FLOOD01888

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

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may affect measurements in a small-scale physical model
of a channel.

b. Wave types.

(1) Chop and swell on the surface of an estuary in a
stiff wind represent gravity waves, which are unlike a
flood wave in a river because the motions of the water
particles are confined to orbits in the upper layers of the
water body. The deeper a measurement is taken below
the surface of such a wave, the smaller are the velocities.
The celerities of such waves depend mainly upon the size
of the wave, and less upon the depth of the water upon
whose surface they travel. Such waves can cause sub-
stantial intermittent wetting, erosion, and even ponding
well above the surface of an otherwise undisturbed water
body. Their short wavelength implies variation of veloci-
ties and pressures in the vertical as well as in the hori-
zontal directions with time; hence, the mathematics of
their calculation is substantially more complicated than
that of flood waves. In typical flood studies, the magni-
tudes of such surface waves are estimated from empirical
formulas and then superimposed upon the surface of the
primary flood wave. Another kind of short wave occur-
ring in very steep channels at Froude numbers (see
paragraph 2-4c) near two results from the instability of
flow on those slopes. This form of wave motion is the
so-called "roll wave," and can be seen in steep channels,
such as spillways with small discharges (e.g.. gate
leakage).

(2) There is anolher variety of short wave that may
be pertinent to some flood waves. In rare instances,
changes in flow are so extreme and rapid that a hydraulic
bore is generated. This is a short zone of flow having
the appearance of a traveling hydraulic jump. Such a
jump can travel upstream (example: the tidal bore when
the tide rises rapidly in an estuary), downstream
(example: the wave emanating from behind a ruptured
dam), or stay essentially in one place (example: the
hydraulic jump in a stilling basin).

c. Flood waves. The essence of flood prediction is
the forecasting of maximum stages in bodies of water
subject to phenomena such as precipitation runoff, tidal
influences (including those from Slorm tides), dam opera-
tions, and possible dam failures. Also of interest are
discharge and stage hydrographs, velocities of anticipated
currents, and duration of flooding. Deterministic
methods for making such predictions, typically called
flood routing, relate the response of the water to a partic-
ular flow sequence. A brief introduction is given here;

EM 1110-2-1416
15 Oct 93

details and examples are in Chapter 5 and Appendix D.
Only one-dimensional situations are discussed here; that
is, river reaches in which the length is much greater than
the width. Similarly, it is assumed that the boundaries of
the reach are rigid and do not deform as a result of the
flow (see Chapter 7 and EM 1110-2-4000, 1989).

(1) Flood routing. Many flood routing techniques
were developed in the late nineteenth and early twentieth
centuries. The fact that water levels during flood events
vary with buth location and time makes the mathematics
for predicting them quite complicated. Various simplify-
ing assumptions were introduced 10 permit solutions with
a reasonable amount of computational effort. While
analytical techniques for solving linear wave equations
were known, those solutions could not, in general, be
applied to real floods in real bodies of water because of
the nonlinearity of the governing equations and the com-
plexity of the boundaries and boundary conditions.
Numerical solutions of the governing equations were
largely precluded by the enormous amount of arithmetic
computation required. The advent and proliferation of
high-speed electronic computers in the second half of the
twentieth century revolutionized the computation of flood
flows and their impacts. Numerical solutions of the
governing partial differential equations can now be
accomplished with reasonable effort.

(2) Data for flood routing. Solution of the partial
differential equations of river flow requires prescription
of boundary and initial conditions. In particular, the
geometry of the watercourse and its roughness must be
known, as well as the hydraulic conditinns at the
upstream and downstream ends of the reach and at all
lateral inflows and outflows (tributaries, diversions) along
the reach. Due to the extreme irregularity of a natural
watercourse, the channel geometry and hydraulic proper-
ties (such as roughness and infiltration) cannot be
specified exactly. The accuracy 10 which they must be
specified 10 yield reliable results is not a trivial issue
(U.S. Army Corps of Engineers 1986, 1989).

(3) Water motion. The motion of water particles at
a cross section during a flood is nearly uniform, lop 10
bottom. The drag of the sides and bottom. possible
secondary currents resulting from channel bends or irreg-
ularities, and off-channel slorage (ineffective flow) areas
create a nonuniform distribution of velocity across a
cross section. The celerity of a flood wave is dependent,
in a fundamental way, on the water depth. In a flood
wave, the pressure distribution is nearly hydrostatic; i.e.,
it increases uniformly with depth below the surface.

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