Teton dam failure, June 5, 1976, Teton Canyon, Idaho.
Flood routing is the calculation of the movement
of a flood wave in space and time along a stream or channel.
The governing equations are the equations of
water continuity and motion of open-channel flow, the so-called
Saint-Venant
The realization that the role of inertia is very often minimal led
This article analyzes the significance of the dispersion term
in both the theory and practice of hydraulic engineering. The online calculator
Table 1, Equation 1, shows
the convection-diffusion-dispersion equation. The convection coefficient is the Seddon, or kinematic wave
celerity (
Table 2, Equation 5, shows
the dimensionless convection-diffusion-dispersion of flood waves
( Lighthill and Whitham, 1955; Ponce
and Simons, 1977). All three
dimensionless coefficients
are shown to be functions only of the Froude and Vedernikov numbers.
It is observed that the
dimensionless convection coefficient
Table 3 shows the results
of script y (Col. 3), and channel bottom slope
_{o}S (Col. 4)
as shown.
The focus was on unit-width discharge (_{o}q =
_{o}u) and
channel bottom slope _{o}y_{o}S _{o}β,
the exponent of the discharge-area
rating, was fixed at β = 1.5Specific observations regarding the coefficients of diffusion and dispersion are the following: Diffusion (Col. 9) increases strongly with an increase in unit-width discharge, i.e., with a simultaneous increase in both *u*and_{o}*y*_{o}(Cols. 2 and 3). Diffusion (Col. 9) increases strongly with a decrease in channel slope (Col. 4). Dispersion (Col. 10) increases very strongly with an increase in unit-width discharge, i.e., with a simultaneous increase in both *u*and_{o}*y*_{o}(Cols. 2 and 3). Dispersion (Col. 10) increases very strongly with a decrease in channel slope (Col. 4).
The magnitude of the dispersion coefficients (Col. 10), particularly for the mild slopes (Lines 3, 6, and 9), indicates that the order of magnitude of the dispersion effect could be comparable to that of the diffusion effect. This remains to be confirmed in actual routing computations.
A convection-diffusion-dispersion
equation of flood flows (
Chow, V. T. 1959.
Ferrick, M. G., J. Bilmes, and S. E. Long. 1984.
Fread, D. L. 1985. "Channel Routing," in
Hayami, I. 1951.
Lighthill, M. J. and G. B. Whitham. 1955.
Ponce, V. M. and D. B. Simons. 1977.
Ponce, V. M. 2014a.
Ponce, V. M. 2014b.
Ponce, V. M. 2020.
Ponce, V. M. 2023.
Saint-Venant, B. de. 1871. Theorie du mouvement non-permanent des eaux avec application aux
crues des rivieres et l' introduction des varees dans leur lit,
Seddon, J. A. 1900. |

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