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107
Rodney J. Sobey
Lateral structure of uniform flow
Journal of Hydroinformatics
06.2
2004
of the depth-integrated flow together with the horizontal
coefficient
of
turbulent
momentum
diffusion.
This
information is provided by the present theory.
`
Chezy model
`
The relationship between C and f is direct:
8g
g
f 82
e OE
(28)
or
.
f
e
|
Figure 3
Natural channel.
As f is dimensionless, the simplest approach would be to
retain the previous algorithm, with a prior translation
from C to f and a subsequent translation from f9 to C9.
From the Stage 1 algorithm, Dh = - 2.00 m, yL = 0 m,
yR = 100 m and A = 300.0 m2. From the Stage 2 algorithm,
e = 2.26 m2/sec and f9 = 0.0011. Figure 2(b) shows the
Manning model
qx(y) profile. The profile is symmetric, as expected. The
The changes are more fundamental for the Manning
near-bank gradients are significantly less steep than those
model. The cross-section-integrated n would be specified
that would characterize a turbulent boundary layer
in place of f and a depth-integrated n9 predicted in place of
between parallel plates. But this is a lateral profile of a
f9. SI units are assumed in the following discussion. For
FSS (footsecondslug) units, n and n9 are replaced by
integrated over the boundary layer profile in the vertical.
n/1.49 and n9/1.49, respectively.
The mean flow velocity gradients near the bed would
Equation (14) becomes
be quite sharp. Figure 2(c) shows the equivalent lateral
profile of qx(y)/[h(y) + Dh], the depth-averaged velocity.
q2
d2qx
x
gdnS0 gn 2
0
Figure 3(a) is a natural channel of roughly similar
(29)
e
dy2
dn/3
7
width and cross-section area. The same S0, f and Q as for
the rectangular channel example are adopted.
and Equation (17) becomes
From
the
Stage
1
algorithm,
Dh = - 4.95 m,
yL = 45.65 m, yR = 96.79 m and A = 240.0 m2. From the
y
yR
q2
Q2
yR
dqx
2
*h
x
Stage 2 algorithm, e = 0.55 m /sec and f9 = 0.0021. Figure
2
4/3
gn
e
gn 2
gAS0
(30)
P
dy.
A7/3
h 7/3
dy
3(b) shows the qx(y) profile, and Figure 3(c) the qx(y)/
L
yL
[h(y) + Dh] profile. As a direct consequence of the irregu-
In Stage 1 of the algorithm, Equation (18) would become
lar bathymetry, the lateral flow profile is asymmetric.
A further application of such structured uniform flow
Q2
solutions would be in the prediction of the longitudinal
43
2
gAS0 gn
f Dh
(31)
7 3P
.
A
dispersion coefficient for contaminant transport in the
same channel. The TaylorElderFischer theory (Fischer
In Stage 2 of the algorithm, Equation (23) becomes
et al. 1979) requires knowledge of the lateral distribution