60
R.H. Charlier and Chr. P. De Meyer
The parabolic distribution is most satisfactory in a physical sense because it is
based on a linear shear stress distribution and a logarithmic velocity profile. A
disadvantage of the parabolic distribution is that it yields a zero-concentration at
the water surface. Sediment mixing coefficients based on the analysis of
measured concentration profiles (Coleman, 1970) indicate a parabolic-constant
distribution rather than a parabolic one, as shown in Fig. 4. Usually, the mixing
or diffusion of the sediment particles is related to the fluid mixing coefficient for
a clear fluid (e~) as follows :
~s,c :]~Ogf~
(11)
2.3.1
J~-factor
The 13-:factor describes the difference in the diffusion of a fluid "particle" (or
small coherent fluid structure) and a discrete sediment particle. Herein, the 13factor is assumed to be constant over the flow depth. Information of the 13-factor
can be obtained from a study carried out by Coleman (1970). Based on eq. (6),
Coleman computed the sediment mixing coefficients (see Fig. 4). We will use
Coleman's results to determine the 13-factor, defined as 13 = es,~x /~f~,x. The
~f~-value was computed from Eq. (2.151) for z/h = 0.5. The escrow-value was
determined as the average value of the es-values in the upper haft of the flow (as
given by Coleman, Fig. 4) where the concentrations are relatively small. The 13factors can be represented by the following function :
, ,(w s )2
Ws
ku.o)
U*~C
(12)
Equation (12) specifies a value larger than unity, indicating a dominant influence
of the centrifugal forces which cause the particles to be thrown to the outside of
the eddies with a consequent increase of the effective mixing length. Given the
limited knowledge of the physical processes involved, it is not advisable to use a
J~-factor larger than 2.
2.3.2
q)-factor
The qb-factor expresses the influence of the sediment particles on the turbulence
structure of the fluid (damping effects). Usually the damping effect is taken into
account by reducing the constant of Van Karman (K).
R.H. Charlier and Chr. P. De Meyer
The parabolic distribution is most satisfactory in a physical sense because it is
based on a linear shear stress distribution and a logarithmic velocity profile. A
disadvantage of the parabolic distribution is that it yields a zero-concentration at
the water surface. Sediment mixing coefficients based on the analysis of
measured concentration profiles (Coleman, 1970) indicate a parabolic-constant
distribution rather than a parabolic one, as shown in Fig. 4. Usually, the mixing
or diffusion of the sediment particles is related to the fluid mixing coefficient for
a clear fluid (e~) as follows :
~s,c :]~Ogf~
(11)
2.3.1
J~-factor
The 13-:factor describes the difference in the diffusion of a fluid "particle" (or
small coherent fluid structure) and a discrete sediment particle. Herein, the 13factor is assumed to be constant over the flow depth. Information of the 13-factor
can be obtained from a study carried out by Coleman (1970). Based on eq. (6),
Coleman computed the sediment mixing coefficients (see Fig. 4). We will use
Coleman's results to determine the 13-factor, defined as 13 = es,~x /~f~,x. The
~f~-value was computed from Eq. (2.151) for z/h = 0.5. The escrow-value was
determined as the average value of the es-values in the upper haft of the flow (as
given by Coleman, Fig. 4) where the concentrations are relatively small. The 13factors can be represented by the following function :
, ,(w s )2
Ws
ku.o)
U*~C
(12)
Equation (12) specifies a value larger than unity, indicating a dominant influence
of the centrifugal forces which cause the particles to be thrown to the outside of
the eddies with a consequent increase of the effective mixing length. Given the
limited knowledge of the physical processes involved, it is not advisable to use a
J~-factor larger than 2.
2.3.2
q)-factor
The qb-factor expresses the influence of the sediment particles on the turbulence
structure of the fluid (damping effects). Usually the damping effect is taken into
account by reducing the constant of Van Karman (K).