Kinematic Wave Controversy
Publication: Journal of Hydraulic Engineering
Volume 117, Issue 4
Abstract
Kinematic and diffusion waves are reviewed prompted by the continuing controversy regarding their nature and applicability. Kinematic waves are shown to be nondiffusive, but to undergo change in shape due to nonlinearity. This latter feature gives kinematic waves the capability of steepening, eventually leading to the formation of the kinematic shock. Kinematic wave solutions using finite differences are shown to possess intrinsic amounts of numerical diffusion and dispersion. These numerical effects are artificial and tend to disappear as the grid size is refined, making the solution dependent on the choice of grid size. Kinematic wave theory can be improved by extending it to the realm of diffusion waves. In this way, the diffusion inherent in many practical runoff computations can be accounted for directly in the modeling, rather than as an afterthought. The use of a kinematic wave method is indicated for small catchments, in cases where it is possible to resolve the physical detail without compromising the deterministic nature of the model. Conversely, the unit hydrograph is advocated for midsize catchments, where the kinematic wave method may prove difficult to implement. The dynamic extension to kinematic and diffusion models shows promise, particularly for modeling channel and flow conditions in which the Vedernikov number is substantially different from zero.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B. (1976). “Computational hydraulics: A short pathology.” J. Hydr. Res., 14(4), 271–285.
2.
Alley, W. M., and Smith, P. E. (1982). “Distributed routing rainfall‐runoff model—version II: User's manual.” Open‐File Report 82‐344, U.S. Geological Survey Water Resources Division, Gulf Coast Hydroscience Center, NSTL Station, Miss.
3.
Chow, V. T. (1959). Open‐channel hydraulics. McGraw Hill Book Co., Inc., New York, N.Y.
4.
“Computer program for project formulation‐hydrology.” (1983). USDA Soil Conservation Service, Tech. Release No. 20 (TR‐20), Washington, D.C.
5.
Cunge, J. A. (1969). “On the subject of a flood propagation computation method (Muskingum method).” J. Hydr. Res., 7(2), 205–230.
6.
Crandall, S. H. (1956). Engineering analysis: A survey of numerical procedures. McGraw‐Hill Book Co., New York, N.Y.
7.
Craya, A. (1952). “The criterion for the possibility of roll wave formation.” Proc., Gravity Waves Symp., Circular 521, U.S. National Bureau of Standards, Washington, D.C., 294–332.
8.
Dawdy, D. R. (1990). Discussion of “Kinematic wave routing and computational error.” J. Hydr. Engrg., ASCE, 116(2), 278–280.
9.
Design of small dams, 3rd ed. (1987). U.S. Bureau of Reclamation, Denver, Colo.
10.
Dooge, J. C. I. (1973). “Linear theory of hydrologic systems.” Tech. Bulletin No. 1468, USDA Agricultural Research Service, Washington, D.C.
11.
Dressler, R. F. (1949). “Mathematical solution of the problem of roll waves in inclined open channels.” Communications in Pure and Appl. Mathematics, 2, 149–194.
12.
Flood studies report. (1975). Natural Environment Research Council, London, England, Vol.III.
13.
Goldman, D. (1990). Discussion of “Kinematic wave routing and computational error.” J. Hydr. Engrg., ASCE, 116(2), 280–282.
14.
Hayami, S. (1951). “On the propagation of flood waves.” Bulletin of the Disaster Prevention Research Institute, Disaster Prevention Research Institute, Kyoto, Japan, 1(1), 1–16.
15.
HEC‐1, flood hydrograph package: Users' manual. (1985). U.S. Army Corps of Engineers, Hydrologic Engineering Center, Davis, Calif.
16.
Hjalmarson, H. W. (1984). “Flash flood in Tanque Verde Creek, Tucson, Arizona,” J. Hydr. Engrg., 110(12), 1841–1852.
17.
Hjelmfelt, A. T. (1984). “Negative outflows from Muskingum flood routing.” J. Hydr. Engrg., ASCE, 111(6), 1010–1014.
18.
Hromadka, T. V., and DeVries, J. J. (1988). “Kinematic wave and computational error.” J. Hydr. Engrg., ASCE, 114(2), 207–217.
19.
Hromadka, T. V., and DeVries, J. J. (1990). Closure of “Kinematic wave and computational error.” J. Hydr. Engrg., ASCE, 116(2), 288–289.
20.
Jolly, P. J., and Yevjevich, V. (1971). “Amplification criterion of gradually varied, single peaked waves.” Hydrol. Paper No. 51, Colorado State University, Fort Collins, Colo.
21.
Kibler, D. F., and Woolhiser, D. A. (1970). “The kinematic cascade as a hydrologic model.” Hydrol. Paper No. 39, Colorado State University, Fort Collins, Colo.
22.
Leendertse, J. J. (1967). “Aspects of a computational model for long‐period water wave propagation.” RM‐5294‐PR, The Rand Corporation, Santa Monica, Calif.
23.
Liggett, J. A. (1975). “Basic equations of unsteady flow.” Unsteady flow in open channels, K. Mahmood and V. Yevjevich, eds., Water Resources Publications, Fort Collins, Colo., Vol. 1.
24.
Lighthill, M. J., and Whitham, G. B. (1955). “On kinematic waves. I: Flood movement in long rivers.” Proc., Royal Society, London, England, A229, 281–316.
25.
Merkel, W. H. (1990). Discussion of “Kinematic wave routing and computational error.” J. Hydr. Engrg., ASCE, 116(2), 282–284.
26.
Morris, E. M., and Woolhiser, D. A. (1980). “Unsteady one‐dimensional flow over a plane: Partial equilibrium and recession hydrographs.” Water Resour. Res., 16(2), 355–360.
27.
Overton, D. E. (1970). “Route or Convolute?” Water Resour. Res., 6(1), 43–52.
28.
Ponce, V. M., and Simons, D. B. (1977). “Shallow wave propagation in open channel flow.” J. Hydr. Div., ASCE, 103(12), 1461–1476.
29.
Ponce, V. M., Li, R. M., and Simons, D. B. (1978). “Applicability of kinematic and diffusion models.” J. Hydr. Div., ASCE, 104(3), 353–360.
30.
Ponce, V. M., and Yevjevich, V. (1978). “Muskingum‐Cunge method with variable parameters.” J. Hydr. Div., ASCE, 104(12), 1663–1667.
31.
Ponce, V. M., Chen, Y. H., and Simons, D. B. (1979). “Unconditional stability in convection computations.” J. Hydr. Div., ASCE, 105(9), 1079–1086.
32.
Ponce, V. M., and Theurer, F. D. (1982). “Accuracy criteria in diffusion routing.” J. Hydr. Div., ASCE, 108(6), 747–757.
33.
Ponce, V. M., and Windingland, D. (1985). “Kinematic shock: Sensitivity analysis.” J. Hydr. Engrg., ASCE, 111(4), 600–611.
34.
Ponce, V. M. (1986). “Diffusion wave modeling of catchment dynamics.” J. Hydr. Engrg., ASCE, 112(8), 716–727.
35.
Ponce, V. M. (1990). “Generalized diffusion wave model with inertial effects.” Water Resour. Res., 26(5), 1099–1101.
36.
Sabol, G. V. (1987). “Development, use, and synthesis of S‐graphs.” Proc., Engrg. Hydrol. Symp., ASCE, New York, N.Y., 627–632.
37.
Sabol, G. V. (1990). “Maricopa County hydrology procedure.” Proc., Watershed Management Symp., ASCE, New York, N.Y., 423–431.
38.
SCS national engineering handbook, section 4: Hydrology. (1985). USDA Soil Conservation Service, Washington, D.C.
39.
Seddon, J. A. (1900). “River hydraulics.” Trans., ASCE, 43, 179–229.
40.
Sherman, L. K. (1932). “Streamflow from rainfall by unit‐graph method.” Engrg. News Record, 108, April 7, 501–505.
41.
Unkrich, C. L., and Woolhiser, D. A. (1990). Discussion of “Kinematic wave routing and computational error.” J. Hydr. Engrg., ASCE, 116(2), 284–286.
42.
“Urban hydrology for Small Watersheds.” (1986). Tech. Release No. 55 (TR‐55), USDA Soil Conservation Service, Washington, D.C.
43.
Vedernikov, V. V. (1945). “Conditions at the front of a translation wave distributing a steady motion of a real fluid.” Comptes Rendus (Doklady) de I[Academie des Sciences de l' U.R.S.S., (in French), 48(4).
44.
Woolhiser, D. A., and Liggett, J. A. (1967). “Unsteady one‐dimensional flow over a plane—the rising hydrograph.” Water Rcsour. Res., 3(3), 753–771.
45.
Woolhiser, D. A., and Goodrich, D. C. (1990). Discussion of “Kinematic wave routing and computational error.” J. Hydr. Engrg., ASCE, 116(2), 278–288.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 117 • Issue 4 • April 1991
Pages: 511 - 525
Copyright
Copyright © 1991 ASCE.
History
Published online: Apr 1, 1991
Published in print: Apr 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.