Geoscience Reference
In-Depth Information
Figure 5.1
Comparison of dynamic and diffusion wave models at channel contraction.
Using the Manning equation, Eq. (5.5) can be rewritten as
A
n
R
2
/
3
S
1
/
2
Q
=
(5.6)
0
The continuity equation (5.1) is still used in the kinematic wave model.
The kinematic wave assumption is generally applicable, if (Dingman, 1984)
U
2
g
S
0
/
>
10
(5.7)
where
represents the length of the channel under study, and
U
is the average velocity
of uniform flow. Eq. (5.7) implies that the kinematic wave model is valid in steep
channels.
5.1.1.2 Imposition of boundary and initial conditions of flow
To establish a well-posed problem, boundary and initial conditions should be provided
for Eqs. (5.1) and (5.2). These dynamic wave equations constitute a hyperbolic system
that has two characteristics:
gh
dx
dt
C
+
=
=
U
+
(5.8)
gh
dx
dt
C
−
=
=
U
−
(5.9)
where
U
and
h
are the flow velocity and depth averaged over the cross-section,
respectively.
