carried by eddies from the lower layer into the upper layer
per time is proportional to the concentration gradient. The sediment falling down from the upper layer into
the lower layer is the product of concentration, S v , and the fall velocity, Ȧ . If the concentration distribution
is in equilibrium, the following equation results:
d S

H

v

S Z 0 (1.18)

y v

d y

in which H y is the diffusion coefficient of sediment and y is the position in the vertical direction. Many
researchers have assumed

hy
Uy

HN (1.19)

y *

h

in which

is the shear velocity, R is the hydraulic radius
of the flow and is equal to the average depth ( h ) in wide river channel, and g is the acceleration due to
gravity Substituting Eq. (1.19) into Eq. (1.18) and integrating yields the vertical concentration profile of
suspended load

N is the von Karman constant,

0.41

* UgsR

z

S § hy a ·

v

¹

(1.20)

¨ ¸

S y h a

©

va

in which a is the elevation from the bed of a reference point, S is the concentration at the point, and Z

va

is given by

Z
N

Z (1.21)

U

*

is a dimensionless number called the Rouse Number .

Fig. 1.12 Concentration profiles of different sizes of suspended sediment in a natural river compared with the
theoretical formula (Eq. (1.20)) (after Wang et al., 2001)

1.1.4.3 Bed Material Load and Wash Load
Einstein, Anderson and Johnson (1940) analyzed a number of size distribution curves of sediment
samples and found that the ratios of fine to coarse sediment in the channel bed and that for the sediment