Geoscience Reference
In-Depth Information
Fig. 2 Results of approximation using (
10
)-(
12
) for the modified tachoida (Data from Stone and
Hotchkiss
2007
)
The examples of results of such calculations are presented in Fig.
2
. Data for
calculation were taken from Stone and Hotchkiss (
2007
). The research performed by
Stone and Hotchkiss (
2007
) was made at a broad natural river (width of ca. 100 m,
and flow of ca. 300 m
3
/s) whose cross-section shape was close to rectangular.
In Fig.
2
, it can be seen that measured and calculated velocities differ from each
other. This concerns especially the upper layer. The measured velocities at the
water surface are bigger than the calculated ones. This comes from the influence of
river banks and will be analyzed in the later part of this chapter.
3
Influence of River Banks upon Tachoida
The influence of river banks is a factor that affects the shape of modified tachoida.
Taking the river banks into consideration requires a two-dimensional model,
u
x
¼ u
x
ð
, to be introduced. This problem can be described in the following
way: The two-dimensional problem needs a second component, the turbulent shear
stress, to be included. So in addition to
z
;
y
Þ
t
xy
.Itis
assumed that the components of shear stress can be described by the relationships:
t
xz
,
there is a new component,
@u
x
@
z
H
t
xz
¼ r
K
z
z
¼
C
z
f
1
ð
y
Þ
1
(14)
and
(15)
K
y
@u
x
@
y
B
t
xy
¼ r
y
¼
C
y
f
2
ð
z
Þ
1
