


107
Rodney J. Sobey
Lateral structure of uniform flow
Journal of Hydroinformatics
06.2
2004
of the depthintegrated 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
nearbank gradients are significantly less steep than those
model. The crosssectionintegrated n would be specified
that would characterize a turbulent boundary layer
in place of f and a depthintegrated 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 depthaveraged 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 crosssection 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