68
R.H. Charlier and Chr. P. De Me),er
Winterwerp et al. did experiments with depth-averaged volume concentrations
ranging from c = 0 to c ~ 0.4. They found a reduction of the K-parameter from r¢
= 0.4 to r¢ = 0.25 for concentrations increasing from c = 0 to c ~ 0.1 , a nearly
constant K-value of about 0.25 for concentrations in the range of c ~ 0.1 to c ,~ 0.2
and an increase of the K value to approximately K ~ 0.4 for concentrations
increasing to c ~ 0.4. (Fig. 8b). According to Winterwerp et al., turbulence
damping due to the presence of large vertical concentration gradients occurs for
concentrations up to c = 0.2. For increasing concentrations (c > 0.2) the
concentration profile tends to become uniform due to dominating hindered
settling effects and turbulence damping disappears because the concentrations
gradients disappear (K nears 0.4, Fig. 8a,b).
2.6
Reference Concentration and Reference Level
2.6.1
Reference Level in Case of a Flat Bed
The most logic assumption for the location of the boundary" (or reference level)
for sediment concentrations is the upper edge of the bed-load layer. For a
perfectly fiat bed a good estimate of the thickness of the bed-load layer can be
obtained by taking the maximum saltation height of the bed-load particles (Van
Rijn, 1984). This leads to a value of the order of 10dso for fiat bed flow in the
upper regime. The concentrations close to the bed will be rather large and hence
the hindered settling effect and the turbulence damping effect must be taken into
account. However, at the present stage of research, the knowledge of these
processes is rather limited which may easily result in large errors of the predicted
concentrations as will be shown by a computation example for a flat mobile bed.
The concentration profile has been computed numerically by applying eqs. (15)
and (A) in combination with a parabolic-constant mixing coefficient. The
suspension number Z = WJ(13Ku.,o) is taken as 0.625. Because of errors in ws, 13,
K and u.,o the inaccuracy of the suspension number will be rather large (say at
least + 25%). Fig. 9 shows concentration profiles for Z = 0.625 + 0.175 (+ 25%).
As can be observed, an error of about 25% in the Z-parameter leads to a
concentration error of a factor 3 at a level ofz = 0.5 h (mid depth) and an error of
a factor 2 at a level of z = 0.1 h. Based on these results, it is evident that the
application of a reference level at the upper edge of the bed-load layer is not very
attractive for reasons of accuracy.
R.H. Charlier and Chr. P. De Me),er
Winterwerp et al. did experiments with depth-averaged volume concentrations
ranging from c = 0 to c ~ 0.4. They found a reduction of the K-parameter from r¢
= 0.4 to r¢ = 0.25 for concentrations increasing from c = 0 to c ~ 0.1 , a nearly
constant K-value of about 0.25 for concentrations in the range of c ~ 0.1 to c ,~ 0.2
and an increase of the K value to approximately K ~ 0.4 for concentrations
increasing to c ~ 0.4. (Fig. 8b). According to Winterwerp et al., turbulence
damping due to the presence of large vertical concentration gradients occurs for
concentrations up to c = 0.2. For increasing concentrations (c > 0.2) the
concentration profile tends to become uniform due to dominating hindered
settling effects and turbulence damping disappears because the concentrations
gradients disappear (K nears 0.4, Fig. 8a,b).
2.6
Reference Concentration and Reference Level
2.6.1
Reference Level in Case of a Flat Bed
The most logic assumption for the location of the boundary" (or reference level)
for sediment concentrations is the upper edge of the bed-load layer. For a
perfectly fiat bed a good estimate of the thickness of the bed-load layer can be
obtained by taking the maximum saltation height of the bed-load particles (Van
Rijn, 1984). This leads to a value of the order of 10dso for fiat bed flow in the
upper regime. The concentrations close to the bed will be rather large and hence
the hindered settling effect and the turbulence damping effect must be taken into
account. However, at the present stage of research, the knowledge of these
processes is rather limited which may easily result in large errors of the predicted
concentrations as will be shown by a computation example for a flat mobile bed.
The concentration profile has been computed numerically by applying eqs. (15)
and (A) in combination with a parabolic-constant mixing coefficient. The
suspension number Z = WJ(13Ku.,o) is taken as 0.625. Because of errors in ws, 13,
K and u.,o the inaccuracy of the suspension number will be rather large (say at
least + 25%). Fig. 9 shows concentration profiles for Z = 0.625 + 0.175 (+ 25%).
As can be observed, an error of about 25% in the Z-parameter leads to a
concentration error of a factor 3 at a level ofz = 0.5 h (mid depth) and an error of
a factor 2 at a level of z = 0.1 h. Based on these results, it is evident that the
application of a reference level at the upper edge of the bed-load layer is not very
attractive for reasons of accuracy.