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where
f
bk
is the nondimensional bedload transport capacity
n
0
¼
d
1
=
6
50
20
is the Manning's coefficient corresponding to the grain roughness
n
is the Manning's coefficient,
t
b
is the bed shear stress
p
ek
0
:
6
p
hk
t
ck
¼
0
:
03
ð
g
s
g
Þ
is the critical shear stress
p
hk
¼
P
and
p
ek
¼
P
N
N
p
bj
d
j
d
k
þ
p
bj
d
k
d
k
þ
are the hiding and exposure probabilities
for the
k
th size class of bed material, respectively.
For this reason, the model of bedload movement for the Białka River was based
on this very formula (the other available were: SEDTRA, Wu et al., Engelund and
Hansen's and Ackets and White's).
The Białka model was made using 40,050 quadrilaterals formed on
I
ð
Þ
ð
Þ
d
j
d
j
j
1
j
1
¼
50
J
801 lines mesh. Roughness coefficient
n
of the flow during the model activity
was computed using Wu and Wang equation (
1999
) based on the diameter of bed
material and relative roughness. In order to improve the precision of the model, the
k-
¼
equation was applied for computing water flow, whereas modeling of bed
material transport was conducted for three layers with a minimum thickness of
0.3 m, enabling fast changes of the bottom configuration. The primary granulation
applied in the model was described by ten fractions measured on measurement
point 3. The thickest bedload layer provided a source of uniformly grained material.
Initial conditions of the bed material movement and the amount of transported
material in the selected reference cross-section were computed using the TRANS
program (Bartnik
1992
) based on MPM-B formula, developed by Bartnik (Bartnik
and Kopka
1991
).
e
5 Presentation and Interpretation of Results
5.1 Cross-Sections
The floodwater which occurred in the spring 2010 in many cross-sections caused
considerable changes in the bottom configuration measured in situ. Also the results
of modeling supplement these characteristics, although they do not represent
precisely the morphodynamic changes which occurred. The results were presented
graphically in Fig.
4
.
In the cross-section V an incision into the concave bank occurred to a depth of
about 23 m. At the same time, a forming accumulation zone was observed on the
left bank. Therefore, concentrated cross-section incised itself into the right bank.
A change of the river arms from cross-section V, in cross-section IV led to the
appearance of a developed river channel on the riverbed axis and a well-developed
left fork. No changes of the right bank part of the riverbed occurred.
The width of the riverbed between cross-sections IV and III has doubled and
there is a flat gravel bank partially reinforced by vegetation in the middle. A division
