Approximate Convection-Diffusion Equations
Publication: Journal of Hydrologic Engineering
Volume 4, Issue 2
Abstract
This paper describes the development of simplified momentum equations, in stage as well as in discharge formulations, governing the transition between the diffusion and the kinematic waves (including the latter). It also describes the application of these equations to arrive at the approximate convection-diffusion equations. The appropriateness of these approximate convection-diffusion equations to model flood waves in the transition range is established, and the characteristics of these equations are studied from the point of view of description of the loop-rating curve. The development of these simplified equations provides a theoretical justification for their use in the well-known “Jones formula” expressed as Q/Q0 = {1 + [1/(S0c)]∂y/∂t}1/2 for converting the stage to discharge of a diffusive flood wave—an approach that has hitherto been considered to be logically incorrect.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chow, V. T. ( 1959). Open channel hydraulics. McGraw-Hill, New York.
2.
Cunge, J. A. (1969). “On the subject of a flood propagation computation method (Muskingum method).”J. Hydr. Res., Delft, The Netherlands, 7(2), 205–230.
3.
Ferrick, M. G. ( 1985). “Analysis of river wave types.” Water Resour. Res., 21(2), 209–220.
4.
Ferrick, M. G., Bilmes, J., and Long, S. E. ( 1984). “Modeling rapidly varied flow in tailwaters.” Water Resour. Res., 20(2), 271–289.
5.
Haizhou, T., and Graf, W. H. (1993). “Friction in unsteady open-channel flow over gravel beds.”J. Hydr. Res., Delft, The Netherlands, 31(1), 99–110.
6.
Hayami, S. ( 1951). “On the propagation of flood waves.” Bull. of Disaster Prevention Res. Inst., Kyoto, Japan, 1, 1–16.
7.
Henderson, F. M. (1963). “Flood waves in prismatic channels.”J. Hydr. Div., ASCE, 89(4), 39–67.
8.
Henderson, F. M. ( 1966). Open channel flow. Macmillan, New York.
9.
Jones, B. E. ( 1916). “A method for correcting river discharge for a changing stage.” U.S. Geological Survey Water Supply Paper No. 375(e), U.S. Geological Survey, 117–130.
10.
Kalinin, G. P., and Milyukov, P. I. ( 1957). “On the computation of unsteady flow in open channels.” Met. i. Gidrologiya Zhuzurnal, Leningrad, Russia, 10, 10–18 (in Russian).
11.
Lighthill, M. J., and Whitham, G. B. ( 1955). “On kinematic waves. I—Flood movement in long rivers.” Proc. Royal Soc. of London, Ser. A, 229, 281–316.
12.
Moots, E. E. ( 1938). “A study in the theory of flood waves.” Am. Geophys. Union Trans., 19, 383–386.
13.
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), 355–366.
14.
Natural Environment Research Council (NERC). ( 1975). “Flood routing studies.” Flood Studies Rep. Vol. III, NERC, London.
15.
Orlandini, S., and Rosso, R. (1996). “Diffusion wave modeling of distributed catchment dynamics.”J. Hydro. Engrg., ASCE, 1(3), 103–113.
16.
Perumal, M. ( 1994a). “Hydrodynamic derivation of a variable parameter Muskingum method: 1. Theory and solution procedure.” Hydro. Sci. J., Oxford, U.K., 39(5), 431–442.
17.
Perumal, M. ( 1994b). “Hydrodynamic derivation of a variable parameter Muskingum method: 2. Verification.” Hydro. Sci. J., Oxford, U.K., 39(5), 443–458.
18.
Perumal, M., and Ranga Raju, K. G. (1998a). “Variable-parameter stage-hydrograph routing method. I: Theory.”J. Hydro. Engrg., ASCE, 3(2), 109–114.
19.
Perumal, M., and Ranga Raju, K. G. (1998b). “Variable-parameter stage-hydrograph routing method. II: Evaluation.”J. Hydro. Engrg., ASCE, 3(2), 115–121.
20.
Ponce, V. M. (1986). “Diffusion wave modeling of catchment dynamics.”J. Hydr. Engrg., ASCE, 112(8), 716–727.
21.
Wong, T. H. F. ( 1984). “Improved parameters and procedures for flood routing in rivers,” PhD thesis, Department of Civil Engineering, Monash University, Victoria, Australia.
22.
Woolhiser, D. A., and Liggett. ( 1967). “Unsteady one-dimensional flow over a plane—The rising hydrograph.” Water Resour. Res., 3(3), 753–771.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 4 • Issue 2 • April 1999
Pages: 160 - 164
History
Received: Sep 23, 1996
Published online: Apr 1, 1999
Published in print: Apr 1999
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.