FLOOD01888

• County: Statewide
• Title: River Hydraulics
• Date: 10/15/1993
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

.

-.

-"

.

...

.

b. Nonuniformity. Only when the nonuniformity of
the flow is primarily the result of nonuniform channel
geometry, rather than because of unsteadiness, can the
local acceleration be small compared to advective
acceleration.

(1) The neglect of all acceleration terms in the diffu-
sion model has advantages and disadvantages. A major
advantage is a more robust model, because the accelera-
tion terms are sometimes the source of computational
fragility, especially in a near-critical or supercritical flow.
To a diffusion model, all flows are infinitely subcritical.

(2) The disadvantages include the inability to simu-
late certain kinds of flow, seiching is infinitely damped,
and bores are imperfectly imitated by relatively gradual
rises in water surface elevation.

(3) The magnitude of the error in outflow hydro-
graph prediction for typical inflow hydrographs depends
on the channel and inflow hydrograph characteristics.

5-14. Kinematic Wave Model

a. Slope. If the slope of the bed is relatively steep
and the change in discharge is moderate, the pressure
term and the acceleration terms become small compared
to the bed and friction slope terms. Hence, the friction
slope and the bed slope are approximately in balance as
shown in Equation 5-11.

Sf= So

(5-11)

This is called the kinematic wave approximation, and the
flow can only be routed downstream. The water surface
elevation at each section can be calculated from
Manning's equation or obtained from a single-valued
rating curve for any discharge. There are no backwater
effects. The physical assumptions in this approximate
method are often justified in overland flow or steep chan-
nels if the flow is well established so that there is little
acceleration.

b. Limitations.

(1) The method is patently useless in horizontal
channels, because there is drag but no stream wise weight
component. It typically overestimates water depth in
channels of small slope. As a rule of thumb, the kine-
matic wave approximation may be applicable for slopes

EM 1110-2.1416
15 Oct 93

greatet than 10 feet per mile, depending upon the shape
of the hydrograph. Experience has shown that kinematic
wave should not be used when analyzing flows in rivers.

(2) A characteristic feature of flood wave behavior
computed with this method is that, in the absence of
lateral inflow/outflow, there is no subsidence of the crest.
Certain numerical schemes introduce a spurious
numerical subsidence, but that cannot be used rationally
to model real subsidence. The phenomenon of kinematic
shock allows flood wave subsidence within the context of
kinematic wave'theory; but does not model real subsi-
dence. When subsidence is important, a kinematic wave
model should not be used.

(3) The major advantage of kinematic wave is that it
displays no computational problems at critical depth.

5-15. Accuracy of Approximate Hydraulic
Models

Numerical criteria are presented in Ponce (1989) for
estimating the relative accuracy of approximate models.
Some of the criteria are based on the relative magnitude
of neglected terms in the unsteady flow equations (5-3
and 5-4). Others, dealing with hydrologic methods, are
concerned with subreach length relative to length of the
flood wave. Still others stem from the results of compar-
ative tests.

a. Kinematic versus diffusion. According to Ponce
(1989), kinematic and diffusion wave models may be
used in reaches with little or no downstream control.
The diffusion wave has a wider range of applicability
than the kinematic wave and should be used unless a
strong case can be made for the latter. Ponce suggests
the following criteria for determining applicability of the
two methods:

The kinematic wave model can be used if

T,Souo > 85 (5-12)
do
The diffusion wave model can be used if

T,So J 8 > IS
do

(5-13)

where

5-29