Geoscience Reference
In-Depth Information
collected, dried, and weighted subsequent to each experiment. By means of these
measurements, a bed load balance is established for each experiment. Water levels
are measured continuously by ultrasonic systems at ten different cross sections
along the channels.
3 Modeling Bed Load
3.1 Problems Arising from Conventional Scaling
Modeling sediment transport implies the conversion of the natural grain size
distribution into model scale. Doing this, the anomaly of the critical dimensionless
shear stress
Y
cr
depending on the particle Reynolds number
Re
*d
, as depicted in the
Shields' diagram (Fig.
4
), has to be considered.
Re
*d
¼
u
*
cr
d
/u with u being the
kinematic viscosity and
u
*
cr
being the critical dimensionless shear velocity:
p
Y
cr
ð
u
cr
¼
r
s
r
=
1
Þ
g
d
(1)
For
Re
*d
cr
>
200,
Y
cr
is considered as a constant value of 0.047. For
Re
*d cr
¼
2 - 200,
Y
cr
varies between 0.03 and 0.047 and for
Re
*d
cr
<
2, the relation
Y
cr
¼
0.1/
Re
*d
cr
is valid.
In gravel bed rivers with highly turbulent supercritical flow conditions, as
Alpbach and Milibach,
Re
*d
is to a great extent higher than 200 for the majority
of grain fractions. The conventional, geometrical conversion of the grain sizes into
model scale by the multiplication with the scale 1:l, however, leads to a reduction
of
Re
*d
and might involve that some scaled grains show values of
Re
*d
<
200.
As
Y
cr
is hence smaller than 0.047 (Fig.
4
), these grains get transported by a smaller
Fig. 4 Shield's diagram (Adapted from Buffington
1999
)
