Rodney J. Sobey
Lateral structure of uniform flow
Journal of Hydroinformatics
of the depth-integrated flow together with the horizontal
information is provided by the present theory.
The relationship between C and f is direct:
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
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.
gdnS0 gn 2
Figure 3(a) is a natural channel of roughly similar
width and cross-section area. The same S0, f and Q as for
the rectangular channel example are adopted.
and Equation (17) becomes
Dh = - 4.95 m,
yL = 45.65 m, yR = 96.79 m and A = 240.0 m2. From the
Stage 2 algorithm, e = 0.55 m /sec and f9 = 0.0021. Figure
3(b) shows the qx(y) profile, and Figure 3(c) the qx(y)/
[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
solutions would be in the prediction of the longitudinal
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